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Growth and Momentum –

Rich and Richer

-A study on momentum and growth on the automotive

Frankfurt stock market

Autors: David Eriksson and Charlie Vindehall

Supervisor: Magnus Willesson

Examinator: Håkan Locking

Semester: VT 20

Subject: Finance

Degree: Bachelor

Course code: 2FE32E

Abstract

Active management funds are associated with higher transaction costs, which is something

that has been acknowledged for a long time. The question is whether these costs can

compensate with a higher return. This paper investigates how two active strategies,

momentum and growth investing, have performed in relation to a passive index. To test this,

we investigated the Frankfurt stock market during 2005-2020 on stocks from the automobile

sector. By doing this, the purpose was investigated whether growth and momentum has had a

higher risk-adjusted return than the benchmark index during the 15 years of observation. The

result showed that both growth and momentum performed better than a passive index fund,

despite its costly variables. However, the risk adjusted return was not significant higher. This

study includes transaction costs in its calculation, which other studies ignore and focus on

one industry with a consistent benchmark index for the same industry. By doing this, we

believe that the test will be more accurate, and avoid potential industry effects on return and

hopefully contribute with new thoughts on the subject.

Key words

Active investing, Growth, Momentum, Efficient market hypothesis, German automotive

sector, CAPM, Alpha, Sharpe ratio,

Acknowledgements

We would like to thank our examiner Håkan Locking and supervisor Magnus Willesson for

giving us good advice and guidance during the thesis. Thereto, the advices and continuous

feedback from our opponents have also been accommodating and have constantly helped us

moving forward with the research.

Table of contents

1.INTRUDUCTION..................................................................................................1-5

1.2 Background.....................................................................................................................1-2

1.3 Problem discussion.........................................................................................................2-3

1.4 Purpose...................................................................................................................... ........4

1.5 Research questions...........................................................................................................4

1.6 Limitation........................................................................................................................4-5

2.THEORY.............................................................................................................6–14

2.1 Growth investing.............................................................................................................6-7

2.2 Momentum.......................................................................................................................7-8

2.3 Momentum short or long time horisont? ........................................................................8

2.4 Momentum vs growth investing: what is the difference?...............................................9

2.5 Efficient market theory................................................................................................9-10

2.6 Critics against efficient market theory.....................................................................10-11

2.7 Transaction costs.........................................................................................................11-12

2.8 Risk models..................................................................................................................12-14

2.8.1 CAPM.......................................................................................................................12–13

2.8.2 Jensens alpha...............................................................................................................13

2.8.3 Sharpe ratio.............................................................................................................. ...14

3. LITERATURE REVIEW ...............................................................................15-17

3.1 Previous results...........................................................................................................15-17

4. METHODOLOGY...........................................................................................18-26

4.1 Investigation design..........................................................................................................18

’4.2 Data collection............................................................................................................18-20

4.3 Portfolio composition..................................................................................................20-21

4.3.1 Benchmark................................................................................................................21-22

4.3.2 German automotive sector.........................................................................................22

4.4 Evaluation of results...................................................................................................23-25

4.4.1 Return..........................................................................................................................23

4.4.2 Risk...........................................................................................................................23-24

4.4.3 Risk adjusted excess return........................................................................................24

4.4.4 Regression…………………………………………………………………………24-25

4.5 Transaction costs.............................................................................................................25

4.6 Potential problems......................................................................................................26-27

4.6.1 Survivorship Bias..........................................................................................................26

4.6.2 Outliers...........................................................................................................................26

4.6.3 Potential problems with the benchmark...............................................................26-27

5 EMPIRICAL RESULTS AND ANALYSIS....................................................27-34

5.1 Returns.........................................................................................................................27-29

5.2 Risk....................................................................................................................................29

5.3 Sharpe ratio......................................................................................................................30

5.4 CAPM and alpha........................................................................................................30-31

5.5 How can momentum be so outstanding?..................................................................31-32

5.6 Results compared to previous results.......................................................................32-33

5.6 Is the result a coincidence?.........................................................................................33-34

5.6.1 Momentum................................................................................................................33-34

5.6.2 Growth..........................................................................................................................34

6. CONCLUSION.................................................................................................35-37

7.FURTHER RESEARCH........................................................................................38

REFERENCES..................................................................................................................39-41

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1. Introduction

1.2 Background

It is not unusual to think those who invest in active funds are naive people that are seduced

by a corrupted and self-interested industry into paying high fees for bad performances. But

does this really reflect the truth? There are a lot of perspectives that should be taken into

account when one should decide if being an active investor is worthwhile or not. It is time

consuming, easy to make errors and there are often a lot of fees included.

According to Damodaran there are even arguments and reasons to believe that being an

active investor is pure luck in the end considering the efficient market hypothesis. Adding

fees to that hypothesis would result in a disadvantage for the active investor in order to

overcome the passive investors yield. Thus, it would question the very need and existence of

portfolio managers and their use of investment strategies (Damodaran, 2012).

If the market is efficient, stock prices fully reflect all available information at any time. This

is what we call the efficient market hypothesis. Stocks that are traded do so in their true fair

value because the market provides accurate and correct signals for resource allocation. A

critical rule for this to hold is that all the information is universally shared among market

precipitations (Damodaran, 2012).

Efficient market hypothesis carries similar conclusions as the random walk theory. Thus, past

trends and movements cannot be used in order to predict the future. This randomness makes

it impossible to exceed the market (Mehwish, 2015). To employ this information, the best

strategy to invest one's money efficiently would be to avoid fees, according to EMH. The

theory suggests buying and hold a diversified portfolio and be as passive as possible in order

to avoid extra costs associated with activity. (Damodaran, 2012).

There is a lot of criticism from earlier studies implying there are flaws in the EMH. For

example, Fama states that information about firms/markets is not freely available for all

investors. There is also disagreement among investors about the implications of given

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information may be potential sources of an inefficient market, even though they are not

necessarily sources (Fama, 1970).

Another argument which Fama brings up is having the null hypothesis; the market “fully

reflects” all available information at any point in time, is extreme. By agreeing with the

assumption that the market is not fully effective would leave room for speculations that

active investments strategies can be able to “beat” the market (Fama, 1970).

One acknowledged investment strategy is momentum which, in simple terms, is when one

capitalizes on previous market trends. It is executed by buying securities that had high returns

in the past, usually within a shorter period. This famous strategy is both investigated and used

by various investors worldwide (Gray, 2016).

Growth investing is when you invest in stocks with high earnings in the past that is expected

to perform in the future as well. Growth investing is when you look at both the price and the

fundamentals of a stock. This strategy is like momentum investing but two factors, the time

period and the focusing on fundamentals, differ the strategies from each other (Gray, 2016).

Gray, Vogel and Foulke examined in their study how active investing strategies, in their case

momentum, growth and value investing, have performed in relation to the index fund SP500.

The result showed that momentum investing outperformed the SP500 index during 1927-

2014. However, the SP500 had a higher return than both growth and value investing during

the time of observation. This means that only one active investing strategy, momentum,

outperformed the passive investing strategy. However, the results from their study are gross

fees, which means that they ignore transaction cost in their observations (Gray, 2016). This

will, according to Damodaran, make the test incomplete since transaction costs have an

impact on the result (Damodaran, 2012).

1.3 PROBLEM DISCUSSION

The stock market is for many people unexplored land. Some do not have the knowledge, time

or the patience that it takes to achieve positive results in the long run. Thereto, active

investing also includes transaction costs like commission, fees and bid ask spread

(Damodaran, 2012).

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According to Karl Erlandzon, investing in index funds is a better alternative than active

investing. He claims that the transaction costs are higher for an active investor because a

passive investor constantly holds the same stocks, while an active investor periodically

changes its portfolio. Since active investing has higher transaction costs than passive

investing will, according to Erlandzon, lead to a higher return for a passive investor in the

end. Only a few investors will beat the market. Additionally, the costs are too high and there

are difficulties in predicting who these investors are. On this basis, Erlanzon claims that

being passive and investing in an index fund, due to its lower transaction costs, is the best

strategy in the long run (Erlanzon, 2019).

Paul Gibson, specialist in financial planning, wrote in 2017 about the Financial Conduct

Authority's report on the asset management industry. More than three of four people in the

UK have exposure to asset management, which makes this report of huge interest for the

individual investor regarding its savings. Active managed funds are associated with higher

transaction costs than passive investing. These higher costs are expected to compensate for

higher return than investing in a passive index fund. From the report the active fund

management became criticized due to its high costs. Despite that active investing is the most

dominant and costly strategy, the report showed that the active funds did not outperform

passive investing, like indexes, after transaction costs had been considered. This made active

funds too expensive in relation to passive investing. The report also demonstrated that the

costs for active investing has been approximately the same for the last ten years, while the

charges for passive investing has become lower every year (Gibson, 2017).

Active investing is associated with higher risk. Transaction costs, namely commissions, bid

ask spread and fees, represent the risk you take for being active. Many investors do not know

if it is worth being active and pay more in the hope of beating the market and get a higher

risk-adjusted return.

However, the main problem by evaluating different investing strategies against each other is

whether the return is luck or purely random. Therefore, this is an important problem in these

kinds of observations in order to decide if the results of the strategies performance are

significant.

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1.4 PURPOSE

The purpose of this paper is to investigate whether two active investing strategies,

momentum and growth investing, have had a higher risk-adjusted return than a passive

benchmark index fund.

1.5 Research questions

To answer the purpose, the paper will examine how the growth and momentum strategy has

performed on a risk adjusted-return basis in relation to a passive index fund. The research

questions are the following:

How has the two different strategies momentum and growth investing performed the past 15

years compared to a benchmark index?

Are the results of the strategies performance significant?

1.6 LIMITATION

This paper will focus on stocks from the Frankfurt stock market. Thereafter, it will be filtered

down to the automobile sector. After this, there remains 71 stocks. The reason for this

limitation is mainly because of the evaluation of growth investing. By looking at one industry

instead of all industries will pick up firm effects rather than mixing it up with potential

industry effects as well. Growth stocks have several characteristics, which are high P/E ratio,

high P/S ratio and low dividend yield. To be able to analyze these fundamentals in an

accurate way for each company, the stocks in the sample needed to be limited. With this in

mind, it would have been too time-consuming analyzing all stocks on the German market.

Simultaneously, the automobile sector is the largest and most important industry in Germany,

which makes it an interesting market to analyze.

The time of observation will last 15 years, from 2005-2020. The reason for this time interval

is because the market has both upward and downward trends during this period, like the

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financial crisis in 2008. Simultaneously, 15 years is quite a long period and should be enough

to give an accurate and reliable result.

Small companies are often illiquid, which can make it hard for trading companies from the

perspective of what the paper aims for, namely private investors. This paper considered

companies “small” when their market cap is under 50 million dollars. Therefore, companies

under 50 million dollars will get excluded from the sample pool.

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2. Theory

2.1 Growth investing

A “growth stock” is a stock that has increased its per share earnings in the past and is

expected to do so in the future as well. The advocates of growth investing mean that these

high growth stocks will outdo the stock-market in the long run. Growth investing focuses on

fundamentals, unlike momentum investing (Christian Schießl, 2013).

The desire to buy high growth stocks became popular in the late 1990s when the internet was

invented. During this time there were a lot of IPO: s (initial public offerings) by companies

with a cheap stock price whose earnings were expected to grow a lot in the future. One

example of this is the case of EMTV on the German stock market. When the company first

was listed in October 1997 the stock price was 35,50 Deutsche Mark (0,35 Euro). In 2000 the

stock price reached its highest point at 120 Euro, which is a remarkable increase. Year 1999

EMTV had generated sales of 317 million Deutsche Mark and had a market value of more

than 15 billion Deutsche Mark. At this point in time, EMTV was as equally valued as the

DAX index. The success ended in 2000 when the stock started to go down, not least because

of the dot com bubble. This means that the high growth company EMTV failed to meet its

expectations. There are other examples where high potential growth companies managed to

fulfill their potential, like Google and Apple (Christian Schießl, 2013).

Growth stocks have some specific characteristics. First, they have high P/E ratios. Price-

earnings ratio, one of the most used multiples, is the market price per share divided by the

earnings per share. This means that you have to pay a high price in relation to the earnings

due to the stock’s high growth potential. Damodaran argues that, especially for high growth

firms, the P/E ratio can be very different depending on which measure of earnings per share

you chose. One reason for this is that there is higher volatility among these high growth firms

compared to other firms. The P/E ratio can be computed using earnings per share, forward

earnings per share, fully diluted earnings per share, primary earnings per share or trailing

earnings per share (Damodaran, 2012).

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Another thing that characterises a growth stock is that it trades at a high P/S ratio. To

compute the price to sales ratio, which is a revenue multiple, you take the market value of

equity divided by revenues. A high growth stock, viewed as expensive due to its potential,

has a high market value of equity in relation to revenues. According to Damodaran, revenue

multiples have several benefits compared to other multiples. Revenue multiples works for

every kind of firm, even the most troubled ones. The consequence of this is that you do not

have to eliminate firms in the sample due to misleading numbers, which lowers the potential

for bias. Second, the volatility is lower compared to for example earnings multiple. The

earnings are much more sensitive than the revenues due to economic changes, which makes

the P/E more volatile than the P/S ratio. One disadvantage using revenue multiples is that

focusing solely on high revenue growth can be a misleading factor. A company needs to

generate high cash flows and earnings for it to have value (Damodaran, 2012).

Low dividend yields are another factor that is typical for a growth stock. Dividend yield is

dividends per share divided by the stock price. Dividend yield is the percentage return you

get from dividends (Damodaran, 2012).

2.2 Momentum

“The dumbest reason in the world to buy a stock because it's going up” - Warren Buffett

Momentum investing is the epitome of a strategy capitalizing on existing market trends. This

is done by taking advantage of the way the market fluctuates. Upward trends mean one

should invest while downwards suggests sell. This whole concept relies on humans being

systematic in their predictions for the future. This way the expectations error can be separated

from efficient market hypothesis and a value can be obtained, “It is the ultimate black eye for

the EMH”. According to Wesley.R the expected error is in average related to an

underreaction to positive news, even though some suggest the opposite. Collected evidence

from the past proves an underreaction. The chain reaction creates mispricing opportunities

which can be exploited. Continuing to argue that two assumptions are usually made in order

to sustain value from the momentum in the future:

“Investors will continue to suffer behavioural bias”

“Investors who delegate will be short-sighted performance chasers”.

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This is caused by erroneous decisions from people after a series of emotional, reflexes and

cognitive biases. For example, people tend to sell stocks that have been going well in order to

earn the profit and keep those which have dropped in value to avoid losses (Gray, 2016).

2.3 Momentum short or long-time horizon?

There are generally three types of time intervals when calculating the momentum of a stock.

These are short-term momentum, intermediate-term momentum and long-term momentum.

The first mentioned is when you look at how a stock has performed a short period back in

time, for example one month. A study made by Bruce Lehmann from 1962-1986, where he

looked at how a one-week look-back affected the next week's return, showed that portfolios

with high past return (winners) had negative returns the following week. These negative

returns the next week after that became positive, which Lehmann said was a short-term

reversal in the returns. Jegadeesh made another study where he focused on a one-month look-

back in the momentum. Jagadeesh found, similar to Lehmann, a short-term reversal in the

returns. Past winners next month became losers who next month again became winners

(Gray, 2016).

Intermediate-term momentum is a 6-12-month look-back in the momentum of a portfolio.

Unlike short term momentum, who exhibited reversal returns, intermediate momentum

showed that past winners became winners and past losers became losers. Jegadeesh and

Titman found that in the time interval of 3-12 months a momentum strategy, namely buying

past winners and selling past losers, performed well. They claimed that the best strategy is to

buy stocks with high past performance the last 12 months and hold these for 3 months. The

reason is that the excess return of these stocks is not that sustained (Gray, 2016).

The third type is long-term momentum, which is a longer look-back in the momentum of

stocks compared to the two other variants. DeBondt and Thaler investigated in their study

how winners and losers the last three to five years continued to perform. The result showed

that losers outperformed winners by quite a large margin, namely 24,6 percent. This means

that for long-term momentum, like short-term, there were reversal returns (Gray, 2016).

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2.4 Momentum vs growth investing: what is the difference?

“With momentum, prices aren't everything; they are the only thing”.

Momentum and growth investing are not the same thing, but it can be easy to mix them up.

Momentum investing is a strategy which claims that past return can predict future return. The

strategy focuses on buying stocks with high past returns (winners) and selling stocks with

low returns (losers). Growth investing says that if a stock has increased its per share earnings

in the past it will continue to do it in the future as well (Gray, 2016). So, what is really the

difference between the two strategies?

The big difference is that growth investing focuses on prices and fundamentals while

momentum investing focuses solely on prices. Growth investing observes the price trend on

the stock and at the same time looks at all the data that affected the stock (fundamental

analysis), including the financial statement. Momentum investing focuses only on the price

trend on the stock, independent of fundamentals like changes in earnings or P/S ratio.

Another difference is the time interval. Momentum investing aims to profit in the short run

while growth investing is a long-term investing strategy (Gray, 2016).

2.5 Efficient market theory

The efficient market theory maintains whether all stocks are perfectly priced with all

available and relevant information to market participants at any given time. If markets are in

fact efficient, then the information reflects the market prices. Thus, the process becomes one

of justifying the price. In this scenario it would be impossible to gain any value since there

are no undervalued or overvalued securities to be invested in.

According to Fama, there are three different forms of efficient market theory. The first level

is called the weak form and suggests that there is no use of analysing prices from the past

considering it has no correlation with future prices. Hence, technical analysis would do no

good for investors since no stock price “patterns” can be found. This implies that information

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that is not involved in the price series, such as fundamental information, would entirely

determine the future prices.

The second level on the ladder is semi-strong and implies that new information comes out to

the public very fast. As follows, this information instantly prices the securities such as no

excess return can be earned by trading that information. Neither technical analysis nor

fundamental analysis can give investors economic advantages over the market in this form.

The only exception would be if one has access to inside information. That is information that

the public does not know about.

The last level is the strong form, which advocates that the share price reflect all information,

both public and private. In this form there is no way to beat the market since the information

and the stock price is already perfectly matched.

2.6 Critics against efficient market theory

An efficient market would carry very negative implications for many investment strategies.

The reasons are the following:

a, It is very costly to research for equity while it would give no benefits back. Thus, it would

always be 50:50 to find undervalued stocks since it would be pure randomness of pricing

errors.

b, Strategies with minimized trading would be preferable. Just sticking to a created portfolio

would require less work and constrain the cost.

c, A strategy that randomly follows the stocks or index carrying minimal execution and

information costs would be a superior tactic.

There is therefore no wonder that there are a lot of controversial and strong views argued

between different individuals about the efficient market hypothesis. However, there is

evidence of irregularities in market behaviour. This is related to systematic factors like price-

earnings ratios, priced book value ratios, size and time, such as weekend and seasons. These

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irregularities tend to be inefficiencies in the market. Continuing, it could be used as an

argument against the efficient market theory (Damodaran, A. 2012).

2.7 Transaction costs

Transaction costs, namely commissions, bid-ask spreads and fees, are costs associated with

the transaction between two investors. Commission, an explicit part, is the payment to your

broker. There are two kinds of brokers: full-service and discount brokers. Full-service

brokers offer executive orders, including recommendation and the completing of buying or

selling a stock. They also provide services dealing with loans, short sales, holding securities

for safekeeping but most importantly they give advice regarding investment alternatives

(Bodie, 2018).

Discount brokers provide the same services as a full-service broker, beside that they do not

give the same information about investment alternatives. The only information they give

about the securities is price quotations. Bid-ask spread is another type of transaction cost

where the broker, instead of taking a commission, is the dealer and collects a fee for the bid-

ask spread (Bodie, 2018).

Many studies exclude transaction costs, although it has an impact on the result. According to

Damodaran, not allowing for transaction costs will make the test incomplete. However, this is

not so easy because investors have different transaction costs and it can be difficult to choose

which transaction cost that should be used in the test (Damodaran, 2012).

Ammann, Moellenbeck and Schmid also point out that to get an accurate result about the

performance of an investment strategy, like momentum, it is important to include transaction

costs. By doing this it will be easier to see if momentum, for example, is as dominating as the

previous results show. According to Moellenbeck, when including transaction costs in the

study, the momentum strategy is not exploitable. They mean that the stocks with high

momentum return are also those with high trading costs (Moellenbeck, 2010).

According to Damodaran, smaller stocks tend to have higher transaction costs than larger

stocks. With this in mind, some writers have tried to rule out smaller firms in their sample by

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for example excluding those with a share price below 5 dollar or by only including larger

stocks (Damodaran, 2012).

2.8 Risk models

2.8.1 CAPM

The capital asset pricing model, created in 1964 by Sharpe, Mossin and Lintner, is still one of

the most famous and used risk models today when calculating the expected return on a stock

or the cost of equity. The model shows that the total risk of a stock is determined by the

market risk and the firm-specific risk. The beta in the model symbolizes the market risk,

which is undiversifiable. A beta of 1 indicates that the stock moves exactly in the same

direction as the market, namely perfectly correlated. A beta higher than 1, an aggressive

stock, means more volatility than the market. A lower beta than 1, a defensive stock, is less

volatile than the market.

According to the CAPM model, a higher beta is higher risk and therefore gives higher

expected return. This means that the reward is larger the more market risk. On the other hand,

the firm-specific risk of a stock can be diversified away by adding more stocks to the

portfolio (Damodaran, 2012).

CAPM: E(ri)= rf+*β(rm-rf)

E(ri)= Expected return of stock i

rf= The risk-free rate

β= The market risk

rm=Expected return of the market portfolio

rm-rf=Market risk premium

The risk-free rate is the return you get from a risk-free investment. Investing in high rated

treasury bonds are usually characterized as a risk-free investment. The market risk premium

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is the difference between the expected return on the market portfolio and the risk-free rate.

This is the premium that investors demand for investing in the market portfolio (Christian

Schießl, 2013).

There are several assumptions about the CAPM-model and some of them can be seen as more

important. Firstly, there is a one-period investment horizon and no transaction costs. Second,

there is unlimited borrowing and lending at the risk-free rate, which is the same for everyone.

Finally, all individuals have the same homogeneous expectations about variance, expected

return and covariances of assets. Taking these assumptions into considerations every

individual will choose the same portfolio of risky assets (the market portfolio). However,

there will be a difference in the proportion of the risk-free asset and the market portfolio

dependent on that individuals have different risk aversion (Szylar, 2013).

2.8.2 Jensen’s alpha

The alpha was created in 1967 by Michael Jensen. It is one of the key metrics for measuring

the risk adjusted return of a stock or a portfolio of stocks (Le Tan Phuoc, 2018) Alpha is the

difference between a stock's required return, denoted as Ri, and its expected return, CAPM.

When the market is efficient, all stocks have an alpha of zero. However, if the market is not

efficient some stocks will have alphas higher than zero. This means that these stocks, or fund

managers, have beaten the market portfolio. In other words, alpha shows if the return is

below or above what CAPM predicted. The following formula is used for calculating Jensen's

alpha (Berk, 2020):

a= Ri-(Rf+β(Rm-Rf))

Ri= Realized return of portfolio or investment

Rm= Realized return of the market index

RF= Risk free rate

βi= The securities sensitivities to the market index, beta of portfolio

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2.8.3 Sharpe ratio

The Sharpe ratio, introduced in 1966 by William Sharpe, is a risk model that measures the

reward-to-volatility provided by a portfolio of stocks. It shows how much reward (return) you

get for every risk (standard deviation) you take. The higher Sharpe ratio, the more return you

get per extra risk. The steepest possible line combined with the risk-free investment must be

found, the so-called tangent portfolio. The slope of of this line is the Sharpe ratio, which is

calculated as follows (Berk, 2020):

Sharpe ratio= Portfolio Excess Return = E(Rp)-rf

Portfolio volatility SD(Rp)

E(Rp)= Return of the portfolio

rf= Risk free rate

SD(Rp)= Standard deviation of the portfolios excess return

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3. Literature review

3.1 Previous results

In the article “Quantitative momentum: A practitioner’s Guide to Building a Momentum-

Based-Stock Selection System”, Gray, Vogel and Foulke discuss if active investing strategy

is a better alternative than passive investment strategy in the long run. From 1927 to 2014

they tested whether value, growth and momentum stocks (active investing strategies) have

been more successful than the SP500 index (a passive investing strategy). Their summarizing

statistics of the period showed that both value stocks and the index fund SP500 had a higher

return than growth stocks. However, momentum stocks outperformed both value and growth

stocks, as well as the SP500 index. This means that between 1927-2014, according to their

results, two active investing strategies, momentum and value investing, was more successful

than the passive investing strategy SP500. However, their results are gross fees, which mean

that the transaction costs have not been taken into account. Their summarizing statistics can

be seen from CAGR, compound annual growth rate, in table 1 (Gray, 2016).

Table 1 (Gray, 2016)

In their study they also made a portfolio combined with both value stocks and growth stocks,

50 % each, to see if this combination could give a better return than what the strategies have

performed individually. The result showed that the standard deviation became lower due to

diversification, but the return stayed unchanged. According to Gray, Vogel and Foulke,

growth investing is not a sustainable investing strategy. Regarding to their result they mean

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that buying and holding growth stocks is not a good choice in the long run. However,

including growth stocks in a portfolio can provide diversification benefits, not least during

bad periods, despite its poor lack of return.

Although growth stocks can be used in a portfolio to prove diversification, the writers find a

better diversifier. They mean that momentum investing, that past return can predict future

return, is a better investing strategy and diversifier (Gray, 2016).

Table 2 (Gray, 2016)

The writers did another test. From 1963 to 2013 they put momentum and growth investing

against each other. They randomly picked 30 momentum stocks and 30 growth stocks and

rebalanced the portfolio of new growth and momentum stocks each month. They calculated

the strategies performance during the years and repeated this step for 1000 times. As table 2

shows, there is not a single time when growth investing has performed better than momentum

investing during 1963 to 2013 (Gray, 2016)

Later in their study they build a quantitative momentum strategy where they included

transaction costs to see if momentum still performed better than the market index. 0,20

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percent were used as a rebalancing cost and 1 percent were paid as commission to a

professional for taking care of the portfolio. The result showed that momentum, despite its

costs, still outperformed the index (Gray, 2016).

Ammann, Moellenbeck and Schmid also point out that to get an accurate result about the

performance of an investment strategy it is important to include transaction costs. By doing

this it will be easier to see if momentum, for example, is as dominating as the previous results

show. Their study was made on the US stock market with the focus on feasible momentum

strategies. The highly large-cap and blue chip stocks were chosen from the S&P100 index.

The investment horizon was between 1982-2009. Their portfolios were held in three different

time intervals, which was 3,6 and 12 months. Ammann, Moellenbeck and Schmid found that

investing long in the single best performing stock and selling short the index where the best

alternative. The long position consists of stocks that has performed the best historically and

the short position is the S&P100. The result showed, when holding a 10-stock portfolio, the

highest monthly return of 0,5 % and the lowest at 0,02 %. The test was significant at a 10 %

level. The conclusion they made was that the momentum strategy is most profitable when

holding the longer portfolio, in other words 12 months rather than three months

(Moellenbeck, 2010).

18

4. Methodology

4.1 Investigation design

This study aims to investigate how the momentum and growth strategy has performed in

relation to a passive index containing 71 stocks. To answer this, a test was made during 2005-

2020 on the Frankfurt stock market on stocks from the automotive sector. The reason for the

filtration down to the automotive sector was explained in section 1,6, Limitation. The data for

growth, momentum and index was collected from Thomson Reuters Datastream. The

calculations were made in Excel.

Previous results from Gray, Voulke and Fogel showed that between 1927 to 2014 momentum

investing outperformed the index SP500, but that SP500 performed better than growth

investing. However, these results were gross of fees while this study is going to include

transaction costs. Thereto, this paper will compare stocks on the Frankfurt market, namely

the automotive sector, while previous results were based on stocks from the American market

(Gray, 2016).

The test will be made from the viewpoint where the one who makes the investment is a

private investor that pays a commission to a full-service broker for taking care of the

portfolio. Simultaneously, fees will be paid to the broker every time each portfolio is

rebalanced.

’4.2 Data collection

4.2.1 Selection of data

When the data was collected it was in focus to use a reliable source, which is also the main

reason why the datastream Thomson Reuters were used. In addition, there are limits within

the study, such as research questions and time limits. Thus, it is of importance to filter the

datastream in order to avoid unnecessary data. A restriction of the parameters was made to fit

the time limits. One restriction was that it had to be listed in the Frankfurt index deutsche

börse. It had to be within the branch automobiles and parts. The data had to come from

19

companies that were active at the time and the data had to be published within the time period

between 2005-2020. The time horizon was chosen with the reason that the study should not

be affected by temporary stock market climate. There have been both sharps up and downs,

the finance crisis 2008 for example, which makes the time period a reliable reflection.

In order to answer the research questions of the paper necessary data was collected, namely

inputs that are needed to apply momentum and growth. The company's share price that is

included in our portfolios was sufficient data for momentum. For growth, however,

additionally data were required. Three financial ratios that take the company’s fundamentals

into account, namely PE, DY and PS, were collected for a ranked summation of the

company’s growth. One could use more different financial ratios when deciding the growth.

However, these three had the highest ranking on Thomson Reuters (the chance of an

accounted value to exist for each company is high) and in addition they are strongly related to

growth.

Year

20

05

20

06

20

07

20

08

20

09

20

10

20

11

20

12

20

13

20

14

20

15

20

16

20

17

20

18

20

19

Original sector 11

568

12

770

14

271

15

161

15

713

16

587

17

266

17

658

18

129

18

800

19

375

19

899

20

642

21

240

21

686

Active 4

231

4

784

5

427

5

775

5

982

6

350

6

574

6

782

7

090

7

529

7

892

8

286

8

893

9

409

9

813

Automobiles and

parts 72 82 88 91 94 105 108 108 109 115 120 125 130 142 147

Major companies 71 79 84 85 88 98 101 101 100 106 110 115 120 132 136

Table 3

4.2.2 Loss of data

The historical data is collected with a starting point of January 2005 where a list of 71

companies is included in the selection pool. Every year from that point on a certain amount of

new companies gets included in the selection pool. The reason behind this is that more

companies get listed each year in the Frankfurt exchange deutsche börse. Additionally, if they

20

are within the filters that are set up for the analysis in this paper, it then gets added to the

pool. A side effect is that the companies are excluded from the research until they get listed.

Also, if the share ceases to exist for various reasons it gets excluded from the pool. Some

examples can be that the company has gone bankrupt due to poor financial performance, the

shares have been bought out of the stock market or just been delisted. Either way it is a loss

of data in the end since the datastream only includes the companies which are listed at the

moment it gets downloaded.

All “small companies” had to be sorted out by the reason that they are unreliable. In addition,

they are often illiquid, which can make it hard for trading companies from the perspective of

what the paper aims for, namely private investors. A company is considered “small” when

their market cap is under 50 million dollars, according to a study made by Greenblatt

(Greenblatt, 2010).

4.3 Portfolio composition

In this study, the intermediate-term momentum will be used. The ten best performing stocks

the last six months will be chosen. These stocks will be held the following six months to see

if they continue to perform well or not. This process will be repeated for the next fifteen

years.

The reason why the intermediate-term momentum will be used in this paper is because this

type was, according to previous results, the only one not showing reversal in their return.

This time interval will therefore facilitate the comparison to the index fund, namely the

passive strategy. According to the results of Jegadeesh and Titman, buying last 12 months

winners and keeping these stocks for 3 months were the best alternatives. However, this

study will instead buy the last six months winners and hold these ten stocks for further six

months. The reason for this is that it is interesting to investigate another time interval for

buying and holding the stocks. This means that the momentum portfolio, during the 15 years

of observation, will be rebalanced 30 times.

In terms of the time interval of growth investing, the ten stocks with the highest P/E ratio, P/S

ratio and lowest dividend yield 2005 will be selected. Said earlier in the paper, these factors

are characteristics of growth stocks. These stocks aim to profit for a longer time, compared to

21

momentum, and are therefore held for five years. After five years, it will be rebalanced with

the ten best growth stocks at that time. This process will continue until 2020, which means

that the growth portfolio will be rebalanced three times.

In Joel Greenblatts study “The little book that still beats the market” a non-weighted ranking

was applied. Greenblatt claimed that the investing strategy magic formula was beating the

market in the long run. Magic formula is built on two financial ratios, return on capital

employed and earnings yield, and Greenblatt ranked the performance of these two-key

metrics for each company in the sample. This is called a non-weighted method because the

companies did not get ranked based on their size but on their performance on return on

capital and earnings yield (Greenblatt, 2010).

Since there are three different financial ratios in comparison for each company, one could

argue how strongly they should be evaluated related to each other and in which way to sum

them up. A non-weighted method, used by Greenblatt, was also applied in this study as a

solution where each financial ratio, in their own category, got ranked from one to the amount

of companies included that particular year. The next natural step was then to sum up the three

different rankings, representing their financial ratios for each company, to achieve a final

result. One can then easily compare how well the different companies are positioned to each

other correlated to their fundamentals: P/E, P/S and DY.

4.3.1 Benchmark

In order to comprehend how well the two different strategies perform, a benchmark is used.

This paper will focus on stocks from the Frankfurt stock market from the automobile sector.

Said earlier, this study will focus on one industry, the automobile sector, with a consistent

benchmark index, Frankfurt, for the same industry. The advantage by doing this gives a more

accurate test and the potential mixed up industry effects on return will be avoided. Mixing up

different industries may lead to a skewed comparison. The reason for this is that some

industries do better than others and this may not reflect the strategies performance in an

accurate way. By looking at one industry instead of several industries will lead to a firm

effect rather than a mixed up industry effect.

22

First, it seemed reasonable to use the German DAX index as a benchmark. However, the

DAX index does not always contain foreign companies that are traded on the Frankfurt stock

exchange, compared to the automotive sector. The comparison would get skewed if the DAX

were chosen as the index. Simultaneously, the prices are not updated in the same time

interval.

Therefore, to facilitate the comparison, a benchmark index was created based on the

companies from the automotive sector. All the stocks in the sector were chosen, namely 71

stocks. These stocks were held for 15 years, representing a passive index fund.

4.3.2 German automotive sector

The production of passenger cars in Germany amounted up to around 5,9 million in 2011.

This made Germany the largest automotive industry in Europe and third in the world, after

Japan and China. Hardly surprising, the automotive sector is the most important part for

Germany in terms of revenue. In 2010 the revenue from vehicles amounted up to 322 billion

euros, which corresponded to about 19 % of Germany's total industry (Wells, 2015).

Nieuwenhuis and Wells wrote in their paper about the global automotive industry. Leading

economies, such as Germany and the United States, are all moving towards the incorporation

of a new manufacturing innovation policy with the purpose to strengthen their automotive

industries. This policy will, among other things, focus on the improvement of technologies,

such as IT and batteries, which are important factors in the development of a more non-

polluting automotive sector (Wells, 2015).

With this in mind, this paper will focus on companies from the automotive sector on the

Frankfurt stock market. It is interesting to investigate this sector since it is the most important

source of revenue for Germany. Simultaneously, the filtration down to this sector will

facilitate when calculating the dividend yield, PE and PS ratios, which are factors that

characterizes growth. Without this limitation it would have been too time consuming for

calculating the growth investing, since a lot more companies then had to be reviewed.

23

4.4 Evaluation of results

Different measures of risk and return have been used to be able to evaluate and compare the

performance of each portfolio in the study. Data such as share price, p/e, dividend yield and

PS ratio was collected from Thomson Reuters Datastream. Further it was used to calculate

CAPM, Sharpe ratio and alpha.

4.4.1 Return

To be able to answer the purpose on how growth and momentum investing have performed in

relation to the passive index, the return for each strategy has been calculated. Due to the fact

that growth and momentum investing are rebalanced in different time intervals, momentum

every sixth month and growth every fifth year, the return will be handled thereafter. Let say

that 10 000 is the starting amount. Then the return or loss of the ten chosen companies in the

momentum portfolio will be added to the starting amount. After six months the portfolio will

be rebalanced. This process will be repeated for the next 15 years, which then will give a

final return. It will be the same for the growth portfolio, but the difference is that it is only

rebalanced three times during the 15 years of observation. Said earlier, the return will be net

of fees. For calculating the return for a stock in the tenfold portfolio the following formula

have been used:

rt=(Pt-Pt-1))/Pt-1

rt= portfolio return at time t

Pt=price today

Pt-1=price at initial investment

4.4.2 Risk

The standard deviation, which is seen as a measure of risk, will be calculated for the

momentum, growth and index portfolio. By doing this it is possible to compare the risk with

the return for each portfolio. The standard deviation shows how much of the monthly returns

that on average deviate from its mean value. According to the efficient market hypothesis, a

24

higher risk (standard deviation) can yield a higher return. Therefore, it is interesting to see if

there is a positive correlation between these two measures (Damodaran, 2012). The standard

deviation is calculated by taking the Excel function “STDEV.S”. To obtain the annual

standard deviation the monthly standard deviations was multiplied with the square root of

12.

4.4.3 Risk-adjusted excess return

The capital asset pricing model (CAPM) will be used to calculate the risk-adjusted return of

each portfolio, which consists of ten stocks. A three-month American treasury bond, which is

associated to be the most riskless investment, will be used as the risk free rate. The beta, a

factor that shows how the portfolio moves in relation to the market index, was calculated by

setting the market's monthly returns against the portfolio's monthly return and then using the

Excel function “SLOPE”.

By comparing the markets risk premium (CAPM) and the risk premium of the portfolio,

Jensen's alpha can be calculated to see if the return of the portfolio has performed better than

what CAPM predicted. If it has, then alpha will be positive, which means that the portfolio

has beaten the market.

4.4.4 Regression

A regression will be made in order to test if the result is statistically significant or not. The

regressions are based on monthly data. Additionally, the alpha is tested for statistically

significance at a five percent level by using the p-value. When testing the statistically

significance for the momentum portfolio the null hypothesis will be stated as follows:

(H0): “The alpha of the momentum is equal to zero”

The alternative hypothesis is defined as:

(H1) “The alpha of the momentum portfolio is not equal to zero”

When testing the statistically significance for the growth portfolio the null hypothesis is

stated as follows:

25

(H0): “The alpha of the growth portfolio is equal to zero”

(H1) “The alpha of the growth portfolio is not equal to zero”

4.5 Transaction costs

Previous results made by Gray, Foulke and Vogel were gross of fees. However, later in their

study they claimed that transaction costs have an impact on the performance of active

investing strategies, like growth and momentum investing. Therefore, they builded a so-

called quantitative momentum model where they included to see if momentum still can beat

the market. They incorporated a 1 percent management fee. This fee represents the cost you

need to pay to a professional for actively taking care of your portfolio and implementing the

desired active strategy. They used a quarterly rebalancing cost of 0,20 percent, which sums

up to an annually trading cost of 0,80 percent. The total transaction cost Gray, Foulke and

Vogel used summed up to 1,80 percent (Gray, 2016)

However, the study will make its own calculations regarding the transaction costs. To get

reliable numbers, information has been taken from Avanza. To get the full- service broker

commission, the paper will look at eight different funds and take the average of those funds’

commissions. By doing this gives a yearly commission of 1,5625 %. However, the

commission is not on a yearly basis, it is a small amount that is paid every day. This gives an

interest on interest effect, which changes the yearly commission to 1,55 %.

Regarding fees, the cost for buying and selling stocks, an approximation has been made.

When buying 10 000 of a stock at Avanza, a fee of 0,28 % was taken for that buy (Avanza).

This paper will therefore use 0,28 % as a fee for buying stocks, namely rebalancing of the

portfolio. The cost will be higher for momentum investing compared to growth investing

because the momentum portfolio is rebalanced more often.

26

4.6 Potential problems

4.6.1 Survivorship Bias

The existing funds in the investment market can be more highly viewed when used as a

representative sample than they should because of the phenomena called survivorship bias.

Therefore, it's important to both understand it and bear it in one's mind when applying the

data that is used in this paper. To explain survivorship bias in a theoretical way from a

finance perspective, one can say that the used databases only contain data about shares that

currently exist without regard to include those that no longer. The sample selection could for

this reason be biased. Shares can cease to exist for various reasons, for example due to poor

financial performance or because the demand for the share is not high enough. Thus, it can

influence the results of the study when there are samples that could have been included but

are excluded due to missing data.

When data was collected for growth, a decent amount of survivorship bias occurred. For

example, a decent amount of all accounted PE values appeared as “null”, which means they

did not get included in the valuation for growth. However, most of these companies had bad

valuation on their other financial ratios meaning they would get excluded anyway.

4.6.2 Outliers

An outlier can be the result of mistakes during the data collection or it can be caused by

variance in the measurement. Either way it can cause some serious problems in the statistical

analyses. The key is therefore to decide whether it should be included in the data or not. The

thumb rule we used in this paper is pretty simple: if the extreme value is due to variance, we

keep it, is it because of a mistake in the collection, we take a deeper look. Thus, if it is not

within our structured parameters for the methods, then without further ado we remove it.

4.6.3 Potential problems with the benchmark

The potential problem with the index constructed can be survivorship bias. This means that

new companies that qualify and should be added are not taken into consideration. This paper

excludes these companies and focuses solely on the 71 automotive stocks in 2005, which can

affect the result.

27

Another potential issue with this study is that an unweighted rank is used on the growth

stocks when creating the growth portfolios. This is a problem because the companies on this

study do not get ranked based on their market capitalization. The higher market

capitalization, the larger the weight should be. However, this factor is ignored and can

therefore affect the final result.

5 Empirical results and Analysis

5.1 Returns

Strategy Average

monthly

return

Average

annual

return

Cumulative

return

2005-2020

Average

monthly

return, with

transaction

cost

Average

annual

return, with

transaction

cost

Cumulative

return 2005-

2020, with

transaction

cost

Momentu

m 1,09% 13,91% 705,40% 1,01% 12,82% 610,45%

Growth 0,722% 9,01% 364,78% 0,682% 8,49% 339,62%

Index 0,60% 7,50% 296% - - -

Table 4

Table 4 above shows the average returns for momentum, growth and the passive index

strategy, both before and after transaction costs have been taken into account. As the picture

shows, both growth and momentum have had a higher monthly, annual and cumulative return

than the benchmark index between 2005-2020. Notable is that both active strategies have had

28

a better return than the index, independent of time interval and when transaction costs are

included. This is truly a remarkable result.

Momentum has been the most dominant strategy of them all during the period with a

cumulative return of 610,45 %, compared to the passive index fund with a cumulative return

of only 296%. This means that momentum has performed more than twice as well as the

passive index fund during the 15 years of observation. This is interesting since the

momentum portfolio has been rebalanced every sixth month, namely 30 times, during the

period. The growth portfolio has only been rebalanced three times and the index fund not a

single time. Rebalancing a portfolio means higher transaction costs. Despite this, momentum

has outperformed both growth and the index fund with quite a large margin. Taking this into

consideration makes the momentum strategy even more outstanding. The growth strategy has

had a cumulative return of 339,62 %, which means that it has beaten the index fund with only

43,62 %. However, it has still performed better both gross and net of transaction costs.

Strategy

200

5

200

6

200

7

200

8

200

9

201

0

201

1

Q1-

Q2

Q3

-

Q4

Q1-

Q2

Q3

-

Q4

Q1-

Q2

Q3

-

Q4

Q1-

Q2

Q3

-

Q4

Q1-

Q2

Q3

-

Q4

Q1-

Q2

Q3

-

Q4

Q1-

Q2

Q3

-

Q4

Momentu

m Yes No No

Ye

s Yes No Yes

Ye

s No

Ye

s No No Yes No

Growth Yes No No No No

Ye

s Yes No No No No

Ye

s Yes

Ye

s

201

2

201

3

201

4

201

5

201

6

201

7

201

8

201

9

Q1-

Q2

Q3-

Q4

Q1-

Q2

Q3-

Q4

Q1-

Q2

Q3-

Q4

Q1-

Q2

Q3-

Q4

Q1-

Q2

Q3-

Q4

Q1-

Q2

Q3-

Q4

Q1-

Q2

Q3-

Q4

Q1-

Q2

Q3-

Q4

29

No Yes Yes Yes Yes No No Yes No No Yes No Yes Yes No Yes

No No Yes No No Yes No Yes No Yes No Yes Yes No Yes Yes

Table 5

Table 5 above shows whether the momentum and growth strategy has beaten the index: Yes,

if it has and No if it has not. The interval is during every six months, which gives 30

intervals. Notable is that momentum has beaten the index almost as many times as it has lost

against it, despite the fact that momentum overall has performed more than twice as well as

the index. This means that momentum must have had a much higher return each sixth month

when it performed better than the index, compared to those half-years when the index won

against momentum. One reason for this can be that the standard deviation is higher for

momentum compared to the index fund, which means that the momentum portfolio is more

volatile and therefore can give extremely high returns in some months.

Another interesting thing is that the index fund has more half-years of better return than

growth. This must also mean that once growth won against the index it must have performed

well, compared to those half-years when the index has beaten growth. Remarkable is that the

annual standard deviation is lower for growth than it is for the index.

5.2 Risk

As showed earlier, momentum and growth have performed better than the index during the

period. One reason for this can be that the standard deviation, the risk, has been higher for the

two active strategies. Momentum has had an average annual standard deviation of 27,48 %,

growth of 21,01 % and the index of 21,50 %. It is clear that momentum has had the highest

volatility, and this can be one reason for its outstanding numbers. However, growth has

performed better than the index but, despite this, have had a lower standard deviation than the

index fund.

30

5.3 Sharpe ratio

Strategy Average

annual

return

standard

deviaton

Average

risk free

rate

Sharpe

Ratio

Average annual

return, transaction

cost included

Sharpe ratio,

transaction cost

included

Momentu

m 13,91% 27,48% 1,31% 0,459 12,80% 0,418

Growth 9,01% 21,01% 1,31% 0,367 8,49% 0,342

Index 7,50% 21,50% 1,31% 0,288 - -

Table 6

The Sharpe ratio is a measure that shows a portfolios risk-adjusted return. It shows the return

you get for every extra risk you take. The average annual return is subtracted from the risk-

free rate and divided by the standard deviation, which represents the risk. Momentum has a

Sharpe ratio (net transaction costs) of 0,418, growth of 0,342 and the index of 0,288. This

means that the momentum has the highest Sharpe ratio, which is not that surprising due to the

fact that it has had the highest cumulative return in the end. However, a Sharpe ratio of 0,418

is not that high. It means that for every 1 % extra risk (SD) you take you only get 0,418 in

return. Though, both momentum and growth have had a higher Sharpe ratio, namely a higher

risk-adjusted return, than the benchmark index.

5.4 CAPM and alpha

Strategy Average excpected return on the market

Average risk free rate

Beta CAPM Alpha

31

Momentum 7,50% 1,31% 0,8453 6,54% 6,30%

Growth 7,50% 1,31% 0,8363 6,49% 2,09%

Table 7

The risk model CAPM has been used to calculate the expected annual return on the

portfolios. The expected return for momentum was 6,5 % and for growth 6,4 %. A beta

higher than zero, which both portfolios have, shows a positive correlation with the market.

For every 1 % the market goes up, momentum increases with around 0,85 %. Both strategies

have similar exposure to market risk (beta), which means that they have barely the same

expected return. However, the average annual return for momentum was 13,91 % and for

growth 9,01 %. This means that both strategies have performed better than what CAPM

predicted.

Jensen's alpha was computed to see how the average annual return has been compared to

CAPM. As table 7 portrays, the momentum portfolio has had 6,3 % more in yearly return

than what CAPM predicted. Simultaneously, the growth portfolio has had 2,09 % more in

yearly return than what CAPM predicted. This means that both growth and momentum

investing have beaten the market in terms of return.

5.5 How can momentum be so outstanding?

Gray, Vogel and Foulke discuss in their article how momentum can be so outstanding, which

is also the case in our result. They mean that the return of momentum is driven by an

underreaction to positive news. They argue that sustainable active strategies, like momentum,

exhibit a mispricing component and a costly arbitrage component. As far as there will be

mispriced assets and investors will suffer from expected error, prices will deviate from its

fundamentals. Gray, Vogel and Foulke mean that, concerning momentum, this expected error

seems to be an underreaction to positive news. Momentum stocks have high past returns and

investors do not seem to react positively enough on these past returns. Therefore, the price is

not driven up (stocks are not bought) and the consequence is higher performance on the

momentum stocks for a period (Gray, 2016). In the result of this study, momentum performed

more than twice as well as the index fund during the years of observation, despite its costly

32

variables. However, the stock with the highest past returns the last six months were bought

and held for further six months (intermediate-term momentum). It seems like the momentum

stocks exhibit momentum in its return for a while. If a longer time interval were tested,

maybe it would have been a completely different result.

It is surprising why not more investors apply momentum strategies with regard to its

outstanding performance. Gray means that the reason for this is that a fund manager needs to

be hired for implementing a momentum strategy. These professionals are often judged based

on their short-term relative performance compared to a benchmark. A momentum strategy

may require patience, but if there is too much deviation for a longer time in the performance

compared to the benchmark, then the strategy probably will be questioned by the investor.

Therefore, it can be hard to implement a momentum strategy due to that many investors are

short-term performance chasers. Gray means that to be a successful investor the most

important thing is to stay long-term dedicated to a strategy, rather than the actual strategy that

is chosen (Gray, 2016). This is something that can be recognized by many investors,

including ourselves. The short-term performance is often very important due to the lack of

patience of many investors who want immediate results. This collides with the idea that it is

important to stay dedicated to an investment strategy for a long time.

Concerning growth, it is the other way around. Investors seem to overreact to the positive

news of growth stocks, for example on fundamentals like high P/E and P/S ratio. The prices

are driven above intrinsic value and therefore the stocks become overvalued. Consequently,

the growth stocks do not manage to fulfill investors’ expectations. Said earlier, Gray, Vogel

and Foulke claim that growth investing is not a sustainable investing strategy. With regard to

their result they mean that buying and holding growth stocks is not a good choice in the long

run (Gray, 2016) However, our result shows that growth investing has performed better than

a passive index fund during the 15 years of observation, despite that growth investing

includes costly variables. On this basis, it is hard to agree with Gray, Vogel and Foulke on

that growth investing is not a sustainable strategy.

5.6 Results compared to previous studies

Gray, Vogel and Foulke tested in their study how momentum and growth investing had

performed in relation to the SP500 index between 1927-2014. Their results showed that

33

momentum outperformed both growth investing as well as the index fund during the years of

observation. Growth investing was beaten by the SP500 and was therefore the least

successful strategy of them all. However, this observation excluded transaction costs in their

calculations of the return. Therefore, they builded a quantitative momentum model where

they included transaction costs to see if momentum investing, despite its costs, still managed

to reach a high level of return. A cost of 0,20 percent was paid every time the portfolio was

rebalanced, and a commission of 1 percent was paid to a professional for implementing the

momentum strategy. The result showed that momentum outperformed the SP500 index even

when transaction costs were included (Gray, 2016).

Previous results are in line with the result of this study. Momentum is the most dominant

strategy both net and gross of transaction cost. However, growth investing performed better

than the index portfolio, compared to previous results. The reason for this difference can be

that their study was made in a longer time interval, in another market and on other types of

stocks. The choice of index can have an impact on the result as well. This study was limited

to stocks from the automobile sector on the Frankfurt market and the index was created based

on these stocks.

5.6.1 Is the result a coincidence?

5.6.2 Momentum

The null hypothesis (H0) is defined as “the alpha of the momentum portfolio is equal to zero”

and the alternative hypothesis (H1) is defined as “the alpha of the momentum portfolio is not

equal to zero”. The regression is based on monthly data. Since we cannot reject the null

34

hypothesis (0,115 > 0,05) at a significance level of 5%, we cannot prove statistically that the

alpha value of the momentum portfolio is significant.

The positive alpha shows that momentum has yielded 0,0071% higher monthly return than

what CAPM predicted. Thus, one could say that 0,0071% of the yield is not explained by

CAPM. This could be associated with the momentum strategy.

5.6.3 Growth

The null hypothesis (H0) is defined as “the alpha of the growth portfolio is equal to zero”

and the alternative hypothesis (H1) is defined as “the alpha of the growth portfolio is not

equal to zero”. The regression is based on monthly data. Since we cannot reject the null

hypothesis (0,2438 > 0,05) at a significance level of 5%, we cannot prove statistically that the

alpha value of the momentum portfolio is significant.

The positive alpha shows that growth has yielded 0,0071% higher monthly return than what

CAPM predicted. Thus, one could say that 0,0071% of the yield is not explained by CAPM.

This could be associated with the growth strategy.

35

6. Conclusion

The purpose of this paper was to investigate whether the active investing strategies,

momentum and growth investing, have had a higher risk-adjusted return than a passive index

fund. The research questions were stated as follows:

How has the two different strategies momentum and growth investing performed the past 15

years compared to a benchmark index?

Does the risk for being active compensate for higher return?

Are the results of the strategies performance significant?

Previous studies have shown that momentum investing has outperformed a passive index, but

that the index fund performed better than growth investing. However, the result of this study

showed that both momentum and growth investing outperformed the passive index fund.

During 2005-2020, momentum has had an average annual return of 13,91 %, growth of

9,01 % and the passive index fund of 7,50 %.

According to the efficient market hypothesis, it is not possible to yield a higher return than

the market since the market is fully effective. The result of this study showed that momentum

and growth investing performed better than the index portfolio in terms of return. However,

the hypothesis test that was made showed that the results were not significant. A regression

of the CAPM model was done, which generated alpha values from the different portfolios.

The result showed a monthly alpha of 0,115 for momentum and 0,2438 for momentum. The

tests were made with a significant level of 5 %. Thus, we couldn´t reject the null hypothesis

for either the momentum portfolio or the growth portfolio, giving us the conclusion that

neither strategy could be statistically significantly proven. This means that we cannot know

for certain if growth and momentum beats the market by taking advantage of flaws in the

market or if it is just by randomness.

36

The results showed that momentum strategy is associated with the highest risk according to a

standard deviation of 27,48% followed by the Index at 21,50% and lastly the growth strategy

at 21,01%. However, after combinating the risk these numbers represent with the return each

strategy yielded it is clear that the return for both active methods have yielded higher than

index in terms of return per unit of risk. The statement still holds after the transaction cost

gets included.

Another way to see the correlation between risk and return was to compute the Sharpe ratio.

It measures how much extra return the portfolio generates compared to the risk-free rate in

relation to the risk that is taken. The Sharpe ratio for the momentum portfolio was 0,459, for

the growth portfolio 0,367 and for the index 0,288. This shows that both active methods have

a better Sharpe ratio than the index. To even more fully reflect the reality, it was also tested

with transaction cost included. The result showed a Sharpe ratio of 0,418 for the momentum

portfolio and 0,342 for the growth portfolio. This means that both active strategies have

performed better than the index with regard to their Sharpe ratio.

What is a bit unusual is the low beta values for the both active strategies, with values of

0,8453 for momentum and 0,8363 for growth. With regard to the standard derivation, both

methods should have a higher risk, although the beta proves otherwise. After a lot of research

about this matter, it still could not be explained why the beta is so low for both the methods

and where the additional risk comes from for the standard derivation.

The conclusion that can be made from the results is that both momentum and growth

investing has had a higher risk-adjusted return than the benchmark index during 2005-2020

on the Frankfurt automobile stock market. The higher risk for growth and momentum

investing, namely transaction costs, compensate with a higher return in the end. However, the

null hypothesis could not be rejected, which means that the risk adjusted return are not

significant higher for either growth or momentum. In other words, it cannot be proved that

they are significant.

The purpose of this paper was to investigate if momentum and growth investing have had a

higher risk adjusted return than a passive index, which turned out to be the case. On the other

hand, the risk adjusted return for momentum and growth was not significantly higher. We

37

hope that the result of this paper has brought more guidance and insight to private investors

on the two active investing strategies growth and momentum and its performance compared

to a passive index fund.

38

7. Further research

To further improve the research, a larger sample can be investigated in a longer time interval.

By doing this, more companies can be selected and hopefully give a more reliable result

about the strategies performance. However, for this work a larger sample would have been

too time consuming and therefore it was limited down to the Frankfurt automotive sector. In

our study, transaction costs were included, which we believe better reflects the reality when

applying investment strategies. Despite that it can be difficult in estimating the total

transaction costs, we hope that further research follows the same track. This will lead to a

better reflection of the performance of growth and momentum compared to a passive index,

which is something that private investors can exploit. It would also be interesting to further

research why the beta is so low compared to the other risk indicators and where this flaw

comes from.

39

References

Literature

Berk Jonathan, DeMarzo Peter. (2020). Corporate Finance. Pearson Education Limited,

Global edition

Bodie Zvi, Kane Alex, Marcus J Alan. (2018). Investments. McGraw-Hill Education, Edition

11

Greenblatt, J. (2010). The little book that still beats the market. John Wiley & Sons

Incorporated, Edition Statement updated ed.

Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the

Value of Any Asset. John Wiley & Sons incorporated, Edition 3e

Wesley R. Gray, Jack R. Vogel and David P. Foulke. (2016). Quantitative momentum: a

practitioner's guide to building a momentum-based stock selection system. John Wiley &

Sons Incorporated, Edition 1

Eugene F. Fama. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work.

New York, Edition 25

Christian Schießl. (2013). Value Stocks beat Growth Stocks: An empirical Analysis for the

German Stock Market. Diplomica Verlag, Edition 1

Jagadeesh, N & Titman, S. (2001). Profitability of Momentum Strategies: An Evaluation of

Alternative Explanations. New York, vol 56

Nieuwenheuis Paul, Wells Peter. (2015-10-12). John Wiley & Sons Incorporated, Edition 1

Richard M .Ennis. (2005). Are Active Management Fees To High? CFA Institute, Vol 61

Szylar Christian. (2013-12-04.). Handbook of Market Risk. John Wiley & Sons Incorporated,

Edition 1

https://lnu-se-primo.hosted.exlibrisgroup.com/primo-explore/fulldisplay?docid=46VAXJO_ALMA5164278570003661&context=L&vid=primo-custom-lnu&lang=sv_SE&search_scope=default_scope&adaptor=Local%2520Search%2520Engine&tab=default_tab&query=any,contains,momentum%2520strategy&offset=0&pcAvailability=false


40

Digital Sources

Wesley R. Gray, Jack R. Vogel and David P. Foulke. (2016). Quantitative momentum: a

practitioner's guide to building a momentum-based stock selection system

https://ebookcentral-proquest-com.proxy.lnu.se/lib/linne-

ebooks/reader.action?docID=4690010

[2020-03-05]

Eugene F. Fama. (1970). Efficient Capital Markets: A Review of Theory and Empirical Work

https://www-jstor-org.proxy.lnu.se/stable/2325486?seq=2#metadata_info_tab_contents

[2020-03-05]

Yasir Bin Tariq and Naseer Mehwish. (2015). The Efficient Market Hypothesis: A Critical

Review of the Literature

https://web-b-ebscohost-com.proxy.lnu.se/ehost/pdfviewer/pdfviewer?vid=1&sid=e86cff19-

6662-4760-aeae-c7ad78fbe880%40pdc-v-sessmgr03

[2020-03-07]

Christian Schießl. (2013). Value Stocks beat Growth Stocks: An empirical Analysis for the

German Stock Market



[2020-03-15]

Jagadeesh, N & Titman, S. (2001). Profitability of Momentum Strategies: An Evaluation of

Alternative Explanations

https://onlinelibrary-wiley-com.proxy.lnu.se/doi/full/10.1111/0022-1082.00342

[2020-03-22]

Avanza. (n.d.). Vad kostar ett fondsparande?

https://www.avanza.se/lar-dig-mer/avanza-akademin/fonder/vad-kostar-ett-

fondsparande.html

[2020-03-22]

Investing. (n.d.). United States 3-Month Bond Yield

https://www.investing.com/rates-bonds/u.s.-3-month-bond-yield

[2020-03-22]



https://ebookcentral-proquest-com.proxy.lnu.se/lib/linne-ebooks/reader.action?docID=4690010


https://www-jstor-org.proxy.lnu.se/stable/2325486?seq=2#metadata_info_tab_contents

https://lnu-se-primo.hosted.exlibrisgroup.com/primo-explore/search?query=creator%252Cexact%252C%2520Bin%2520Tariq%252C%2520Yasir&tab=default_tab&search_scope=default_scope&vid=primo-custom-lnu&offset=0

https://lnu-se-primo.hosted.exlibrisgroup.com/primo-explore/search?query=creator%252Cexact%252CNaseer%252C%2520Mehwish%2520&tab=default_tab&search_scope=default_scope&vid=primo-custom-lnu&offset=0

https://web-b-ebscohost-com.proxy.lnu.se/ehost/pdfviewer/pdfviewer?vid=1&sid=e86cff19-6662-4760-aeae-c7ad78fbe880%2540pdc-v-sessmgr03

https://web-b-ebscohost-com.proxy.lnu.se/ehost/pdfviewer/pdfviewer?vid=1&sid=e86cff19-6662-4760-aeae-c7ad78fbe880%2540pdc-v-sessmgr03



https://onlinelibrary-wiley-com.proxy.lnu.se/doi/full/10.1111/0022-1082.00342

https://www.avanza.se/lar-dig-mer/avanza-akademin/fonder/vad-kostar-ett-fondsparande.html

https://www.avanza.se/lar-dig-mer/avanza-akademin/fonder/vad-kostar-ett-fondsparande.html

https://www.investing.com/rates-bonds/u.s.-3-month-bond-yield

41

Yahoo finance. (n.d). market cap

https://finance.yahoo.com/

[2020-03-25]

Mehwish Naseer, Yasir bin Tariq. (2015-12-01). The Efficient Market Hypothesis: A Critical

Review of the Literature

https://web-b-ebscohost-com.proxy.lnu.se/ehost/pdfviewer/pdfviewer?vid=1&sid=55d01fc0-

4746-4e30-8dad-8001a4512412%40pdc-v-sessmgr04

[2020-03-25]

Erlanzon Karl. (2019-02-11). Därför är indexfonder ett bättre alternativ

https://www.realtid.se/debatt/darfor-ar-indexfonder-ett-battre-alternativ

[2020-03-28]

Gibson Paul. (2017-02-20). Fees for active fund managers are excessive

http://www.granitefp.co.uk/index.php/granite-guidance/98-active-fund-management-fees-are-

too-high

[2020-03-29]

Nieuwenheuis Paul, Wells Peter. (2015-10-12). The Global Automotive Industry



[2020-04-02]

Richard M .Ennis. (2005). Are Active Management Fees To High?

https://www-tandfonline-

com.proxy.lnu.se/doi/pdf/10.2469/faj.v61.n5.2755?needAccess=true

[2020-04-12]

Ammann Manuel, Moellenbeck Marcel, Schmid M Marcus. (2010-10-06). Feasible

momentum strategies in the US stock market

https://web-b-ebscohost-com.proxy.lnu.se/ehost/pdfviewer/pdfviewer?vid=1&sid=af977dee-

fa9c-4a5d-82e2-01d06162a45a%40pdc-v-sessmgr02

[2020-04-14]

Szylar Christian. (2013-12-04.). Handbook of Market Risk



[2020-04-14]

Le Ta Phuoc. (2018). Jensen's Alpha Estimation Models in Capital Asset

https://finance.yahoo.com/

https://web-b-ebscohost-com.proxy.lnu.se/ehost/pdfviewer/pdfviewer?vid=1&sid=55d01fc0-4746-4e30-8dad-8001a4512412%2540pdc-v-sessmgr04

https://web-b-ebscohost-com.proxy.lnu.se/ehost/pdfviewer/pdfviewer?vid=1&sid=55d01fc0-4746-4e30-8dad-8001a4512412%2540pdc-v-sessmgr04

https://www.realtid.se/debatt/darfor-ar-indexfonder-ett-battre-alternativ

http://www.granitefp.co.uk/index.php/granite-guidance/98-active-fund-management-fees-are-too-high

http://www.granitefp.co.uk/index.php/granite-guidance/98-active-fund-management-fees-are-too-high



https://www-tandfonline-com.proxy.lnu.se/doi/pdf/10.2469/faj.v61.n5.2755?needAccess=true

https://www-tandfonline-com.proxy.lnu.se/doi/pdf/10.2469/faj.v61.n5.2755?needAccess=true

https://web-b-ebscohost-com.proxy.lnu.se/ehost/pdfviewer/pdfviewer?vid=1&sid=af977dee-fa9c-4a5d-82e2-01d06162a45a%2540pdc-v-sessmgr02

https://web-b-ebscohost-com.proxy.lnu.se/ehost/pdfviewer/pdfviewer?vid=1&sid=af977dee-fa9c-4a5d-82e2-01d06162a45a%2540pdc-v-sessmgr02



42

Pricing Model

http://jafeb.org/journal/article.php?code=62849

[2020-04-22]

http://jafeb.org/journal/article.php?code=62849

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