Active versus passive investment : market timing model extended

(1)

Active versus Passive Investment

Market timing model extended

UNIVERSITY OF AMSTERDAM

BSc Economics & Business

Bachelor Specialisation Finance & Organisation

Author:

Bram van de Water

Student number:

10559663

Thesis supervisor: Dr. Jan Lemmen

Finish date:

January 2018

(2)

ABSTRACT

This paper investigates if there is any reason to invest in actively managed mutual funds comparing to passively managed funds. 113 active mutual funds are compared with the Russell 1000 to conclude if there is a selection ability or market timing ability. This paper investigates if the market timing model of Treynor and Mazuy (1966) is valid and if this model must be extended with a cubic variable. The paper concludes that there is no selection ability, no market timing ability and it cannot be concluded if the market timing model is valid or not.

Keyword: Active management, passive management, market timing, mutual funds. JEL Classification: G11, G12, G19, G20, G29.

Statement of Originality

This document is written by student Bram van de Water who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

(3)

CHAPTER 1 Introduction

Should investors invest in actively managed mutual funds who are seeking for higher annually returns than the stock market? Or do investing skills not exist and is it rather being lucky to outperform the stock market? These questions are part of a major topic in investment. Warren Buffet recommends investors to invest in passive funds in his yearly letter. So, a big industry of mutual and hedge fund managers has no rights to exist according to Warren Buffet.

1.1 Market timing ability

Warren Buffet’s advice is supported by the main literature existing about this subject. It is known that on average actively managed mutual funds even underperform compared to stock markets returns (French, 2008). But is there any reason to invest in actively managed mutual funds? Still, it cannot be said that fund managers do not have any ability to outperform the market. Treynor and Mazuy (1964) found evidence that fund managers can have market timing ability. Market timing ability is the ability to reduce losses when stock markets returns are negative and increase returns when stock markets returns are positive. So, market timing ability is the ability choosing the right moment to join and leave the market. The model of Treynor and Mazuy is also known today as the market timing model. This is the Capital Asset Pricing Model with a quadric variable of market risk premium added. This paper investigates if this market timing model has a better fit than the common capital asset pricing model. There are papers like Bauer, Otten and Rad (2006) that even a cubic variable added has a better fit than the market timing model, but there is not much research about this yet. So, this paper

investigates if an added new cubic variable of market risk premium has a better fit than the market timing model of Treynor and Mazuy.

1.2 Subprime crisis

The investigated period in this paper is 2004 till 2017. This period is interesting to investigate, because the subprime crisis is in this period. The subprime crisis causes a volatile period and it is interesting to investigate how mutual funds perform during and after the subprime crisis, especially when

investigating market timing ability. For example, in this period there are years like 2014 with an annually return of 30% and 2009 with an annually return of -38%.

1.3 Paper built up

This paper is built up in different chapters. First, the existing literature will be discussed in the next chapter. Second, chapter three will explain how the used data is collected and which criteria are used for selecting the right mutual funds. Third, chapter four explains the used research method. fourth, chapter 5 discusses the results. And last, chapter 6 will answer the research question and summarize the main results.

(5)

1.4 Main results

There are several results that can be extracted from this paper. There is no selection ability for the tested mutual funds for the period 01/01/2004 till 01/01/2017, there is even underperformance comparing with the benchmark the Russell 1000 index. There is no evidence of market timing ability for the tested mutual funds for the period 01/01/2004 till 01/01/2017. Also, this paper did research if the known market timing ability model is valid, and so must be extended with a cubic variable of the market premium risk. Because there is no evidence of market timing ability it cannot be concluded that the market timing model is valid or not and if the model must be extended with a cubic variable.

(6)

CHAPTER 2 Literature review

The existing literature about mutual fund performance and stock performance will be discussed in this chapter. It starts with the CAPM and the Jensen’s alpha and will be extended till a multiple factor regression equation that will be used to evaluate the performance of the dataset and market timing ability. There are a lot of extended versions of the CAPM and Fama-French three factor model with different variables. But only the control variables needed will be discussed.

2.1 CAPM and Jensen’s alpha

It starts with the Capital Asset Pricing Model or CAPM. This model calculates expected returns using the relationship between risk and expected returns. For example, small market capitalised stocks outperform stocks with large market capitalisation, but they are more volatile and so, riskier. Investments with same levels of risk will have same levels of returns is the fundamental assumption for CAPM. This model is designed by Harry Markowitz. Wiliam Sharpe (1964) is one of the first who published about the CAPM. The equation of the CAPM is as follows:

(1) 𝐸(𝑅) = 𝑅𝑓+ 𝛽1∗ (𝐸(𝑅𝑚) − 𝑅𝑓) + 𝜀𝑖

Where 𝐸(𝑅) is the expected return, 𝑅𝑓 the risk-free rate and 𝐸(𝑅𝑚) the expected market return, and so

𝐸(𝑅𝑚) − 𝑅𝑓 is the market risk premium. The beta in this model measures the systematic risk. It is the

sensitivity of an asset with the total stock market.

According to CAPM there are two categories of risks: firm-specific risk and systematic risk. Firm-specific risk, for example employee strikes or financial distress of the firm, is risk that can be solved by diversification and so the investor will not be compensated for. Systematic risk, for example macro -economic crises or other event that cannot be avoided, is the part that cannot be solved by diversification and so the investor wants to be compensated for holding this risk. When the beta is high, the asset is sensitive for systematic risk and vice versa. Thus, speaking about market timing ability, it is the ability to increase the beta when expected market returns are high and decrease the beta when expected markets are low or negative.

Jensen (1968) used the CAPM for mutual fund performance. It is called the Jensen’s alpha and the equation is as follows:

(2) 𝐸(𝑅) − 𝑅𝑓= 𝛼 + 𝛽1 ∗ (𝐸(𝑅𝑚) − 𝑅𝑓) + 𝜀𝑖

Here, the risk-free rate is brought to the left side of the equation and a constant appears. When

investments with same levels of risks have same levels of returns this alpha is zero. When this constant is positive then this asset or portfolio of assets outperforms similar assets. When investigating mutual

(7)

fund performance this alpha is a measure of performance. If a mutual fund manager claims he can outperform the market every year, he has an asset portfolio that has a significant positive alpha every year.

2.2 Fama-French three-factor model

Eugene Fama and Kenneth French (1993) extended the capital asset pricing model with two variables. They found evidence that expected returns are not only determined by market’s returns, but also on size and book-to-market ratio. The returns of stocks with small market capitalisations are higher than predicted by CAPM and so there must be a variable included to compensate that, the SMB or Small- Minus-Big variable. This is the case for firms with a higher book-to-market ratio as well, so they added the High-Minus-Low or HML variable to the regression equation. This is the difference between growth stocks and value stocks. Growth stocks have a low book-to-market ratio and are stocks where investors expect their cashflow will grow in the future. Value stocks have a high book-to-market ratio and are stocks where the assets already generate value. The equation of the Fama-French three-factor model is as follows:

(3) 𝐸(𝑅) − 𝑅𝑓= 𝛼 + 𝛽1∗ (𝐸(𝑅𝑚) − 𝑅𝑓) + 𝛽2∗ 𝐸(𝑆𝑀𝐵) + 𝛽3∗ 𝐸(𝐻𝑀𝐿)

This new two variables are needed to include, because otherwise the same levels of risks, same levels of returns would be violated and so the alpha will reflect different risk factors instead of superior returns. Thus, otherwise the original capital asset pricing model would be biased and cannot be used for evaluating mutual fund performance.

2.3 Carhart four-factor model

But, adding the two variables for size and book-to-market ratio is not enough yet. Jegadeesh and Titman (1993) found evidence for another variable. They found that bad performing stocks will perform bad over several months. This also accounts for good performing stocks. It is called a momentum factor.

Carhart (1997) includes this momentum factor to the existing Fama-French three-factor model, and so turned the three-factor model into a four-factor model for evaluating mutual fund performance. The equation of the Carhart’s four-factor model is as follows:

(4) 𝐸(𝑅) − 𝑅𝑓 = 𝛼 + 𝛽1∗ (𝐸(𝑅𝑚) − 𝑅𝑓) + 𝛽2∗ 𝐸(𝑆𝑀𝐵) + 𝛽3∗ 𝐸(𝐻𝑀𝐿) + 𝛽4∗ (𝑀𝑂𝑀)

SMB and HML factors control different risk factors. It can be discussed if this is the case with the variable that controls the momentum factor. Carhart leaves the risk interpretation to the reader. It can be that a superior investing strategy does not mean more risks. But Jegadeesh and Titman conclude

(8)

that because the significant higher returns on a strategy to buy previous winners and sell previous losers there can be a bias in investor’s expectations. This bias is a risk that must be controlled.

This has to do with efficient market theory. The theory about how well information is

available and priced in asset prices. Eugene Fama (1969) published about this subject and divided this in three hypothesises. First the strong form, where all existing information is available and fully priced in asset prices. Second the semi-strong form, where all information that is publicly available for investors is quickly priced in. And third the weak form, stock prices reflect all information that can be derived. Market inefficiency can be exploited by investors with stock picking abilities and so must be controlled for with a control variable.

For the momentum factor it is not important which form stock markets are in, but it helps explaining investor’s expectations bias. When new information occurs or is available and it is priced in the stock price, then investors change their expectations. When it is priced in wrongly because of expectation bias then this forms a risk for investors, because the market does not know how this information must be priced in. Thus because of the investor’s expectation bias it is necessary to add the control variable for momentum in the regression equation for evaluate mutual fund performance.

2.4 Performance measurement and underperformance

When looking at performance of mutual funds we must determine which comparison is made, which methods are used and how to judge performances evaluations. The methods described previous are the most common methods to use for evaluating mutual funds’ performances. This section discusses what the status quo is about mutual fund performance.

The consensus is that actively managed funds underperform the market index, even before cost reduction. This is the conclusion from studies like Fama and French (1993) and Malkiel (1995). Carhart researched persistence in mutual fund’s managers performance. He concluded there is a short-term persistence in performance and so a momentum effect. But long-short-term persistence, thus

persistency longer than one year is not found.

The benchmark is important as well. When CAPM is used the benchmark is the market index. This makes sense as well when comparing passive strategy and active strategies. The passive

investment strategy is closely following the market index. But what is the market index? According to Bodie and Kane (2014) the Wilshere index 5000 is common to use as a benchmark when comparing active investment strategies with US stocks. This is an index sorted on market capitalisation of the 5000 US stocks with the largest market capitalisation. This index is not used in this paper as a benchmark because the focus is on large cap stocks and so the Russell 1000 index is a better benchmark to compare mutual funds.

(9)

2.5 Market timing ability model

This subject is different than what is discussed in this chapter. If we speak about market timing ability it has nothing to do with the constant or alpha, because the alpha measures mutual fund manager’s selection ability. It is about the slope of the regression equation, and thus about the betas in the models.

Market timing ability is the ability to increase the beta for market risk premium when market returns are positive and decrease the beta when market returns are negative. Treynor and Mazuy were the first coming with the idea that a non-linear relation would indicate market timing ability, but the sample of mutual funds Treynor and Mazuy (1966) investigate there was no indication that market timing ability would exist. If market timing exists, then the beta of the added variable would be significantly different from zero. The regression equation using the CAPM equation would be as follows:

(5) 𝐸(𝑅) − 𝑅𝑓= 𝛼 + 𝛽1∗ (𝐸(𝑅𝑚) − 𝑅𝑓) + 𝛽2∗ (𝐸(𝑅𝑚) − 𝑅𝑓) 2

+ 𝜀𝑖

Here, there is a squared variable added and so the CAPM changed from a linear model to a non-linear model.

But some say that there is evidence that this model is not complete to measure accurate market timing ability. For example, Bauer, Otten and Rad (2006) wrote that there is cubic variable needed to measure market timing ability. It is especially needed to measure the ability to decrease the beta when market returns are negative. Because the slope of the cubic variable is flatter when negative than the squared variable, this would have a better fit and so a better model to estimate market timing ability. When market returns are positive the relation is the same non-linear relation as the quadric variable and so there will be no difference between them. Thus, a significant cubic variable would mean that fund managers have more ability to decrease the beta when market returns are negative than predicted by the model of Treynor and Mazuy. The regression equation for estimating market timing ability would be as follows: (6) 𝐸(𝑅) − 𝑅𝑓 = 𝛼 + 𝛽1∗ (𝐸(𝑅𝑚) − 𝑅𝑓) + 𝛽2∗ (𝐸(𝑅𝑚) − 𝑅𝑓) 2 + 𝛽3∗ (𝐸(𝑅𝑚) − 𝑅𝑓) 3 + 𝜀𝑖

Bauer, Otten and Rad (2006) investigated this for New Zealand mutual funds and found no market timing ability for these funds. But they wrote that they investigate this model, because there is

evidence for Australian mutual funds for better fit for this cubic model than the squared model. So, for this reason this paper will investigate for US mutual fund’s performance evaluation which of the following regression equations has the better fit to answer the research questions.

(10)

CHAPTER 3 Data

It is hard to find data about returns of mutual funds. First the right funds must be selected. Then the data about daily returns must be available during 2004 till 2017. This chapter discusses which criteria is used for mutual funds and how the returns, the data about the other control variables and the risk-free rate are collected.

3.1 Mutual funds

Several criteria are used by collecting the right mutual funds for research. The chosen mutual funds must invest mainly in US stocks of companies with large market capitalisations. This criterion is included because this paper wants to narrow the performance comparison to US stocks that are listed on the S&P 500 or Russell 1000. These stocks are common for investors and new information about these stocks are easily available for all investors. So, fund managers cannot outperform stock markets by inefficient stock markets. The second reason is because small market capitalisation stocks

outperform stocks with large market capitalisations. This paper wants to compare performances with equal levels of risks. Still, there is included a control variable for size in the regression equations, because most mutual funds describe that they will invest for 85% or sometimes for 60% in stocks who are listed on the S&P 500 or Russell 1000 index.

3.1.1 Mutual fund size

The size of the mutual funds can be important for selection. According to Elton, Gruber and Blake (2011) expense ratios decline when mutual funds are increasing in size. This is because the fact that the costs are mostly fixed components. Larger mutual funds are not constrained in their expenses for research. It is important for determining selection ability and market timing ability that a lack of these skills is not because funds can afford the research needed to have these abilities.

Chen et al. (2004) found evidence that fund size erodes the fund’s return. This counts especially for funds trading in stocks with small market capitalisations. Because this paper selects funds which invest mainly in large market capitalisation stocks this effect is not important for the selection. In this paper there is not strictly selected on fund size, but funds were selected with a size as large as possible. The smallest funds are 200 million in size and the largest around the 50 billio n.

3.1.2 Survivorship bias

The last criterion for the mutual funds is that there is data available during the period of 01/01/2004 till 01/01//2017. The advantage for holding this criterion is that by this way the sample size will be equal for every day, so there is no risk that the sample size will be too small for a day. The disadvantage is that there is no data included of funds that dropped out because of bad performances during 2004 and 2017. This is called survivorship bias. This is the bias that bad performing funds dropped out of the

(11)

dataset and so returns of the remaining mutual funds are higher on average (Bodie, Kane and Marcus, 2014, p. 439).

3.1.3 Collection mutual funds data

First, Reuters’ fund screener is used. For finding the right funds several filters are used in the funds screener. Equity funds, US stock and Large cap core are used as filters. Then there is looked closely if the fund existed before 01/01/2004 and which strategy those funds followed. Funds with strategies like closely following the return of the S&P 500 or Russell 1000, or seeking for returns like the S&P 500 or Russel 1000 are not included. This would indicate they followed a passive investment strategy. Funds with strategies like searching for undervalued stocks or aiming for higher returns than the returns of S&P 500 of Russell 1000 are included to the sample. Only one of the different funds from the same company and following the same strategy are included to prevent endogeneity. Finally, 122 mutual funds met all the conditions to be included.

Second, the mutual funds’ unique codes are written down, so they can be used for searching the returns in the database DataStream. Nine mutual funds were not available on DataStream, so 113 mutual funds are left over. With the second codes founded on DataStream there is created a list for time-serie requests. Then collected the data for daily, weekly, monthly, quarterly and yearly returns for the period 01/01/2004 till 01/01/2017.

And third, a graph of the quarterly data is used if there were strange outliers. There were no substantial differences between these 113 mutual funds. With substantial difference is meant: When all mutual funds have negative returns and one fund has an extreme positive return or vice versa. When this would be the case than it might be possible that this fund follows a different strategy, which would deviate from the criteria to be included in the dataset.

3.2 Control variables, risk-free rate and the Russell 1000 index

The control variables’ data and the risk-free rate data are collected on the website of Fama and French. Daily data for all variables for the Fama-French three-factor model can be downloaded on the website of Fama and French. The daily data of the momentum control variable for the Carhart four-factor model is available as well. The risk-free rate data is daily compounding till a one-month US treasury bill.

For the benchmark the Russell 1000 index is used. This data is collect with DataStream and the precise data is the iShares Russell 1000 index. This is an ETF of Blackrock that closely follows the return of the Russell 1000 index and so is available to use for the benchmark. The table on the next page describes the collected data of the variables.

(12)

Descriptive statistics table

The table shows that the return of mutual funds in the dataset has on average a daily return that is almost 1% lower than the average daily return of the Russel 1000 index. This can be a first indication of underperformance of mutual funds. Further, the table shows that the minimum daily return of the Russel 1000 index is lower than the minimum of the mutual fund’s daily return. It can be an indication that mutual funds can leave the market on time, but because the maximum daily return of the mutual funds is lower than the maximum daily return of the Russel 1000 index it can be an indication that the daily return of the mutual funds is less volatile than the return of the Russel 1000 index. The number of observation of 3390 means that there is data collected of 3390 days.

Mean Std. Dev Median Min Max Number of observations

Russel 1000 index 0,0285 0,0199 0,0462 -9,3700 11,3725 3390 Mutual funds 0,0186 0,0191 0,0276 -8,5430 10,6805 3390 SMB 0,0046 0,0098 0,0100 -3,7500 3,8300 3390 HML 0,0032 0,0109 -0,0100 -4,2200 4,8300 3390 Risk-free rate 0,0046 0,0001 0,0010 0,0000 0,0220 3390 MOM 0,0036 0,0164 0,0500 -8,2000 7,0100 3390

(13)

CHAPTER 4 Research method

In this chapter will be discussed how to investigate selection ability and market timing ability. And so, if there is enough evidence that the market timing ability of Treynor and Mazuy must be extended with a cubic variable.

4.1 Preparing data

After the data is collected it must be prepared to be used in STATA. The daily returns of the 113 mutual funds must be in columns and the daily average returns must be calculated. This average will be used as the returns of the mutual funds. Because there are 113 observations each day we can assume that the average return is normally distributed. So, there the results can be generalised for all existing mutual funds with mainly US stocks large market capitalisation companies.

In Excel the average return and benchmark return will reduced with the risk-free rate, because the models used evaluate returns minus risk-free rate, or risk premium called. So, there are no further transformations needed in STATA.

The regressions in STATA will use the robust function. Because the standard errors differ for each different period during 2004 till 2017. This is the result of the robustness test performed. This is because volatility differs each period and so homoscedasticity cannot be assumed.

4.2 Robustness test

A robustness test is performed to conclude if robust standard errors must be used for the empirical research. The standard errors of the market return, the Russel 1000 index, of different periods are compared to analyse if they differ or if standard errors do not change and so homoscedasticity can be assumed. Period 1 is 1/1/2005 till 1/1/2007, period 2 is from 1/1/2009 till 1/1/2011 and period 3 is from 1/1/2015 till 1/1/2017. The table below explains the results of the regressions.

Table Results Robustness test

Coef. Std. Err. t-value P-value 95% Conf. Interval 𝐸(𝑅𝑚) − 𝑅𝑓 period 1 0.8758 0.0102 86.03 0.000 0.8558 0.8957 Constant .0027 0.0068 -0.39 0.698 -0.0161 0.0107 𝐸(𝑅𝑚) − 𝑅𝑓 period 2 0.9463 0.0039 242.73 0.000 0.9387 0.9541 Constant 0.001 0.0055 0.18 0.856 -0.0099 0.0119 𝐸(𝑅𝑚) − 𝑅𝑓 period 3 0.9693 0.0064 150.48 0.000 0.9566 0.9819 Constant -0.0182 0.0057 -3.18 0.002 -0.0295 -0.0069

The standard error in period 3 is almost two times larger than in period 2 and the standard error in period 1 is larger than in period 3. So, because the standard error differs in different periods robust standard errors will be used when performing the regressions equations in STATA.

(14)

4.3 Selection ability

Before determining if there is selection ability or market timing ability this paper will investigate which variables will be needed for evaluating mutual fund performances. In the previous chapter there are four variables described which are common to use for evaluating performances. This are the variables market risk premium, HML, SML and MOM.

First, the Jensen’s alpha equation will be tested. If the coefficient of the market risk premium is statistical different from zero than it is a relevant variable to include in the model to evaluate the performances of the dataset.

Second, the three-factor Fama-French model will be tested. The control variables HML and SML will be included in the model after the first regression of the Jensen’s alpha. If the added variables HML and SML are statistical significant from zero, they are relevant to include in the regression equation.

And third, the Carhart four-factor model will be tested. The last discussed control variable for the momentum factor will be included after the second regression of the Fama-French four-factor model. If MOM is statistically significant it will be relevant to include MOM in the regression equation for researching selection ability.

The regression equation that will be used for determining selection ability will be used for determining market timing ability as well.

4.3.1 Testing Selection ability

After determining which model has the best fit this paper will research if there is selection ability. So, if the constant alpha will be statistical significantly positive from zero. The testing of the constant alpha can be done after the variables about market timing ability are tested and determined if they are relevant to be included. Otherwise the constant can be correlated with an omitted variable for market timing ability. This will give biased results. Testing the constant can be tested with a student t-test. The following hypothesis will be tested.

𝐻0: 𝛼 = 0 𝑜𝑟 𝐻1: 𝛼 > 0

So, the first statement says there is no selection ability and so there will be not enough evidence to conclude that the alpha is statistical significantly different from zero. And the H1 says there is enough evidence to conclude that the alpha is statistical significantly positive different form zero. This testing can be easily done with STATA at the same moment when the coefficients are determined. But STATA will only perform a two-sided test. So, the p-value of the two-sided test must be multiplied by two.

According to the existing literature there is an underperformance of active managed mutual funds against passive funds. So, if in the previous test states that alpha is not statistically significant

(15)

different form zero, it can be tested if there is an underperformance of this dataset comparing to the benchmark. The following hypothesis will be tested.

𝐻0: 𝛼 = 0 𝑜𝑟 𝐻1: 𝛼 < 0

So, if underperformance is the case, the H0 will be rejected at 5% significance level. There will be concluded that there is no selection ability for this dataset. This conclusion is in line with the existing literature, thus these results can be expected.

4.4 Market timing ability

The second stage in this research is about market timing ability. In the previous section different control variables are tested if they are relevant to include in the regression equation for determining selection ability. The final regression equation used for determining selection ability will be the start equation for determining market timing ability.

First, the quadric market risk premium variable will be added to the regression equation. So, the market timing model as described by Treynor and Mazuy (1966), with control variables HML, SMB and MOM if needed. Then the interesting part is if the coefficient will be significant positive, significant negative or will be not significantly different from zero, because from the coefficient can be concluded if there is market timing ability. If the coefficient is statistical significantly positive from zero than existing of market timing ability can be concluded for the tested mutual funds. If the

coefficient will be statistical significantly negative than mutual funds perform even worse when the stock market is more volatile. So, the first test will be if the coefficient of the quadric term is

significantly different from zero. This test will be performed by STATA at the same moment when the regression is run. When the coefficient differs from zero than market timing is determined if the coefficient is positively different from zero. The following hypothesis will be tested.

𝐻0: 𝛽 = 0 𝑜𝑟 𝐻1: 𝛽 > 0

So, if H0 can be rejected at 5% significance level than the quadric term is relevant to include in the regression equation and market timing ability can be assumed. If the coefficient is statistical significant negative it is relevant to include in the equation as well.

4.4.1 Extend the market timing ability model

The next step is to include the new cubic term and test if this variable is relevant to include in the regression equation. This is the last term for the regression equation and can be compared with the other regressions that follows from existing literature. So, the cubic variable will be included in the regression equation with the control variables and the quadric variable form Treynor and Mazuy. The hypothesis that will be tested are as follows.

(16)

𝐻0: 𝛽 = 0 𝑜𝑟 𝐻1: 𝛽 > 0

If the coefficient is not significantly different from zero and the quadric variable is positively significant different from zero than market timing ability exist and there is no need to extend the market timing ability with a cubic variable.

If the coefficient of the cubic variable is positively significant different from zero and the quadric variable is positively significant different from zero, market timing ability exist and the market timing model of Treynor and Mazuy must be extended with a cubic variable. Otherwise result would be biased and so the constant alpha is biased positive, and so selection ability is assumed, but is not significantly different from zero in real.

If the coefficient of the cubic variable is negatively significant different from zero that would not indicate market timing ability. It means that when market returns are negative, mutual fund returns are positive and when market returns are positive, mutual fund returns are negative. This outcome is not what would be expected.

As mentioned before, the regression with the best fit will be used to answer the question if there is selection ability and if there is market timing ability for mutual funds with mainly US large market capitalisation stocks. To conclude which regression equation has the best fit the adjusted R-squared will be used. This is the R-R-squared multiplied with a factor that decreases when a variable is added to the equation. So, if an added variable explains more of the depend variable than decrease of the factor than the regression equation has a better fit than without the added variable.

(17)

CHAPTER 5 Results

This chapter discusses the results of the research in this paper. The results arise from the regressions performed in STATA. For all regressions performed the number of observation is 3390. The adjusted R-squared is 0,9815 and did not change, because the R-squared did not change and because the high number of observation the factor 𝑛−1

𝑛−𝑘−1 did not change when adding a variable. When a coefficient or

a constant is significantly different from zero at 5% significance level a * will be used.

5.1 Jensen’s Alpha

The first performed regression is the Jensen’s Alpha as displayed below. The results can be seen in table 1 below.

(2) 𝐸(𝑅) − 𝑅𝑓= 𝛼 + 𝛽1 ∗ (𝐸(𝑅𝑚) − 𝑅𝑓) + 𝜀𝑖

Jensen’s Alpha regression

Variables Coef. Std. Err. t-value P-value 95% Conf. Interval 𝐸(𝑅𝑚) − 𝑅𝑓 0.9501* 0.0040 235.2000 0.0000 0.9422 0.9580 Constant -0.0086* 0.0026 -3.3000 0.0010 -0.0137 -0.0035 Table 1 shows that the t-value of the 𝐸(𝑅𝑚) − 𝑅𝑓 is high and so a relevant variable to include in the model. The coefficient is 0.9501 and that means when market risk premium goes up with 1% or 0.01, the expected return of the mutual funds goes up with 0.95%. The constant alpha is significantly negative, but for now it is too early to conclude if the mutual funds underperform, because not all variables that are relevant to include according the existing literature are added to the equation. The adjusted R-squared is 0,9815 which is high. If the R-squared is 1 than the independent variables can estimate every value of the dependent variable. So, this value of R-squared shows that the market risk premium and the constant are good estimators for the returns of the mutual funds.

5.2 Fama-French three-factor model

The table displays the result of the second regression is the Fama-French three-factor model. Fama-French three -factor model regression

Variables Coef. Std. Err. t-value P-value 95% Conf. Interval 𝐸(𝑅𝑚) − 𝑅𝑓 0.9501* 0.0040 235.3700 0.0000 0.9422 0.9580

SMB 0.0015 0.0050 0.3000 0.7610 -0.0082 0.0112

HML 0.0060 0.0047 1.2800 0.2020 -0.0032 0.0153

Constant -0.0086* 0.0026 -3.3200 0.0010 -0.0138 -0.0035 The table displays the results of the second regression equation.

(18)

The coefficient for the market risk premium and the constant alpha did not changed, the added control variables for size and book-to-market ratio are not significantly different from zero and the value of the adjusted R-squared did not change in comparing to the Jensen’s alpha model. This shows that the added control variables are not relevant estimators to include in the equation for evaluating mutual fund performance.

The SMB variable has a very high P-value, and thus not relevant to use. The reason for that is that the tested mutual funds have a strategy to invest in US stocks with a large market capitalisation. So, the main investments are in stocks of the Russell 1000 index and some funds claim mainly to invest in S&P 500 stocks. Thus, there is no need to correct the mutual funds returns for size of the stocks. The HML variable corrects returns for growth versus value stocks. This variable is not significantly different from zero. The reason for that is on average the fraction invested in growth stocks and the fraction invested in value stocks is not significant different than the fraction of growth stock and the fraction in value stocks in the Russel1000 index. Individual funds have different strategies according to value and growth stocks. There are funds with the strategy of investing in undervalued stocks and seeking for higher return than the market return. And other funds have the strategy to invest in growth stocks and so seeking for higher return than the market return. But

speaking of averages a correction on growth versus value stocks is not a relevant variable to include in the regression equation for now. Again, final conclusions can be drafted after are variables are

concluded.

5.3 Carhart four-factor model

The third regression is the Carhart four-factor model and table 3 shows the results. Carhart four-factor model regression

Variables Coef. Std. Err. t-value P-value 95% Conf. Interval

𝐸(𝑅𝑚) − 𝑅𝑓 0.9501* 0.0040 234.7500 0.0000 0.9421 0.9580

SMB 0.0015 0.0050 0.3100 0.7580 -0.0082 0.0113

HML 0.0049 0.0054 0.9000 0.3680 -0.0058 0.0156

MOM -0.0014 0.0045 -0.3100 0.7570 -0.0103 0.0075

Constant -0.0086* 0.0026 -3.3100 0.0010 -0.0138 -0.0035

The Carhart four-factor regression equation is as follows:

(4) 𝐸(𝑅) − 𝑅𝑓 = 𝛼 + 𝛽1∗ (𝐸(𝑅𝑚) − 𝑅𝑓) + 𝛽2∗ 𝐸(𝑆𝑀𝐵) + 𝛽3∗ 𝐸(𝐻𝑀𝐿) + 𝛽4∗ (𝑀𝑂𝑀)

The control variable for the momentum factor is added in the regression equation, making this

equation the Carhart four-factor model. Again, the coefficient of the market risk premium, the constant alpha and the adjusted R-squared did not change. The coefficient of the SMB variable did not change as well. Adding MOM did change the coefficient of HML and its P-value. So, HML is correlated with MOM. The coefficient of the momentum factor has a high P-value, and thus not significant different from zero. The reason for that is the same as for HML. The fraction of ‘momentum’ stock, stocks

(19)

which have a positive or negative momentum, is not significant different from the fraction of stock with a momentum in the Russel 1000 index.

There are funds who follow a momentum strategy, but the average return in not affected enough by the funds with this strategy. It can be the case that funds following this strategy are not able to have higher returns than the market index. Further research is needed if these funds have an ability to find stocks with a momentum and so having a higher return than the market return.

5.4 Market timing ability model

In the next stage the quadric variable will be added to the existing variables. Table 4 shows the results of the regression of the market timing ability model.

Market timing model regression

Variables Coef. Std. Err. t-value P-value 95% Conf. Interval 𝐸(𝑅𝑚) − 𝑅𝑓 0.9500* 0.0040 236.2100 0.0000 0.9421 0.9579 SMB 0.0015 0.0050 0.3000 0.7670 -0.0083 0.0113 HML 0.0045 0.0053 0.8500 0.3930 -0.0059 0.0150 MOM -0.0015 0.0044 -0.3400 0.7350 -0.0102 0.0072 (𝐸(𝑅𝑚) − 𝑅𝑓)2 _-0.0004 _0.0012 _-0.3300 _0.7380 _-0.0028 _0.0020 Constant -0.0081* 0.0027 -3.0300 0.0030 -0.0133 -0.0028 Adding the (𝐸(𝑅𝑚) − 𝑅𝑓)2 variable did not change the existing variables and it P-values. The coefficient of the quadric variable is not significantly different from zero and so there is no indication of market timing ability according to the model of Treynor and Mazuy.

The reason that these mutual funds have no market timing ability is because they are hold to their strategy they follow. These funds are equity funds and they promise the investor to invest only in US stocks with a large market capitalisation, so if the US stock market declines they cannot invest in bonds or in stocks from a different region. The only option to decrease the beta is to invest in stocks in the index with a low beta with the index. This makes it harder to decrease the beta when the only investment option is to invest in that declining stock market. For increasing the beta when market returns are high count the same reasons. Mutual funds can only increase their beta when investing in stocks in the market index with a high beta with the index.

(20)

5.5 Market timing ability model extended

Now the final variable (𝐸(𝑅𝑚) − 𝑅𝑓)3_{will be added the existing variables. Table 5 shows the final}

results.

Market timing model extended regression

Variables Coef. Std. Err. t-value P-value 95% Conf. Interval 𝐸(𝑅𝑚) − 𝑅𝑓 0.9467* 0.0040 237.4000 0.0000 0.9389 0.9545 SMB 0.0016 0.0050 0.3200 0.7480 -0.0082 0.0114 HML 0.0044 0.0053 0.8300 0.4040 -0.0059 0.0147 MOM -0.0017 0.0043 -0.4000 0.6870 -0.0102 0.0067 (𝐸(𝑅𝑚) − 𝑅𝑓)2 _-0.0007 _0.0015 _-0.4900 _0.6260 _-0.0036 _0.0021 (𝐸(𝑅𝑚) − 𝑅𝑓)3 _0.0002 _0.0002 _0.9200 _0.3560 _-0.0002 _0.0005 Constant -0.0076* 0.0028 -2.6700 0.0080 -0.0132 -0.0020 Only the coefficients of the variables about market risk premium changed a bit. The reason for that could be multicollinearity. This is the correlation between variables. Because all these variables are the market risk premium or modified versions of the market risk premium. Still, the significance of the quadric variable did not change.

The cubic variable is not significantly different from zero. So, the first conclusion is that adding the cubic variable is not relevant when determining market timing ability and there is still not enough evidence to conclude that the tested mutual funds have market timing ability.

The first conclusion that the cubic variable in not relevant to include is too premature. First, there must be market timing ability according to the old model of Treynor and Mazuy to conclude if adding this cubic variable. If there is market timing ability than the cubic variable must be tested if it is relevant to include this variable and if this extended market timing ability function has a better fit than the old version of the model. Further research is needed to conclude if the cubic variable is relevant or not.

According to all results the constant is statistical significant negative from zero and so the tested mutual funds underperform the benchmark, the Russel 1000 index. This is in line with the existing literature and these results do not deviate from the expectations before obtaining the results.

(21)

CHAPTER 6 Conclusion

This paper investigates if there is any reason why active investing strategy could be an option for investing. It was already known that active strategy underperforms in comparing with passive strategy, even before cost reduction. But maybe if mutual fund managers can decrease the beta when there is a bear market and increase the beta when it is a bull market, might be a reason to invest in actively managed mutual funds. This paper also investigates if the market timing ability model of Treynor and Mazuy (1966) is valid and if this model must be extended with a cubic variable.

There is on average no selection ability found for the 113 tested mutual funds which mainly invest in large market capitalisation US stocks. The funds even underperform in comparing to the benchmark. These results are in line with the existing literature. Further investigation can be done on this dataset by searching selection ability for each fund. The funds follow different strategies to have a superior return in comparing to the market index. There are funds which invest in growth stock or seeking for a momentum in stocks. And there are funds which seeking for undervalued stocks. It can be interesting to research if one of these strategies can outperform the benchmark and how the funds perform in comparing to each other.

There is on average no market timing ability found for the 113 tested mutual funds which mainly invest in large market capitalisation US stocks. The reason for these results can be that mutual funds cannot switch between regions, asset classes and market capitalisations of stocks. Because the mutual funds must stick to the strategy. It is interesting to investigate market timing ability for funds that can switch, for example hedge funds. Further investigation can be done with this dataset about market timing ability by testing the funds individually. After that can be concluded if mutual funds are able to increase the beta when there is a bull market and decrease the beta when there is a bear market, given the constrains these mutual funds have.

At last, this paper investigates if the market timing model of Treynor and Mazuy (1966) is still valid. Because there is no market timing ability found, it cannot conclude if the model is valid and if it must be extended with a cubic variable. For further research it is needed to find funds that have market timing ability and then test if the cubic variable is significant different from zero.

Although the research has enough data available to perform this research there are some limitations. First, the dataset did not include mutual funds that drop out of the dataset in the used period. So, if there was selection ability determined than it cannot be said that there is selection ability because of survivorship bias. Second, the recent studies about mutual fund performance use CRSP dataset which include all mutual funds and so is free of survivorship bias. When using CRSP mutual funds dataset much more mutual funds can be used and so makes the research better.

(22)

REFERENCES

Bauer, R., Otten, R., Rad, A.T., 2006, New Zealand mutual funds: measuring performance and persistence in performance, Accounting and Finance 46, 237-363.

Bodie, Z., Kane, A., and Marcus, A. J., 2014, Investments (10th ed.). Maidenhead, USA: Mc Graw Hill education.

Cahart, M.M., 1997, On Persistence in Mutual Fund Performance, Journal of Finance 52 (1), 57-82.

Chen, J., Hong, H.G., Huang, M., Kubik, J.D., 2004, Does Fund Size Erode Mutual Fund

Performance? The Role of Liquidity and Organization, The American Economic Review 34, 73-95.

Elton, E.J., Gruber, M.J., Blake, C.R., 2012, Does Mutual Fund Size Matter? The Relationship Between Size and Performance, Review of Asset Pricing Studies 2 (1), 31-55.

Fama, E.F., 1969, Efficient Capital Markets: A Review of Theory and Empirical Work, Journal of Finance 25 (2), 383-417.

Fama, E.F., French, K.R., 1993, Common Risk Factors in the Returns on Stocks and Bonds, Journal of Financial Economics 33 (1), 3-56.

French, K. R., 2008, The cost of active investing, Journal of Finance 63 (4), 1537-1573.

Jegadeesh, N., Titman, S., 1993, Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency, Journal of Finance 48 (1), 65-91.

Jensen, M. C., 1968, The performance of mutual funds in the period 1945-1964, Journal of Finance 23 (2), 389-416.

Malkiel, B. G., 1995, Returns from investing in equity mutual funds: 1971-1991, Journal of Finance 50 (2), 549-572.

Sharp, W.F., 1964, Capital Asset Prices: a theory of market equilibrium under conditions of risks. Journal of Finance 19 (3), 425-442.

Treynor, J., and K. Mazuy, 1966, Can mutual fund outguess the market, Harvard Business Review 44, 131–136.

Active versus passive investment : market timing model extended