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
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
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
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).
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
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.
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.
financial crisis in 2008. Simultaneously, 15 years is quite a long period and should be enough to give an accurate and reliable result.
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).
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”
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).
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.
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.
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).
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
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
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
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)
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)
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
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
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
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.
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
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
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
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”
(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 %.
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
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 4a 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.
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
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 6The 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
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
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
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
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.
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 %.
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.
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
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,
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
https://ebookcentral-proquest-com.proxy.lnu.se/lib/linne-ebooks/reader.action?docID=1640416
[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
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
https://ebookcentral-proquest-com.proxy.lnu.se/lib/linne-ebooks/reader.action?docID=4038798
[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
https://ebookcentral-proquest-com.proxy.lnu.se/lib/linne-ebooks/reader.action?docID=1481180
[2020-04-14]
Pricing Model
http://jafeb.org/journal/article.php?code=62849
