can quantitative screening of uk smaller company portfolios result in superior investment returns

IMPERIAL COLLEGE OF SCIENCE, TECHNOLOGY AND MEDICINE

(University Of London)

The Management School

Can Quantitative Screening of UK Smaller Companies Result in

Superior Investment Returns?

By

Ian J. Lancaster

A report submitted in partial fulfilment of the requirements for the MBA

degree and the DIC

September 1999

“Money machines don’t exist – not for long, anyway”

Brealey and Myers

“There is nothing so dangerous as the pursuit of a rational

investment policy in an irrational world”

John Maynard Keynes

“Its different this time”

Anon

Contents

CONTENTS

Page

LIST OF FIGURES vii

SYNOPSIS x

DECLARATION xi

ACKNOWLEDGEMENTS xi

1.0 INTRODUCTION 1

1.1 Background 3

1.2 Aims of this study 4

1.3 Data sources 4

1.4 Definitions 5

2.0 LITERATURE REVIEW 7

2.1 Introduction 8

2.2 The CAPM and efficient markets 9

2.3 The APT and efficient markets 11

2.4 Evidence of market inefficiencies 12

2.4.1 The price to earnings ratio 12

2.4.2 The price to book ratio 16

2.4.3 The price to sales ratio 20

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Contents

2.4.4 The return on equity 21

2.4.5 Equity market value 22

Page

2.4.6 Other ratios associated with market inefficiency 23

2.4.6.1 Yield 23

2.4.6.2 Debt to equity ratio 23

2.4.7 Patterns in equity price reaction 26

2.4.7.1 Past share price performance 26

2.4.7.2 January effect 28

2.5 The information content of reported earnings 29

2.6 Evidence for the sustainability of accounting ratios 33

2.6.1 Return on equity 33

2.6.2 Earnings per share growth 33

2.7 The use of earnings forecasts 37

2.7.1 Earnings models 41

2.7.2 Cash flow models 42

2.7.3 Other predictive models 45

2.7.3.1 The T-Model 45

2.7.3.2 Jacobs and Levy Model 46

2.7.3.3 Brennan and Subrahmanyam Model 46

2.8 Are the market inefficiencies a proxy for risk? 47

2.9 Conclusion of the literature review 51

ii

Contents

Page

3.0 INTRODUCTION TO EQUITY VALUATION 60

3.1 The dividend discount model 60

3.1.1 The relationship between the DDM and accounting

ratios 62

3.1.2 Price to earnings 64

3.1.3 Price to book value 66

3.1.4 Price to sales 67

3.1.5 Debt to equity ratio 69

3.2 Cash flow valuation 70

3.3 Conclusion of the introduction to equity valuation 71

4.0 DETERMINANTS OF COMPANY FINANCIAL PERFORMANCE 73

4.1 Equity growth rate 73

4.2 Issues of cash flow 75

4.2.1 Depreciation charge 75

4.2.2 Working capital 75

4.2.3 Free cash flow 76

4.3 The value drivers 77

4.4 Operational gearing 81

4.5 Risk of failure 82

4.6 A test for correlation between accounting ratios and outperforming

companies 84

iii

Contents

Page

5.0 RANKED PORTFOLIO TESTS FOR MARKET INEFFICIENCY :

UK SMALLER COMPANIES 86

5.1 Tests for market inefficiencies 87

5.2 Methodology 89

5.2.1 Definition of FTSE Smaller Company Index 89

5.2.2 Data collection 90

5.2.2.1 Constituents of the proxy smaller company

index 90

5.2.2.2 Portfolio creation dates 92

5.2.2.3 Time period 96

5.2.2.4 Test portfolios 96

5.3 Consideration of the significance of the results 98

5.3.1 The Student’s t test 98

5.3.2 Portfolio risk 100

5.3.3 Stage of business cycle 102

5.4 Portfolio ranking, performance and analysis 103

5.4.1 The proxy universe 103

5.4.2 Price to earnings 105

5.4.2.1 Discussion 111

5.4.3 Price to book 114


iv

Contents

Page

5.4.4 Price to sales 118


5.4.5 Return on equity 122


5.4.6 Cash EPS % of EPS 125


5.4.7 Dividend Yield 127


5.4.8 Share price momentum 129


5.5 Summary of single factor tests 132

5.6 Combination portfolios 134

5.6.1 PER and momentum 135


5.6.2 PSR and momentum 136


5.7 Summary of combination portfolios 138

5.8 Conclusion of data analysis 139

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Contents

Page

6.0 CONCLUSION AND FURTHER STUDY 143

6.1 Can the quantitative screening of UK Smaller Companies result in

superior investment returns? 143

6.2 Further study 145

7.0 REFERENCES 147

8.0 APPENDICES 158

8.1 Test of whether the proxy index companies perform in line with

the FTSE Smaller Company Index

8.2 Test of portfolios by single factor

8.3 Test of combination portfolios

8.4 Regression of ROE on Log PTBV

8.5 Test of high ROE, low PTBV screen

vi

List of Figures

LIST OF FIGURES

Page

Figure 2.01: Average Annual Return by PER Quintile. Compustat data

1956-1971 13

Figure 2.02: One-Year Total Return by PER Quintile. Compustat data

1968-1990 14

Figure 2.03: One-Year Total Return by PTBV Quintile. Compustat data

1963-1990 17

Figure 2.04: Average Excess Annual Return by Ranked MV and PTBV Quintile.

Compustat data 1982-1992 18

Figure 2.05: Price to Book Value against Beta 19

Figure 2.06: Compounded Annual Returns for Varying Balance Sheet Strength 25

Figure 2.07: Cumulative Return on a Neutral, Six-Month Relative Strength,

Winner/Loser Portfolio. Compustat data 1965-1989 27

Figure 2.08: Average Return 1926-1986 of 5-Year Relative Strength Stocks

by Calendar Months 28

Figure 2.09: Monthly Difference between Winner and Loser Portfolios at

Earnings Announcement Dates 31

Figure 2.10: Relative Subsequent EPS Growth in Quintiles of the EP Ratio 35

Figure 2.11: Earnings Surprise versus PE Ratio Compustat Data 1980-1994 37

Figure 2.12: Studies of the Accuracy of Analysts Earnings Estimates 38

Figure 2.13: Studies on the Accuracy of Analysts Earnings Estimates versus

Mechanical Earnings Models 39

vii

List of Figures

Page

Figure 2.14: Zero Net Investment, Long Low Accrual, and Short High Accrual.

Compustat data 1962-1992 44

Figure 2.15: The relationship between Beta and the PE Ratio 47

Figure 2.16: The Annual Returns of High vs. Low Volatility Portfolios 49

Figure 2.17: Annualised Excess Return for Investment Strategies 55

Figure 5.01: Market Capitalisation Cut-Off Points for the Proxy Smaller

Company Index 91

Figure 5.02: Year-End Distribution for December 1994 Proxy-Index 94

Figure 5.03: Portfolio Creation Dates 95




Figure 5.07: UK GDP Growth (% YOY) 6/1990 – 6/1999 102

Figure 5.08: Test of the Acceptability of Portfolios as a Proxy the FTSE

Smaller Company Index 104

Figure 5.09: Theoretical PE Ratios for High and Low Growth Companies 108

Figure 5.10: Performance of Portfolio Quartiles by PE Ratio 110

Figure 5.11: Performance of Portfolio Quartiles by PTBV Ratio 116

Figure 5.12: Performance of Portfolio Quartiles by PS Ratio 120

Figure 5.13: Performance of Portfolio Quartiles by ROE 123

Figure 5.14: Performance of Portfolio Quartiles by CEPS/EPS 126

viii

List of Figures

Page

Figure 5.15: Performance of Portfolio Quartiles by Dividend Yield 128

Figure 5.16: Performance of Portfolio by Share Price Momentum 130

Figure 5.17: Statistically Significant Results for the Single Factor Screens 132

Figure 5.18: Outperforming Single Factor Strategies 133

Figure 5.19: Performance of Portfolio by PER and Share Price Momentum 135

Figure 5.20: Performance of Portfolio by PSR and Share Price Momentum. 137

Figure 5.21: Performance of Combination Strategies 138

Figure 5.22: Sharpe Ratios of Outperforming Strategies 139

ix

Synopsis

SYNOPSIS

Academic research on stock market inefficiencies was surveyed to indicate which factors

might be relevant when looking for potential inefficiencies within the UK Smaller

Company Index.

The relationship between equity valuation, and the theoretical basis for company

financial performance was explored in order to lay the foundations for more complex

accounting based screens of UK Smaller Companies.

It was found that the quantitative screening of UK Smaller Companies by a simple

combination of an accounting ratio, and share price momentum resulted in an excess to

Index return of 5.2 % p.a. The trade off between the risk and return of this strategy was

superior to that of the FTSE Smaller Company Index. Nine other statistically significant

inefficiencies were recorded.

The results of the value screens for UK Smaller Companies are the opposite of the results

of previous research on the wider market index. This indicates that there are distinct

differences between profitable investment strategies for Smaller Companies as compared

to Larger Companies.

x

Declaration and Acknowledgements

DECLARATION

Plagiarism: the presentation of another person’s words, ideas, judgement or data as

though they were your own.

I have read the above definition of plagiarism. I am fully aware of what it means and I

hereby certify that, except where indicated, this project report is entirely my own work.

ACKNOWLEDGEMENTS

I would like to thank my supervisor, Dr. Colin Clubb, for his guidance and comments,

and the lesson that data always has a deeper meaning than the numbers alone would

suggest.

I would also like to thank my girlfriend, Amanda, for her support both before, and

throughout this course.

This project is dedicated to my father, like a true contrarian, he always supported the

underdog.

xi

Introduction

1.0 INTRODUCTION

1

Introduction

1.0 INTRODUCTION

Like modern day alchemists, portfolio managers attempt to refine the components of a

market index into a portfolio of equities that will outperform that index. There is

however, little evidence that the expensive process of fundamental research and careful

stock selection adds any value, in fact as a whole, managed portfolios underperform

(Malkiel (1995), Jensen (1968)). It could be argued that the complex interactions that

occur between economic forces, companies, management and those who value financial

assets is beyond human understanding. The inroads that chaos theory is making into the

world of financial theory seems to support this view. An interested reader should see

Fogler (1995) for an excellent synopsis of the emerging opportunities created by non-

linear forecasting models.

In the search for a leading edge in portfolio selection, it is becoming common for vast

databases to be interrogated for patterns between share prices and financial attributes. In a

similar vein, this study focuses on investigating patterns in the share price behaviour of

UK Smaller Companies. As UK Smaller Companies account for only 3.84% (31/8/99) of

the market capitalisation of the UK equity market, this data set is rarely examined by

academics.

For larger, more frequently traded companies, arbitrage would be expected to eliminate

valuation anomalies. However UK Smaller Companies are relatively under researched, so

2

Introduction

within this sub sector there may be the opportunity of achieving risk-adjusted excess

returns.

1.1 Background

The FTSE Smaller Company Index excluding investment trusts (FTSC X-IT), consists of

364 companies. These range in size from £30m to £406m. I worked within a team of 3

UK Smaller Company analysts on behalf of a large institution investor (assets of £15bn.,

£650m. in Smaller Companies). We considered that each individual could cover 35

companies sufficiently well to justify a holding within the portfolio, and follow the

fortunes of a further 20 companies for possible inclusion. Between three analysts, this

totaled only 165 companies. A key management problem was deciding which of the 364

index companies, should become part of the list of the 165 companies that were covered

by the analysts. It was therefore essential for a screening process to take place.

The investment screens were both quantitative and qualitative. Qualitative decisions

could only be made after meeting with the company management and exploring the

prospects for a company’s product or service. This was time consuming, and in any case,

it was not feasible to meet all of the companies in the Smaller Company Index. Due to

this, it was considered necessary to consider various quantitative screens in order to

eliminate certain ‘poor prospects’.

3

Introduction

1.2 Aims of this study

It is the primary aim of this study to establish whether it is possible to use quantitative

screens in order to achieve risk-adjusted excess returns for a portfolio of UK Smaller

Companies. A secondary aim is to increase the readers understanding of the interaction

between accounting ratios, equity valuation and the theoretical basis for equity

outperformance. In the Literature Review, academic research is surveyed in order to

establish whether market inefficiencies exist, and if so how best to exploit them. In the

portfolio screening tests of this study, a high-low ranking of companies by historic

accounting ratios is used to select portfolios that express a similar attribute. The total

return of these portfolios is then assessed against the total return of the FTSE Smaller

Company Index over the subsequent year in order to measure their performance.

1.3 Data Sources

Compustat is a US database of company account data and share prices from 1925 to

present day. It is the prime source of information for the academic literature.

Datastream is a UK database of financial and economic time series. The data set is used

in this study for accounting ratios and price information.

I/B/E/S is the Institutional Broker Estimate System. It is used extensively by Investment

Managers to track Analysts forecasts.

4

Introduction

1.4 Definitions

APT - Arbitrage Pricing Theory

Beta or β - The β coefficient of the CAPM

BV - Book value

BVP - Book value to price

BVPS - Book value per [ordinary] share

CAPM - Capital Asset Pricing Model

CEPS - Cash earnings per [ordinary] share

CFO - Cash flow from operations

DDM - The dividend discount model (Gordon growth model)

DER - The debt to equity ratio

DPS - Dividends per [ordinary] share

DYLD - Dividend yield

EP - Earnings yield (1/EPS)

EPS - Earnings per [ordinary] share

Excess Return - Provide a higher return (capital plus income) than the relevant stock

market index (capital plus income)

FTSC Index - FTSE Smaller Company Index

Micro-cap - Used to describe a very small quoted equity (sub £55m MV)

MV - Market value of equity

Net - After interest and tax

Outperform - Provide a higher return (capital plus income) than the relevant stock


5

Introduction

Payout ratio - DPS / EPS

PCEPS - Price to cash EPS

PEG ratio - Price to earnings ratio / EPS growth rate

PER - Price to earnings ratio

PS - Price to sales

PSR - Price to sales ratio

PTBV - Price to book value

Retention ratio- 1-Payout Ratio

ROCE - Return on capital employed

ROE - Return on ordinary shareholders equity

SPS - Sales per [ordinary] share

Underperform - Provide a lower return (capital plus income) than the relevant stock


6

Literature Review

2.0 LITERATURE REVIEW

7

Literature Review

2.0 LITERATURE REVIEW

2.1 Introduction

Early empirical research tested the association between the returns of portfolios against

the predicted returns of the CAPM framework (see Section 2.2, (Sharpe (1964), Lintner

(1965), and Black (1972)). Subsequently, Gibbons (1982) and Stambaugh (1982) tested

the hypothesis that expected returns were predicted solely by the Beta value. Following

the development of the APT (Ross (1976)), similar tests of this model were conducted.

Tests of the CAPM and APT models were based upon the theory that the excess return of

a portfolio was also dependent upon non-risk security characteristics. These included firm

size (Banz (1981)) book to market ratios, dividend yields, past sales growth, debt to

equity ratios (Bhandari (1988)), low share price (Stoll and Whaley (1983)), and earnings-

price ratios (Basu (1977,1983)). See also Black and Scholes (1974), Rosenberg, Reid and

Lanstein (1985), Lakonishok, Shleifer and Vishny (1994), and Haugen (1995).

In addition, relationships have been demonstrated between a reversal in long term returns

of three to five years (De Bondt and Thaler (1985)) and, in contrast, a tendency for short-

term (up to one year) performance to continue (Jegadeesh and Titman (1993), Asness

(1994)).

8

Literature Review

2.2 The CAPM and efficient markets

The Capital Asset Pricing Model (CAPM) has been an axiom of financial analysis since

its conception by Sharpe (1964) and Lintner (1965). The CAPM states that the expected

return of a stock is a function of the risk free rate of return plus the Beta (β) value of the

stock multiplied by the equity market risk premium.

Expected return = Rf +β (ERm – Rf)

Where Rf = The risk free rate of return (the return on long term bonds)

β A measure of the historic share price return to the historic market return

ERm = Expected return for the market

Beta is calculated from a regression of past stock returns on past market returns, and thus

describes the sensitivity of a stocks return to that of the market. The equity risk premium

is the compensation for the additional risk that investors take on when investing in the

stock market as opposed to a risk free asset. The risk premium is defined as the expected

return of the equity market minus the expected return from a risk free asset (i.e. a

government bond). As a stock with a high Beta has a high price variance compared to the

market, then consequently investors will require a higher return from the stock in order to

compensate for the higher risk (standard deviation of returns). By definition the market

has a β value of one, and government bonds a Beta value of zero.

9

Literature Review

A central principle of the CAPM is that arbitrage by investors (between theoretical and

actual value) is expected to keep all stocks at the correct expected return. In the most

literal of terms, the CAPM states that investors will be unable to achieve higher returns

for a particular portfolio, without taking on extra risk. Markets are therefore considered

efficient at equating risk with return. Brealey and Myers (1996) state that the CAPM’s

resilience is because “The Capital Asset Pricing Model captures [the idea of] risk in a

simple way.”

However critics of the CAPM theory point to evidence that market inefficiencies are

demonstrated to exist when Beta is controlled for. For example, if companies are sorted

into groups of similar Beta, and similar market capitalisation (MV), at a particular value

of Beta, the lower MV companies tend to outperform. If the outperformance is

compensation for the risk that the investors in low MV companies endure, then evidently

the risk is not captured by Beta alone. Various other inefficiencies are discussed in this

chapter and these suggest that the single risk factor of Beta is inadequate.

The CAPM theory has expanded to include varying Beta models. These are based upon

the theory that risk is not constant over time. Howton and Peterson (1998) have shown

that during bull (bear) markets, if Beta is allowed to vary, then Beta is significantly

positive (negative). However Ghysels (1998) warns that, in practice, the estimation errors

of varying Beta models can prove to be higher than stable Beta models.

10

Literature Review

2.3 The APT and efficient markets

The Arbitrage Pricing Theory (APT, Ross (1976)) splits stock risk into two components.

First, there is macroeconomic factor risk, that is the risk from economic or general factors

that influence equity return such as the oil price, inflation etc. (General factors may also

include potential inefficiencies such as the PER, PTBV etc). Second, there is the risk

from factors that are unique to a particular company, this is termed ‘noise risk’. The APT

assumes that, the noise risk can be reduced as a portfolio becomes more diversified.

Mathematically the APT can be expressed as,

Stock expected return, (Er) = a + b1 (Rp factor 1) + b2 (Rp factor 2) + … + noise

Where ‘a’ is the risk free rate of interest, ‘Rp factor n’ is the risk premium for economic

or general factor n (i.e. the excess return that a sample portfolio would have earned in the

past for taking on the particular factor risk), and ‘bn’ is the sensitivity of the return of a

stock to factor n. The value of ‘bn’ is calculated by regressing factor n on the historic

share price return.

The risk premium of a stock therefore depends upon the associated risk premium of each

factor and the sensitivity of the stock to each factor.

Stock risk premium = Er - Rf

= b1(Rp factor 1 – Rf) + b2(Rp factor 2 – Rf) + … + bn(Rp

factor n – Rf)

11

Literature Review

Where ‘Rf’ is the risk free rate of return (the return on government bonds).

There are no standard factors, so a standard model cannot be used to test for the

availability of excess returns vs. those predicted by the APT theory1. Chen et al. (1986)

have suggested that five macroeconomic factors are common, these are industrial

production, changes in default premium, shifts in the term structure of interest rates,

unanticipated inflation, and changes in the real rate of return. The factor specific nature of

APT makes it superior to the simple one factor (β) CAPM, however its mathematical

complexity means that, so far, the CAPM still dominates in terms of practical use.

2.4 Evidence of market inefficiencies

2.4.1 The price to earnings ratio

The price to earnings ratio (PER) is an established valuation screen. Its simplicity and

empirical success made it the cornerstone of early portfolio strategy. In his seminal book

“The Intelligent Investor” Benjamin Graham (1973) discusses the merits of low PER

stocks, but he warns against the use of low PER combined with low MV, because

“market neglect” [possibly due to stock illiquidity and lack of research] can result in low

PER and MV stocks remaining undervalued for some time.

1 Certain studies have concluded that relevant factors are: Yield spread (long govt. bond-30 treasury bill), Δ interest rate, Δ exchange rate, Δ real GNP forecast and Δ inflation forecast.

12

Literature Review

A number of studies (for example Basu (1977,1983) indicate that low PER stocks

outperform. In these studies it was hypothesised that a low PER effect could also be

associated with a size effect, so returns were compared against the size group of which a

company is a member. The results however, showed that the low PER effect continues

regardless of the size (MV) of the company.

Basu (1977) tested the low PER screen on 1400 companies from the NYSE between 1956

and 1971. He used the CAPM framework to show that low PER stocks earn excess

returns relative to the market. The results of the study are shown below.

Figure 2.01: Average Annual Return by PER Quintile. Compustat data 1956-1971

PER Quintile Average Annual Return BetaA (Highest) 9.3% 1.1121A* 9.6 1.0579B 9.3 1.0387C 11.7 0.9678D 13.6 0.9401E (Lowest) 16.3 0.9866

Source: Basu, S., 1977, “The Investment performance of Common Stocks in Relation to their Price-Earnings: A test of the Efficient Markets Hypothesis,” Journal of Finance, 32, pp. 663-682.

A* = Highest PER quintile excluding stocks with negative earnings.

One argument against the use of a low PER strategy is that low PER stocks outperform in

order to compensate investors for higher risk. This is partly refuted by the demonstration

that lower PER stocks, in fact, have lower Beta values (of course, this depends upon ones

acceptance of the CAPM). If Beta captures risk then it would seem, from this study, that

there is an inverse relationship between risk and reward. See Figure 2.01 above.

13

Literature Review

In one of the first papers to focus on contrarian investment strategies, Lakonishok et al.

(1994) examined the Compustat data over the period of April 1968 to April 1990, and

formed portfolios based upon ranked quintiles of PE ratios. The results are shown below.

Figure 2.02: One-Year Total Return by PER Quintile. Compustat data 1968-1990

Source: Dreman, D.,N., 1998, “Contrarian Investment Strategies: The Next Generation,” Simon and Schuster, New York, p. 154. Adapted from Lakonishok, J., Shleifer, A., and Vishny, R., 1994, “Contrarian Investment, Extrapolation, and Risk,” Journal of Finance, 49, pp. 1541-1578.

It can be seen that over the period of 1968 to 1990, a low PER strategy would have

outperformed by an average of 2.7% p.a.

In an extension of the preceding studies, Goodman and Peavy (1983) tested stocks with a

PER that was low relative to the PER of their industrial categorisation, the low PER

effect continued.

14

Literature Review

There are various arguments for the (Beta controlled) low PER phenomena.

First, is that the CAPM consistently underestimates the Beta values of low PER stocks

and overestimates the Beta values of high PER stocks; however as low PER stocks are

often large, stable (and consequently less ‘risky’) companies this argument is not

compelling.

Second, is that the tax considerations of investors cause the anomaly as investors are

adverse to the high yield of low PER stocks (Ball (1989)); however tax rates on capital

gain and income are now at similar levels and the effect continues.

Third, and most compelling, is that investors systematically pay too much for growth

(high PER) companies. The reassurance of being part of ‘the crowd’, pushes many

investors into the same limited number of growth companies, and consequently they

force the PE ratio to (theoretically) high levels. It is for this reason that those who follow

a low PER strategy are called ‘contrarian’ investors; they are happy to go against the

crowd.

To try and eliminate the possibility of the overvaluation of high PER stocks, Peters

(1991) tested the strategy of buying portfolios of low “PER / EPS Growth” companies.

This screen was applied in order to incorporate a basis of ‘reasonable value’ i.e. high

PER stocks could be held if the earnings growth rate was correspondingly high. The

lowest decile outperformed in 26 out of the 30 quarters measured, and provided a return

of 1,536% vs. 356% for the S&P 500 over the seven and a half year period.

15

Literature Review

Damodaran (1994) suggested that significant explanatory factors for a regression

calculation of the PE ratio in any one year, include the payout ratio, β, and the earnings

growth rate. He found that for the individual years of 1987 to 1991, the R2 ranged from

32% to 92%.

However the regressions are unstable year by year, quite possibly because investors

‘price in’ the effects of the business cycle on earnings. I.e. investors will pay a high PER

for a company at the low point of its earnings cycle and visa versa. Hence whilst the PER

regressions may demonstrate relationships, they are poor long-term predictors.

2.4.2 The price to book ratio

Rosenberg, Reid, and Lanstein (1985) looked at the period of 1973 to 1984 and found

that low PTBV portfolios provided an excess return of 36 bp. per month. In addition,

Fama and French (1992) further confirmed the relationship in a study of the period 1963

to 1990. They found that a low PTBV portfolio earned an average monthly return of

1.83% vs. an average monthly return of 0.3% for a high PTBV portfolio.

16

Literature Review

Figure 2.03: One-Year Total Return by PTBV Quintile. Compustat data 1963-1990

Source: Dreman, D.,N., 1998, “Contrarian Investment Strategies: The Next Generation,” Simon and Schuster, New York, p. 152. Reference: Fama, E.,F., and French K.,R., 1992, “The Cross-Section of Expected Returns,” Journal of Finance, 47, pp. 427-466.

The low PTBV quintile outperformed the market on average by 4.6% annually, whilst the

high PTBV quintile underperformed the market by 5.7%.

In order to counter the arguments of survivorship bias (often databases delete the history

of failed companies) in the Fama and French paper, De Silva (undated) used the

Compustat data for the 1982-1992 period (for which survivorship bias was not a

problem). In his study he segmented the sample to see whether there was an underlying

size effect. The results are illustrated below.

17

Literature Review

Figure 2.04: Average Excess Annual Return by Ranked MV and PTBV Quintile.

Compustat data 1982-1992

Source: Adapted from Haugen, R.,A., 1995, “The New Finance: The Case against Efficient Markets,” Prentice Hall, Englewood Cliffs, New Jersey, p. 5. Reference: De Silva, H., “What Underlies the Book-to-Market Effect,” Working Paper, Graduate School of Management, University of California, Irvine.

In the De Silva paper the size effect is quite evident, however the results have been

questioned as the small MV quintile may be based upon very small illiquid companies.

This study will incorporate a market value cut off in order to insure that a tradable

strategy is formulated.

Interestingly, Capaul, Rowley and Sharpe (1993) found that between 1981 and 1992, a

low PTBV portfolio earned excess returns in every international market that they

analysed.

18

Literature Review

Fama and French (1992) hypothesised that a low PTBV is a proxy for risk. This is

because low PTBV stocks are more likely to be in financial trouble. However during the

course of their study they found that lower PTBV stocks in fact had lower Beta values

(see also Basu (1977), Figure 2.01 above, in relation to low PER).

Figure 2.05: Price to Book Value against Beta

Source: Fama, E.,F., and French, K.,R., 1992, “The Cross Section of Expected Stock Returns,” Journal of Finance, 47, pp. 427-466.

Damodaran (1994) found that the most significant explanatory factors for the PTBV ratio

are the payout ratio and earnings growth rate. For the period of 1987 to 1991 the

predicted PTBV ratio was stable year on year i.e. the model had a stable R2 of between

86.0% to 88.5%.

There is a theoretical relationship between the return on equity (ROE) of a company and

the PTBV ratio at which it should be priced (see Section 3.1.3). To test this relationship,

Damodaran screened all NYSE stocks from 1981 to 1990 into “top 25% ROE – bottom

19

Literature Review

25% PBV” and “bottom 25% ROE – top 25% PBV” portfolios. Over the period the first

portfolio outperformed by 8.1% and the second portfolio underperformed by 6.8%.

2.4.3 The price to sales ratio

Senchack and Martin (1987) conducted one of the few tests of the performance of low

price to sales ratio (PSR) portfolios. They used the Compustat database to study the

returns of US stocks (AME and NYSE) between 1976 and 1984. Their conclusion was

that low PSR companies outperformed the market, but low PER was both dominant and

more consistent than low PSR.

Minard (1984) has argued that a low PSR strategy is superior to a low PER strategy as,

1) Sales are more stable over time.

2) The PSR can be used when companies are loss making.

3) That a low PER strategy is distorted by the elimination of high PER stocks that have

temporarily depressed earnings, and the selection of low PER cyclical stocks at the

peak of their earnings cycle.

In a study of the PS ratio that used regression analysis, Jacobs and Levy (1988) found

that a low PSR factor was significant in providing an excess return of 0.17% a month, it

also remained a significant factor when PER and MV were included.

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There is a theoretical relationship between the PSR and net profit margin (see Section

3.1.4.). To exploit this relationship, for the period of 1981 to 1990, Damodaran (1994)

created “undervalued” portfolios consisting of the lowest quartile PSR stocks and highest

quartile net profit margin stocks, and “overvalued” portfolios consisting of the highest

quartile PSR stocks and lowest quartile net profit margin stocks. Damodaran’s

“undervalued” portfolio outperformed the S&P 500 by 6.2% and “overvalued” portfolio

underperformed by 2.0%.

In addition, for the period of 1987 to 1991, cross sectional regressions were performed

on the net profit margin, dividend payout ratio, Beta, and the growth rate in earnings.

The R2 ranged from 44% to 88%, however it is not stable over time.

2.4.4 The return on equity

Wilcox (1984) found that a strong cross sectional relationship existed between the Log of

price to book value (PTBV) and return on equity (ROE). The derived formula was,

Log PTBV = α + β1ROE

Where α and β1 are factors from a multiple regression of ROE on Log PTBV for a single

year.

The Wilcox PTBV – ROE model is based on the relationships that define the expected

growth rate of book equity (see Section 4.1). Wilcox suggests that analysts should use the

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model to compute a forecast PTBV ratio based upon the consensus ROE. Stocks with a

lower PTBV ratio than that forecast by the model should be bought. For the period of

1976 to 1980, the Wilcox model demonstrated a lower mean squared error than a PER

regression model when used for predicting the value of US companies.

This model is useful, as unlike the earnings growth rate, past ROE has been shown to be

a good predictor of future ROE (see Babcock (1980), Paynor (1966) and Sections 2.6.1

and 2.6.2). However, the PTBV – ROE relationship does not hold for stocks were the

past ROE is not a good predictor of the future ROE, so it should only be used for

companies with a five-year standard deviation in ROE < 0.05.

2.4.5 Equity market value

Over extended periods, size (MV) has be shown to be a better predictor of expected

returns than Beta (Banz (1981), Reinganum (1981), Keim (1983), Fama and French

(1992,1993,1996)). Ball (1992) has suggested that the size anomaly is a candidate for an

expected return model as,

1) The information is publicly available, but the anomaly persists

2) Information processing costs are likely to decrease as market size increases

3) As there is a correlation between size and the yield component of expected return

then taxation of income becomes a factor

4) It is possible that Beta estimates are skewed by the non representative sample of

assets in equity indexes, Stambaugh (1982)

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5) Bid-ask spreads are a decreasing function of size

6) The size effect is possibly as a consequence of short-interval Beta measurement,

Handa et al. (1989)

2.4.6 Other ratios associated with market inefficiency

2.4.6.1 Yield

The result of a high yield (DYLD) screen is counter-intuitive. It is assumed that high

yield stocks are predominantly in low growth industries, however high yield stocks tend

to outperform. The results of a study by Dreman (1998) on the Compustat 1500 data base

(largest 1500 US stocks) showed that for the 27 years ending December 1996, a high

quintile DYLD portfolio that was re balanced annually, provided average annual returns

of 16.1% vs. 14.9% for the market. [The second highest DYLD quintile is the best

performer, with an average annual return of 17.5%]. The downside protection of high

yield was also demonstrated in the study, as for all down quarters (bear markets) the high

DYLD strategy averaged a loss of only 3.8% vs. a loss of 7.5% for the market.

2.4.6.2 Debt to equity ratio

In general, a higher debt to equity ratio (DER) would be expected to result in greater risk

for the common equity holder. This is because when the DER increases, so does the

interest cost as a proportion of operating profits. As debt interest is in effect a fixed cost,

then if operating earnings were to fall (rise) the consequence of debt would be to amplify

profits negatively (positively) at the net level. However, Bhandari (1988) demonstrated

that after controlling for Beta and firm size, the expected common stock return is

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positively related to the ratio of debt to equity. In an extension to this line of reasoning,

Ross-Healy and Sgromo (1993) showed that portfolio returns can be enhanced by

decreasing exposure to companies with balance sheet excess (defined as both under and

over leveraged), increasing exposure to companies with improving balance sheet

strength, and decreasing exposure to companies with deteriorating balance sheet strength.

The data was taken from S&P 500 companies in the period of 1983 to 1990 and the

results are shown below. The data shows that for a portfolio of companies that had

improving Balance Sheet strength, an excess return of 7.7% p.a. was achieved.

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Figure 2.06: Compounded Annual Returns for Varying Balance Sheet Strength

Source: Adapted from, Ross-Healy, C., and Sgromo, E., 1993, “How to Beat the S&P 500 Index Using Credit Analysis Alone,” Journal of Portfolio Management, Winter, pp. 25-31, Exhibit one.

NB: A1 C denotes Strong Weak Balance Sheet

pA1 pB denotes balance sheet strength quartile promotion, eg pA1 indicates promotion from A to A1, pA indicates promotion from B to A.

dA dC denotes balance sheet strength quartile demotion, eg dA indicates demotion from A1 to A, dB indicates demotion from A to B.

The S&P 500 returned 9.78% compound during the period.

Whilst the Ross-Healy and Sgromo paper uses a specific ‘SAC’ score (developed by

Solvency Analysis Corporation), the issues can be related to other measures of financial

strength available in the UK. For example, Professor Richard Taffler, of the City

University Business School (1997) found the Z-Score rating of Syspas (UK) to be useful

in predicting company failure, see Section 4.5.

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2.4.7 Patterns in equity price reaction

2.4.7.1 Past share price performance

De Bondt and Thaler (1985) propose a contrarian trading strategy that buys stocks that

have performed poorly over a 3 or 5 year period. Over the subsequent 3 or 5 year holding

period these stocks go on to outperform those that had performed well in the past period.

Other studies (Jegadeesh (1990)) have illustrated a similar short-term (week/month)

return reversal. However these findings are at odds with the medium term (less than 12

month) relative strength screens that are used by many investment professionals.

Jegadeesh and Titman (1993) posited that relative returns may be time variable, that is

that contrarian strategies may provide excess returns in the short and long term, and that

relative strength strategies may provide excess returns in the medium term. In their study

stocks were classified as winners (the 10% of stocks with the best returns over the

preceding six months), and losers (the 10% of stocks with the worse returns over the

preceding six months). The chart below shows the returns to the relative strength

strategy.

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Figure 2.07: Cumulative Return on a Neutral, Six-Month Relative Strength,

Winner/Loser Portfolio. Compustat data 1965-1989

Source: Adapted from, Jegadeesh, N., and Titman, S., 1993, “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency,” Journal of Finance, 48, pp. 65-92. Table VII.

The strategy return is negative for periods of less than one month and of greater than

twelve months. It corresponds to the short-term contrarian view, the medium term

practitioner view and the long-term contrarian view. However the t-stats of the study

decline for the longer periods. The conclusion of the Jegadeesh and Titman study is

replicated in non-US markets for the period of 1957 to 1986 by Poterba and Summers

(1988). They found positive autocorrelation of stock prices for periods of less than twelve

months and negative autocorrelation for periods of greater than twelve months.

The most profitable Buy-Hold-Sell strategy [in the De Bondt and Thaler study] was

based upon test period returns of twelve months for a portfolio that was held for three

months, this strategy yielded an excess return of 1.31% per month.

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Various explanations for price overreaction have been put forward. One is behavioural

insomuch as analysts and investors are systematically over (under) enthusiastic about

short-term winners (losers) (Dreman (1998). Another is based upon liquidity, there is

simply not enough stock in the system to accommodate the buying and selling pressure

post valuation relevant surprises (Grossman and Miller (1988) and Jagadeesh and Titman

(1995)).

2.4.7.2 January effect

In addition to the excess returns associated with earnings announcements, (detailed in

Section 2.5), there is also evidence of a ‘January effect’ (De Bondt and Thaler (1985),

Chopra et al. (1992)). In Figure 2.08 below, portfolios are ranked 1-20 in order of share

price return over the previous five years (portfolio 20 is high).

Figure 2.08: Average Return 1926-1986 of 5-Year Relative Strength Stocks by

Calendar Months

Source: Adapted from Chopra, N., Lakonishok, J., and Ritter, J.,R., 1992, “Measuring abnormal performance: Do Stocks Overreact?,” Journal of Financial Economics, 31, pp. 235-268, Table 3.

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It can be seen that, in January, the return of underperforming stocks (over the previous

five years) is disproportionately high. An explanation for this could be that of the

‘window dressing’ of portfolios at the calendar year-end. Professional investors may do

this in order to present blue chip portfolios to clients for year-end fund reports. In

January, the subsequent ‘bottom fishing’ of these badly performing stocks results in their

outperformance.

2.5 The information content of reported earnings

In 1968, Ball and Brown were the first to record the observation that abnormal rates of

return followed earnings increases as reported at annual earnings announcements.

Subsequent US studies by Bernard and Thomas (1990) extended the research to quarterly

earnings announcements. They looked at over 100,000 announcements during the period

of 1974 to 1986 and concluded that,

1) A zero exposure, long-short portfolio, that each quarter takes a long position in the

top decile of earnings performers and a short position in the bottom decile, earns an

average excess return of +4.19% over the 60 days following the announcement. The

abnormal return is positive for 46 of the 50 quarters in the study.

2) The excess returns were a decreasing function of size

3) One sixth of the 60 day excess return is achieved in the first five days

4) Over 180 days the excess return is +7.74%.

5) There is no price drift post 180 days

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They note that “a significant component of the predictable post-announcement abnormal

return occurs at the announcement of the following quarters earnings.” It seems that the

market ignores the information about future earnings contained in earnings

announcements. One reason put forward for the lagged share price response is that

analysts take up to three quarters to correct for an earnings surprise, (Abarbanell and

Bernard (1992)).

The Jegadeesh and Titman (1993) study, (see Section 2.4.7.1) also looked at the

performance of winner/loser portfolios in relation to earnings announcements (top and

bottom decile, ranked by six month share price performance relative to the index). The

performance of each group of stocks was measured over the two days before, and the day

of, the next quarterly results following portfolio formation. It was found that for seven

months winner stocks continued to outperform at earnings announcements. This implies

that the market failed to recognise that good earnings numbers foretold of more to come,

and likewise that earnings disappointment would continue. See below.

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Figure 2.09: Monthly Difference between Winner and Loser Portfolios at Earnings

Announcement Dates

Source: Haugen, R.,A., 1990, “Modern Investment Theory,” Englewood Cliffs, N.J., Prentice Hall, p.21. Reference: Jegadeesh, N., and Titman, S., 1993, “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency,” Journal of Finance, 48, pp. 65-92. Table IX.

By the sixteenth month post the date of portfolio construction, the loser portfolio was

outperforming the winning portfolio. This implies that if the strategy of six-month

relative share price strength is to be used, then the investor should sell the portfolio after

eight months. Another strategy would be to take a position in the stocks that have

underperformed over fourteen months. I.e. the six-month test period, plus the eight

months during which the information contained in the earnings announcements are

absorbed by the market.

Hawkins, Chamberlin and Daniel (1984) put forward evidence that the revision of

earnings forecasts has informational value. Twelve-month risk adjusted returns of 14.2%

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were available for investors in stocks with the largest upward revisions in consensus

earnings forecasts. Richards and Martin (1979) found that the revisions in the first quarter

contain more price sensitive information than revisions later in the year.

Mott and Coker (1993) investigated the effect of earnings surprise on the subsequent

performance of Smaller Companies. A positive surprise is defined by a Standardised

Unexpected Earnings (SUE) ratio of greater than one, where:

SUE = Actual EPS – Consensus EPS estimate Standard Deviation of Consensus

Their conclusion was that for Smaller Companies exhibiting a positive surprise, the

relative outperformance (from one-week post announcement) was +2.1% for the first

month and +12.9% for the first twelve months. Overall, ninety percent of these

companies outperformed over the following twelve months. The corresponding one

month and twelve month relative performance for negative surprise (SUE<1) was –0.9%

and –3.5% respectively. Ninety percent of negative surprise companies underperformed

over the following twelve months.

Analysts seem to fail to incorporate the information contained in announcements that

report an earnings surprise. In the Mott and Coker sample, in a reflection of the

inaccuracy of analysts earnings estimates (see Section 2.7), positive surprises were seen

20% of the time and negative surprises 26% of the time. In addition, for the positive

surprise sample, a repeat surprise was seen 34% of the time, and for the negative surprise

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sample, a repeat surprise was seen 41% of the time. For positive and negative repeaters

the subsequent 12-month relative performance was 19.3% and –3.6% respectively. ‘Third

time’ positive or negative surprises were seen post the repeat surprise for 39% and 44%

of the time respectively. These observations of systematic error should prove useful in the

construction of screening models.

2.6 Evidence for the sustainability of accounting ratios

2.6.1 Return on equity

The Return on Equity has been shown to be a relatively consistent accounting ratio over

time (Wilcox (1984) Babcock (1980), Paynor (1966), see also Section 2.4.2).

2.6.2 Earnings per share growth

In a UK study of the period of 1951 to 1961, the statistician I.M.D.Little (1962, 1966)

found limited evidence that past earnings growth indicates future earnings growth. He

wrote that,

“My impression is that many stockholders, financial journalists, economists and

investors believe that past growth behaviour is some sort of guide to future growth…

For the privilege of holding these particular growth stocks, the investor has been

willing to forego a considerable amount of income…[in a belief that] firms which

have grown relatively better than others in the past will continue to do so in the

future”.

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Little split a sample of stocks into two five-year sub periods. For the first period,

quartile groupings of low to high EPS growth were formed. The EPS growth for the

second period was then compared to that of the first. The average correlation of

earnings growth rates was just 0.02. There was therefore no consistency demonstrated

in persistence of respect of earnings growth. An updated study for the periods of 1981

to 1985 and of 1986 to 1990 supported the findings. Given the emphasis that

professional investors place on past EPS growth rates, this is an interesting finding. It

leads to the conclusion that the EPS growth rate experienced in the past, will not be a

useful investment screen.

However investors also screen by other quantitative and qualitative factors. Fuller et al.

(1993) tested whether they were able to use other data available to them in order to make

judgements about future growth prospects. During the period 1973-1990, Fuller ranked

stocks by the EP ratio (the inverse of the PER ratio) and then compared the subsequent

EPS growth over each of the next 8 years.

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Figure 2.10: Relative Subsequent EPS Growth in Quintiles of the EP Ratio

Source: Fuller, R.,J., Huberts, L.,C., and Levinson, M.,J., 1993, “Returns to E/P Strategies; Higgledy Piggledy Growth; Analysts Forecast Errors; and Omitted Risk Factors,” Journal of Portfolio Management, Winter, Exhibit 6.

NB: The middle quintile grew EPS by 10.2% in the first year. Analyst forecast error was similar and low across quintiles.

Figure 2.10 shows that the earnings growth rate of low EP (high PER) stocks, is greater

than that of the earnings growth rate of the middle quintile stocks for some years into the

future. If it is assumed that a low EP ratio is a reflection of investor’s anticipation of high

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future EPS growth, then the data suggest that investors can use fundamental analysis to

form reasonable judgements about the future EPS growth prospects for a company. With

reference to Figure 2.10, it seems that investors are able to judge the prospects of

premium earnings growth for a company, for around six years into the future.

Given the demonstrated underperformance of low EP stocks (see Section 2.4.1) and the

fact that low EP stocks achieve premium earnings growth, then it is interesting to

speculate as to why low EP stocks underperform. One explanation may be that the

valuation of these stocks is forced to too high a level for the achievable growth rate. This

is difficult to test for, as the growth expectation of investors cannot be measured directly,

it can only be inferred via the high EP ratio.

Another logical explanation as to why high PER stocks underperform, could be because

of the revision of over-optimistic forecasts by analysts. Figure 2.11, illustrates the finding

of Bauman and Miller (1997) that as PE ratios increase, then earnings surprise also

increases.

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Figure 2.11: Earnings Surprise versus PE Ratio Compustat Data 1980-1994

Source: Bauman, W.,S., and Miller, R.,E., 1997, “Why Value Stocks Outperform Growth Stocks,” Journal of Portfolio Management, Spring, pp. 57-68, Exhibits 1 and 2.

NB: Earnings Surprise is defined as (reported earnings - forecast earnings)/standard deviation of forecasts.

The evidence suggests that high PE ratios tend to reflect past high EPS growth rates, and

as there is no correlation between past and future rates of earnings growth, then it is not

surprising that these high PER stocks systematically disappoint investors. The under

performance of high PER stocks could well be a combination of both over valuation, and

disappointment with ‘over estimated’ future earnings performance.

2.7 The use of earnings forecasts

By showing that companies that beat the consensus earnings forecast out performed the

market, Beaver, Clark, and Wright (1979) emphasised the advantage of being able to

predict large, unexpected, changes in earnings. This suggests that a forecast of earnings

per share in a valuation model would aid predictions of equity performance.

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However there is evidence that consensus earnings forecasts from analysts have such a

high error rate that given the sensitivity of valuation models, they can add little useful

information, see below.

Figure 2.12: Studies of the Accuracy of Analysts Earnings Estimates

Study Period Number of Companies

Mean Error (%)

Stewart, Jr., 1973 1960-64 14 10 to 15Barefield and Cominsky, 1975

1967-72 100 16.1

Richards, 1976 1972 93 8.8Richards and Frazer, 1977

1973 213 22.7

Richards et al., 1977 1972-76 92 24.1Richards et al., 1977 1969-72 50 18.1

Mean estimate error over all studies 16.6

Source: Dreman, D.,N., 1998, “Contrarian Investment Strategies: The Next Generation,” Simon and Schuster, New York, p.99.

NB: Mean Error is defined as the absolute difference between the actual earnings and the forecast for the next quarter, as a percentage of the forecast.

In addition, the three studies illustrated below show that the earnings forecasts of analysts

for the next quarter are only slightly more accurate than those based upon mechanical

forecasts that simply rely on historic earnings.1

1 Three time-series models have been shown to be useful see: Bathke, A.,W., and Lorek, K.,S., 1984, “The Relationship between Time Series Models and the Security Markets Expectation of Quarterly Earnings,” The Accounting Review, 59, pp. 163-176. For a more recent paper examining time-series models, see Elgers and Murray (1992).

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Figure 2.13: Studies on the Accuracy of Analysts Earnings Estimates versus

Mechanical Earnings Models

Mean Error (%)Study Analyst Group Analyst Forecasts Mechanical ModelsCollins and Hopwood, 1980

Value Line Forecasts 1970-75

31.7 34.1

Brown and Rozeff, 1979

Value Line Forecasts 1972-75

28.4 32.2

Fried and Givoly, 1982

Earnings Forecaster 16.4 19.8

Source: Damodaran, A., 1994, “Damodaran on Valuation,” John Wiley & Sons, New York, p81.

NB: Mean Error is defined as the absolute difference between the actual earnings and the forecast for the next quarter, as a percent of the forecast.

The evidence also suggests that the superior forecasting ability of analysts declines, as the

forecast period increases. O’Brien (1988) found that the forecasts of analysts were more

reliable than mechanical models for 1 and 2 quarters ahead, equal for 3 quarters ahead

and worse for 4 quarters ahead.

Even though forecasts may be inaccurate, the extent of disagreement between analysts, as

measured by the standard deviation of growth predictions, has been shown to be a useful

indicator as to the reliability of the consensus earnings estimates. The lower the standard

deviation, the more likely is the forecast to be accurate. See Givoly and Lakonishok

(1984).

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Research from Strathclyde University concluded that 1) forecasts tend to err towards

optimism, 2) that the further ahead the time period, the greater the degree of error, and 3)

that forecasts made more than one period ahead were little more accurate than a naive

extrapolation of past earnings.

Over and above the normal difficulty of predicting future events, forecaster optimism

(and inaccuracy) possibly stems from the conflict of interests within Investment Banks.

Analysts are constrained by the fact that, as well as providing impartial advice and

forecasts for companies to institutional investors, the same companies are often corporate

clients. As corporate clients would rather a high share price to a low share price, the

Corporate Finance department will ensure that forecasts lead to the highest possible share

rating.

For Smaller Companies, the consequences of this conflict of interest can be magnified.

Due to the relatively low turnover of shares it would be reasonable to assume that

corporate, rather than institutional brokerage is the main driver of revenue. In addition,

securities analysts are paid in relation to the stock they sell rather than the accuracy of

their forecasts (Dorfman (1991)). The fact that only a few stock brokerage houses follow

Smaller Companies adds to forecast unreliability, as the corporate brokers forecast is

usually taken as a guide by other competing analysts. This reduces the benefit of a range

of independent analysis.

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2.7.1 Earnings models

As discussed above, a simple extrapolation of the past earnings growth rate is not

sufficient. However certain studies have produced reasonably accurate forecasts of future

earnings from historic accounting data.

Ou and Penman (1989a) hypothesized that there is underutilised information about future

earnings contained in a variety of financial variables. They examined the Compustat

database for the period of 1965 to 1972 in order to form a strategy for investment during

the period of 1973 to 1983. A summary measure named ‘Pr’ was constructed from

published financial ratios. The Pr measure was used to indicate the direction of change of

one-year forward earnings. The forecast direction of change in earnings was then

compared to previous earnings (including a drift value that was based upon the last four

years earnings growth, cf. Section 2.6.2). Following the Ou and Penman strategy,

companies that were forecast to beat their ‘drift adjusted’ earnings were bought. Over a

two-year holding period, the average return of a portfolio that was made up of positive

earnings (long) and negative earnings (short) predictions was 7.0%. Out of the 34 (50%

of sample) attributes shown to be significant over one period, 26 of them were found to

indicate the same direction of forecast earnings for the second period.

Ou and Penman found that a high Pr was associated with prior earnings declines and

future price increases and vice versa. They also found that the results were improved

when the model was combined with a low PER strategy (Ou and Penman (1989b)).

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Stober (1992) found that where brokers estimates are available (via I/B/E/S) the brokers

estimates are marginally more accurate than the prediction of Ou and Penman’s Pr

measure (72.8% vs. 70.9%, respectively). Interestingly the predictive performance of Pr

when the forecast of Pr and I/B/E/S estimates agree, rose to 78.2%, and when Pr and

I/B/E/S predictions disagree the analysts predictions are correct in 54% cases vs. 46% for

the Pr strategy. So the Pr model is best used, if at all, in combination with estimates from

analysts.

It should be noted that in promoting their own forecasting model, Holthausen and Larcker

(1992), demonstrate that the Pr strategy ‘breaks down’ in the 1983-1988 period.

2.7.2 Cash flow models

Sloan (1996) put forward the hypothesis that because investors “fixate on current

earnings”, they fail to use the information in accruals and cash flows that provides a good

forecast of future earnings. Sloan showed that companies with a high (low) level of

accruals experience negative (positive) future abnormal stock returns. He argued that the

value of cash flow from operations (CFO) when compared to net earnings is due to the

fact that aggressive accruals are not sustainable over long periods of time. This

information can be used to gain a position in a stock before the share price reacts when

the next earnings figures are announced. Sloans definition of accruals is,

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Accruals = ( ΔCA – ΔCash ) – ( ΔCL – ΔSTD – ΔTP ) – Dep

| Current Assets | | Current Liabilities | | Depreciation |

Where ΔCA = change in current assets

ΔCash = change in cash/cash equivalents

ΔCL = change in current liabilities

ΔSTD = change in debt included in current liabilities

ΔTP = change in income taxes payable

Dep = depreciation and amortisation expense

In order to scale for size (MV) the accruals measure should be divided by Average Total

Assets.

The result of a ‘long’ bottom decile accrual, ‘short’ top decile accrual portfolio over a

one-year holding period is shown below.

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Figure 2.14: Zero Net Investment, Long Low Accrual, and Short High Accrual.

Compustat data 1962-1992

Source: Sloan, R.,G., 1996, “Do Stock Prices Fully Reflect Information in Accruals and Cash Flows about Future Earnings,” The Accounting Review, 71, July, pp. 289-315, Table 6.

The returns are relatively stable with an average size adjusted excess return of 10.4%

over the thirty-year study period.

In support of the above strategy, Bernstein (1993) states that,

“Analysts [should] relate CFO to reported net income, as a check on the quality of that

income. A company with a high net income and a low cash flow may be using income

recognition or expense accrual criteria that are suspect”

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2.7.3 Other predictive models

2.7.3.1 The T-Model

Tony Estep (1987) developed the T-Model, this expresses expected stock return in three

terms—Growth, Cash flow yield, and Valuation change. It was demonstrated that 94% of

the return of a stock during 1982-1985 could be forecast if ROE, growth rate of

shareholders equity, and change in PTBV were known with hindsight. The Estep

proposition is that if the dependent variables are accurately forecast, then the model has

predictive ability.

The T-Score = g + ROE – g + PTBV * (1 + g) PTBV PTBV

| Growth | | Cash flow yield | | Valuation change |

Where,

T-Score = Total return

g = Growth in shareholders equity over the period

ROE = Net Income during the period / Opening Shareholders Equity

PTBV = Opening Market Value of firms common stock / Opening Shareholders

Equity

PTBV = Change in PTBV during the period

During the period of the study, portfolios with a high expected return according to the T-

Model, outperformed the S&P 500 by 9.8%, the portfolios had a standard deviation of

13.8% vs. 13.2% for the S&P 500.

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2.7.3.2 Jacobs and Levy Model

Over the test period of 1982 to 1987, for a sample of 1000 stocks, Jacobs and Levy

(1988) looked at the prediction of the dividend discount model (DDM) return vs. a model

comprising of 25 equity attributes. They found that the DDM (see Section 3.1) was

insignificant when placed in a multivariate model with the 25 attributes. The attributes

that provided statistically significant abnormal returns were: PSR, short term tax loss,

neglect, relative strength, residual return reversal (-1 month, -2 months), trends in

analysts estimates (-1 month, -2 months), sigma, and earnings surprise (-2 months, -3

months) the R2 of the model was 43.93%.

They also tested PER, book/price, cash flow/price, yield, Beta, coskewness, size, earnings

growth consistency, low price, tax rate, trends in analysts estimates (-3 months), and

earnings surprise (-1 month). However these attributes were not found to be statistically

significant.

2.7.3.3 Brennan and Subrahmanyam Model

In addition to other attributes, Brennan and Subrahmanyam (1996) assessed liquidity as a

factor that effects returns. They used the dollar volume of trading as a reasonable proxy

for liquidity, and in one of the few studies to test the APT, they found the returns to

Volume, MV, PTBV, and 3, 6, and 12 month lagged share price performance to be

significant.

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2.8 Are the market inefficiencies a proxy for risk?

A major debate in Finance has been as to whether the rational asset pricing paradigm

(CAPM or APT) holds. Are the accounting characteristics (discussed above), that

empirically provide excess returns, a proxy for risk, or do they explain predictable excess

stock returns at constant risk?

Damodaran (1994, see Section 3.1.2), rearranged the DDM relationship, to show that,

P0/E0 = (Payout ratio * (1 + gn))/ (Er-gn)

Where gn is the expected growth rate of earnings, and Er is the required rate of return.

Keeping other values constant, the relationship between PER and β can then be

demonstrated (from the CAPM relationship, via a change in Er).

Figure 2.15: The relationship between Beta and the PE Ratio

Source: Damodaran, A., 1994, “Damodaran on Valuation,” John Wiley & Sons, New York, p. 204.

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Literature Review

It can be seen that, the PER will fall as β increases. This is because under the CAPM (see

Section 2.2) Er, the required rate of return, is a positive function of β. If the CAPM holds

then a low PER is a proxy for risk as defined by Beta. However this is not demonstrated

in empirical tests, in fact the relationship is reversed. See Figure 2.01, and Section 2.4.1.

Fama and French (1993, 1994, 1996) have theorised that the various market inefficiencies

are related to each other, and can be amalgamated into a three-factor model. The FF

model is defined as:

E(Ri) - Rf = bi [E(RM) – Rf] + si E(SMB) + hi E(HML)

Where E(Ri) - Rf, is the expected return of a portfolio in excess of the risk free rate. This

is dependent upon three factors. (1) the excess return of a broad market portfolio, (2) the

difference in return of a portfolio of small stocks and the return of a portfolio of large

stocks (SMB), and (3) the difference in return of a portfolio of high book-to-market

stocks and the return of a portfolio of low book-to-market stocks (HML). The historic

return of a low PTBV (high book-to-market) portfolio is around 20.5 percent per year

(see Figure 2.03), so for the stocks with a low EP, low cash flow per share and high sales

growth (which tend to have a high PTBV ratio), the expected return is lower. Fama and

French propose this model as an equilibrium pricing model and find that in a regression

of the three factors on price an R2 of 92% is demonstrated.

48

Literature Review

In collaboration with Baker, Haugen (1995) studied the relationship between volatility

and return. In this US study, Larger Companies were classified as those stocks in the

S&P 500 Index, and Smaller Companies were those in the Russell 2000 Index

(MV<$200m.). For the period of 1928 to 1992, Haugen formed portfolios that were

based upon stocks with (24 month historic) low and high volatility. Interestingly, the

results show that the low volatility stocks provided higher future annual returns.

Figure 2.16: The Annual Returns of High vs. Low Volatility Portfolios

Source: Haugen, R.,A., 1995, “The New Finance: The Case against Efficient Markets,” Prentice Hall, Englewood Cliffs, New Jersey, p. 86.

NB: Large Cap. (S&P 500) sample 1928-1992.Small Cap. (Russell 2000) sample 1979-1992.

The effect is even more pronounced for Smaller Companies, as measured by the Russell

2000 Index. These results are in direct contrast to the CAPM theory, which states that

higher rewards can only be achieved by taking higher risk (volatility).

49

Literature Review

Fuller et al. (1993) produced one of the few studies that make use of the BARRA

database. This sophisticated risk management system is widely used amongst investment

management companies. The BARRA system attempts to identify the sources of alpha

(excess return) in terms of fifty-five industry classifications and thirteen other potential

risk factors. However, Fuller et al. found that their sorted EP portfolios provided a better

explanation of stock performance than that of the complex BARRA model.

It would seem that investment risk is difficult to express in a simplified manner. This is

not surprising given the many factors that influence share prices. It may be that risk

occurs in different ways for different strategies. For example, low PER stocks may

outperform because investors are compensated for the risk of company failure. However

investors in high PER stocks would also seem to be taking risk, insomuch as they are

relying on a premium level of earnings growth, that is difficult (impossible) to forecast.

Both sectors then, suffer a different type of risk.

The Fama and French measure (above) is an extension of the CAPM model, and in a

sense, is a simplification of the APT model. Their measure has a high predictive ability

but, if remains to be seen whether irregularities are found in this model, either over time,

or over explanatory factors.

Until more complex models are developed that can consistently classify the risk of

holding a particular stock, it is perhaps best to express risk in simple terms, as the

variability of total return. All investors will understand that, in practice, the risk of

50

Literature Review

holding equities is a combination of the average return that they provide and the

variability of that return.

Consequently, this study will assess risk as the standard deviation of total return, and will

avoid the misleading simplification of using Beta values.

2.9 Conclusion of the literature review

Whilst many of the studies reported in this section are US based, it seems that value

strategies are also profitable in other international markets (Capaul et al. (1993)).

The strategy of value investing (that is, of investing in low rated stocks) was first

documented the 1930s (Graham and Dodd (1934)). One of first academic studies to

demonstrate the benefits of the low PER strategy was undertaken by Basu (1977,1983).

In 1994, Lakonishok et al. extended the work of Basu, and calculated that over a period

of 22 years a low PER investment screen provided, an average excess (to market) return

of 2.7% p.a.

Fama and French (1992) investigated the result of following a low PTBV strategy. They

found that over the period of 1963 to 1990, an excess (to market) return of 4.6% p.a.

would have been achieved.

Fewer studies have focused on the potential benefits of following a low PSR strategy, but

the results, nevertheless, have been impressive with excess returns of 2.04% p.a.

available over an 8 year study period (Jacobs and Levy (1988)).

51

Literature Review

In a test of a high yield screen Dreman (1988) found that over a 27 year period, these

stocks provided an average excess return of 1.2 % p.a.

The most striking aspect of the value strategies, is the magnitude of the outperformance

recorded. With the benefit of compounding over a 20 year period, an excess return of

2.7% or 4.6% p.a. for the PER or PTBV strategies respectively, results in phenomenal

total returns.

Strategies that exploited the patterns detected in share price behaviour were found to be

even more profitable. Jegadeesh and Titman (1993) were able to demonstrate a one-

month and long-term (three year or five year) share price return reversal, along with the

continuation of share price momentum over shorter time periods. A long-short portfolio

of the companies with the highest, and lowest, six-month relative share price momentum,

provided an excess return of 9.5% over the following twelve months.

The information value of earnings (growth) announcements was investigated by Bernard

and Thomas (1990). They found that a portfolio that takes a long position in the top

decile of earnings performers, and a short position in the bottom decile of earnings

performers, provided an excess return of 7.74% over a 180 day holding period.

52

Literature Review

Jegadeesh and Titman (1993) noted that those shares that outperformed at earnings

announcements also tended to be those with positive six-month share price momentum.

It has been shown that analysts are poor forecasters of company earnings (Damodaran

(1994), Dreman (1998)). In one of the few studies of Smaller Companies, Mott and

Coker (1993) reported that companies that reported an earnings surprise tended to

outperform by 12.9% over the following twelve months. Interestingly, a high proportion

of companies (34%) continued to surprise the market at future announcements. For these

‘positive repeaters’ the excess return over twelve months accelerated to 19.3%.

Bauman and Miller (1997) looked at earnings surprise by equity characteristics. They

found that earnings surprise tended to be negative for high PER companies and positive

for low PER companies. This provides a partial explanation as to why low PER stocks

outperform the market.

Hawkins, Chamberlin and Daniel (1984) put forward evidence that the revision of

earnings forecasts has informational value. Twelve-month risk adjusted returns of 14.2%

were available for investors in stocks with the largest upward revisions in consensus

earnings forecasts.

The above trading strategies are relatively simple. Greater rewards were thought to be

available for investors who could use the information within company accounts that was

deemed relevant to the future share price.

53

Literature Review

Ross-Healy and Sgromo (1993) devised a complex strategy that identified companies

with improving Balance Sheet strength. During the period of 1983 to 1990 this strategy

outperformed the market by 7.7% p.a.

The strategy of Ou and Penman (1989a) was to use published accounting data in order to

create a long-short hedge portfolio consisting of companies that were forecast to beat (or

not beat) their ‘drift adjusted’ earnings. Over a ten-year test period, the portfolio provided

a size adjusted excess return of 3.5% p.a.

A more profitable (and less complex) strategy was developed by Stober (1992). He

constructed a long-short hedge portfolio based upon accounting accruals. Over a period

of thirty years, this portfolio provided an average excess return of 10.4%.

Finally, the T-Model developed by Estep (1987) was shown to produce an excess return

of 9.8% p.a. However the time period of the test was relatively short (3 years), and other

researchers have had difficulty in replicating the results. Nevertheless, the use of the

PTBV ratio in a theoretical way is of interest.

A summary of the profitable investment screens found during the course of this Literature

Review is documented below.

54

Literature Review

Figure 2.17: Annualised Excess Return for Investment Strategies

NB: The strategies of Accounting accrual, Ou and Penman ‘Pr’, Share price relative strength, and Earnings growth are based upon long and short (hedge) portfolios, consequently they also benefit from the returns of the short position. The other strategies are long only.

One criticism of the studies is that they all rely on the integrity of Compustat. There is

bound to be little disagreement over the market inefficiencies as there is no comparative

data set. Consequently there is a debate about the accuracy of the data. One argument is

that there is a survivorship (selection) bias (Kothari et al. (1995), Breen and Korajczyk

(1994)). This is that, we may expect to see a correlation, for example between low PER

firms and outperformance, if those low PER firms were in financial distress at the time

that they were included in test portfolios and subsequently survived. If those companies

that had correspondingly low PERs, but went bankrupt, were removed from the database,

then there would be a bias in the results towards low PER companies. However a great

55

Literature Review

deal of effort has been spent on trying to clean up the data base (De Silva (undated)) and

as yet no major reversals in the findings have been reported.

The recorded excess return of certain strategies may also be as a consequence of the

miss-measurement of expected returns because, 1) the processing of financial information

is not costless and 2) that the prices recorded on Compustat are sometimes not prices that

could be traded at. In addition, transaction costs will erode a proportion of the returns.

These are not insignificant, for instance, the average bid-ask spread on the NYSE has

been calculated as 2.8% (Keim (1989)).

With reference to Figure 2.17 the returns that the strategies provide are far superior to

those achieved by traditional active Investment Management. It is fair to ask why, in a

world where outperformance is substantially rewarded in terms of large bonuses, have the

inefficiencies not been exploited and consequently arbitraged away?

One answer may be that whilst the idea of value strategies have been documented since

Graham and Dodd (1934), the computing power to ‘prove the case’ has been available for

considerably less time.

An additional explanation as to why Institutional Investors fail to exploit the

demonstrated inefficiencies, would be that their time horizons are so short that they

cannot take the risk of pursuing a value strategy that might take a number of years to

outperform. This is irrational given that Trustees should be seeking outperforming

56

Literature Review

strategies, but is not incomprehensible in a world where investment mandates are

reviewed yearly, if not more frequently.

It is also possible that the answer as to why market inefficiencies persist, lies in human

psychology. The behavioural scientist Amos Tversky (1995) commented,

“Rather than operating on rational expectations, people are commonly biased in several

directions: they are optimistic; they overestimate the chances that they will succeed, and

they overestimate their degree of knowledge, in the sense that their confidence far

exceeds their ‘hit rate’”,

and also that,

“Recognising our limited ability to predict the future, is an important lesson to learn”.

I.M.D.Little (1962, 1966) theorised that investors put undue weight on past events, and

that these are poor predictors of the future (see Section 2.6.2). The desire to be part of

‘The Crowd’ pushes investors towards well-known and proven companies. Trustees are

unlikely to question blue chip investments, whereas value stocks are often considered to

be the shares of companies that face severe problems. Detailed discussions of the field of

Behavioural Finance are to be found in Jacobs and Levy (1988), Hunter (1988), Thaler

(1993), and Wood (1995).

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Literature Review

One of the most striking findings in the process of this Literature Review, was that of the

work of Fuller et al. (1993). They found that investors are able to identify, and award a

high PER to those stocks with superior earnings potential. However it is shown in other

work that the same high PER stocks, and investment funds as a group, tend to

underperform (Malkiel (1995), Jensen (1968), and Section 2.4.1). Consequently, it seems

that fund underperformance is due to a combination of overaggressive valuation of those

equities that are (rightly) considered to be superior earnings performers, and also of the

earnings disappointment that is a consequence of analyst forecast error (Damodaran

(1994), Dreman (1998), Figure 2.11).

Finally, there is the thorny issue of risk. Principally the studies calculate the risk-adjusted

return of a strategy, from the expected return as defined by the CAPM. However the

CAPM depends upon stock Beta values that have been shown to be poor predictors of

future return (Gibbons (1982), Stambaugh (1982), Fama and French (1993, 1994, 1996)).

Due to this, the results must be viewed with caution. Market capitalisation has been

demonstrated to be a better predictor of stock performance than Beta, so this has also

been used as a proxy for risk. But it is not clearly understood for what reasons MV is a

proxy for risk, and indeed how consistent this factor may be. (Note that in the UK, the

beginning of the underperformance of the FTSE Smaller Company Index relative to the

FTSE All-Share Index coincided almost exactly with the publication of articles about the

UK ‘Small Cap [outperformance] effect’ in the late 1980’s). Size as a measure of risk,

may prove to be as inconsistent as Beta.

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Literature Review

However the Efficient Market Theory cannot be refuted until the complex subject of risk

has been fully understood. Even though so many ‘inefficiencies’ have been demonstrated

that it is temping to reject the theory merely on the weight of evidence alone, it is not yet

possible to precisely specify the risk that any of these strategies suffer, so this temptation

should be avoided.

It is interesting to consider that as soon as risk is properly understood, those strategies

that really do provide risk-adjusted excess returns will be exploited. When this occurs,

the anomaly will cease to exist, and the Efficient Market Theory will dominate once

more.

59

Introduction to Equity Valuation

3.0 INTRODUCTION TO EQUITY VALUATION

60


3.0 INTRODUCTION TO EQUITY VALUATION

In the Literature Review, the various market inefficiencies that have been presented to

date were discussed. However the demonstration of the existence of a pattern between a

share price and an equity attribute, is not sufficient to prove the relationship. It is possible

that the occurrence of the pattern may be due to chance, or due to circumstances that may

not be repeated in the future. It is therefore essential for a proposed market inefficiency to

have some theoretical basis. The subjects of equity valuation, and company financial

performance are explored in this, and the following chapter.

3.1 The dividend discount model

The Dividend Discount Model (DDM) states that the value of a company is the sum of

the discounted dividend flows that the company will produce over its lifetime.

Company Value = D0 + D1___ + .… + Dn___

(1+r)1 (1+r)n

Where D is the forecast dividend in each time period, r is the discount rate and n is the

life time of the company or investment.

When the term structure of both interest rate and equity risk premium is flat, and earnings

growth is constant, the value of an equity can be calculated via a rearrangement of the

61


perpetuity formula. This is called the Gordon Growth Model after Gordon (1962). It is

expressed below.

P = D0 * (1+g)/r-g

Where P = Share price, D0 = Current dividend per share, g = Growth rate of earnings per

share and r = the discount rate.

3.1.1 The relationship between the DDM and accounting ratios

Miller and Modigliani (1961) show that the DDM can be rewritten in terms of various

accounting ratios. This is due to the fact that 1) a constant dividend growth rate model is

mathematically similar to that of an annuity, and 2) that accounting ratios are interrelated.

As various accounting ratios are related to the dividend, a DDM valuation can be

expressed in terms of earnings (via a constant payout ratio), cash flow (via constant

depreciation rate, working capital adjustment and payout ratio), sales (via a constant net

margin and payout ratio) and book value (via a constant ROE and payout ratio).

Consequently, a high DDM valuation would be characterised by a high dividend (yield),

high earnings (i.e. low PER), high cash flow (low PCF), high sales (low PSR) or high

book value (low PTBV).

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In a study, Sorensen and Williamson (1980) found that a DDM ranked portfolio had a

16% excess return for undervalued stocks and 15% negative excess return for overvalued

stocks. This was supported by similar findings from Haugen (1990).

It would seem then, that some of the value-based inefficiencies that are discussed in the

Literature Review could be thought of as a failure of investors to price stocks correctly on

the basis of the DDM. However, this could also be seen in terms of risk. It is not

uncommon for the DDM to place over 80% of the value of a company on dividends

forecast more than five years ahead 1. Therefore, the reward for holding low PER stocks

(which are often indicated as undervalued by a DDM) could be for the risk that investors

take when trying to forecast so far into the future.

Given the complexity of data input into a DDM, and the fact that low PER and high yield

strategies outperform DDM strategies, then on its own, the DDM seems of little use as a

portfolio filter.

However it does provide a theoretical basis for the observed outperformance of high

yield, low PER, low PCF, low PSR and low PTBV stocks.

1 This is easy to calculate. From the MV of a quoted company, deduct the DDM valuation of the dividends expected over the next five years, the remainder is the DDM value of the company post year five.

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3.1.2 Price to earnings

The following derivations of the DDM in terms of accounting ratios are based upon the

work of Damodaran (1994).

From the constant growth DDM,

P0 =__DPS1__ (1)( r-gn )

Where, P0 is the Price at time 0, DPS1 is the dividend for next period, r is the cost of

equity (from the CAPM), and gn is the expected growth rate in equity and earnings.

If DPS1 is rewritten as,

DPS1 = EPS0 * Payout ratio1 * (1 + gn)

where EPS0 is the earnings per share at time 0, and Payout ratio1 is the payout ratio for

period 1, then equation (1) can be expressed as,

P0__ = Payout ratio1 * (1 + gn) (2)EPS0 (r-gn)

64


And in terms of the EPS for the next time period as,

P0__ = Payout ratio1_EPS1 (r-gn)

This model can be extended into multiple time periods via the equation:

P0___ = Payout ratio * (1+g) * (1- ((1+g) n /(1+r) n )) (3)EPS0 (r-g)

+ Payout ration * (1+g) n * (1+g n)__(r-gn) * (1+r)n

Where,

n = Number of years of high growth (and/or visibility of a particular growth rate)

g = Expected growth rate in equity and earnings in the first n years

gn = Expected growth rate in equity and earnings in the subsequent years

Payout ratio = Payout ratio for first n years

Payout ration = Payout ratio after n years

For companies with low/no dividend payments, the ratio of FCF to earnings can be

substituted for the payout ratio.

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3.1.3 Price to book value

From the two period growth DDM in terms of the PER, (equation (3))

P0___ = Payout ratio * (1+g) * (1- ((1+g) n /(1+r) n )) (4)EPS0 (r-g)

+ Payout ration * (1+g) n * (1+g n)__(r-gn) * (1+r)n

If EPS0 is expressed as, EPS0 = BVPS0 * ROE, (this is from a simple accounting identity

where BVPS0 is the Book value per share in time period 0), and substituted into (4) then,

P0___ = ROE * Payout ratio * (1+g) * (1- ((1+g) n /(1+r) n )) BVPS0 (r-g)

+ Payout ration * (1+g) n * (1+g n) (r-gn) * (1+r)n

The PTBV ratio is seen to be dependent upon the ROE. In other words, companies with a

high ROE should sell for a higher PTBV ratio than companies with a low ROE.

Therefore, if the DDM holds, then the stocks that investors should look for (i.e. those that

are undervalued), are stocks with a low PTBV ratio and a high ROE.

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3.1.4 Price to sales

The main benefit of the Price to Sales Ratio (PSR) is that it can be used to value

companies that are making a loss. In addition, the sales figure is not subject to the

vagaries of accounting policy to the same extent as are the PE and PTBV ratios. The PSR

is also more stable over time.

From the one period stable growth DDM in terms of the PER (equation (2)),

P0__ = Payout ratio1 * (1 + gn)EPS0 (r-gn)

Substituting in, EPS0 = Net Profit Margin0 * SPS0, (where SPS0 is the Sales per share in

period 0),

P0 = Net Profit Margin0 * SPS0 *_Payout ratio1 * (1 + gn) ( r-gn )

P0__ = Net Profit Margin0 * Payout ratio1 * (1 + gn) SPS0 ( r-gn )

If the profit margin is based upon the earnings in the next time period then,

P0__ = Net Profit Margin1 * Payout ratio1 SPS0 ( r-gn )

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For the two stage model,

P0_ = Net Profit Margin1 * Payout ratio * (1+g) * (1- ((1+g) n /(1+r) n )) SPS0 (r-g)


From the above relationships, it is evident that firms with higher net profit margins will

sell for higher PS ratios than firms with lower net profit margins. This is for two reasons,

one is direct, and the other is via the lower expected growth rate.

With reference to Section 4.1, the effect on the growth rate (g) is due to following

relationship,

Fundamental EPS Growth (g)= Retention ratio * ROE

= Retention ratio * (Net profit/Sales) * (Sales/BV of

Equity)

= Retention ratio * Net Profit Margin * (Sales/BV of

Equity)

As the Net profit margin is reduced the expected growth rate will reduce, unless Sales

increase proportionately.

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For an investment screen, companies with low PS ratios and high net profit margins

should be considered undervalued and companies with high PS ratios and low net profit

margins should be considered overvalued.

3.1.5 Debt to equity ratio

A high debt to equity ratio (DER) enhances a company’s valuation by increasing the

ROE. This can be demonstrated via the following relationship.

ROE = ROA + (DER * (ROA – i (1 – t))) (5)

Where,

ROA = Return on Assets (Pre-interest)

DER = Book Value of Debt / Book Value of Equity

i = Interest Expense

t = Tax rate on ordinary income

Equation (5) can then be substituted into,

Earnings Growth = Retention ratio * ROE

Earnings Growth = Retention ratio * [ROA + (DER * (ROA – i (1 – t)))]

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So, the higher the DER, the higher is the fundamental earnings growth of a company.

This provides a theoretical basis for the finding of Bhandari (1988), Section 2.4.6.2, that

companies with a high DER provided positive excess returns.

3.2 Cash flow valuation

In his book, Alfred Rappaport (1986) argues that managers and investors judge company

performance by looking at the wrong financial measures. He highlights some of the

shortfalls of earnings which are discussed below.

1) Rappaport argues that the PER as a theoretically sound valuation ratio is flawed. He

asserts that the leap from dividend, which is a cash measure, to earnings, which are an

accounting measure, is like comparing “apples and pears”. For example, earnings can

be effected by a change in accounting policy, i.e. a change in stock valuation from

LIFO to FIFO, however cash flow will not alter as a consequence.

The difference between cash flow and earnings stems from the fact that accountants

measure revenue from the point of sale and purchases from the point of invoice.

Whereas in reality, there is a delay until actual cash leaves or is received by a

business. This is why a company can be declared bankrupt, even though the P&L

account (and hence EPS) looks healthy. The difference in approach between cash

flow and EPS valuation is apparent for growth companies. Growth Companies would

normally have to increase inventory before cash from sales is received. In this case,

the cost of sales figure will understate the cash outflow for inventory. Obviously there

70


is a counter balance in the increase in payables, however the miss-match of cash to

reported earnings will lead to EPS being greater than cash EPS for a growth

company.

2) Depreciation smoothes the deterioration in the book value of an asset over its

estimated life. However the extent of the charge is subjective. For example, the

estimated life of computer equipment has proved difficult to judge, with some now

arguing that IT spend should be fully written off at the date of purchase. Over time,

errors in predicting asset life can accumulate and prove misleading when certain

accounting measures (particularly Book Value) are assessed.

3) In addition, two companies may produce the same earnings growth however the

leverage of one company could be higher, and consequently the variance of expected

earnings would also be higher. A single measure of EPS does not account for the

increased risk.

Consequently, Rappaport argues that investments should be valued (and compared) on

the basis of discounted cash flow. This supports the findings in Section 2.7.2 where the

positive excess return of low accrual portfolios (Sloan (1996)) was noted.

3.3 Conclusion of the introduction to equity valuation

Valuation theory can justify the market inefficiencies that have been demonstrated for the

ratios of PER, PCEPS, PSR, PTBV, DER, and DYLD and of accounting accruals.

71


In Chapter 5.0 these measures will be tested for potential market inefficiencies within the

sub sector of UK Smaller Companies.

72

Determinants of Company Financial Performance

4.0 DETERMINANTS OF COMPANY FINANCIAL

PERFORMANCE

73


4.0 DETERMINANTS OF COMPANY FINANCIAL PERFORMANCE

4.1 Equity growth rate

It is not sufficient just to seek out companies with a high Return on Equity (ROE). If the

return is high, but the ability to absorb cash (i.e. reinvest) is low, then the growth in value

will be lower than for a similar company that can reinvest more of its cash flow (at the

same ROE). The retention ratio (RR) can be used as an indication as to the investment

opportunities available for a company, the higher the RR, the more opportunities. The

achievable growth rate is defined as,

Achievable Growth Rate = ROE * RR

Where, RR = (EPS-DIV)/EPS

An additional consideration, is that a company may face an incremental Return on

Investment that is higher/lower than the historic rate. The incremental ROI (IROI) can be

calculated as below,

Incremental ROI = OP NI

Where OP = Change in Operating profit less interest, less tax over a period

NI = Net investment in working capital and fixed assets over a period

74


One of the benefits of calculating the IROI is that it is not distorted by out of date

Balance Sheet asset valuations, as is the ROE.

4.2 Issues of cash flow

4.2.1 Depreciation charge

Depreciation is a provision out of profit towards the cost of replacing an asset at the end

of its life. However the rate of depreciation is almost always determined by the

management, so it would be reasonable to be suspicious of companies where the

depreciation rate is substantially lower than that of the peer group.

4.2.2 Working capital

Over time, the increase in working capital (stock + debtors - creditors) should be

proportionate to the increase in sales. However for growth companies, expansion causes

stock and debtors to increase disproportionately. As accounting measures accruals, this

causes a mismatch, for example, earnings are recorded on sales that are not yet paid

(debtors), and assets are recorded when no contracted buyer has yet been found for them

(stock). In addition trade creditors are not reported in the P&L account, although these

are debts that must be paid. The P&L account can therefore mask the true cash position

of a company.

One test that is used in order to assess earnings manipulation is to compare EPS growth

over a period, with cash flow per share (CEPS) growth over the same period. A shortfall

75


in cash growth would be seen as a negative indicator. Also, an expanding working capital

to sales ratio would warn of a potentially unsustainable growth rate.

4.2.3 Free cash flow

The cash flow statement is split into three sections. These are net cash from Trading,

Financing, and Investing. Any surplus or loss on the sale of businesses or fixed assets is

deducted from the operating profit and included in the Investing account. Any cash from

operating activities that is left after financing activities is then available for capital

expenditure and dividends to equity shareholders. Capital expenditure is not segmented

further, but it has two distinct uses. First to grow the business organically, and second to

replenish worn out assets. The replenishment of assets is necessary in order to maintain

present cash flow, and is therefore essential spending. Free cash flow is that which is left

after this expenditure. Despite the reservations stated above, the depreciation charge is

often taken as a proxy for replenishment spend, as for an outside investor it is difficult to

assess the true need for replacement capital expenditure.

Free cash flow as a percentage of Pre-tax profit is a reasonable measure of the spare cash

resources that a company has after funding capital expenditure, dividends, tax, interest,

and working capital. A ‘high’ percentage indicates that a company has the flexibility to

invest in acquisitions or organic growth, or has the ability (if the free cash flow is

consistent) to service higher debt levels in order to grow.

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Free cash flow can also be used as an indicator for potential corporate activity. For

example, if free cash flow is able to finance debt (at a rate of 2% above LIBOR, and with

repayment over 15 years) of greater than the market capitalisation of the company it is a

prime target for an MBO or takeover.

During the period 1992-1996, Philips (1998) found that seventy eight percent of

companies in the UK Engineering sector with free cash flow as a percentage pre-tax

profit of greater than 120% outperformed the market. In his analysis Philips created an

index of ‘average operating cash as a percentage of pre tax profit’ * ‘average return on

capital employed’, the higher the value, the better the prospects for company.

The results of tests of CEPS as a percentage of EPS for UK Smaller Companies are

reported in Chapter 5.0.

4.3 The value drivers

The Du Pont Formula splits the Return on Equity into components in order to quantify

the value drivers of a business.

Return on Equity = Attributable profit / Book Equity

= Attributable profit * Sales_ * Assets_____Sales Assets Book Equity

= Earnings Margin * Asset Turn * Equity Solidity

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An increase in the Earnings Margin, Asset Turn, or Equity Solidity Ratio will increase

the ROE and hence the achievable growth rate of a company (see Section 4.1).

Although a higher earnings margin can compensate for a lower asset turn, the best

companies outperform on all measures. This is because high margins and high asset turns

generally provide high cash flow to 1) Invest in more high return assets, 2) Retire equity,

or 3) Pay high dividends.

The Drivers of Earnings Margin are:

Depreciation Turnover

This ratio may decline if previously owned assets are converted to leases. Whilst

operating leases are charged against operating profits, and finance leases are charged to

the interest account, in both cases Asset Turn would increase. If the ratio of depreciation

to turnover has reduced without a corresponding increase in Asset Turn then depreciation

rates may have been relaxed.

Staff costsSales

The above ratio is a useful measure of the service element of a business. High staff cost

to sales = high service = high margin = high PSR (see Section 3.1.4).

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Sales______________Number of Employees

This is measure of how labour intensive the business is.

Operating profitEmployees

This is a measure of how much a business can charge for the time of its employees.

A business that is both labour intensive and has a high profit per employee is therefore

attractive.

Per capita profit Per capita sales

A ratio of greater than one can indicate a positive change in product or service mix. [Less

than one can indicate pursuit of turnover for its own sake].

The Drivers of Capital Efficiency are:

Sales_______________________________________ = Asset turnAverage of opening and closing Tangible fixed assets

Asset turn will rise if the capital spend of a business is producing an increase in sales

over and above the increase in assets. A static asset turn with higher sales is not

satisfactory if the increase in assets is essentially a requirement in order to carry on

trading.

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Working CapitalSales

If there is a divergence between operating profit and cash inflow from operations, then

the cause is normally that sales growth requires further investment in working capital

(e.g. stocks and debtors).

Sales___________________________________ = Intangible asset turnAverage of opening and closing intangible assets

Acquisitive companies can seem to be more profitable than they are, for example, by

writing down assets to ‘fair value’, writing off the goodwill to reserves, and then selling

the stock at higher than carrying value, therefore inflating profit. Similarly over-provision

can be made for (not so) doubtful debtors. However working capital as a percentage of

sales will then be seen to increase, as both are replenished at normal values, and under

FRS 10 companies that buy-in turnover will show a deteriorating intangible asset turn.

Cost of goods sold________________ = Stock turnAverage of opening and closing stock

This indicates the speed at which a company can turn its inventory into saleable goods.

Average of opening and closing trade debtors = Debtor daysSales/365

The timely collection of debt indicates both good working capital management and the

strength of a company’s bargaining position.

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Average of opening and closing trade creditors = Creditor daysCost of goods sold / 365

As long as supplier relationships are not damaged, the more interest free credit that a

company can gain, the better.

4.4 Operational gearing

In general the resilience of the profits of a company to volume and price pressures, is

determined by the margin structure of the profits. The resilience to volume declines

depends upon operational gearing, and resilience to price falls depends upon the

operating margin. However it is the relationship between fixed and variable costs, that

determines the degree of the resilience.

Resilience to volume declines:

The profit sensitivity to a decline in volume is determined by the relationship between

direct variable costs, and fixed overhead costs. However it is not just that fixed costs are

negative and that variable costs are positive. The most important ratio is the amount by

which gross profit covers net profit, that is the extent by which profits, after variable

costs, exceed the fixed overhead.

Traditionally if a company had a gross margin of 40% and a net margin of 20% then if

sales declined by 10% profits would be expected to fall by 20%. This is illustrated by the

relationship below,

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Profit gearing = Gross margin * Change in sales Net margin

However in the short term “Gross margin” costs such as Labour are likely to be relatively

fixed. If the charge for Labour moves to below the calculation of gross margin then the

sensitivity of profits to sales declines increases greatly. In general, Labour costs could be

defined as 80-90% fixed, other costs 90% fixed, and depreciation and R&D, 100% fixed.

Resilience to price declines:

A 5% price fall for a company earning a net profit margin of 15% will result in the net

profit margin falling to 10%. So, the higher the net margin the less destructive is a given

price fall.

Depending upon the stage of the business cycle operational gearing can be either useful

or destructive. It may prove advantageous to use a screen for operational gearing as a

check on whether, for example, a value stock is on a low rating because it has a high level

of operational gearing and is about to enter a cyclical downturn.

4.5 Risk of failure

Syspas Z-Score:

Syspas looked at a sample of failed companies in order to see whether these companies

had similar accounting characteristics leading up to the point of failure. Companies

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deemed ‘at risk of failure’ were given a negative Z-Score. The findings are summarised

below,

1) Turnover - At risk companies had 30% of the turnover of the sample

2) Profits - 44% report losses vs. 3% for strong firms

Profitable at risk companies had margins of 6% compared to 12%

for profitable strong firms

3) Assets - At risk companies spend less on fixed assets, typically 4.5% of

turnover vs. 7.5% of turnover for strong companies.

4) Capital Structure -

Healthy At Risk

Net Worth 47 13

Creditors 27 36

Long Term Debt 16 36

Provisions 8 3

Short Term Debt 2 12

Theory suggests that investing in high-risk (negative Z-Score) companies would provide

greater returns. However Professor Richard Taffler (1997) of the City University

Business School, found in a sample of all UK quoted companies over the period 1983-

1994, that those with a negative Z-Score underperformed the positive Z-Score portfolio

by an average of 4.7% p.a.

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There were however dramatic periods of low Z-Score outperformance ( 6/1984 - 1/1987 )

and underperformance ( 1/1987 – 1/1992 ), reflecting a strong business cycle effect.

The Z-Score could be used in the process of portfolio, screening in order to make sure

that low PER or low PTBV stocks are not reflecting a risk of company failure.

4.6 A test for correlation between accounting ratios and outperforming companies

In their book “In Search of Excellence” Peters and Waterman (1982) attempted to define

the characteristics of a company with better than average growth prospects. They took a

list of companies that were regarded as superior by businessmen and screened them for

common attributes. These were found to be,

Attribute 1961-1980 Average

1) Rate of growth in corporate assets 21.78 %

2) Rate of growth in book value 18.43 %

3) Average ratio of market price to book value 2.46 x

4) Average return on corporate assets 16.04 %

5) Average return on book value 19.05 %

6) Average ratio of net income to sales 8.62 %

In a study of the subsequent performance of these companies, Clayman (1987) found that

the share prices of the group that she called the ‘unexcellent’ (the 39 companies with the

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worse combination of the six characteristics) had risen by 297%. Whilst, the share prices

of the excellent companies had risen by only 181%. In addition, the rates of growth in

assets and book value nearly halved for the excellent group and reductions were seen in

other attributes as well.

Clayman’s study clearly demonstrates the concept of ‘reversion to the mean’ (as

discussed in Section 2.6.2). This strengthens the case for value based strategies as

creating a portfolio of the days best performing companies (in terms of accounting ratios)

is shown to prove unsuccessful.

85

Ranked Portfolio Tests: UK Smaller Companies

5.0 RANKED PORTFOLIO TESTS FOR MARKET

INEFFICIENCY: UK SMALLER COMPANIES

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5.0 RANKED PORTFOLIO TESTS FOR MARKET INEFFICIENCY:

UK SMALLER COMPANIES

5.1 Tests for market inefficiencies

In the chapters of the Literature Review, Introduction to Equity Valuation, and

Determinants of Company Financial Performance it was demonstrated that exposure to

the following factors would have produced portfolio returns in excess of the market

index.

1) Low firm Size

2) Low price to book

3) Low price to sales

4) High dividend yield

5) Mid-high debt to equity ratio

6) Low PE ratio

7) Low three/five year historic share price performance (positive return over 3-5 year

holding period)

8) High six month historic share price performance (positive return over one year

holding period)

9) High twelve month historic share price performance (positive return over three month

holding period)

10) Low accruals (scaled for MV)

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11) Top 10% of earnings performers

12) Positive earnings surprise

13) High upward revision in earnings forecasts

14) Ou and Penman (1989a) ‘Pr’ value of greater than 0

15) Attractive Estep (1987) valuation

In addition, Valuation Theory indicates that those companies with a high Return on

Equity and those companies that convert a high level of earnings into cash should

perform well.

The factors of positive earnings surprise and high upward revision in earnings forecasts

would seem worth investigating for UK Smaller Companies but unfortunately, it has not

been possible to gain access to the I/B/E/S earnings forecast data set. This is

disappointing given the high returns of these strategies. In the case of Ou and Penman’s

Pr measure and Estep’s T valuation, these are too complex to calculate given the time

frame of this study.

Therefore tests for possible inefficiencies within the FTSE Smaller Company Index, were

conducted on the following attributes.

1) Low price to book

2) Low price to sales

3) High dividend yield

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4) Low PE ratio

5) High six month historic share price performance (positive return over one year

holding period)

6) ROE

7) Cash EPS as a percentage of EPS

Plus, combinations of any strategy that was found to be successful.

5.2 Methodology

5.2.1 Definition of the FTSE Smaller Company (Ex IT) Index

The FTSE Smaller Company Index is made up of all companies in the FTSE All-Share

Index that are not in the FTSE 350 Index. The FTSE 350 Index consists of the 350 largest

(by market capitalisation) companies that are quoted on the London Stock Exchange, and

the FTSE All-Share Index consists of companies representing the top 98% (by market

capitalisation) of quoted companies. The FTSE Smaller Company (Ex IT) Index,

(referred to as the FTSE Smaller Company Index from here on) is the FTSE Smaller

Company Index after eliminating all Investment Trust companies. This is the usual

benchmark index for UK Smaller Company portfolio managers as they specialise in UK

equities, whereas the Investment Trusts that are included in the FTSE All-Share Index (of

which 82 are in the ‘Smaller Company’ market capitalisation band) can invest

internationally.

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5.2.2 Data collection

The data for this study was extracted from the Datastream database.

5.2.2.1 Constituents of the proxy smaller company index

In order to test the index-relative performance of quartiles of portfolios of companies

ranked by a particular accounting ratio, it was necessary to have a list of the constituents

of the benchmark index for past years. However it was found that FTSE International will

only make the data available on a commercial basis, and that Datastream does not hold

the FTSE Smaller Company Index constituent data.

Due to this, it was necessary to assemble a universe of stocks that could act as a proxy

index. The proxy index contained the stocks that would have been candidates for the

FTSE Smaller Company Index at a particular point in time.

Datastream holds the constituents of the FTSE All-Share index from the period 1994 to

date (as of 29/12 of each year). From this constituent list it is possible to construct a

reasonable proxy for the FTSE Smaller Company Index by eliminating companies below

and above the FTSE Smaller company threshold level at that date. These levels are based

upon market capitalisation, and are detailed below.

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Figure 5.01: Market Capitalisation Cut-Off Points for the Proxy Smaller Company

Index

Year-End Low Mkt. Cap. Company High Mkt. Cap. Company

1994 £8.46m Ross Group £285.79 Lex Service

1995 £10.10m Calderburn £470.60m Trinity Int.

1996 £4.92m NSW £354.83m Chiroscience

1997 £8.56m Automotive Hldgs. £370.83 Micro Focus

1998 £37.95m Fortune Oil £338.40m AMV

Source: FTSE International PLC.

The constituents of the FTSE All-Share Index for each year were down loaded into an

Excel file and ‘stripped’ in order to leave only companies whose market capitalisation

was between the above bands. At this point Investment Trusts were removed.

Next, three more sectors were eliminated. These were Pharmaceutical (Biotech)

companies, Oil and Gas exploration companies, and Real Estate companies. This was

because the above sectors are valued based upon their assets (or more correctly, their

projected assets). Often they do not have current earnings or sales, and consequently if

they were kept in the proxy index, they would distort the results.

By this process, a proxy universe, (constituents of a proxy Smaller Company Index) of

stocks was created on the 31st of December for the years of 1994 to 1998.

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5.2.2.2 Portfolio creation dates

Important requirements for test portfolio formation are,

1) Like for like ratios are compared.

The selection universe must consist of companies with the same financial year-end.

This is because the information value of, for example, the historic PE ratio erodes

over time. Consider the historic PE ratio of a company on the day before and the day

after it reports its earnings. On the day after the results are reported, the information is

current, an investor can assess the earnings of last year on that days share price.

However, on the day before the results, the ratio is almost a year out of date. On that

day investors will pay a higher historic PE ratio, as the company has had almost a

year to improve on its historic earnings. For this reason, at a particular date,

companies with different year-ends will be at a different point in their reporting cycle.

Selection rule: At a particular date select companies from a universe of companies

that share the same financial year-end.

2) Ratios are calculated at their most useful point in time

To have a reasonable chance of identifying market inefficiencies, ratio information

must be assessed when it is most relevant. For this exercise, this would be the day that

the results were reported.

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Selection rule: At a particular date select companies from a universe of companies

with the same financial year-end. The date should be the day that results were

reported.

3) The screening criteria must be available at the portfolio creation date.

If a company has a financial year-end in December, then full-year results will

normally be announced to the Stock Market in March of the following year. Thus, for

tests of portfolios consisting of companies with year-ends in December, ratios were

calculated using the stock price as at the first day of April of the following year. It is

assumed that all companies would have reported their results by three months after

their financial year-end.

Selection rule: At a particular date, select companies from a universe of companies

with the same financial year-end. The date for the share price should be three months

after the financial year-end.

4) Within the sample portfolios, company-specific risk must be minimised.

One problem with portfolio formulation by criteria is that the sample size reduces

fairly quickly. For the tests, it was considered that the minimum number of shares in a

portfolio should be eighteen. Although not ideal, (this is a function of the size of the

universe of around 450 companies and the aim to assess quartile ranked share price

performance), this size of portfolio is large enough to diversify away approximately

80% of the company specific risk. Due to the constraint of a minimum quartile size of

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eighteen stocks, only companies with a December and March year-end have sufficient

representation. See below.

Figure 5.02: Year-End Distribution for December 1994 Proxy-Index

Month of YE 1 2 3 4 5 6 7 8 9 10 11 12

No. of Cos. 18 5 86 27 11 30 7 6 34 9 6 115

5) A reasonable number of sample portfolios must be built in order to achieve statistical

significance.

The more samples that are taken, the more the data will reflect the characteristics of

the Population. Around thirty data points are regarded as sufficient in order to start to

draw statistically significant conclusions about the Population.

If the selection rules are adhered to with regard to point 4 above, and as the index

constituents are only available from December 1994, then only 8 data points would be

collected. I.e. Full-year results for March and December year-end companies, for a period

of four and a half years. In order to increase the sample size, it was thought reasonable to

include interim results, as these provide new valuation information. However, this still

results in only 15 data points. So, due to the limited data availability, it was considered

acceptable to create portfolios with a ‘six month from financial year-end’ time lag. In

support of this decision, recall the finding that it takes up to three months for analysts to

incorporate new information into forecasts (see Section 2.5). These lagged portfolios give

investors three months to disseminate the information reported in the Company Accounts

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(as opposed to portfolio formation on (or near to) the day of the results for the non-lagged

samples).

For companies with December and March year-ends the tables below illustrate the

portfolio formation dates, and the proxy index from which the companies are selected.

Figure 5.03: Portfolio Creation Dates

Constituents from Proxy Index at 31/12

December Year-end, Full-year results. Ratios at:

December Year-end, Interim results. Ratios at:

19941995 1/4/95 1/10/951996 1/4/96 1/10/961997 1/4/97 1/10/971998 1/4/98



December Year-end, Full-year results. Lagged; Ratios at:

December Year-end, Interim results. Lagged; Ratios at:

19941995 1/7/95 1/1/961996 1/7/96 1/1/971997 1/7/97 1/1/981998 1/7/98



March Year-end, Full-year results. Ratios at:

March Year-end, Interim results. Ratios at:

1994 1/1/951995 1/7/95 1/1/961996 1/7/96 1/1/971997 1/7/97 1/1/981998 1/7/98

95




March Year-end, Full-year results. Lagged; Ratios at:

March Year-end, Interim results. Lagged; Ratios at:

19941995 1/10/95 1/4/951996 1/10/96 1/4/961997 1/10/97 1/4/971998 1/10/98 * 1/4/98

* All share price performance tests are for the period of 1/10/98 – 1/8/99

5.2.2.3 Time Period

The measurement of share price performance against the FTSE Smaller Companies Index

was over the twelve months following the formation of the portfolio. It was considered

(in line with the Literature) that this was a sufficiently long period for share prices to

react to information contained in the financial ratios. In addition, fund managers are often

assessed over a rolling twelve-month period.

5.2.2.4 Test portfolios

With regard to Figures 5.03-5.06, it will be noted that the year for the proxy index

universe is sometimes different to that of the year of the formation of the test portfolio.

This was in order to match the period during which the performance of the portfolios was

measured, with the universe from which the stocks were selected. See, for example,

“March year-end, interim results, ratios at: 1/1/95”, the proxy index for this portfolio is

from 31/12/94, as this is nearer to the portfolio creation date than 31/12/95.

Portfolios were each allocated a code based upon Year of proxy portfolio, Month of

creation of test portfolio, Year of creation, Year of end of measurement period of return,

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Month of financial year-end, and whether the sample was taken after full-year, or interim

figures. If ‘L’ is within the code, then this signifies a portfolio that has been created with

a Lag, i.e. three months after figures were released.

For example, 9419596MINT, represents a portfolio consisting of companies from the

1994 proxy universe, with a March year-end, that have recently presented their interim

results; the portfolio is constructed in January 1995, and total return is measured from

January 1995 until January 1996.

For the portfolio screening tests, each list of possible portfolio constituents from the 30

date points was taken in turn; then companies were sorted in order of the attribute that

was being assessed. First a screen to eliminate outliers was made, then the portfolio was

ranked into quartiles. Over the subsequent year, the total return of each quartile was noted

and compared against the total return of the FTSE Smaller Company Index. This was

then repeated for other attributes.

In a laborious process, 300 different portfolios were constructed in order to measure the

total return for the 10 test characteristics, over the 30 time periods.

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5.3 Consideration of the significance of the results

It was necessary to assess the total return for the portfolios in two ways. First there was

the possibility that the data could mislead if a number of results distorted the calculated

mean value (i.e. they may not be representative of the true population). To quantify

whether the mean value was representative, the two tailed Student t test was used.

Second, as investors are concerned about both the absolute return of a particular strategy,

and the volatility (standard deviation) of the return, then some assessment had to be made

as to the trade off between return and the consistency of that return. This was evaluated

by calculating the Sharpe Ratio.

5.3.1 The Student’s t test

The Student t test was used to calculate whether the average performance of a particular

quartile was significantly different from zero. The Student t distribution was used

because the population standard deviation was not known and also because the sample

size was small (30 portfolios). In using the t distribution it was assumed that the

population was approximately normal.

The central (null) hypothesis of the test was that the portfolio did not outperform the

FTSE Smaller Company Index, i.e. the outperformance was zero. This is denoted as:

H0: μhe alternate hypothesis was that the performance of the portfolio was not

equal to zero, H1: μ≠. As the level of outperformance could be greater than, or equal

to, zero then a two-tailed test was appropriate.

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The level of significance of the test is the probability of accepting the alternate hypothesis

(in this case “that the characteristic outperforms the FTSE Smaller Company Index”)

when, in fact, the sample mean is not significantly different from zero. The higher the

level of significance is, the more sure that we can be in accepting the alternate

hypothesis. The tests were undertaken at 10, 5, 2, and 1% levels of significance (1% is

high, 10% is low). The process of the t test is detailed below.

The sample size was 30, so the test was for 29 ‘degrees of freedom’. (n=30, d.f.=29)

H0: μ

H1: μ≠

The Estimated standard error of the mean, σ = __ σ __ n

The sample mean was then ‘standardised’ by subtracting the hypothesised mean (H0:

μ), and dividing by the Estimated standard error of the mean, σ . The test statistic

is,

t = - μH0

σ

If the value of t was greater than + or - the critical value of t (that is the value of t from

the t distribution for a given level of significance and degrees of freedom) then the null

99


hypothesis (in this case the ‘sample does not outperform’) was rejected. The critical

values for t in the tests were,

100


To 10% significance: +/- 1.699

5% significance: +/- 2.045



5.3.2 Portfolio risk

A rational investor would prefer a higher level of return for a given level of risk.

However the trade off between risk and return is the subject of much debate. The Sharpe,

Jensen alpha (αp) and Treynor ratios are most commonly used to assess this relationship.

The Sharpe ratio is defined as,

Sharpe ratio = (Rp - Rf)/Rp)

Whilst the Jensen αp is defined as,

Jensen αp = p (Rm - Rf) - (Rp - Rf)

(This is derived from yearly regressions of the portfolio return)

And the Treynor ratio is defined as,

Treynor measure = (Rp - Rf)/p,

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Where for each ratio,

Rp - Rf = portfolio excess return

Rf = average risk free holding-period return,

Rm = market holding period-return,

Rp = average portfolio holding period-return,

Rp) = standard deviation of excess (to risk free) returns for portfolio p.

p = portfolio p’s index of systematic risk,

The Treynor ratio is dependent upon calculating a β value for the portfolio. In effect, the

portfolio return is standardised by the CAPM expected return. The Jensen alpha assesses

portfolio risk in a similar fashion. As there is an ongoing debate about the usefulness of β

(See the Literature Review), and as the calculation of 300 portfolio Beta values would be

time consuming, it was decided not to use the Treynor ratio or Jensen alpha to assess the

risk-reward relationship.

For the Sharpe ratio the excess return is defined as the portfolio return over the risk free

rate. The Sharpe ratio, scales excess return by the volatility (standard deviation) of the

excess return. This is a basic statistical measure, and is relatively easy to understand. The

higher the excess return that is achieved per unit of risk (standard deviation), the higher is

the Sharpe ratio. Due to its simplicity of understanding and calculation, this study

measures the risk-adjusted excess return of portfolios by their Sharpe ratio.. Datastream

does not construct a benchmark yield for one-year UK Government Bonds so the yield

for three-month Bonds is taken as the risk free rate.

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5.3.3 Stage of business cycle

This study focuses on the performance of Smaller Company shares during the period of

1/1/95 to 1/8/99. In the analysis of a data sample it is important to note any variables that

may have affected the results. To help achieve this, the year on year percentage change in

UK GDP during the study period is shown below in Figure 5.7.

Figure 5.07: UK GDP Growth (% YOY) 6/1990 – 6/1999

Source: Datastream

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On the chart, the trend growth of UK GDP is plotted at 2.25% p.a. This is, approximately,

the rate of real growth that the UK economy has enjoyed over the medium term. It can be

seen that during most of the period of this study the UK economy was growing at a rate

above its normal trend. Consequently the most rigorous interpretation of the results of the

tests would be that UK Smaller Companies perform in the way indicated, during a period

of above trend economic growth.

5.4 Portfolio ranking, performance and analysis

The total returns (capital plus income) of the individual portfolios formed for each test of

market inefficiency are detailed in Appendix 8.2.

5.4.1 The proxy universe

The first test to be conducted was to see whether the thirty proxy-index portfolios

performed similarly to the FTSE Smaller Company Index. If these did not perform

similarly, then the usefulness of the subsequent results would be limited to proxy

universes constructed in the same way, rather than to the FTSE Smaller Companies

Index.

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Figure 5.08: Test of the Acceptability of Portfolios as a Proxy the FTSE Smaller

Company Index

Portfolio Mean Outperformance (%)

Portfolio Mean Outperformance (%)

9419596MINT -6.85 9549596LMINT -4.59519697MINT -11.3 9579596LDFY 1.99549596DFY 2.9 95109596LMFY -6.69579596MFY -3.1 9519697LDINT -2.795109596DINT -0.4 9649697LMINT -11.79619798MINT -2.8 9679697LDFY -5.49649697DFY -7.6 96109697LMFY -7.19679697MFY -12.9 9619798LDINT 1.896109697DINT -1.8 9749798LMINT -6.69719899MINT 4.5 9779798LDFY 09749798DFY -4.9 97109798LMFY 1.19779798MFY -1.9 9719899LDINT 4.397109798DINT 3.7 9849899LMINT 4.89849899DFY -3.7 9879899LDFY -5.49879899MFY 1.9 981098To899LMFY 6.6

Mean (%) -2.5Standard Deviation 5.18

Null Hypothesis Outperformance =

0

Degrees of Freedom 29Estimated standard error of Pop. mean

2.02

Standardised Value -1.22

Critical values for t: 10% significance: +/- 1.699@ 29 d.f. 5% significance: +/- 2.045

2% significance: +/- 2.4621% significance: +/- 2.756

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The t statistic for the thirty portfolios with H0: μand H1: μ≠ is –1.22. This

indicates that to the 10% significance level, the null hypothesis of zero outperformance

against the FTSE Smaller Company Index cannot be rejected.

Therefore the thirty test portfolios are representative of the FTSE Smaller Company

Index.

5.4.2 Price to earnings

Datastream definition:

This is the ratio of the current share price divided by the earnings per share reported over

the last twelve months.

Earnings per share = Net Profit after Tax, minority interest and preference dividends,

(excluding pre tax extraordinary items, non-operating provisions

and transfers to tax-exempt reserves and any other items not

considered to normal trading activities of the company), divided by

the average number of shares in issue during the period, (adjusted

for scrip and rights issues).

Each test portfolio was sorted by the PE ratio of its constituents. Within the data set there

were found to be extreme values for the PE ratio. At the low end were companies that

were loss makers (i.e. with negative PE ratios), and at the high end were companies that

were making insignificant earnings per share relative to their share price. In order to

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screen the test portfolios so that a general investment rule could be established (if any),

then the outliers needed to be eliminated.

This is a difficult stage of data analysis as the researcher could be accused of data mining.

Data mining is when a sample is manipulated in order to achieve the results that are

required. One approach that is used to eliminate outliers is to delete all data points that

are above, and below, two standard deviations from the mean. The rule would result in a

portfolio that incorporates 95% of the data points. Although, even the choice of two

(rather than one, or three…) standard deviations from the mean could be questioned.

This study takes a different approach. Whilst wishing to be academically rigorous (i.e.

not wishing to be accused of data mining), the aim of this project is to create investment

rules that have a theoretical backing. A two standard deviation rule still leaves companies

in the data set with very low and very high PE ratios, these will tend to be companies in

financial distress, and the aim is to use the investment rules to invest in companies that

are acceptable to an institutional investor.

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With reference to Section 3.1.2, Damodaran has expressed the PE ratio as,

P0___ = Payout ratio * (1+g) * (1- ((1+g) n /(1+r) n )) EPS0 (r-g)

+ Payout ration * (1+g) n * (1+g n)__ (r-gn) * (1+r)n

Where,

n = Number of years of high growth/visibility





r = Cost of equity

In order to calculate upper and lower bounds for PE ratios a high-growth company and a

low-growth company were characterised.

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Figure 5.09: Theoretical PE Ratios for High and Low Growth Companies

Factor Low Growth High GrowthNumber of years of high growth/visibility 6 6ROE for first n years 10.6% 25%Payout ratio for first n years 33% 25%Expected growth rate in equity and earnings in the first n years

7% 19%

ROE after n years 10.6 13Payout ratio after n years 33% 25%Expected growth rate in equity and earnings in the subsequent years

7 10

Cost of equity 10.57 10.57Damodaran PE ratio 10.13x 53.29x

The ‘number of years of high growth/visibility’ is set at six years. This follows from the

work of Fuller et al. (1993) as discussed in Section 2.6.2. (They found that investors are

able to correctly judge the relative EPS growth rate of a company for up to six years

ahead.)

The ‘Expected growth rate in equity’ is calculated as Growth Rate = Return on Equity *

Retention ratio. For an explanation of this relationship, see Section 4.1. The retention

ratio is defined as 1- the payout ratio.

The cost of equity is the yield on a 10 year benchmark bond (@9/7/99) plus an assumed

equity risk premium (ERP) of 5%. (There is currently a debate as to whether the ERP is

declining from historic levels. For UK Equities, the ERP for the period of 1919-1993 was

6.14% 1. Five percent was considered a reasonable assumption).

1 BZW Equity and Gilt Study 1993

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Based upon the above assumptions the Damodaran PE ratio ranges from approximately

10x for a low-growth company to approximately 50x for a high-growth company. As 10x

is a theoretical rating for a low growth company, and because we wish to leave in the

sample companies that are ‘under priced’, then the low PER band is set at 7x historic

earnings. The high band is set at 50x historic earnings.

For the test, companies in each proxy index universe with a December or March year-end

and PE ratios of between 7x and 50x were sorted into ascending order of PER, and then

into PER quartiles. The total return of each quartile was then measured over the

following year and noted, along with the average size of the market capitalisation of the

quartile. This process was repeated for the 30 portfolio creation dates, in order to

calculate an average value.

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The results of the PE Ratio screen are summarised below.

Figure 5.10: Performance of Portfolio Quartiles by PE Ratio

Quartile FTSE SC Index

1 (Low)

2 3 4 (High)

Strategy Performance relative to the FTSC Index

Mean (%)

-4.29 -6.45 -3.44 3.87

Standard deviation

13.82 5.94 7.58 7.16

Estimated standard error of the population mean

2.57 1.10 1.41 1.33

t value -1.67 -5.84 -2.44 2.91Sharpe ratio 4.9 -8.5 12.9 59.6 39.6



The t values for quartiles 2, 3, and 4 are highly significant. This means that the null

hypothesis of zero outperformance can be rejected. The null hypothesis of zero

outperformance can also be rejected for the first quartile (but only at the 10% level).

Over the period, the forth quartile of PE ratios outperformed the FTSE Smaller Company

Index by an average of 3.87%. This value is significant at a level of 1% (critical value of t

= +/- 2.46). The strategy outperformed in nineteen out of the thirty periods measured, so

positive returns were recorded for 63% of the time.

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The Sharpe ratio of the FTSE Smaller Company Index is 39.6 (this will remain constant

over all of the tests). The average Sharpe ratio of the forth quartile portfolios is 59.6, so

the benefit of the excess return of the strategy is not hindered by excessive volatility

relative to the volatility of the return of the FTSE Smaller Company Index.

Therefore, from the evidence above, it is statistically valid to state that “Investments

should be in made in companies with a PE ratio in the forth quartile of an ascending PER

ranking.”

5.4.2.1 Discussion of the PER screen

Interestingly, the result of the PER screen for UK Smaller Companies is the opposite of

the result of earlier studies. Graham (1973), Basu (1977,1983), Lakonishok et al. (1994),

and Goodman and Peavy (1983) all found that low PER stocks tend to outperform.

Whereas this study found that high PER stocks have outperformed, and that low PER

stocks have underperformed.

First the differences between previous studies and this must be addressed. Previous

studies have assessed all companies quoted on the stock market, whereas this study has

deliberately focussed on Smaller Companies. In earlier studies of the market as a whole,

it was noted that Smaller Companies tend to outperform, and that they also have lower

than market PE ratios; for this reason previous work has attempted to eliminate the ‘size

bias’ in results, by scaling for market capitalisation. This was done to counter the (pro-

CAPM) argument that low PER stocks outperformed in order to compensate investors for

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the higher default risk of investing in Smaller Companies. One would expect then, that

the results of this study would reflect the previous non-MV scaled finding that low MV,

low PER stocks outperform. Is it possible that there is a different size effect happening

within the Smaller Company sector?

In terms of the distribution of the PE ratio, the sample seems quite similar to the non-MV

scaled ‘all market’ studies. For the PER test in this study, the average MV of Q1, Q2, Q3

and Q4 was £137m, £157m, £165m and £162m respectively. The MV of Q4 is higher

than Q1, so in a similar fashion to the ‘all market’ studies, the PE ratio is a positive

function of size; however in this study Q4 outperforms, rather than Q1.

If the reason for the variance in quartile performance was due to risk, then in common

with past research, this study would be expected to show that a high PER strategy

underperforms. This is because investing in larger ‘Smaller Companies’ is considered

less risky by investors, for example, because of higher liquidity, see Brennan and

Subrahmanyam (1988), Section 2.7.3.3.

This study illustrates that in the case of Smaller Companies, investing in high risk/ low

MV / low PER companies is penalized: once again, reward does not equal the risk taken.

See also Figures 2.01 and 2.05.

However, this does not explain why the high PER stocks in the sample outperform.

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Another way of looking at the result is to say that investors are systematically paying too

low a PE, for a high PE ratio company. Relative to the market, over a twelve-month

period, the price of a high PER company is seen to increase. In ‘all market’ studies, it is

theorised that the low PER sector, outperforms because companies tend to revert to mean

performance, and that high PER stocks tend to underperform investors expectations. See

for example, Figures 2.10 and 2.11.

In this study, the outperformance of high PER stocks could be due to the earnings of

these companies surprising on the upside. It may be that the expected earnings growth for

the high PER sector was too low, or it could be that earnings growth remained higher

than investor’s original expectations.

During the period of this study the UK economy was growing fairly strongly, see Figure

5.07. The best (high PER) Smaller Companies would be expected to benefit from this

growth environment. During the period the rate of inflation was also reducing, companies

would be reporting high earnings growth, but in a climate of low inflation, investors may

have been cautious as to the sustainability of the high earnings growth demonstrated by

high PER companies.

If a less favorable economic environment were forecast, then PE ratios would normally

be expected to discount lower earnings in the future. However, as the economic

environment continued to be positive and above trend, then the market may have been

consistently ‘surprised’ by strong company earnings. Share prices would have to adjust

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upwards in order to maintain a constant PE ratio. The longer the boom continued, the

longer growth stocks (high PER stocks) remained attractive, and the longer the low PER

stocks remained unattractive. During the Literature Review, a long-term study of the

Smaller Company sector by PER was not found, so it is not possible to cross check the

results of this study. The ‘growth phase’ argument seems a reasonable explanation as to

the outperformance of high PER Smaller Companies, over the time period studied.

Until a longer-term data set is available (one that incorporates a number of business

cycles), the investment rule should be limited to “During periods of above trend

economic growth, invest in Smaller Company shares with a high PER”.

Rule One: During periods of above trend economic growth, invest in

companies with a PER in the highest 25% of all companies. Avoid companies

with a PER in the lowest 75% of all companies.

5.4.3 Price to book


This is the ratio of the current share price divided by the Book value per share.

Book value per share = Share capital reserves minus intangible and deferred assets,

divided by the average number of shares in issue during the

period, (adjusted for scrip and rights issues).

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A price to book value ratio of less 0.5x would mean that investors are willing to pay only

50 pence, or less, for each £1 of balance sheet assets. This would indicate that a company

is in financial distress. In order to select companies that were not in financial distress, the

lower bound of the price to book value ratio was set at 0.5x. To check whether this was a

reasonable level, the Damodaran value for the PTBV ratio was calculated for the low

growth company in Figure 5.09. The Damodaran formula for the PTBV ratio is discussed

in Section 3.1.3 and restated below.

P0___ = ROE * Payout ratio * (1+g) * (1- ((1+g) n /(1+r) n )) BV0 (r-g)


Where,

n = Number of years of visibility





r = Cost of equity

Based upon the above assumptions, the Damodaran value for the PTBV of a Low Growth

company is 1.29x. The limit of 0.5x would therefore seem a reasonable indicator of a

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company in distress. There was no upper bound set for book value, as book value is

relatively stable over time. This means that (in contrast to the problem with high PE

ratios) there are few companies on extremely high PTBV ratios. NB: According to the

assumption in Figure 5.09, the price for a high growth company could be justified up to a

PTBV ratio of 18x.

The results of the PTBV screen are summarised below.

Figure 5.11: Performance of Portfolio Quartiles by PTBV Ratio


1 (Low)

2 3 4 (High)


Mean (%)

-1.18 -3.70 -5.80 -2.66

Standard deviation

5.21 6.26 11.01 9.18


0.97 1.16 2.04 1.70

t value -1.22 -3.19 -2.84 -1.56Sharpe ratio 31.3 10.7 -3.7 14.4 39.6



The t statistics for quartile 1 and quartile 4 are not significant to 10 %. However quartiles

2 and 3 are significant to the 1% level.

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If the sample is assessed by bottom half of PTBV and top half of PTBV, the means are

-2.2 and -4.3, and the t statistics are –2.67 and –2.64 respectively. These figures are

significant to the level of 2%. The data shows that price to book value cannot be used as a

screen for investments to buy. Another basis for rejecting the PTBV as a screen is that the

Sharpe ratio for each quartile is below the Sharpe ratio for the market. Although as the

figures for quartiles 2 and 3 are highly significant, the PTBV screen could be used in the

sense that stocks with a PTBV in quartiles 2 and 3 should be avoided.

5.4.3.1 Discussion of the PTBV screen

The PTBV was found to be a useful screen by Rosenberg, Reid, and Lanstein (1985), and

Fama and French (1992). In addition, De Silva (Figure 2.04) scaled companies by MV

and found the low PTBV effect to be more pronounced in Smaller Companies.

It is difficult to interpret the PTBV test in this study, as only Q2 and Q3 are significant.

The underperformance of Q3 is greater than Q2, so it is possible that the data displays a

trend for higher PTBV ratio companies to underperform lower PTBV ratio companies,

but unfortunately the mean values for Q1 and Q4 are not significant to 10% so the trend

cannot be confirmed further. In addition the whole sample underperforms the market.

Theoretically, this is possible, as the test portfolios are equally weighted, and the FTSE

Smaller Company Index is Market Value weighted. (The reason that this study tests

equally weighted portfolios, is because Smaller Company investors do not track the index

in the same way as larger company investors. I.e. they are happy to take on more

company specific risk.)

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It is possible that at the level of MV for Smaller Companies, the results of the PTBV tests

are inconclusive, as investors do not see the PTBV ratio as a relevant valuation measure.

When valuing a small growth company the main concern is likely of intangible assets

rather than physical property. A market cap weighted test over a longer time period

would further aid understanding.

Rule Two: The tests do not indicate that PTBV is a relevant portfolio screen

for Smaller Companies.

5.4.4 Price to sales


This is the ratio of the current share price divided by sales per share.

Sales per share = Goods and services to third parties relating to the normal activities of

the company, (net of sales related taxes), divided by the average

number of shares in issue during the period, (adjusted for scrip and

rights issues).

The price to sales ratio is relatively stable over time, see Section 2.4.3. In addition its use

as a valuation tool benefits from the fact that sales are not subject to the accounting

adjustment of depreciation that distorts the PER and PTBV ratios, see Section 4.2.1.

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The Damodaran derivation for the PS ratio (see Section in 3.1.4) is given below.

P0___= Net Profit Margin1 * Payout ratio * (1+g) * (1- ((1+g) n /(1+r) n )) S0 (r-g)


With a Net Profit Margin of 15%1, and a sustainable ROE of 10.6% as the required equity

return, (i.e. assuming mean reversion of the ROE at year six), the high growth company

in Figure 5.09, would be correctly valued at a price to sales ratio of 3.6x. It was therefore

considered appropriate to set an upper bound of 10x for the price to sales ratio in order to

screen out companies for which the prospect of meaningful sales can only be at some

time in the very distant future. (E.g. Internet Companies).

1 According to Company Refs. data the market median net margin is 5.5 %, with the upper quartile at 10.5%

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The results of the PSR screen are summarised below.

Figure 5.12: Performance of Portfolio Quartiles by PS Ratio


1 (Low)

2 3 4 (High)


Mean (%)

-2.54 -7.24 -4.16 2.25

Standard deviation

8.62 6.60 10.52 8.25


1.60 1.23 1.95 1.53

t value -1.59 -5.91 -2.13 1.47Sharpe ratio 16.3 -16.2 5.7 46.3 39.6



The t statistics for Q2 and Q3 are significant to the level of 1 and 5 percent respectively.

Therefore both of these quartiles underperform the FTSE Smaller Company Index to a

significant degree. The underperformance of Q1 is not significant to 10%. Unfortunately

the outperformance of Q4 is also not significant to 10% (it is significant to 15%).

However due to the higher than market Sharpe ratio (46.3), this quartile will be

considered further in a screen of a combination of factors. Q4 PSR outperformed the

FTSE Smaller Company Index in 56% of periods.

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5.4.4.1 Discussion of the PSR screen

Senchack and Martin (1987) and Jacobs and Levy (1988) found that a low PS ratio was a

significant factor in determining stock outperformance. The results of the PSR test in this

study seem to indicate a trend in the other direction. High PSR outperforms (but not

significant to 10%), whereas Q2 PSR underperforms.

In a similar argument to that of the PER test (Section 5.4.2.1), high PSR stocks should

benefit from a positive economic environment. High PSR stocks will tend to have a high

net margin (see Section 3.1.4). As sales will tend to increase in a period of growth, each

additional £ of sales for a higher net margin company, will translate into a higher level of

profitability (than for a low net margin company). Consequently, the outperformance of

the high PSR sector could be due to the positive economic environment during the time

period of the study, rather than a discernable long-term trend for high PSR companies to

outperform.

Rule Three: During periods of above trend economic growth, avoid investing

in companies in the second and third quartiles of companies ranked by PSR,

(possibly) invest in Q4 PSR companies.

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5.4.5 Return on equity


ROE = Net Profit after Tax, minority interest and preference dividends (this excludes pre

tax extraordinary items, non-operating provisions and transfers to tax-exempt

reserves and any other items not considered to be normal trading activities of the

company), divided by equity capital and reserves (less intangibles, plus deferred

tax).

Companies with a Return on Equity of between 0 and 100 percent were included in the

test portfolios. This eliminates loss making companies and those companies that have a

ROE that is abnormally high (this maybe due to writing down assets excessively, etc).

The results of the ROE screen are summarised below.

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Figure 5.13: Performance of Portfolio Quartiles by ROE


1 (Low)

2 3 4 (High)


Mean (%)

-4.55 -3.14 -4.08 -0.31

Standard deviation

7.91 6.36 9.43 11.78


1.47 1.18 1.75 2.19

t value -3.10 -2.66 -2.33 -0.14Sharpe ratio 5.2 13.2 6.1 29.0 39.6



The t statistics for Q1 and Q2 (the lower half of the sample) are significant to 1% and 2%

respectively. These quartiles underperform the FTSE Smaller Company Index. The same

is true of the Q3 sample (to 5%). The result for the forth quartile is not statistically

significant. This sample indicates that avoiding low ROE companies will be beneficial

for portfolio performance.

5.4.5.1 Discussion of the ROE screen

In Section 4.1, it was noted that the ROE is a driver of the rate of growth of earnings per

share. In Section 2.6.1 it was shown the ROE is also relatively stable over time.

Therefore it would be expected that high ROE companies would have high stable rates of

growth. In addition, in Section 5.4.3 it was shown that the PTBV and ROE ratios are

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mathematically related, accordingly if low PTBV stocks were to outperform, then low

ROE stocks should also outperform. The low PTBV strategy stems from the results of the

contrarian (mean reversion) strategies discussed in the Literature Review. However

because ROE is relatively stable, this could mean that mean reversion might not occur

within the time scale of this study. In addition, it seems (from Section 5.4.3) that the

PTBV ratio is also an unreliable screen for UK Smaller Companies.

The results indicate the opposite of previous research, at least to the level of Q1 and Q2

ROE underperformance. Once again this could be a reflection of a growth economy

during the period of the study. High ROE stocks achieve high EPS growth, see Section

4.1, these stocks would be highly rated and at some point contrarian theory suggests that

they would disappoint; but in the period of 1994-1999, they continued to perform well.

During the period, investors may have sold companies with a low ROE in order to buy

the high ROE companies that were benefiting most from the positive economic

environment. Another possibility is that whatever the environment, Smaller Company

investors do not wish to invest in low ROE companies. However to prove this statement,

data over a longer time period would be necessary.

Rule Four: During periods of above trend economic growth, avoid investing

in companies in the lowest 75% of companies ranked by ROE.

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5.4.6 Cash EPS % of EPS

Datastream definition of Cash EPS (CEPS):

CEPS = Net Profit after Tax, minority interest and preference dividends, (this excludes

pre tax extraordinary items, non-operating provisions and transfers to tax-

exempt reserves and any other items not considered to normal trading activities

of the company), + [depreciation + adjustment for assets sold + depreciation of

assets leased out] + deferred tax + overseas tax equalisation, divided by the

average number of shares in issue during the period, (adjusted for scrip and

rights issues).

CEPS_ * 100 = Datastream definition of CEPS (see above) * 100 EPS Datastream definition of EPS (see Section 5.4.2)

Cash EPS as a percentage of EPS measures how much of the accounting earnings of a

company are converted into cash. For the test samples, a figure of 100 indicates that all

earnings have been converted into cash, below 100 indicates that cash is being absorbed,

above 100 indicates that cash is being released.

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The results of the CEPS/EPS screen are summarised below.

Figure 5.14: Performance of Portfolio Quartiles by CEPS/EPS


1 (Low)

2 3 4 (High)


Mean (%)

-3.05 -5.53 -1.86 -0.49

Standard deviation

7.95 8.47 8.13 7.56


1.48 1.57 1.51 1.40

t value -2.07 -3.51 -1.23 -0.35Sharpe ratio 13.4 -2.5 21.1 34.1 39.6



The t statistics for Q1 and Q2 are significant to 5% and 1% respectively. Companies that

do not convert EPS into Cash EPS tend to underperform the FTSE Smaller Company

Index over the following year. The results of Q3 and Q4 are not statistically significant

(to 10%).

5.4.6.1 Discussion of the CEPS % of EPS screen

Alfred Rappaport (1986), see Section 3.2, emphasised the importance of real cash, rather

than accounting profitability in company valuation. Sloan (1996) and Bernstein (1993),

see Section 2.7.2, put forward the theory, and demonstrated that, companies that had low

127


levels of accruals tended to outperform. In addition, Philips (1998), see Section 4.2.3,

found that companies that generated high levels of cash as a percentage of profits tended

to outperform. All of the above studies noted the superiority of cash flow over accounting

earnings.

The test of cash EPS as a percentage of EPS indicates that a low conversion rate of

profits into cash tends to result in share price underperformance. The results for Q1 and

Q2 agree with previous research.

Rule Five: During periods of above trend economic growth, avoid investing in

companies in the lowest 50% of companies ranked by Cash EPS as a

percentage of EPS

5.4.7 Dividend Yield


Yield is calculated as the current share price, divided by dividends paid in the last

(rolling) twelve-month period.

It was not possible to draw a distinction between companies that do not pay a dividend

because of 1) financial distress or 2) a high re-investment rate (presumably as a

consequence of superior investment returns). So it was decided to eliminate zero yield

companies from the selection universe. There was no upper bound put on yield.

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The results of the DYLD screen are summarised below.

Figure 5.15: Performance of Portfolio Quartiles by Dividend Yield


1 (Low)

2 3 4 (High)


Mean (%)

2.26 -2.29 -6.52 -5.07

Standard deviation

9.39 7.64 8.25 9.04


1.74 1.42 1.53 1.68

t value 1.30 -1.61 -4.26 -3.02Sharpe ratio 42.1 19.4 -11.1 0.7 39.6



The results for quartiles 3 and 4 are highly significant with t statistics that are significant

at the 1% level. Companies that have yields in the top half of yield ranking tend to

underperform the FTSE Smaller Company Index over the following year. The results for

quartiles 1 and 2 are not significant at the 10% level. The Sharpe ratio for Q1 is slightly

higher than that for that for the FTSE Smaller Company Index, however this figure

cannot be relied upon as the quartile outperformance may be due to chance.

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5.4.7.1 Discussion of DYLD screen

Dreman (1998) found that stocks with a high yield tend to outperform, see Section

2.4.6.1. In contrast, over the period studied in this test, high yield stocks have

underperformed.

As Miller and Modigliani (1961) showed, see Section 3.1, the dividend yield and PE ratio

are interrelated (via the payout ratio). Consequently, high yield stocks would tend to be

those stocks that are also low PER stocks. With reference to Section 5.4.2.1, the

underperformance of high yield stocks could be as a result of the positive economic

environment. Alternatively, the result may indicate that Smaller Company investors wish

to invest in companies with high a ROE and retention rate (for which a low dividend

yield could be a proxy).

Rule Six: During periods of above trend economic growth, avoid investing in

companies in the highest 50% of companies ranked by Dividend Yield.

5.4.8 Share price momentum

Definition of test ratio:

Price Change = Current share priceInitial Share Price

Index Change = Current FTSE Smaller Company Index ValueInitial FTSE Smaller Company Index Value

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Share price momentum = [Price Change – Index Change] x 100Index Change

Share price momentum was measured over the six months prior to the formation of the

test portfolio. Companies within the test portfolio were split into two groups, those with

negative momentum (underperformers) and those with positive momentum

(outperformers).

The results of the Momentum screen are summarised below.

Figure 5.16: Performance of Portfolio by Share Price Momentum

Momentum FTSE SC Index

Negative Positive


Mean (%)

-7.00 1.81

Standard deviation

8.96 6.34


1.66 1.18

t value -4.21 1.54Sharpe ratio -11.3 50.6 39.6



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In the year following negative six-month share price momentum, companies

underperformed the FTSE Smaller Company Index by an average of 7%. As the mean

performance figure is significant to 1%, then this is clearly a factor to be avoided. The

positive momentum sector outperformed by 1.8% over the following year and the Sharpe

ratio (50.6) is higher than that of the FTSE Smaller Company Index (39.6), however the t

statistic is not significant to 10% (only to 13%). The positive momentum sector

outperformed in 21 out of 30 time periods (70%) and the negative momentum sector

underperformed for 25 out of 30 time periods (83%).

5.4.8.1 Discussion of the share price momentum screen

The tendency for six-month and twelve month share price momentum to persist, was

noted by Jegadeesh and Titman (1993), see Section 2.4.7.1. The results of the momentum

test indicate quite strongly that stocks with negative momentum should be avoided. The

degree of the under performance (7%), and the significance of the t Statistic (to 1%),

suggests that this screen may prove useful in a combination test.

Rule Seven: During periods of above trend economic growth, avoid investing

in companies with negative share price momentum over six months.

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5.5 Summary of single factor tests

The single factor strategies that displayed statistically significant t statistics are illustrated

below.

Figure 5.17: Statistically Significant Results for the Single Factor Screens

NB: The figures below (and above) the data columns indicate the level of significance of a two tailedStudent t test of the mean performance of the strategy.

In addition, to a level of significance of 1%, stocks with negative share price momentum

underperformed by 7.0%.

The objective of this study was to provide practical indications as to the investment

screens that could lead to portfolio outperformance. Although sixteen statistically

relevant inefficiencies have been demonstrated (by quartile), we cannot take practical

133


advantage of any of the inefficiencies that indicate predictable underperformance,

because it is not possible to take short positions in the shares of Smaller Companies.

Therefore, the quartiles that underperformed would best be viewed as sectors to avoid.

The strategies that outperformed the FTSE Smaller Company Index, and that have a

Sharpe ratio of higher than the FTSE Smaller Company Index, are shown below.

Figure 5.18: Outperforming Single Factor Strategies

Strategy Q4 PER Q4 PSR + Momentum Q1 DYLD

Strategy Performance relative

to the FTSC Index (%)

3.87 2.25 1.18 2.26

Sharpe ratio 59.6 46.3 50.6 42.1

% of Time periods in which

the strategy outperforms

63 56 70 60

t value 2.91 1.60 1.54 1.3

NB: FTSE Smaller Company Index Sharpe ratio = 39.6



The Q4 PER strategy has a high Sharpe ratio and a t statistic that is significant to 1%. The

next highest Sharpe ratios are for the + Momentum, followed by Q4 PSR, followed by

Q1 DYLD strategies. These are not significant to the level of 10%, however the t

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statistics of the + Momentum and PSR strategies are not too far away from the 10% level

(they are significant to the level of 13% and 15% respectively). It was decided to see

whether a combination of these strategies would enhance returns, over and above, the

returns of the individual strategies.

Dividend yield was not assessed further as 1) Statistically, it was the least significant and

2) It could be considered as a proxy for the PER.

5.6 Combination portfolios

The total returns of the individual portfolios formed for each combination test of market

inefficiency are detailed in Appendix 8.3.

As stated in Section 5.1.2.1, it was important to monitor the number of shares in each

portfolio to make sure that they had enough stocks in them to diversify away the majority

of stock-specific risk. When combination screens were run, the number of stocks that

satisfied the first criteria would be by definition only one quarter of the number of stocks

in the initial portfolio. The second screen would then reduce the sample further. For this

reason, quartiles could not be used in the combination tests, either for the initial criteria,

or for the reporting of results. This is as a consequence of the unavoidably small sample

size of the initial portfolios (e.g. there were only 80 stocks in 9419596MINT).

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5.6.1 PER and momentum

Stocks that had PE ratios within the top one third of a PER ranking were selected for the

initial screen. This group was chosen to reflect the outperformance demonstrated by the

top quartile PER strategy, and in order to satisfy the need to hold more than 18 stocks in

the test portfolio. Taking those stocks with positive momentum and those stocks with

negative momentum two test portfolios were then created.

The results of the PER-Momentum screen are summarised below.

Figure 5.19: Performance of Portfolio by PER and Share Price Momentum

Top Third PER FTSE SC Index

NegativeMomentum

PositiveMomentum


Mean (%)

-1.81 5.07

Standard deviation

10.35 8.24


1.92 1.53

t value -0.94 3.31Sharpe ratio 20.3 63.4 39.6



The outperformance of 5.07 % for the top third PER, positive momentum strategy is

significant to 1%. The strategy outperformed for 21 out of thirty periods, that is 70% of

136


the time, and the Sharpe ratio is 63.4. The result for the top third PER, negative

momentum portfolio is not statistically significant to 10%.

5.6.1.1 Discussion of top third of PE ratio and positive momentum screen

The combination screen of PER and share price momentum, provides better results than a

screen of either of the two strategies taken individually (see Figure 5.2.2). The mean

outperformance is highly significant, and has consistently beaten the FTSE Smaller

Company Index (70% of time periods). Whilst the result may be limited to a positive

economic environment, see Section 5.4.2.1, when that environment persists, it would

seem that the strategy is far superior to that of traditional stock picking, see Malkiel

(1995) and Jensen (1968), Section 1.0.

Rule Eight: During periods of above trend economic growth, invest in

companies in the top third of companies ranked by PE ratio that have positive

six-month share price momentum.

5.6.2 PSR and momentum

Stocks that had a PS ratio within the top one third of the sample were selected on the

initial screen. Taking those stocks with positive momentum and those stocks with

negative momentum two test portfolios were then created.

The results of the PSR-Momentum screen are summarised below.

137


Figure 5.20: Performance of Portfolio by PSR and Share Price Momentum.

Top Third PSR FTSE SC Index

NegativeMomentum

PositiveMomentum


Mean (%)

-4.09 5.20

Standard deviation

10.49 9.56


1.95 1.77

t value -2.10 2.93Sharpe ratio 5.9 67.7 39.6



The t statistic for the top one third of stocks rated by PS ratio with positive six-month

share price momentum is significant to 1%. The portfolios outperformed the FTSE

Smaller Company Index by an average of 5.2%, and have a Sharpe ratio of 67.7. The

portfolios outperformed the market in 21 out of 30 periods (70%).

The t statistic for the negative momentum portfolios is significant to 5%. The mean

underperformance was 4.09 %, with the strategy underperforming in 19 out of 30 periods

(63%).

5.6.2.1 Discussion of top third of PS ratio and positive momentum screen

The result is highly significant, and has consistently beaten the FTSE Smaller Company

Index.

138


Rule Nine: During periods of above trend economic growth, invest in companies in

the top third of companies ranked by PS ratio that have positive six-month share

price momentum. Avoid companies in the top third of companies ranked by PS

ratio that have negative six-month share price momentum.

5.7 Summary of combination portfolios

The statistically significant results from the combination portfolios are summarised

below.

Figure 5.21: Performance of Combination Strategies

Strategy Top 1/3 PER,

+ Momentum

Top 1/3 PS, +

Momentum

Top 1/3 PS, -

Momentum

Strategy Performance relative to

the FTSC Index (%)

5.07 5.20 -4.09

Sharpe ratio 63.4 67.7 5.9

% of Time periods that strategy

outperforms or underperforms

70 70 63

t value 3.31 2.93 -2.1

NB: FTSE Smaller Company Index Sharpe ratio = 39.6



139


5.8 Conclusion of data analysis

Figure 5.22: Sharpe Ratios of Outperforming Strategies

NB: The figures above the data columns indicate the level of significance of a two tailed Student t test of the mean performance of the strategy.

With reference to Figures 5.18 and 5.21, the results of the combination portfolios show

that risk adjusted returns can be enhanced through screening a stock universe by more

than one factor.

Over 56% of time periods, the Q4 PSR strategy outperformed by an average of 2.25%

p.a., with a Sharpe ratio of 56.0. Over 60% of time periods the + Momentum strategy

outperformed by an average of 1.18% p.a., with a Sharpe ratio of 42.1. Together, the

140


strategies outperformed for 70% of time periods by an average of 5.2% p.a., with a

Sharpe ratio of 67.7. The joint strategy increased return and risk-adjusted return.

The combination of an accounting ratio screen (PSR) and a momentum screen seems

helpful in picking the high PSR stocks that had the greatest potential for continued

outperformance. In addition, the underperformance of the high PSR and negative

momentum strategy indicated that within the high PSR group, there were certain stocks

that were being de-rated (as contrarian theory would suggest).

Momentum is demonstrated to be a useful indicator of those companies whose results

will disappoint or surprise investors over the following twelve months.

The top 1/3 PSR and positive momentum strategy beats the top 1/3 PER and positive

momentum strategy in terms of both average total return, and Sharpe ratio.

There are a few points that need to be noted before these strategies are followed.

1) A straight comparison between the single and combination strategies was not possible

as in the single factor test, the top quartile of stocks was held, rather than the top 1/3.

2) A disadvantage of including some three-month lagged portfolios, is that over the

three months post the results, the share price may have already reacted, and hence

outperformance may not be registered over the year-long holding period. This

141


increases the likelihood of accepting the null-hypothesis that the selection criterion

does not outperform the FTSE Smaller Company Index. However as indicated in the

Literature Review (see Section 2.4.7.1) share price reaction tends to continue for up

to one year ahead.

3) In addition incorporating overlapping time periods could lead to a misleadingly high,

standardised t-statistic. This is because some of the same companies will have been

selected for both periods, and consequently the standard deviation of the mean

outperformance of the strategy will be reduced (i.e. some of the companies share

prices will perform in exactly the same way for a 9-month period). However a

cursory glance at the lagged and non-lagged portfolios, does not indicate as high a

degree of portfolio similarity as feared.

4) The test period of 1994 to 1999 does not incorporate enough business cycles to enable

a general strategy to develop. A particular strategy is only valid if the economic

environment is similar to that of the test period.

The above criticisms would be resolved if a longer time series of Smaller Company Index

constituents were available for analysis.

Nevertheless, the criticisms do not mitigate the results for the study, which are

statistically significant and indicate that a high level of outperformance can be achieved,

by following very simple rules.

142


Two further tests were conducted. The first was a test of the Wilcox (1984) ROE - Log

PTBV relationship for which a high R2 between the two variables is demonstrated for UK

Smaller Companies (see Appendix 8.4).

The second (see Appendix 8.5) was a test of a low PTBV and high ROE combination

screen proposed by Damodaran (1994, Section 3.1.3). The results of following this

strategy indicate no significant outperformance.

143

Conclusion and Further Study

6.0 CONCLUSION AND FURTHER STUDY

144


6.0 CONCLUSION AND FURTHER STUDY

Past studies have indicated patterns (market inefficiencies) in share price behaviour that

are predictable and profitable. The credibility of these patterns is enhanced as they have a

foundation in valuation theory. The contrarian strategies, the share price reversal, and the

momentum strategy, exist for the same reasons. These are 1) the desire of Investors to be

associated with success (consequently they overpay for stock), and 2) the failure of

Investors to accept that the performance of successful companies will eventually ‘revert

to the mean’. As these are basic human traits, which prove hard to counter, then there is

the possibility that the inefficiencies will continue; they are part of human nature.

6.1 Can the quantitative screening of UK Smaller Companies result in superior

investment returns?

In this study, the UK Smaller Company market has been shown to be inefficient. Seven

single factor quantitative screens, and three combination quantitative screens were

demonstrated to provide statistically significant excess returns.

During the period of the tests, through holding a portfolio of the top one third of

companies ranked by the PSR that had also outperformed the FTSE Smaller Company

Index over the preceding six months, it was possible to earn an excess return (vs. the

FTSE Smaller Company Index) of 5.2% p.a. The Sharpe ratio of the strategy was 67.7 vs.

39.6 for the Index. This means that the volatility of the total return of the strategy was not

excessive as compared to the volatility of the Index. Even in the unlikely event that the

145


whole portfolio is turned over each year, (as some stocks will remain in the screen), the

bid-offer spread of 2.8% (Keim (1989) does not erode the gain excessively, in contrast

with many reported inefficiencies.

The results of the study are all the more interesting as the inefficiencies found in the PER,

PSR and DYLD screens go against the findings of previous research. There are three

possible reasons (or combinations of reasons) for this. First is that FTSE Smaller

Company Investors do not overpay for stock 1, second is that the financial performance of

Smaller Companies does not mean revert as quickly as Larger Companies. Third is that,

as the period of the study coincides with above trend economic growth, there is a

business-cycle-variant nature to whether high or low rated stocks outperform.

Given the high statistical significance of the reported results, reasons for the perverse

nature of Smaller Company share price performance warrant further investigation.

6.2 Further study

Due to the lack of I/B/E/S data the earnings based strategies that proved profitable in all-

market studies were not tested, these should be tested for UK Smaller Companies. Also

within the time frame of this study, it was not possible to test for all of the relationships

established in the review of the determinants of company financial performance. Now

that the relationships are understood, it would be interesting to see whether the share

price of companies that express the desired characteristics outperform the index.1 Even at a high PER, the super-normal earnings growth a Smaller Company may reduce the PER very quickly. Indeed this is one of the main reasons for investing in Smaller Companies.

146


In addition, if a longer-term data set were available then a study of the performance of

ratio sorted portfolios during different points of the business cycle would further aid

understanding.

147

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158

Appendices

8.0 APPENDICES

159

can quantitative screening of uk smaller company portfolios result in superior investment returns

Economy & Finance

equity price reaction26

beta19 figure

average return

share price momentum129

equity market value22

calendar months28 figure

ep ratio35 figure

cumulative return