Author: Shaole Hu
Student number: s3267032
Supervisor: Dr. J. J. Bosma
Date: 07/06/2018
Master Thesis Finance Rijksuniversiteit Groningen
Abstract
1. Introduction
Investing in mutual funds can be costly, due to the fees charged to investors. Many mutual fund managers claim to justify their fees by having extraordinary forecasting skills, which makes it able for them to outperform the market. One of the biggest questions for a mutual fund investor is: Do mutual funds actually have the extraordinary forecasting skills to outperform the market? Henriksson and Merton (1981) separate these forecasting skills into selectivity skills and market timing skills. Therefore, more specifically the question raised is: If mutual funds do outperform the market, which of the two before mentioned forecasting skills, stock selectivity or market timing, are they applying to do so? This paper focuses on answering the latter forecasting skill, market timing, through the means of a multifactor model. Instead of using the conventional models (see, e.g., Treynor and Mazuy (1966) and Henriksson and Merton (1981)), to measure market timing ability of a mutual fund. This paper expands the current literature on mutual fund performance with an alternative multifactor model to capture this market timing ability of mutual funds.
In 2008, the legendary investor, Warren Buffett, challenged abovementioned question. He challenged the actively managed fund industry by claiming that an actively managed fund, including fees, costs, and expenses, cannot outperform an S&P 500 index fund. One actively managed fund accepted this challenge and conceded the loss even before the actual challenge end date. Whereas the index fund eventually gained 85.4%, the actively managed fund only got an average return of 22.0%. The result of this challenge does not come by surprise according to the literature. Many studies have been conducted on the performance of actively managed funds and found that they underperform the market after all costs are taken into account (see, e.g., Fama and French (2010)). On the other hand, some studies have been conducted and found that actively managed funds do outperform passively managed funds (see, e.g., Ippolito (1989)).
the net asset value (hereafter NAV) price, which represent a part of these holdings. Holding those shares sometimes comes with large fees to the investor. A mutual fund can be divided into a load mutual fund or a no-load mutual fund. In a load mutual fund the investors pays the mutual fund manager a manager fee. This is rather expensive compared to a no-load mutual fund, which does not charge a manager fee. But a no-load mutual fund is not entirely free; it comes with a 12b-1, which charges between 0.25 to 1% of its net assets annually to the investor. In both cases, they are more expensive to hold than a passively managed fund. Next to distinction between no-load mutual funds and load mutual funds, a mutual fund can be classified as open-end or closed-end funds. Commonly mutual funds are open-end funds. An open-end fund sells and buys back fund shares from investors that wish to leave the fund. A closed-end has a limited number of shares that are traded on the market.
In passively managed funds, a manager adjusts the portfolio in accordance with a pre-determined strategy that does not involve any forecasting. Hereby they are able to minimize costs of investment and do not take the risk of unsuccessfully predict the market. An index fund is an example of a passively managed fund. An index fund attempts to replicate the performance of a certain market index of stocks and therefore believes that one cannot outperform the market. The basic idea behind this is that by following a specific benchmark, one holds a well-diversified portfolio with low costs.
The abovementioned alternative multifactor model, in this paper referred to as the five factor model, is an extension to the Carhart (1997) four factor model, and takes the following form,
𝐸(𝑟!) = 𝑟!+ 𝛽!,!"# 𝐸(𝑟!") − 𝑟!" + 𝛽!,!"#𝐸(𝑆𝑀𝐵) + 𝛽!,!"#𝐸(𝐻𝑀𝐿) + 𝛽!,!"#𝐸(𝑊𝑀𝐿) + 𝛽!,!"𝐸(𝑀𝑇) (1)
where (𝑟!") − 𝑟!" 𝐸(𝑆𝑀𝐵), 𝐸(𝐻𝑀𝐿), 𝐸(𝑊𝑀𝐿), and 𝐸(𝑀𝑇) are expected premiums, and the
betas represents the factor sensitivity of a mutual fund or portfolio to these expected premiums. In this paper I demonstrate that this five factor model captures more of the average excess return of mutual funds than the Carhart (1997) four factor model does. Furthermore, I demonstrate that the five factor model captures market timing ability better than the widely used Treynor and Mazuy (1966) and Henriksson and Merton (1981) models, in case of evaluating mutual funds’ performance.
2. Literature review
According to Fama (1970) the financial market is efficient, meaning when information arises, the information incorporates into the security price without a delay. Henriksson & Merton (1981) mentions that portfolio managers forecasting skills can be split into two components: micro forecasting and macro forecasting. The former is also known as security analysis or selectivity skills and the latter is referred to as market timing. If a manager can show significant forecasting skills, this will infer that the efficient market hypothesis would be violated and therefore not hold. In this study I focus on the latter, the market timing ability of mutual fund managers. Several researches have investigated whether mutual fund managers were able to time the market (e.g. Treynor & Mazuy (1966)). I extended the Carhart (1997) four factor model by adding a market timing factor. With this model, a mutual fund investor will be able to evaluate a mutual fund manager and whether the manager successfully times the market if it behaves like a market timer. Furthermore, I compare and contrast the momentum factor with the market timing factor. I do this to understand whether or not the momentum factor already captures the market timing factor.
Efficient market hypothesis
In 1970, Fama (1970) published its paper on the efficient capital markets, which is formally known as the efficient market hypothesis (EMH). Fama (1970) defines an efficient market as a market in which prices always fully reflect all available information. Fama (1970) describes three forms of this efficient market, the weak form, the semi-strong form and the strong form. Each form is set to have its own particular available information included in the security price. The weak form only includes historical prices, the semi-strong form includes historical prices and publicly available information and the strong form includes all aforementioned information plus the private available information. Therefore, the EMH states that one cannot beat the market, by neither stock selectivity ability nor market timing ability (Sharpe (1975)).
Mutual fund performance
and showed that the sample of 115 mutual funds were on average not able to outperform a buy-the-market-and-hold (passive) strategy over the period 1945 to 1964. Studies after the Jensen (1968) paper, found similar results (see e.g., Malkiel (1995), Carhart (1997), Bogle (2002), French and French (1997), Wermers (2000), Fama and French (2010), Yang & Liu (2015), and Blake et al. (2017)). Malkiel (1995), Carhart (1997), French (2008), Fama and French (2010), and Blake et al. (2017) found that one of the main reason of underperforming are the costs and fees that mutual funds charge for their services. French (2008) found that an investor who avoids excessive fees, expenses, and trading costs, by switching to a passive market portfolio, on average can increase his annual returns by 0.67% over the period 1980 to 2006. Wermers (2000) found that mutual funds outperform the market by 1.3% annually, but after fees and transaction costs of the funds, underperform by 0.3%.
Whereas the aforementioned studies show that actively managed funds on average are not able to outperform, other studies shown that actively managed funds indeed are superior to passively managed funds (see e.g. Ippolito (1989); Grinblatt & Titman (1992); Cremers & Petajisto (2007)). Ippolito (1989) focused on the performance of 143 mutual funds over the period 1965 to 1984, and found that mutual funds are indeed superior to passively managed funds, even after all costs, except load charges.
Henriksson and Merton (1981) mentions two important skills an actively managed fund manager can separate himself from a passively managed fund manager by the means of security analysis, and market timing. Security analysis refers to micro forecasting or better known as stock selectivity skills, this involves forecasting the price of an individual security. Market timing, also known as macro forecasting, refers to forecasting the general market itself. According to Bollen and Busse (2001), a manager with market timing ability increases a fund’s exposure to the market index, by shifting the portfolio assets into high-beta stocks, prior to a bull market and decreases exposure to the market, by shifting the portfolio assets into low-beta stocks or holding cash, prior to a bear market.
found that stock selectivity ability of portfolio managers are not able to provide excess returns. Sharpe (1975) acknowledged the existence of market timing ability, even though being a big supporter of the efficient market hypothesis. However, Sharpe (1975) showed that unless a portfolio manager can predict the market seven out of ten times correctly, he should probably avoid attempting to use market timing ability. Chua, Woodward and To (1987) agrees with Sharpe (1975), but instead of the 70% correctly predicting the market, the portfolio manager requires a minimum of 80% in forecasting both bull and bear markets correctly in order to achieve excess return over passive managed funds. On the other hand, Henriksson (1984) used the Henriksson and Merton (1981) method to find that mutual fund managers are not able to successfully time the return on the market portfolio at all over the period 1968 to 1980. Bello and Janjigian (1997) found that some of the negative market timing ability in previous studies are a result of misspecification of the model they used. Bello and Janjigian (1997) introduced an alternative model to show that 633 actively managed funds for the period 1984 to 1994, exhibit significantly positive market timing ability. Furthermore, Bello and Janjigian (1997) show that there exist a negative correlation between market timing and stock selectivity. Bollen and Busse (2001) found that using daily data, mutual funds may possess more market timing ability than monthly data which have been widely used in the literature in the past. Furthermore, Chance and Hemler (2001) used four types of tests and three benchmark portfolios to find that all tests and portfolios showed evidence of significant market timing ability. Swinkels and Tjong-A-Tjoe (2007), found evidence of a group of 153 mutual funds that market timing ability do exist, but were not able to use this to successfully outperform the passively managed funds. Friesen and Sapp (2007) also supports the existence of market timing ability over the period 1991 to 2004, but show that this market timing ability reduces the investor average returns by 1.56% annually. The negative relation of the market timing ability on returns is greater on load funds and funds with relatively large risk-adjusted returns.
Factor theory
Factor theory is useful to evaluate mutual funds’ performance. If applied on the excess returns of mutual funds, it can display the mutual fund’s type of manager and the ability to evaluate the skills of this manager. Before factor theory existed, risk was thought to be an assets’ own volatility. It was not until the CAPM of Sharpe (1964), Lintner (1965) and Mossin (1966) that used Markowitz’s (1952) two-parameter portfolio analysis model as basis that showed that assets’ own risk can be diversified away and that the only relevant measure of risk was how the asset co-vary with the market portfolio – the beta of the asset. The CAPM takes the following form,
where,
𝑟!" − 𝑟! = the excess return of the market portfolio
𝛽! = the beta, sensitivity, to the market portfolio, formerly known in the
literature as the factor loading of a security or portfolio
The market portfolio is a tradeable portfolio in the market due to low-cost index funds, exchange-traded funds, and stock futures. The CAPM states that the factor underlying the asset, the market portfolio factor, determines asset risk premium and that this premium is a compensation for losses during bad times. Furthermore, the CAPM stipulates that expected returns are linear functions of the market portfolio factor only. This linear function to only the market portfolio can be represented graphically with beta on the X-axis and expected return on the Y-axis, more formerly known as the security market line (SML). Equation (2) represents the CAPM-based return-generating model, where the dependent variable is the excess return of a single security. Given the expected return of the market portfolio, the CAPM-based return-generating model can be transformed into the expected return of a single security, which is equal to,
𝐸(𝑟!) = 𝛼! + 𝑟!+ 𝛽!,!"#[𝐸(𝑟!) − 𝑟!] (3)
Equation (3) shows that, if the market is efficient, an investor should expect a certain return on a security, based on the beta, the sensitivity to the market portfolio, of that security. The intercept in equation (3) represents the abnormal return over this expected return, according to the CAPM.
Graphically 𝛼! shows the vertical distance between the security market line and the security. A
positive 𝛼! shows that the security lies above the security market line and a negative 𝛼! below the
security market line. When the intercept is positive or negative, it can be concluded that the market is inefficient and not priced well, when the intercept is indifferent from zero, it shows that the market is indeed efficient.
After the publication of the CAPM, many criticized the model. The most cited one criticism is the Roll (1977) critique, where Roll (1977) states that the true market portfolio cannot be observed. After the CAPM, other factors were identified, but many researches still continued using the CAPM’s, market portfolio factor, as a factor to explain average excess returns.
In 1993, Fama and French (1993) (hereafter FF) found that the CAPM prediction of positive relation between average stock returns and the beta on market portfolio holds during the pre-1969 period. However, they found this relationship disappears during, in their time, more recent 1963-1990 period. FF (1993) extended the traditional CAPM market portfolio factor with two additional factors to capture the size- and value effect, now formally known as the FF (1993) three factor model. The FF three factor model takes the following form,
𝐸(𝑟!) = 𝑟!+ 𝛽!,!!"[𝐸(𝑟!) − 𝑟!] + 𝛽!,!"#𝐸(𝑆𝑀𝐵) + 𝛽!,!"#𝐸(𝐻𝑀𝐿) (4)
𝐸(𝑟!) − 𝑟! = the expected excess return on the market portfolio
(𝑆𝑀𝐵) = abbreviation for Small Minus Big, which represents the size effect
(𝐻𝑀𝐿) = abbreviation for High Minus Low, which represents the value effect.
The betas represents the sensitivity of the security to the factors market portfolio, size, and value. In 1981, Banz (1981) introduced the size factor, showing that small firms tends to do on average better than large stocks, after adjusting for risk. Therefore, showing that the CAPM market portfolio factor is not the only factor explaining returns. The value factor states that value stocks tend to outperform growth stocks, measured by book-to-market values of companies.
During the same year FF (1993) introduced its factor model, Jegadeesh and Titman (1993) shed light to the momentum factor. Momentum is a winners and losers strategy, where an investor purchases stocks that have gone up in the past (winners) during a certain period and sells stocks with the lowest return (losers) over the same period. The momentum effect refers to that winner stocks continue to win and losers continue to lose. Carhart (1997) eventually extended the FF (1993) three factor model with the momentum factor. The Carhart four factor model takes the following form,
𝐸(𝑟!) = 𝑟!+ 𝛽!,!"#[𝐸(𝑟!) − 𝑟!] + 𝛽!,!"#𝐸(𝑆𝑀𝐵) + 𝛽!,!"#𝐸(𝐻𝑀𝐿) + 𝛽!,!"#𝐸(𝑊𝑀𝐿)
(5)
Where the first three factors represents the same factors as the FF (1993) three factor model of equation (4), (𝑊𝑀𝐿) represents the momentum effect and is an abbreviation for Winners Minus Losers.
Market timing methods
In 1968, Jensen (1968) reformulated the CAPM in order to measure the performance of a mutual fund, now formally known as Jensen’s alpha. The following is the ex post version of this formula,
𝑟!"− 𝑟!" = 𝛼! + 𝛽! 𝑟!" − 𝑟!" + 𝜀!" (6) Where,
𝛼! = intercept of the regression
𝑟!"− 𝑟!" = the excess return of a portfolio
Treynor and Mazuy (1966) (hereafter TM) took equation (6) and reformulated in order to capture the market timing ability of a portfolio manager. The TM model takes the following form,
𝑟!"− 𝑟!" = 𝛼!+ 𝛽! 𝑟!"− 𝑟!" + 𝛾!(𝑟!"− 𝑟!)!+ 𝜀
!" (7)
Where the intercepts 𝛼!, 𝛽!, and 𝛾! are regression coefficients on the market portfolio factor and
the market portfolio factor squared. The 𝛾! coefficient is a tool to evaluate a portfolio managers’
market timing ability. Negative 𝛾! indicates negative market timing ability, zero or not
significantly different from zero 𝛾! indicates no market timing ability, and positive 𝛾! indicates
positive market timing ability. When markets go up and a portfolio manager forecasted this and anticipated before it went up by allocating his portfolio into high beta stocks, is expected to have
a positive 𝛾!. When markets go up and a portfolio manager forecasted a market decrease and
anticipated by allocating his portfolio into low beta stocks, is expected to have a negative 𝛾!. TM
(1966) used this equation to evaluate 57 mutual funds and found that only one fund’s 𝛾!
coefficient was significantly above zero. The TM (1966) model has been widely used in the literature to evaluate portfolio managers’ market timing ability (see e.g. Bello and Janjigian (1997), and Grinblatt and Titman (1994)).
Henriksson and Merton (1981) (hereafter HM) introduced an alternative methodology in combination with equation (6) in order to capture the market timing ability of a portfolio
manager. HM (1981) assumed that a portfolio manager either forecasts 𝑟!">𝑟!" or 𝑟!! ≤ 𝑟!". The
HM (1981) model takes the following form,
𝑟!"− 𝑟!" = 𝛼!+ 𝛽! 𝑟!"− 𝑟!" + 𝜑!𝐷!(𝑟!"− 𝑟!) + 𝜀!" (8)
Where 𝐷! is a dummy variable that takes the value 0 if 𝑟!">𝑟!", and -1 if 𝑟!" ≤ 𝑟!". The 𝜑!
coefficient is similar to 𝛾! coefficient of the TM model. Henriksson (1984) used equation (8) to
evaluate 116 mutual funds for the period 1968 to 1980. Henriksson (1984) found that there was little evidence that portfolio managers successfully timed the market. Just like the TM (1966) model, the HM (1981) model has also been widely used in the literature to evaluate portfolio managers’ market timing ability (see e.g. Henriksson (1984), and Bollen and Busse (2001)).
3. Data and methodology
A. Data
came to existence, and went out of existence over the period 2002 to 2017. The CRSP survivor bias free US mutual fund database gave a total of 423,851 mutual funds. I only include funds that are classified as growth funds, and growth & income funds under the Lipper Objective Code. Lipper characterize a growth funds as funds that are actively managed in order to earn excess returns, they do this by investing in companies with long-term earnings expected to grow significantly faster than the earnings of the stocks represented in the major unmanaged stock indices. Lipper characterizes growth & income funds as funds that combine a growth-of-earnings orientation and an income requirement for level and/or rising dividends. The selection on growth funds and growth & income funds are in line with other widely cited literature on mutual funds’ performance (see e.g. Carhart (1997) and Bollen and Busse (2001)). Other literature also include balanced funds (see e.g. Jiang, Tao & Yu (2007)), in this study I did not include balanced funds, due to the fact that a balanced funds objective is to maintain a certain stock/bond ratio typically 60 /40, at all time. I do this first of all because of the high percentage of allocation to bonds, since I research the market timing ability of equity market and high percentage of allocation to bonds will significantly influence the change in Net Asset Value (hereafter NAV), due to non-equity activity. Furthermore, Belo and Janjigian (1997) found that balanced funds exhibit no timing abilities. Just like Fama & French (2010), I manually exclude index funds and exchange traded funds (hereafter ETFs), to mainly focus on active managers. Index funds and ETFs replicate a predetermined market index and therefore are not actively managed funds. Furthermore, just like Brown and Goetzmann (1995), I omit mutual funds with less than 12 consecutive return observations over the entire sample period. After filtering the data on exclusion basis, I found 10,474 mutual funds.
In the United States, the Securities and Exchange Commission (hereafter SEC) protects investors of mutual funds. The SEC requires all mutual funds to compute and publish their NAVs per share on a daily basis. They also require selling and redeeming their shares only at their current NAV. Therefore, the return of a mutual fund is equal to the change of the NAV that period, which is defined as
𝑁𝐴𝑉! =!"#$%& !"#$% !" !"" !""#$" !" !!!"#$%"&'!
!! !"!#$ !"#$"!"%"&' !" !
!"#$%& !" !!!"#$ !"#$#%&'(&) !" !"#$ ! (9)
Also Bollen & Busse (2001) use the NAV as a way to calculate the returns of mutual funds, but they also include ex-dividends of fund. Due to lack of information, I do not include this. Therefore, I assume that the dividends that a mutual fund receives are reinvested in the fund.
Furthermore, Dichev (2004) mentions that using monthly data is a reasonable compromise between the annual and daily data, allowing to properly calculate the distributions for the internal rate of returns (hereafter IRR), which will be explained later in this paper. Therefore, using monthly data is sufficient enough for this study. I was able to retrieve 8012 mutual funds’ monthly NAVs from the Thomson Reuters Datastream database. After omitting mutual funds with less than 12 consecutive return observations over the entire sample period, my final dataset consist of 7084 mutual funds. Table 1 provides summary statistics of the mutual funds used in this study and their investment characteristic.
Table 1 Summary statistics of mutual funds used
This table shows the number of funds and the characteristics of mutual funds in the sample categorized into 6 types based on investment objectives, which are large-cap, mid-cap, small-cap, multi-cap, mixed-asset, and others (specialty diversified and retirement income) funds. This table also shows what the current status, dead or alive, is of the funds used. The information obtained on the NAVs are found in the Thomson Reuters Datastream and the current status are found in the CRSP survivor bias free US mutual fund database.
Current status Number of
funds
Average NAV Median NAV Dead funds Alive funds
All funds 7084 17.928 13.320 2920 4164 Large-cap funds 2630 20.043 15.070 1310 1320 Mid-cap funds 264 19.650 15.060 105 159 Small-cap funds 199 20.778 14.550 60 139 Multi-cap funds 1963 18.737 14.110 855 1108 Mixed-asset 1953 12.495 11.150 577 1376 Others 75 12.723 10.550 13 62 B. Methodology
determine the actual return of an active investor, because this takes both the cross-sectional and time-series aspects of weighting by market value into account. The intuition behind this method is that investments made by an active investor are seen as an investment project. The active investor in this study is the mutual fund manager. The returns of the mutual fund manager are reflected in the NAV of the fund. To compute the IRR, I use the net distributions formula, proposed by Dichev (2004).
𝐷𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛𝑠! = 𝑀𝑉!!!∗ 1 + 𝑟! − 𝑀𝑉! (10)
Where MV is market capitalization and 𝑟! is the total return for that period. The formula
provides the net distribution to investors. Instead of net distributions to investors, I use the distributions on the mutual fund managers, which is reflected in the change of the NAV of the
fund. Therefore, in the case of a mutual fund, MV is NAV and 𝑟! is the total lognormal return on
the NAV for that period. Positive distributions indicate a positive cash flow of the mutual fund and negative distributions indicates a negative cash flow of the mutual fund. Hence, it can be said that when the distribution is positive, an active portfolio manager was successful in his ability to increase the NAV and, when the distribution is negative, unsuccessful. This should not be confused with the fact, whether the manager outperformed or underperformed the market. The intuition behind this is that the NAV of a mutual fund changes resulting from returns of its investments and not from fresh cash inflow of investors. Dichev (2004) mentions three advantages of this method. First, it is simple and easy to use. Second, it has minimal data requirements. Third, it automatically adjusts for all capital distributions. Furthermore, the dollar-weighted return approach has also been supported by other literature to measure market timing ability (see e.g. Friesen and Sapp (2007)).
mutual funds that are in the top 10 percent, based on the IRR, and I create an equally-weighted (losers) portfolio of the mutual funds that are in the bottom 10 percent, also based on the IRR. Finally, I take the excess return of the winners’ portfolio of the following months, for a year, and subtract this with the excess return, of the same periods, of the losers’ portfolio. The excess return is the lognormal return on NAV minus the risk-free rate of that period. I obtain the risk-free rate from Kenneth French’s data library, which is the one-month Treasury bill rate from Ibottson and Associates, Inc. The basic principle of this procedure is to go long each year in the top 10 percent market timers and short each year the bottom 10 percent market timers. The average difference between the winners’ portfolio and losers’ portfolio will give a monthly market timing factor. Table 2 shows the amount of funds used each year and their corresponding IRRs. Note the low average IRR of the year 2008 and 2009. This might suggest that during the 2007 crisis, the majority of mutual funds unsuccessfully timed the market.
Table 2 Numbers of funds used for each year
This table shows the amount of funds used for each year in the process of building the market timing factor. Each year the IRR is calculated from July to June. Notable is the increasing number of funds used every year. This indicates that every year the number of growth and/or growth and income funds is increasing.
Year N Funds Average IRR Highest IRR Lowest IRR
2003 1939 0.4198 3.4797 -10.0568 2004 2115 1.1979 3.0258 -2.2603 2005 2283 0.6564 3.1779 -7.7305 2006 2519 -0.1572 1.5338 -4.3079 2007 2779 0.8379 2.6661 -6.5355 2008 3032 -1.8034 1.5106 -10.4839 2009 3266 -3.2124 1.0524 -11.3185 2010 3423 0.2967 2.2838 -4.8689 2011 3499 1.5227 6.5976 -3.6763 2012 3514 -0.2449 1.6211 -5.3405 2013 3698 1.1432 3.1063 -6.3144 2014 3857 0.8892 6.7296 -13.7838 2015 4006 -0.1597 2.1581 -24.4999 2016 4116 -0.9701 1.6591 -22.1215
I add the market timing factor to the Carhart four factor model. The FF (1993) three factors are obtained from the Kenneth French’s data library. The momentum factor (WML) is also obtained from the Kenneth French’s data library. After adding the market timing factor, the five factor model takes the following form,
Fama and French (2010) mention the criticism on whether the average returns of factors are rewards for carrying the risk of those factors during bad times or the result of mispricing of those stocks with these characteristics. Just like Fama and French (2010), I conclude that this is not an issue in this paper. I interpret these risk factors of equation (11) as diversified passive benchmark returns that capture patterns in average excess returns during my sample period, whatever the source of the average excess returns.
In table 3 I provide the summary statistics of the five factors of equation (11) and the cross-correlation between each other on 168 months of observations, July 2003 to June 2017. Most notable in this table is the negative correlation between the momentum factor, WML, and all the other factors except for the market timing factor.
Table 3 Summary statistics of the five factor model
Summary statistics of the five factor model of equation (11). The market portfolio, size, value and momentum factor are obtained from the Kenneth French’s data library, the market timing factor are obtained by the abovementioned procedure. The table also contains the average monthly returns in percentages and the standard deviation of the five factors. Furthermore, the correlation matrix shows how the five factors correlates with each other.
Cross-correlations Average monthly return Standard deviation Mkt-Rf SMB HML WML MT Mkt-Rf 0.73625 4.00587 1 SMB 0.17345 2.28801 0.38118 1 HML 0.07208 2.51735 0.28021 0.13356 1 WML 0.02595 4.43933 -0.32359 -0.04529 -0.38501 1 MT 0.30078 1.55817 0.23093 0.12737 -0.04991 0.14296 1 B. Regressions
In order to test the validity of the five factor model, I conduct both time-series regressions and cross-sectional regressions. The regression analysis is split into individual fund level and portfolio level. The individual fund level is all the mutual funds, both in existence and not in existence anymore, of the whole sample set. This indicates that 7048 individual funds are tested over 168 months, July 2003 to June 2017.
years, July to June, to be included in the sample. Then I rank all the mutual funds that are in existence and report a full year of returns afterwards, on their IRRs ranking from highest to lowest IRR. After this, these funds are split into 10 equally-weighted portfolios. This results in 10 portfolios and each portfolio includes 168 months, July 2003 to June 2017, of average excess returns.
B.1. Time-series regression
The main regression framework is the five factor model of equation (11). The five factor model of equation (10) takes the following regression form,
𝑟!"− 𝑟!" = 𝛼! + 𝛽!,!"# 𝑟!" − 𝑟!" + 𝛽!,!"#𝐸(𝑆𝑀𝐵) + 𝛽!,!"#𝐸(𝐻𝑀𝐿) + 𝛽!,!"#𝐸(𝑊𝑀𝐿) + 𝛽!,!"𝐸(𝑀𝑇) (12)
Where the left hand side represents the excess return of each individual fund or portfolio. The betas of market portfolio, size, value, momentum, and market timing factors can be described as a passive benchmark. This benchmark can be replicated by creating a portfolio that has the same exposures to the factors, as the fund or portfolio on the left hand side. The intercept in equation (12) can be interpreted as a measure of outperformance or underperformance on a comparable fund or portfolio that has the same exposures to the five factors. A positive intercept is interpreted as an outperformance of the benchmark portfolio, and a negative intercept as an underperformance of the benchmark portfolio. I conclude that the five factor model describes the average excess returns well if the intercept is close to zero.
The second and third time-series regression is to analyze whether there is a difference observable in the intercept when omitting the momentum factor or the market timing factor. The second time-series regression is the Carhart (1997) four factor model, which takes the following regression form,
𝑟!"− 𝑟!" = 𝛼! + 𝛽!,!"# 𝑟!"− 𝑟!! + 𝛽!,!"#𝐸(𝑆𝑀𝐵) + 𝛽!,!"#𝐸(𝐻𝑀𝐿) + 𝛽!,!"#𝐸(𝑊𝑀𝐿) (13)
The third time-series regression is similar to equation (12), but without the momentum factor. This takes the following regression form,
𝑟!"− 𝑟!" = 𝛼!+ 𝛽!,!"# 𝑟!"− 𝑟!" + 𝛽!,!"#𝐸(𝑆𝑀𝐵) + 𝛽!,!"#𝐸(𝐻𝑀𝐿) + 𝛽!,!"𝐸(𝑀𝑇)
(14)
equation (12) is closer to zero than the average intercept of the Carhart (1997) four factor model, then I conclude that market timing factor has a better explanatory power than the momentum factor. This might indicate that the momentum factor is already incorporated in the market timing factor. Therefore, via the time-regression series I observe whether market timing is a factor on its own or has more explanatory or less explanatory power than the momentum factor, by comparing and contrasting equations (12), (13), and (14).
B.2.1.1. Cross-sectional regression on portfolio level: Gibbons, Ross, and Shanken test
After running the time-series regression I obtain the sensitivity, betas, for each of the five factors in equation (12) for each portfolio. To test the validity of the factor model, similar to Fama and French (1996), I ran the Gibbons, Ross, and Shanken (1989) (hereafter GRS) test. Originally the GRS test is developed to test the CAPM using a multivariate statistical method. The CAPM theory states that the market portfolio is mean-variance efficient, the GRS test tests whether any particular portfolio is ex-ante mean-variance efficient. If the CAPM is valid the intercept should be zero for all assets. That is, the CAPM implies that the intercept estimate should not be statistically significantly different from zero for all individual assets or portfolios. GRS test uses a simultaneous test of the null hypothesis:
𝐻!: 𝛼! = 𝛼! = ⋯ = 𝛼! = 0
The GRS test suggest the following test statistic for the simultaneous test, which is an F-statistic with degrees of freedom N and (T – N – L),
𝐹!"# = ! !!!!!! !!! !!!∑!!!!
!!!!! ~𝐹(𝑁, 𝑇 − 𝑁 − 1) (15)
Where,
T = number of time-series return observations,
N = number of test assets
𝛼!! = (𝛼
!!, 𝛼!!, … , 𝛼!! )
∑ = covariance matrix of the residual returns,
𝜃!! = ( !!!!!
!! )
!
𝑟!− 𝑟!= average excess market return,
𝑠! = standard deviation of excess market returns (𝑟!"− 𝑟!")
The original GRS test tests for the CAPM, but in this paper I test the five factor model. In order to include the four other factors into the formula, I compute the following GRS-statistic,
𝐹!"#= !! !!!!!!!!!! !!!∑!!!!
L = amount of factors used
𝜇 = average factor over the sample period
Ω = covariance matrix of the factors
The null hypothesis stays the same, that is, the intercept estimate does not statistically significant differ from zero for all individual assets or portfolios. To compare and contrast the different models described above, I apply this GRS test on the factor models of equations (2), (4), (5), (12), and (14). The factor model with the lowest GRS-statistic is said to be the model with the most explanatory power.
B.2.1.2. Cross-sectional regression on portfolio level: Fama and Macbeth test
Next to testing the five factor model with the GRS test, I also test the factor model with the methodology of Fama and Macbeth (1972) (hereafter FM). The FM methodology has been widely acknowledged and used in the literature of factor model testing (see e.g. Fama and French (1996)). The FM methodology provides a practical way to test factor models. The FM method is a two-step regression that estimates the premium rewarded on taking the risk of a factor. The first step is running a time-series regression, similar to the ones done at section B.1. The second step, the estimation of the factor premium, is to run a cross-sectional regression at each time period. In this paper, this results in 168 cross-sectional regressions. The regression takes the following form,
𝑟!,!− 𝑟!,! = 𝛼! + 𝛾!"#,!𝛽!,!"#+ 𝛾!"#,!𝛽!,!"#+ 𝛾!"#,!𝛽!,!"# + 𝛾!"#,!𝛽!,!"# + 𝛾!",!𝛽!,!"
⋮ (17)
𝑟!,!− 𝑟!,! = 𝛼!+ 𝛾!"#,!𝛽!,!"#+ 𝛾!"#,!𝛽!,!"#+ 𝛾!"#,!𝛽!,!"# + 𝛾!"#,!𝛽!,!"#+ 𝛾!",!𝛽!,!"
The risk premium for each factor is the average of each gamma, 𝛾!,!, over the whole sample
period, resulting in one gamma for each factor. To test the validity of the factor models, I average the alphas over the whole sample period to get one single alpha. The methodology uses a simple t-statistic to test whether the gammas and alpha are statistically different from zero. The t-test null hypothesis takes the following form,
𝐻!: 𝛼! = 0
The same null hypothesis holds for the gammas tested. If the null hypothesis is rejected, it indicates that the factor has explanatory power to explain the average excess return of mutual funds. I also apply this FM test on the factor models of equations (2), (4), (5), (12), and (14), to compare and contrast these factor models with each other.
In order to test validity of the factor model on individual fund level, I also regress two cross-sectional regressions. One of the two regressions is the same as the FM methodology. The other regression is similar to the cross-sectional procedure similar to the FM methodology but combined with an alternative method of the GRS test. The GRS method is a multivariate test, it requires the number of investigated assets to be less than the number of time-series observations (N < T). Therefore, I use an alternative approach to the GRS-statistic. The FM procedure is split into two parts. The first step is similar to the time-series regression on equation (12). In the second step I took the betas, obtained by the first step and regressed a cross-sectional regression with, on the left-hand side the average excess return of each individual fund over all the available data on that fund, and on the right-hand side the betas estimated in step one. This result into one risk premium for each factor. Then I took the risk premium on each factor and multiply it with the betas of step one of each individual fund. The residual that is not explained by this model is the intercept of the cross-sectional regression. To test the hypothesis similar to the GRS test, I use the following formula,
𝐹!"#$%&'()! !!"#!
!!"#! ~𝐹(𝑁, 𝑇 − 𝑁 − 𝐿) (18)
Where,
𝛼!"#! = the average sum of squared intercept, 𝛼
!, of each individual fund
calculated in step one, the time-series intercept.
𝛼!"#! = the average sum of squared intercept, 𝛼
!, of each individual fund
calculated in step two, the cross-sectional residuals.
If the five factor model is valid, it implies that the intercept estimate, 𝛼!, should not be
statistically significantly different from zero for all individual funds. Note that this metric comes with the caveat that it does not incorporate the effect of correlation among residuals stemming from the underlying regression models. To also compare and contrast the different models described above I also applied the pseudo- GRS test on the models of equations (2), (4), (5), (12), and (14). The model with the lowest pseudo-GRS-statistic is said to be the model with the most explanatory power.
4. Results
4.1. Portfolio level: Time-series regression
the momentum factor is redundant, when adding the market timing factor into the FF (1993) three factor model.
Table 4 R-squares of three different factor models
R-squares and adjusted R-squares on the time-series regressions of equation (12), (13), and (14), respectively, on 10 portfolio based on IRRs.
Five factor model Carhart (1997) Four factor model
Equation (14) Four factor model Portfolios R-squared Adjusted
R-squared R-squared Adjusted R-squared R-squared Adjusted R-squared 1(Low) 0.933 0.931 0.821 0.817 0.933 0.931 2 0.937 0.935 0.890 0.887 0.937 0.936 3 0.930 0.928 0.901 0.899 0.930 0.928 4 0.939 0.937 0.922 0.920 0.939 0.937 5 0.941 0.940 0.923 0.921 0.941 0.940 6 0.945 0.944 0.934 0.933 0.945 0.944 7 0.953 0.952 0.946 0.945 0.953 0.952 8 0.953 0.952 0.950 0.949 0.953 0.952 9 0.956 0.954 0.955 0.954 0.956 0.954 10(High) 0.937 0.935 0.936 0.935 0.937 0.935 Average 0.943 0.941 0.918 0.916 0.942 0.941
Table 5 shows the results of the time-series regression conducted of the five factor model on portfolio level. The table shows that portfolios with higher IRR tend to have higher average excess return than lower IRR portfolios. The intercepts are all close to zero, slightly negative, but all significant. This indicates that the five factor model of equation (11) describes the average excess returns of the portfolio of mutual funds well. Notable is that for every portfolio, the momentum factor and the size factor is insignificant and has low coefficients. Furthermore, the high portfolio has the only positive market timing coefficient, but it is statistically insignificant.
Table 5. Results of time-series regression on portfolios
Mutual funds are sorted at the end of June each year, beginning from 2002, into 10 portfolios based on their IRR of the previous year. The portfolios are equally weighted. Fund with the lowest IRR of the previous year comprise decile 1 and fund with the highest comprise decile 10. The average monthly excess returns are in percentage points. Mkt-rf, SMB, and HML are Fama and French (1993) market proxy and mimicking portfolios for the size and value effect. WML is Carhart’s (1997) factor-mimicking portfolio for the momentum effect. MT is the additional factor added to the Carhart (1997) four factor model and is a factor-mimicking portfolio for the market timing effect. Alpha is the intercept of the model. The t-statistics are in parentheses. Note: a single asterisk indicates significant at 10% level (two-tailed t-test), a double asterisk indicates significant at 5% level, and triple asterisk indicates significant at 1% level.
Portfolio Average excess return Alpha Mkt-Rf SMB HML WML MT 1(Low) -0.02 -0.005 (-5.70)*** 1.021 (40.94)*** 0.058 (1.46) -0.159 (-4.36)*** 0.005 (0.21) -0.930 (-16.49)*** 2 0.07 -0.005 (-6.02)*** 1.026 (42.53)*** 0.026 (0.69) -0.128 (-3.63)*** -0.010 (-0.46) -0.606 (-11.10)*** 3 0.07 -0.005 (-6.19)*** 1.041 (40.24)*** 0.002 (0.04) -0.133 (-3.51)*** -0.017 (-0.75) -0.481 (-8.21) 4 0.07 -0.006 (-7.00)*** 1.023 (43.02)*** 0.020 (0.52) -0.123 (-3.53)*** -0.004 (-0.21) -0.360 (-6.69)*** 5 0.21 -0.004 (-5.35)*** 1.032 (44.36)*** 0.002 (-0.06) -0.127 (-3.74)*** 0.003 (0.13) -0.382 (-7.25)*** 6 0.20 -0.005 (-6.02)*** 1.031 (45.46)*** -0.008 (-0.22) -0.099 (-2.99)*** -0.009 (-0.47) -0.291 (-5.66)*** 7 0.25 -0.004 (-6.00)*** 1.027 (49.50)*** -0.019 (-0.58) -0.107 (-3.53)*** -0.009 (-0.50) -0.235 (-5.00)*** 8 0.26 -0.004 (-6.05)*** 1.019 (49.18)*** -0.011 (-0.34) -0.109 (-3.59)*** -0.007 (-0.38) -0.162 (-3.44)*** 9 0.30 -0.004 (-6.19)*** 1.013 (49.79)*** 0.013 (0.40) -0.084 (-2.84)*** -0.002 (-0.12) -0.057 (-1.23) 10(High) 0.29 -0.005 (-5.70)*** 1.020 (40.96)*** 0.058 (1.46) -0.159 (-4.36)*** 0.005 (0.21) 0.070 (1.24)
4.1.2. Portfolio level: Cross-sectional regression: Gibbons Ross, and Shanken test
Table 6 shows the results of the GRS tests conducted on portfolio level. Every GRS-statistic rejects the null hypothesis of,
𝐻!: 𝛼! = 𝛼! = ⋯ = 𝛼! = 0
at significance levels of 1%, 5%, and 10%. This indicates that the intercepts of all factor models tested, are statistically significant different from zero at portfolio level. On the other hand, it does show that the five factor model, has the lowest GRS-statistic and equivalent intercept as the equation (13) four factor model. This indicates that the five factor model, captures most of the average excess returns at portfolio level.
Table 6 Gibson, Ross, and Shanken (1989) test results at portfolio level
Test statistics on five evaluated factor models using the GRS-statistics. Each test uses a set of 10 portfolios formed by its IRRs. The underlying sample contains a total of 168 monthly observations from July 2003 to June 2017.
Factor model Average intercept GRS-statistic P-value
Five factor model -0.00476 6.43 0.00
Carhart (1997) model -0.00548 6.84 0.00
FF (1993) model -0.00556 6.91 0.00
Equation (14) four factor model -0.00476 6.44 0.00
4.1.3. Portfolio level: Cross-sectional regression: Fama and Macbeth test
Table 7 shows the results of the FM tests conducted on five different factor models. Contrary results are found here to the GRS test conducted on the five different factor models, the five factor model intercept is insignificant, indicating that it does not reject the null hypothesis of intercept being zero. Therefore, the five factor model captures most of the variation of the average excess return on portfolio level. On the other hand, the Carhart (1997) four factor model has the nearest to zero intercept, but is statistically significant, and therefore does not explain all of the average excess returns. In addition, both the market timing factor and momentum factor are statistically significant. This indicates that, including both factors in the model, have more explanatory power in explaining the average excess return, than omitting one factor. Furthermore, note that the value factor, HML, is insignificant for every factor model. But when omitting the value factor, the intercepts of all the factor models tested, becomes insignificant. Therefore, I continue including the value factor into the model.
Table 7 Fama and Macbeth (1973) test results at portfolio level
Test statistics on five different factor models using the FM methodology. Each test uses a set of 10 portfolios formed by its IRRs. The underlying sample contains a total of 168 monthly observations from July 2003 to June 2017. Note: a single asterisk indicates significant at 10% level (two-tailed t-test), a double asterisk indicates significant at 5% level, and triple asterisk indicates significant at 1% level.
Five factor model
Factor model Alpha Mkt-Rf SMB HML WML MT
Five factor model 0.01220 (0.983) -0.00870 (-0.716)*** -0.01604 (-3.203)*** 0.00072 (0.287) 0.05387 (4.310)** 0.00297 (9.406)*** Carhart (1997) model 0.01148 (3.952)** -0.00797 (-2.788)** -0.01593 (-3.136)** 0.00093 (0.280) 0.05452 (9.861)*** FF (1993) model -0.03423 (-4.314)*** 0.03653 (3.956)*** 0.00597 (0.424) 0.00409 (0.279) Equation (14) four factor model 0.03992 (3.650)** -0.03694 (-3.291)** -0.01865 (-1.902) -0.00844 (-0.972) 0.00306 (11.515)*** CAPM -0.03503 (-7.808)*** 0.03757 (8.000)***
4.2.1. Individual fund level: Time-series regression
with the highest market timing coefficient also has an intercept of 0.00918, indicating that the fund outperforms the benchmark. As expected, the mutual fund with the lowest market timing coefficient, has a negative intercept of -0.01033, indicating that the fund underperforms its benchmark. Over the whole sample I found 1382 individual funds with a positive market timing coefficients and 5702 negative market timing coefficients. Of the 1382 individual funds with a positive market timing coefficient, 1130 of them has a positive average excess return. Indicating that when an individual fund exhibit a positive market timing coefficient, about 80% of the time they are be able to receive positive average excess return on my whole sample period. On the other hand, there is little relation between negative market timing coefficient and average excess return, because of the 5702 negative market timing coefficients, 1782 of them has a negative average excess return. Furthermore, I found 2082 positive alphas and 5002 negative alphas, with coefficients ranging from 0.01180 to -0.0286 and an average of -0.00252. The small spread between alphas and the close to zero average indicate that, on average, funds do not outperform the benchmark of the five factor model, and that the five factor model of equation (11) describes the average excess returns well.
The second time-series regression, Carhart (1997) four factor model (equation (13)), on individual fund level resulted in a slightly higher average alpha, -0.00296, than using the five factor model. I found 1687 positive alphas and 5397 negative alphas with coefficients ranging from 0.01475 to -0.03390. The higher spread and higher average alpha indicates that, over the whole sample, the five factor model describes the average excess returns better than the Carhart (1997) four factor model on individual fund level.
alpha is even lower at the five factor model, indicating that a model with both the market timing factor and momentum factor, explains the average excess returns of individual funds the best.
4.2.2. Individual fund level: Cross-sectional regression: Gibbons, Ross, and Shanken test
Table 8 shows the results of the GRS-tests conducted on portfolio level. Every pseudo GRS-statistic does not reject the null hypothesis,
𝐻!: 𝛼! = 𝛼! = ⋯ = 𝛼! = 0,
at all significance levels. This indicates that the intercepts of all factor models tested, are not statistically significant different from zero at individual fund level. This is contrary to the portfolio level, where the GRS tests rejected every multifactor model. Furthermore, table 8 shows that the cross-sectional average intercept is the lowest for the equation (13) four factor model. However, similar to the tests conducted on portfolio level, the five factor model exhibit the lowest pseudo GRS-statistic. This indicates that the five factor model explains the average excess returns the best compared to the other factor models.
Table 8 Gibson, Ross, and Shanks (1989) tests results at individual fund level
Test statistics on five different factor models using the GRS-statistics. Each test uses a set of 7048 individual funds. The underlying sample contains a total of 168 monthly observations from July 2003 to June 2017. TS stands for time-series and CS stands for cross-sectional.
Factor model Average
intercept (TS) Average intercept (CS) Pseudo GRS-statistic P-value
Five factor model -0.00252 0.00076 0.54523 0.85567
Carhart (1997) model -0.00296 0.00072 0.66212 0.75807
FF (1993) model -0.00303 0.00068 0.67598 0.74550
Equation (14) four factor model -0.00254 0.00063 0.70537 0.71842
CAPM -0.00301 0.00085 0.62506 0.79080
4.2.3. Individual fund level: Cross-sectional regression: Fama and Macbeth test
the average excess return on individual funds. The nearest intercept to zero, and at the same time is insignificant, is the FF (1993) three factor model.
Table 9 Fama and Macbeth (1973) test results at individual fund level
Test statistics on five different factor models using the FM methodology. Each test uses a set of 7048 individual funds. The underlying sample contains a total of 168 monthly observations from July 2003 to June 2017. The t-statistics are in parentheses. Note: a single asterisk indicates significant at 10% level (two-tailed t-test), a double asterisk indicates significant at 5% level, and triple asterisk indicates significant at 1% level.
Five factor model
Factor model Alpha Mkt-Rf SMB HML WML MT
Five factor model 0.00019 (2.713)*** 0.00199 (14.692)*** 0.00137 (1.752)* -0.00339 (-8.205)*** 0.00655 (5.460)*** 0.00293 (11.137)*** Carhart (1997) model 0.00009 (1.347) 0.00159 (12.706)*** 0.00158 (2.020)** -0.00251 (-5.896)*** 0.00876 (6.937)*** FF (1993) model 0.00003 (0.433) 0.00126 (10.982)*** 0.00204 (2.640)*** -0.00358 (-8.955)*** Equation (14) four factor model 0.00018 (2.577)** 0.00192 (14.646)*** 0.00154 (1.974)** -0.00399 (-10.299)*** 0.00301 (11.066)*** CAPM 0.00025 (3.804)*** 0.00109 (8.983)***
5. Robustness tests
5.1. Market timing factor versus Treynor and Mazuy (1966)
Table 10 compares and contrasts the market timing factor with the conventional TM (1966) (see equation (7)) model, by adding the market timing factor to the TM (1966) model. The table shows that, except for portfolio two, where the TM factor is significant, the significance of the market timing factor is stronger. Furthermore, in most portfolios the market timing factor is able to capture market timing, and TM (1966) not. This indicates that the market timing factor is able to capture market timing, where the TM (1966) model cannot. Therefore, I conclude that, when adding the market timing factor to a factor model, the TM factor becomes redundant.
Table 10 Regression to explain average monthly excess returns on Treynor and Mazuy (1966) model and market timing factor
𝑟!"− 𝑟!" = 𝛼!+ 𝛽! 𝑟!" − 𝑟!" + 𝛽!,!"𝐸 𝑀𝑇 + 𝛾!(𝑟!"− 𝑟!)!+ 𝜀!" (19)
10% level (two-tailed t-test), a double asterisk indicates significant at 5% level, and triple asterisk indicates significant at 1% level.
Factors Portfolios Alpha Mkt-Rf MT TM 1(Low) -0.00414 (-4.022)*** 0.99403 (43.356)*** -0.89097 (-15.386)*** -0.39287 (-1.374) 2 -0.00361 (-4.493)*** 0.99466 (55.534)*** -0.03917 (-0.867) -0.38993 (-1.746)* 3 -0.00338 (-4.101)*** 0.99034 (53.867)*** -0.14310 (-3.084)*** -0.51223 (-2.234)** 4 -0.00351 (-4.231)*** 0.99942 (54.074)*** -0.21904 (-4.695)*** -0.42492 (-1.843)* 5 -0.00398 (-4.427)*** 1.00842 (50.348)*** -0.27625 (-5.465)*** -0.39297 (-1.573) 6 -0.00371 (-3.934)*** 1.00256 (47.715)*** -0.35362 (-6.668)*** -0.29954 (-1.143) 7 -0.00512 (-5.350)*** 0.99986 (46.926)*** -0.33613 (-6.250)*** -0.31931 (-1.202) 8 -0.00495 (-4.765)*** 1.01777 (43.989)*** -0.46403 (-7.946)*** -0.30160 (-1.045) 9 -0.00422 (-4.359)*** 1.00403 (46.541)*** -0.58361 (-10.719)*** -0.42238 (-1.570) 10(High) -0.00414 (-4.020)*** 0.99393 (43.358)*** 0.10954 (1.893)* -0.39389 (-1.378)
5.2. Market timing factor vs Henriksson and Merton (1981)
Table 11 compares and contrasts the market timing factor with the conventional HM (1981) (see equation (8)) model, by adding the market timing factor to the HM (1981) model. Whereas, every HM factor is insignificant at portfolio level, market timing are at most portfolios significant. This indicates that the market timing factor is able to capture market timing, where the HM (1981) model cannot. Therefore, I conclude that, when adding the market timing factor to a factor model, the HM factor becomes redundant.
Table 11 Regression to explain average monthly excess returns on Henriksson and Merton (1981) model and market timing factor
𝑟!"− 𝑟!" = 𝛼!+ 𝛽! 𝑟!"− 𝑟!" + 𝛽!,!"𝐸 𝑀𝑇 + 𝜑!𝐷!(𝑟!"− 𝑟!) + 𝜀!" (20)
Factors Portfolios Alpha Mkt-Rf MT HM 1(Low) -0.00414 (-2.975)*** 0.97722 (23.557)*** -0.89427 (-15.368)*** -0.04410 (-0.657) 2 -0.00340 (-3.131)*** 0.97130 (29.955)*** -0.04289 (-0.943) -0.05667 (-1.080) 3 -0.00298 (-2.663)*** 0.95528 (28.639)*** -0.14826 (-3.169)*** -0.08287 (-1.535) 4 -0.00339 (-3.016)*** 0.97741 (29.169)*** -0.22286 (-4.741)*** -0.05511 (-1.016) 5 -0.00380 (-3.130)*** 0.98590 (27.213)*** -0.27993 (-5.508)*** -0.05514 (-0.940) 6 -0.00376 (-2.959)*** 0.99165 (26.133)*** -0.356001 (-6.688)*** -0.02996 (-0.488) 7 -0.00508 (-3.942)*** 0.98529 (25.604)*** -0.33887 (-6.277)*** -0.03762 (-0.604) 8 -0.00505 (-3.609)*** 1.00843 (24.143)*** -0.46633 (-7.959)*** -0.02698 (-0.399) 9 -0.00406 (-3.107)*** 0.98103 (25.136)*** -0.58748 (-10.730)*** -0.05693 (-0.901) 10(High) -0.00413 (-2.970)*** 0.97694 (23.570)*** 0.10623 (1.827)* -0.04448 (-0.663)
6. Conclusion
The main purpose of this paper is to create a factor model to evaluate the performance, with focus on the market timing ability, of mutual funds. Instead of using the conventional Treynor and Mazuy (1966) and Henriksson and Merton (1981) models to identify the market timing ability. In this paper I extended the Carhart (1997) four factor model with an additional factor to evaluate the performance of a mutual fund with focus on the market timing ability of the fund. The five factor model is easily applicable and is a factor-mimicking portfolio to capture the market timing effect of managers of a mutual fund. The five factors can be considered as diversified passive benchmark returns that capture patterns in average excess returns. The importance of the market timing factor is to identify whether funds behaves like market timers and whether they are successful in doing so. This might be an answer to whether an investor should pay the additional fee to a mutual fund or rather invest in a passively managed fund, that has no market timing ability.
funds, in existence in the CRSP survivorship bias free database from the period between 2002 and 2017.
The five factor model has been tested on both portfolio and individual fund level. At the portfolio level there are 10 portfolios formed by its IRRs. To compare and contrast the five factor model with other factor models, I used five different factor models at portfolio level. Although the GRS test rejected all the factor models tested, the FM test conducted showed that there is enough evidence to take market timing factor into account when evaluating on portfolio level. Furthermore, I have showed that the market timing factor has more explanatory power than both the conventional TM (1966) and HM (1981) models.
On the individual fund level, using a pseudo GRS-statistic, I find that every factor model tested is not rejected. Therefore, the intercepts of all factor models tested, are not statistically significant different from zero at individual fund level. This indicates that the models all describes the average excess return of actively managed funds well. The five factor model in particular did well on the GRS test, with the closest to zero intercept, -0.00252, and the lowest GRS-statistic, 0.54523. Although the FM test rejects the intercept of the five factor model, the market timing factor is significant, and therefore has explanatory power on individual fund level as well as on portfolio level.
Furthermore, time-series regressions on individual fund level showed that around 80% of the funds that exhibit a positive market timing coefficient, have a positive average excess return over the whole sample period. No relation was found between negative market timing coefficient and its average excess return.
The main result of this paper is the five factor model that includes the following factors: market portfolio, size, value, momentum, and the market timing. For the period 2003 to 2017, this five factor model captures most of the cross-sectional variation in average excess returns of mutual funds. This paper showed that market timing factor is a factor on its own and makes the conventional TM (1966) and HM (1981) redundant to evaluate market timing ability of mutual funds.
using the performance gap, also suggested by Dichev (2004) named by Friessen and Sapp (2007). The performance gap is computed as the difference between the dollar-weighted return and the buy-and-hold return. The buy-and-hold return is computed using the geometric average return of an investment project.
References
Banz, R. W., 1981. The relationship between return and market value of common stocks. Journal of Financial Economics 6, 103-26.
Bello, Z. Y., Janjigian, V., 1997. A reexamination of the market-timing and security-selection performance of mutual funds. Financial Analysts Journal 53, 24-30.
Blake, D., Caulfield, T., Ioannidis, C. & Tonks, I., 2017. New Evidence on Mutual Fund Performance: A Comparison of Alternative Bootstrap Methods. Journal of Financial and Quantitative Analysis, 1-21.
Bogle, J., 2002. An Index Fund Fundamentalist. Journal of Portfolio Management - J PORTFOLIO MANAGE 28, 31-38.
Brown, S. J., and Goetzmann, W. N., 1995. Performance persistence. Journal of Finance 50, 679-698.
Carhart, M. M., 1997. On persistence in mutual fund performance. Journal of Finance 52, 57-82. Chance, D. M. and Hemler M. L., 2001. The performance of professional market timers: Daily evidence from executed strategies. Journal of Financial Economics 62, 377–411.
Chau, J. H., Woodward, R. S. and To, E. C., 1987. Potential gains from stock market timing in Canada. Financial Analysts Journal 43, 50-56.
Chen, L. and Chen, H., 2016. Applying a Bootstrap Analysis to Evaluate the Performance of Chinese Mutual Funds. Journal of Emerging markets Finance and Trade 53, 865-876.
Cremers, K.J. and Petajisto, A., 2007. How Active Is Your Fund Manager? A New Measure That Predicts Performance. The Review of Financial Studies 22, 3329–3365.
Cumby, R.E., J.D. Glen, 1990. Evaluating the Performance of International Mutual Funds’, The Journal of Finance, vol 45-2, p. 497-498, 521
Daniel, K., Grinblatt, M., Titman, S., Wermers, R., 1997. Measuring Mutual fund performance with characteristic-based benchmarks. Journal of Finance 52, 1035-1058
Del Guercio, Diane, and Tkac, P. A., 2002. The determinants of the flow of funds of managed portfolios: Mutual funds vs. pension funds, Journal of Financial and Quantitative Analysis 37, 523–557.
Dichev, I. D., 2007. "What Are Stock Investors’ Actual Historical Returns? Evidence from Dollar-Weighted Returns." American Economic Review 97, 386-401.
Fama, F. E., 1972. Components of Investment Performance. Journal of Finance, vol. 27, p. 551-567
Fama F. E., and Macbeth, J. D., 1973. Risk, returns, and equilibrium: Empirical tests. Journal of Political Economy 81, 607-636.
Fama, F. E. and French, K. R., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3-56.
Fama, F. E. and French, K. R., 1996. Multifactor explanations of asset pricing anomalies. Journal of Finance 51, 55-84.
Fama, F. E. And French, K. R, 2010. Luck Versus Skill in the Cross Section of Mutual Fund Returns. Journal of Finance 65, 1915-1947.
Friesen, G. C. And Sapp T. R., 2007. Mutual fund flows and investor returns: An empirical examination of fund investor timing ability. Journal of Banking and Finance 31, 2796– 2816. Gibbons, M. R., Ross, S. A., and Shanken, J., 1989. A test of the efficiency of a given portfolio. Econometrica 57, 1121-1152.
Grinblatt, M. and Titman, S., 1992, The persistence of mutual fund performance, Journal of Finance 47, 1977-1984.
Grinblatt, M. and Titman, S., 1994, A study of monthly mutual fund returns and performance evaluation techniques. Journal of Financial and quantitative analysis 29, 419-444.
Henriksson, D. R., 1981. On Market Timing and Investment Performance. II. Statistical Procedures for Evaluating Forecasting Skills, Journal of Business 54, 513-533.
Henriksson D. R., 1984. Market timing and mutual fund performance: An empirical investigation. Journal of Business 57, 73-96.
Jegadeesh, N., and Titman, S., 1993. Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance 48, 65-91.
Jensen, M. C., 1968. The performance of mutual funds in the period 1945-1964. Journal of Finance 23, 389–416.
Jiang, G. J., Yao, T. and Yu, T., 2007. Do mutual funds time the market? Evidence from portfolio holdings. Journal of Financial Economics 86, 724–758.
Lintner, J., 1965. The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47, 13-37.
Malkiel, B. G., 1995. Return from investing in equity mutual funds 1971 to 1991. Journal of Finance 50, 549–572.
Markowitz, H., 1952. Portfolio selection. The Journal of Finance 7, 77-91.
Mossin, J., 1966. Equilibrium in a Capital Asset Market. Econometrica 34, 768-783.
Yang, L. and Weidi, L., 2015. Luck Versus Skill: Can Chinese Funds Beat the Market? Emerging Markets Finance and Trade 53. 1-15.
Roll, R., 1977. A critique of the asset pricing theory’s tests Part I: On past and potential testability of the theory. Journal of Financial Economics 4, 129-176.
Sharpe, W. F., 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance 19, 425-442.
Sharpe, W. F., 1966. Mutual fund performance. Journal of Business 39, 119–138.
Swinkels, L. and Tjong-A-Tjoe L., 2007. Can mutual funds time investment styles. Journal of Asset Management 8, 123–132.
Treynor, J., 1965. How to rate management of investment funds. Harvard Business Review 43(1), 63-75.
Treynor, J. and Mazuy, K., 1966. Can mutual funds outguess the market? Harvard Business Review 44, 131-136
