accounting for risk a fundamental beta prediction...

ACCOUNTING FOR RISK

A FUNDAMENTAL BETA PREDICTION MODEL

CRYSTAL MICHELLE SWAFFORD

UNIVERSITY OF NORTH CAROLINA AT ASHEVILLE

SENIOR ECONOMICS RESEARCH

DECEMBER 2010

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Accounting for Risk

A Fundamental Beta Prediction Model* 1

Crystal Swafford

Economics Department, University of North Carolina at Asheville

Abstract Beta coefficients are the most commonly used measure of the systematic risk

associated with financial assets. Rather than focusing only on historical returns,

fundamental betas incorporate a firm’s accounting data to explain the sources of

systematic risk. Consumer confidence is an important component systematic risk since it

affects all firms in the economy. Fisher and Statman find that consumer sentiment greatly

influences the behavior of individual investors, but not institutional investors. In a similar

study, Lemmon and Portniaguina conclude that stocks held primarily by individuals are

more likely to be mispriced. These studies suggest that there is a connection between a

firm’s distribution of ownership and its sensitivity to systematic risk. A fundamental beta

prediction model is developed to test the hypothesis that nonfinancial firms’ distribution

of ownership influences systematic risk as measured by historical betas.

Keywords: beta coefficient, distribution of ownership, systematic risk

I. Introduction

The assessment of risk is one of the most important aspects of finance and has

significant implications for the way investors manage their exposure to uncertainty. Beta

coefficients are widely used by investors to estimate systematic risk, that is, the

variability in returns that cannot be avoided through diversification. They are the most

commonly used proxy of systematic risk used by financial analysts, portfolio managers,

and individual investors to evaluate many types of financial assets.2 Traditionally, betas

are calculated by finding the correlation between a stock’s return and the return on the

market overall.

* I would like to extend my sincere thanks to Dr. Chris Bell and Dr. Pamela Nickless for their invaluable

support during the entire research process. 2 Diana R. Harrington, “Whose Beta is Best?” Financial Analysts Journal 39, no. 4 (1983): 67.

3

In contrast, fundamental betas incorporate an analysis of a firm’s financial data to

gain insights into the sources of systematic risk. Betas derived this way reveal that

although all companies experience systematic risk, they differ in their sensitivity to

macroeconomic conditions due to their underlying accounting characteristics. As a result,

fundamental betas suggest that systematic risk is a function of various accounting

variables, such as liquidity, leverage, and the dividend payout ratio.3

However, fundamental beta prediction models developed by previous research do

not consider the impact of consumer confidence, which is a systematic risk for all

companies. Fisher and Statman find that changes in consumer sentiment are highly

correlated to stock returns. Additionally, they find that individual investors are very

responsive to consumer sentiment, whereas institutional investors are not at all. 4

Lemmon and Portniaguina found the same relationship between the behavior of

individual investors and they conclude that stocks held primarily by individuals are more

likely to be mispriced.5

Although these researchers did not analyze the relationship between the

distribution of ownership and systematic risk, their findings suggest that a firm that has a

relatively high proportion of individual stockholders may see more volatility in the value

of its common stock. Therefore, it is likely that a firm’s distribution of ownership may

3 Don M. Chance, “Evidence on a Simplified Model of Systematic Risk,” Financial Management 11, no.3

(1982): 53-63. Edward A. Dyl and J. Ronald Hoffmeister, “A Note on Dividend Policy and Beta,” Journal

of Business Finance & Accounting 13, no. 1 (1986): 107-115; Eugene F. Fama and Kenneth R. French,

“The Capital Asset Pricing Model: Theory and Evidence,” Journal of Economic Perspectives 18, no. 3

(2004): 25-46; Barr Rosenberg and Walt McKibben, “The Prediction of Systematic and Specific Risk in

Common Stock,” Journal of Financial and Quantitative Analysis 8, no. 2 (1973): 328; James M. Gahlon

and James A. Gentry, “On the Relationship Between Systematic Risk and the Degrees of Operating and

Financial Leverage,” Financial Management 11, no. 2 (1982): 15-23. 4 Kenneth L. Fisher and Meir Statman, “Consumer Confidence and Stock Returns: What Sentiment Tells

Us,” Journal of Portfolio Management 30, no. 1 (2003): 119. 5 Michael Lemmon and Evgenia Portniaguina, “Consumer Confidence and Asset Prices: Some Empirical

Evidence,” Review of Financial Studies 19, no. 4 (2006): 1524-1526.

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influence its’ sensitivity to systematic risk. This paper develops a fundamental beta

prediction model to test the hypothesis that an individual firm’s distribution of ownership

impacts the level of systematic risk associated with its common stock. In other words,

this study seeks to provide an additional explanatory variable for the level of systematic

risk experienced by individual firms. In this way, investors may be able to more

effectively manage their exposure to risk and choose securities that best suit their

objectives and are compatible with their existing holdings.

Section two of this paper presents an overview of the existing research. Section

three presents the methodology and a description of the data used to create the

fundamental beta prediction model. The empirical results are discussed in section four,

suggestions for future research in section five, and section six contains the concluding

remarks. The appendix provides a glossary of financial and accounting terms used in this

paper.

II. Literature Review

Risk evaluation and management are two of the primary components of finance.

Harrington demonstrates that beta coefficients are widely considered to measure the

riskiness of securities and their relationship to fluctuations in financial markets overall.6

Beta remains the most commonly used measure of systematic risk despite the great

variation in betas reported by various agencies. The variance in beta results from

differences in the time period analyzed, the frequency of observations, and the proxy

used for the market portfolio. The work of Rosenberg and McKibben, Fama and French,

Chance, Dyl and Hoffmeister, and Gahlon and Gentry suggests that fundamental betas

6 Harrington, 67.

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have important advantages over historical betas. They argue that this is because

fundamental betas provide better indications of the sources of systematic risk experienced

by firms.

The research of Fisher and Statman and Lemmon and Portniaguina implies that

consumer confidence may be a contributing factor in the systematic risk of common

stock.7 They find that individuals are much more affected by changes in consumer

confidence and that stocks held primarily by individuals are more likely to be mispriced.

Extending these arguments, I hypothesize that the distribution of a firm’s common stock

ownership may have important implications for the level of systematic risk it

experiences.

The findings of Fisher and Statman and Lemmon and Portniguina gives support to

the hypothesis that fundamental betas should incorporate ownership data in addition to

accounting variables. In this way, the systematic risk of common stock may be better

explained since companies likely differ in their sensitivity to systematic risk due to

changes in consumer sentiment. As a result, investors may acquire a more effective tool

to evaluate securities.

The vast majority of recent research in fundamental beta prediction models

focuses on the creation of hypothetical portfolios to test the models’ efficiency. In fact,

Fama and French discuss that, when testing beta models, grouping stocks with a similar

level of beta is now standard.8 The assumption that investors “evaluate the risk of a

portfolio as a whole, rather than the risk of each asset individually” is the basis of these

7 Fisher and Statman, 119. Lemmon and Portniaguina, 1524-1526.

8 Fama and French, 31.

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types of studies. The foundation of this argument is the expectation that people take

advantage of diversification and the risk any particular stock does not matter.9

Although diversification is a very influential factor in the decision making of

investors, one must understand the risks inherent in individual securities in order to

evaluate their effects on a portfolio. Fama and French argue that the portfolio method of

analysis has important weaknesses in that it reduces the range of betas represented in the

sample. This diminishes the quality of the statistical results and reduces predictive

power.10

An additional factor overlooked by the portfolio method is that investors who

assemble their own portfolios, rather than buy mutual funds, choose single assets at a

time and not complete portfolios. In this case, the risk of individual assets does matter,

and an analysis of individual stocks will be more representative of the actual behavior of

investors. The approach of analyzing individual firms was at the height of its popularity

in the 1970’s but appears to have been largely abandoned in recent research although a

few modern studies use this method. Consequently, this paper will analyze individual

firms’ betas in order to evaluate whether they differ in their sensitivity to systematic risk

as a result of their distribution of ownership.

In order to test this hypothesis, I will apply information about the ownership

distribution of stock to a fundamental beta prediction model. The majority of studies that

analyze the impact of consumer confidence seek to relate it to patterns in the pricing of

stock or the behavior of investors. In this way, it may be possible to fill a gap in the

9 Marshall, E. Blume, “On the Assessment of Risk,” Journal of Finance 26, no.1 (1971): 2.

10 Fama and French, 31.

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literature between fundamental economic analysis and firms’ responsiveness to changes

in consumer confidence.

III. Methodology

To test the hypothesis that a firm’s distribution of ownership influences its level

of systematic risk, a fundamental beta prediction model was created and estimated using

multiple regression. Such an approach is appropriate for this type of study since multiple

regression allows for the analysis of a large number of observations with many variables.

In this model, the estimated historical beta is the dependent variable and various

accounting risk factors and ownership profiles are the independent variables.

The data set is composed of 84 firms listed on the S&P 500 index, with

observations over a five-year period from 2002 to 2006. The companies included in the

data set represent a proportional sample of the industries included in the S&P 500 with

the exception of financial firms.11 The firms were selected randomly from their industry

category in proportion to each industry’s representation on the S&P 500.12 Table 1

describes the composition of the sample by industry.

11 Although I initially attempted to include financial companies and use a proportional sample of 100 firms,

the finance companies eventually had to be eliminated since the balance sheets of banks list assets and

liabilities in a way that is not comparable to that of firms in other industries. For this reason, it was not

appropriate to compare the liquidity of financial firms to nonfinancial firms. This is particularly the case

with banks, since they do not use a category on their balance sheets for current and noncurrent assets and

liabilities. Additionally, financial firms are subject to much government regulation, which dramatically

affects their accounting ratios, as with reserve requirements for banks. The firms were randomly selected

from their industries. 12 To do so, the list of companies was sorted by industry in Excel and using the function to randomly select

row numbers within the range occupied by each industry.

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Table 1: Sample Composition

Industry Number

Consumer Discretionary 17

Consumer Staples 8

Energy 7

Health Care 10

Industrials 12

Information Technology 15

Materials 6

Telecommunication Services 2

Utilities 7

Total 84

Although beta is the most commonly used measurement of systematic risk, the

values of beta coefficients for the same firm can vary widely among subscription data

services, investment firms, and security rating agencies. Such differences are likely due

to differences in the period analyzed, the frequency of observations, and which proxy is

used to represent the market return. To avoid such variations and maintain consistency

throughout the data set, I first estimated the yearly historical betas using the Ordinary

Least Squares method. To do so, I used a simple regression of the daily return of each

stock and the daily return of the S&P 500, which is the most commonly used proxy for

the market portfolio used by professional researchers and security rating agencies.13 In

this way, the model utilizes pooled time series data since it incorporates five yearly

observations for each firm, yielding 420 observations.

13Harrington, 69. Chance, 56. Carl R. Chen, "Time-Series Analysis of Beta Stationarity and Its

Determinants: A Case of Public Utilities,” Financial Management 11, no.3 (1982): 67. Here, the firms’

daily return refers to the adjusted closing price obtained from Yahoo Finance, Yahoo Inc.

http://finance.yahoo.com. This way, inconsistencies from stock splits and dividend payments was avoided.

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The independent variables included in the model represent measures of sources of

systematic risk experienced by a firm. 14 The volatility of cash flows is the primary source

of risk from the stockholder’s perspective, so business and financial risk are likely to be

important factors in the riskiness of common stock. Because business risk is associated

with the degree of uncertainty associated with a firm’s earnings and cash flow, it

indicates a company’s ability to meet its operating expenses. Similarly, financial risk is

associated with a firm’s ability to meet their financial obligations and can influence the

amount of growth the firm experiences through retained earnings, as well as their ability

to pay dividends.

The fundamental beta prediction model will incorporate ratios for operating and

financial leverage and debt to equity to serve as proxies for business and financial risks.15

Economic theory and the empirical results of Chance, Chen, and Gahlon and Gentry

suggest that this model will indicate a positive relationship between the systematic

variability of returns for common stock and both measures of leverage. A similar

relationship is likely with debt to equity ratios, as indicated by the research of Fama and

French. This hypothesis is consistent with economic theory since a higher amount of debt

financing is associated with more variation of cash flows due to interest payments. It is

probable liquidity is also an important component of the systematic risk borne by

14 With the exception of market capitalization and the distribution of ownership, all data for the accounting

variables was obtained from Morningstar.com, Morningstar Inc. http://www.morningstar.com/?t1=

1287965787.The values of market capitalization and ownership were obtained from archived versions of

Yahoo Finance and MSN Money. Microsoft Corporation. http://moneycentral.msn.com/home.asp. 15 In this model, debt to equity ratios were calculated using the formula, total liabilities divided by

shareholder equity. Although many professional financial analysts and subscription data services, such as

Morningstar, use only long term debt in the calculation, many firms do not include such a category on their

balance sheets, which would prevent consistency within the model. The use of total liabilities is also more

conservative since all debt is considered, rather than only long term debt.

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shareholders.16 The work of Rosenberg and McKibben lends support to the expectation

that a negative relationship is likely to be found between a firm’s liquidity and the

riskiness of its stock.

Many researchers found the size of companies a significant contributing factor in

the systematic risk of common stock, although there was great variation the proxies used

to indicate growth. Chen’s model uses the change in assets, as did that of Rosenberg and

McKibben, although they also incorporate the change in net sales. Chen’s empirical

results show a slightly positive relationship between the growth in assets and beta. He

attributes this to be most likely due to increased sensitivity to market fluctuations when

assets grow more rapidly.17 Rosenberg and McKibben do not find a statistically

significant relationship with the growth in assets, although they do find a weak, positive

relationship with the growth of revenue.18

Both changes in assets and revenue will be included in the model as proxies for

company growth. Consistent with the research of Chen and Rosenberg and McKibben, a

positive relationship is expected for both variables. However, the effect of company size

on the systematic variability of returns for stock is indeterminate because it is possible

that larger companies are actually less risky. This is because they are more likely to have

achieved economies of scale, are in a more mature phase of their lifecycle, and have a

longer record of performance available to investors.

16 While ‘acceptable’ levels of liquidity vary greatly by industry and what stage the firm is in its lifecycle,

the ability to convert assets into cash quickly is an important indicator of risk since it can have implications

on the survival of a company when faced with fluctuations in the business cycle. In this model, the quick

ratio is used since it is somewhat more conservative because it does not consider inventories to be a liquid

asset, as does the current ratio. Excluding the impact of inventories may allow for a more consistent

comparison between industries. This is particularly the case since some industries tend to keep a larger

inventory on hand, such as those in basic materials, whereas others do not, as with telecommunications

firms. 17 Chen, 66.

18 Rosenberg and McKibben, 326.

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Lui, Markov, and Tamayo, who use market capitalization as an indicator of size,

find that smaller companies are more risky.19 Studies that use this proxy for company size

are probably misspecifiying their models because, although companies with a larger

market capitalization are almost always larger and do tend to be perceived as less

volatile, it actually measures only a firm’s valuation rather than its growth. For this

reason, using market capitalization to indicate a firm’s size is not appropriate.

Through its direct connection to stock prices, market capitalization is more an

indicator of investors’ expectations of the value of the stock’s future cash flows because

firms receive no funds from the secondary market. Consider the case of a stock whose

price falls during an economic contraction. Even if nothing changes in the structure of the

firm or its financial position, its market capitalization, or valuation, will fall while the

actual size of the company remains unchanged.

Market capitalization is included in this model to indicate valuation, rather than

size.20 This variable may exhibit a negative relationship with beta, but not likely for the

same reason as changes in assets or revenue. Rather, such a relationship would likely

result because a stock that is more highly valued is more likely to provide investors with

capital gains as when the stock’s price rises before being sold. For this reason, market

capitalization is used here to represent the systematic risk faced by investors associated

with cash flow. Although a negative relationship is expected similar to that found by Lui,

19 Lui, Daphne, Stanimir Markov, and Ane Tamayo, “What Makes a Stock Risky? Evidence From Sell-

Side Analysts’ Risk Ratings,” Journal of Accounting Research 45.3 (2007): 637. 20 The data for market capitalization was obtained using Wayback Machine, Internet Archive,

http://www.archive.org/web/web.php with which I viewed archived webpages of Yahoo Finance and MSN

Money. In this model, market capitalization was converted to real dollars using the GDP deflator and a base

year of 2005. The GDP deflator was obtained from United States Bureau of Economic Analysis. Implicit

Price Deflators for Gross Domestic Product. National Income and Products Accounts Table 1.1.9.

http://www.bea.gov. 3 Sept. 2010.

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Markov, and Tamayo, such a correlation would indicate the effect of capital gains, not

size.

Return on equity is also likely to be an appropriate measure of company growth

since it indicates the amount of earnings reinvested into the company, thus fueling its

growth. Additionally, it demonstrates how effectively a firm generates profits from the

funds invested by stockholders. So a firm that has a higher return on equity is expected to

experience a lower level of systematic risk since their reinvestment of profits is often

associated with greater future earnings. Although none of the studies I reviewed

incorporated return on equity in their models, it may prove to be an additional

explanatory variable in the riskiness of common stock and a positive relationship is

expected.

Since dividends are a very important component of the returns received by

investors, it is logical that a firm with a higher dividend payout ratio would be experience

less systematic risk since it would provide shareholders with a greater amount of income.

This ratio may represent the profitability of stock since it indicates how much of a firm’s

net income is distributed to shareholders. The desired ratio depends greatly on each

investor’s goals, whether they are seeking high capital gains, as is common with newer

firms whose stocks pay very low or no dividends, or a steady stream of current income as

with more mature firms. Consistent with the research of Dyl and Hoffmeister who find a

negative relationship between the dividend payout ratio and beta, a negative relationship

is expected.21

As an extension of the arguments of Lemmon and Portniaguina and Fisher and

Statman, I anticipate a connection between a firm’s distribution of ownership and its

21 Dyl and Hoffmeister, 113.

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exposure to systematic risk. A variable will be included in this model for the proportion

of a firm’s stock held by individuals.22 Consistent with the work of these researchers, I

expect that the empirical results will find a positive relationship between beta and the

distribution of ownership of common stock. The variable is included in this study as a

pure experiment without any prior fitting of the data. The data for the ownership profiles

of the firms included in the sample were obtained from archived web pages since the

proportions reported are only indicative of the current conditions and do not indicate

previous years’ values.23

Reeb, Kwok, and Baek maintain that exchange rate and political risks are also

very influential on the variability of a firm’s cash flow, and by extension, the systematic

risk associated with common stock. Their research suggests that it is important to

incorporate measures of a firm’s level of internationalization in fundamental beta

prediction models.24 Although an attempt was made to incorporate these variables into

this model, lack of access to the appropriate databases prevented their inclusion.

Table 2 provides a summary of the variables included in the model, their

abbreviations, and their anticipated relationship to the systematic risk of common stock.

22 Here, the proportion of individual investors was obtained by subtracting the percentage of institutional

and mutual fund owners from one. The quality of this variable could be possibly be improved by using the

distribution of ownership at the end of each firm’s fiscal year when the rest of the accounting data is

reported. However, archived webpages for these dates were not always available, and the closest possible

date was used. 23 This was achieved by using the Wayback Machine with which I viewed archived webpages of Yahoo

Finance and MSN Money. 24 David M. Reeb, Chuck C.Y. Kwok, H. Young Baek, “Systematic Risk of the Multinational Corporation,”

Journal of International Business Studies 29, no.2 (1998): 263-279. Although an attempt was made to

incorporate these variables into this model, lack of access to the appropriate databases prevented their

inclusion.

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Table 2: Variables

Variable Symbol Anticipated Relationship

Estimated Historical Beta HB

Degree of Operating Leverage DOL Positive

Degree of Financial Leverage DFL Positive

Dividend Payout Ratio DPR Negative

Liquidity L Negative

Debt to Equity Ratio DE Positive

Return on Equity ROE Negative

Real Market Capitalization in

2005 dollars M Negative

Change in Revenue from

Previous Year R Positive

Change in Assets from Previous

Year A Positive

Percentage of Shares Held by

Individuals II Positive

The estimated equitation of the fundamental beta prediction model is as follows:

^HBi = a+ b1DOL + b2DFL + b3DPR + b4L + b5DE +

b6ROE + b7M + b8R + b9A + b10II + ε

To determine whether its relationship to beta is statistically significant, the

ownership variable will be evaluated with an analysis of its t-statistic using a 95%

confidence level.

IV. Empirical Results

The multiple regression produced many unexpected results. Only the degree of

financial leverage and market capitalization were found to be statistically significant as

indicated by their t-statistics. The residuals were not at all random and produced many

outliers, which likely skews the results. Additionally, the mean squared error was

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extremely high at 131.197 and the adjusted R2 was exceptionally low at 0.061, indicating

that only 6.1% of the variation in beta is explained by the independent variables.

If multicollinearity was present, it would indicate that two variables are highly

correlated and move together, and could distort the empirical results. However,

multicollinearity between the independent variables does not appear to be a problem

since the greatest correlation coefficient among them was only -0.233 between the

change in assets and dividend payout ratio. The empirical results do suggest that some

relationship exists between at least one of the independent variables and beta as

evidenced by the F-statistic test.

The resulting fundamental beta prediction model is as follows. Table 3 presents a

summary of the regression results.

^HBi = a+ 0DOL + 0.017DFL + (-0.042)DPR +

(-0.037)L + (-0.015)DE + 0ROE + 0.003M +

0.023R +(-0.047)A +(-0.238)II

Since the initial empirical results indicated such little explanatory power, I ran a

second regression with only the variables found to be significant in studies that analyze

individual assets.25 The motivation being that perhaps some accounting data does explain

the systematic risk of portfolios, but is not important when studying individual securities.

In this regression, only the change in assets and revenue, degree of operating and

financial leverage, and dividend payout ratio were included.

25 See Dyl and Hoffmeister, Chen, Rosenberg and McKibben, and Gahlon and Gentry.

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Table 3: Regression Results*

Adj. R2 = 0.061 MSE = 131.197 Standard Error = 0.566


Slope Coefficients

(T-statistics)



0.000

(-0.627)

Degree of Financial Leverage DFL Positive 0.017

(2.301)


-0.042

(-1.104)

Liquidity L Negative

-0.037

(-1.632)

Debt to Equity Ratio DE Positive

-0.015

(-1.102)

Return on Equity ROE Negative

0.000

(1.242)

Real Market Capitalization in

2005 dollars M Negative

0.003

(5.383)



0.023

(0.513)


Year A Positive

-0.047

(-0.895)

Percentage of Shares Held by

Individuals II Positive

-0.238

(-1.458)

*Values in bold indicate the variables that were found to be statistically significant, as indicated by their

t-statistics.

The empirical results were even poorer than for the initial regression using all ten

variables. The degree of operating leverage was again found to be statistically significant,

but no other variable indicated any relationship to beta. The adjusted R2 was even lower

with a value of 0.001 and the mean squared error was much greater at 141.392. These

results suggest that even less explanatory power results from using a more simplified

model. Table 4 presents the results of this multiple regression.

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Table 4: Regression Results from Simplified Model*

Adj. R2 = 0.001 MSE = 141.392 Standard Error = 0.584


Slope Coefficients

(T-statistics)



0.000

(-0.408)

Degree of Financial Leverage DFL Positive 0.013

(2.064)


-0.021

(-0.548)



0.021

(0.453)


Year A Positive

-0.037

(-0.674)


t-statistics.

In their article, “The Capital Asset Pricing Model: Theory and Evidence,” Fama

and French briefly discuss the possibility that beta prediction models whose samples

include stocks from a variety of industries may produce unreliable empirical results. 26

They argue that this could occur since systematic risk may not affect all sectors of the

economy in the same way. Testing this hypothesis, I ran separate regressions for each

industry in the sample, with the results summarized in Table 6.27

These eight industry regressions yielded results that support the argument of

Fama and French. All the regressions possessed mean squared errors that were much

lower than for the initial statistical results. Additionally, all of the regressions indicated

much more of the variation in beta was explained by the independent variables, as

evidenced by the improvement in the adjusted R2, especially for consumer staples and

26 Fama and French, 31

27 A separate regression was not performed for the telecommunications services firms since it would

include a sample of only two firms, so they were excluded completely from the industry specific

regressions.

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health care firms. Still, the distribution of ownership was found to be significant only for

the industrials, materials, and utilities firms. This suggests that a model that uses a sample

composed of a single economic sector, as analyzed by Chen, could gain more insight

about the industry-specific association between the distribution of stock ownership,

accounting data, and beta coefficients.28

Table 6: Statistical Details from Industry Regressions*

Industry

#

Observations Adj R2

Standard

Error MSE

II Slope

Coefficient

(t-statistic)

Consumer

Discretionary 85 0.350 0.461 15.718

0.085

(0.222)

Consumer

Staples 40 0.514 0.264 2.016

-0.474

(-1.261)

Energy 35 0.058 0.535 6.873

-0.706

(-0.969)

Health Care 50 0.459 0.232 2.093

0.109

(0.301)

Industrials 60 0.359 0.405 8.034 1.606

(2.101)

Info Tech 75 0.221 0.657 27.601

-0.186

(-0.270)

Materials 30 0.285 0.700 9.316 -2.230

(2.131)

Utilities 35 0.266 0.353 2.999 1.542

(2.579)


t-statistics.

The empirical results of this study do not lend support for the hypothesis that the

distribution of common stock ownership is influential in the level of systematic risk

experienced by nonfinancial firms. Overall, the results were not consistent with the

literature or with economic theory. Additionally, this model does not indicate that the

financial characteristics of an individual firm are reliable indicators of the systematic risk

28 Chen 64-70.

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inherent in its common stock. Therefore, it is likely that the lack of explanatory power is

specific to this model.

V. Potential Improvements of the Model for Future Research

Discouragingly, the multiple regressions, no matter the number of variables or the

composition of the observations, produced beta predictions that were reliable in any way.

One possible explanation is that some of the variables in the model were replicated from

studies analyzing hypothetical portfolios. Again, some of the relationships found by

researchers using this method may not hold for individual assets.

Additionally, many of the studies that analyze individual stocks, as did this

model, were conducted several decades ago. In recent years, much has changed in the

way investors trade securities and evaluate risk. This is particularly the case with the use

of computers and more sophisticated quantitative methods, so it may possible that the

statistical relationships found by these early studies may no longer hold and that the

sources of systematic risk have changed.

Another possible explanation for the poor quality of the results is that some the

variables included in this model may not be good proxies of the relationships they are

intended to analyze. The ambiguity of publicly available information increases the

possibility that this is the case. The data that composed the variable for distribution of

ownership is particularly problematic in this sense. In the case of MSN Money and

Yahoo Finance, it is possible that street name securities are included in the percentage of

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stock owned by institutional investors.29 Although individuals own these assets, they are

held in the name of a brokerage to ease the transfer of ownership when the security is

sold. If these assets are included in institutional ownership, then the variable in this model

is misspecified and does not accurately reflect the percentage of shares held by

individuals.

Additionally, company insiders such as employees, were included in the counts of

individual ownership because they do not manage a large volume of assets for others, as

do pension funds for example. Counting insiders as individuals may not be appropriate,

however, since insiders may not be as responsive to consumer sentiment as other

investors. This may occur because they could be more reluctant to sell their holdings of

their own employer’s stock, as when it is part of their compensation. Indeed, they may

not even be able to sell if they are not considered vested until after a certain length of

time, so their investing behavior may depend on company policy rather than a response to

consumer sentiment.

Future researchers may obtain better empirical results if they incorporate a longer

time horizon in their analysis. Harrington and Levy found the period of analysis to be

influential in the predictive power of fundamental betas.30 It is possible that yearly

observations, such as those here, are too short to reflect trends in betas and accounting

data. If a longer time period is used, it is important to consider the possibility that betas

29 Despite numerous attempts to verify if this was the case, no satisfactory resolution could be obtained.

Edgar Online, which supplies the ownership information to MSN Money and Yahoo Finance, was not

responsive to email inquiries and could not be reached by telephone. 30 Harrington, 70. Levy, 58.

21

may not be stationary over time and may tend to regress toward the mean of one, as is

suggested by the work of Rosenberg and McKibben and Martin and Simin.31

The time period used in this model may be particularly problematic because each

of the historical betas that served as the dependant variables were produced from an

entire year’s return on the stock and the S&P 500. However, the values of the accounting

variables were obtained from the year-end financial statements, which indicated

accounting data as of the last day of the firm’s fiscal year. Essentially, the historical betas

represented a year’s average, whereas the accounting variables denote only one day’s

values.

Therefore it may be optimal to construct the data set so that the financial data are

also represented as averages over the course of one or more years using quarterly

financial statements. Rosenberg and McKibben and Chance used this method in their

studies, incorporating five year averages for their accounting variables and achieved

empirical results that were much more reliable than those produced by this model.32

Despite the large number of variables included in this model, it likely contains

omitted variable risk in that there are undoubtedly many additional factors that affect the

level of systematic risk borne by shareholders. This is the case since this model did not

include variables for all of the potential sources of systematic risk. In addition to

business, financial, and liquidity risks, an analysis of exchange rate and political risks

may prove to be helpful in attaining higher quality statistical results, as examined by

Reeb, Kwok, and Baek.

31 Rosenberg and McKibben, 328. R. Douglas Martin and Timothy T. Simin, “Outlier-Resistant Estimates

of Beta,” Financial Analysts Journal 59, no. 5 (2003): 56. 32 Rosenberg and McKibben, 324. Chance, 58.

22

It is possible that this model uses the wrong functional form to estimate the

relationships between the independent variables and beta. Rather than using the ordinary

least squares method, a logarithmic or quadratic function may be more appropriate, for

example. Also, Microsoft Excel, which was used in this model, is widely considered to

have limitations for econometric analysis. Therefore, the use of another program, such as

MiniTab or Gretl may improve the statistical results.

Despite due diligence, many improvements to the fundamental beta prediction

model developed by this study could be made in future research. Such improvements may

better indicate the relationship between a stock’s systematic risk and its distribution of

ownership. The use of better proxies for the systematic risk factors of common stock and

a longer period of analysis may prove to be particularly helpful. Future studies will also

likely benefit from using extreme caution when collecting and interpreting publicly

available information that is used to inform the variables contained within the model.

Although this study did not produce the expected results, it provides a good starting point

for others in that it demonstrates potential hazards faced by researchers in developing a

fundamental beta prediction model.

VI. Conclusion

This study sought to include an additional explanatory variable, the distribution of

ownership, into a fundamental beta prediction model. Multiple regression is used with

pooled time series data to analyze the relationship between distribution of ownership and

the beta of a nonfinancial firm’s common stock. By recognizing the connection between a

firm’s distribution of ownership and the impact of consumer confidence, I analyzed an

23

additional aspect of systematic risk to demonstrate that firms differ in their sensitivity to

macroeconomic conditions due to the distribution of their ownership.

Although there is good support in the literature for the hypothesis that the

ownership distribution of individual firms affects a company’s sensitivity to systematic

risk, the results of this study did not support my hypothesis. The variable for the

ownership data was not found to be statistically significant in the initial multiple

regression, and did not display a consistent relationship to beta across industries. The

short time period analyzed and the potentially poor quality of data sources were likely the

most likely reasons the empirical results displayed so little explanatory power.

Given the importance of risk evaluation and management in finance, there is still

an important role for the fundamental analysis of firms. More research is needed into

fundamental beta prediction models to determine what role consumer confidence plays in

the level of systematic risk experienced by a firm. This study provides a contribution to

the literature in that it demonstrates the complexity of developing systematic risk

forecasts from publicly available information and possible implications of the sample’s

composition. Although this study did not produce a model with reliable forecasting

ability, it may help other researchers obtain empirical results with more explanatory

power so that investors can better manage their exposure to risk.

24

Appendix A: Glossary* 33

Beta: a measure of systematic risk that describes the relationship of a security/portfolio’s

return in relation to the market overall. A beta of zero indicates that the return is

independent of the market’s performance. A positive value of beta indicates that

the security/portfolio’s return moves in the same direction as the market, and vice

versa. The coefficient of the beta indicates the magnitude of the relationship.

Consumer confidence: a measure of the level of optimism consumers feel regarding the

state of the overall economy. The most commonly reported levels of consumer

confidence are developed by The Conference Board and the University of

Michigan.

Equity: the amount of money invested in a company by its owners or shareholders.

Institutional investor: an organization that manages large volumes of assets on the behalf

of others such as pension funds, insurance companies, or mutual funds.

Liquidity: the ability to quickly convert an asset into cash.

Market portfolio: a hypothetical portfolio that contains a weighted average of every asset

available in financial markets. Typically, only domestic stocks are included, but

there is much dispute in the literature regarding which specific types of securities

should be included in the market portfolio, such as whether bonds, foreign assets,

or consumer durable goods should be included. However, the S&P 500 is the

most commonly used proxy for the market portfolio.

Multicollinearity: a condition in which two or more independent variables in a statistical

model are highly correlated, indicating that the variables are closely related and

can distort the empirical results.

Regression: a statistical process that attempts to demonstrate the relationship between a

dependant variable and one or more independent variables.

Secondary securities market: the financial market in which previously issued securities,

including stock, are traded. As opposed to the primary market in which new

issues are sold and the issuing firm receives funds.

Street name security: an asset that is owned by an individual but is held in the name of a

brokerage to ease the transfer of ownership when the security is sold.

Systematic risk: caused by factors that affect financial markets overall. As opposed to

nonsystematic risk, systematic risk is specific to individual firms.

* Although many of these terms have multiple meanings, all terms in this glossary are explained in context

of their usage in this paper.

25

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