The insignificant effect of return dispersion on value-, growth- and
minimum volatility investing.
Student number: 2576740 Name: Tijmen Schagen Study program: MSc Finance
Supervisor: Dr. A. Plantinga
Field keywords: Return dispersion, value investing, growth investing, minimum volatility investing.
Abstract
1.Introduction
On average active managers tend to underperform their benchmark, especially after expenses1. However, De Silva, Sapra and Thorley (2001), argue that the availability of
opportunities to outperform the market, which is measured as the level of return dispersion, should be included in the benchmark managers are supposed to beat. Return dispersion is cross-sectional standard deviation of returns, and measures the deviation between
individual stock returns and the market return. High levels of return dispersion imply more opportunities for managers to either select winning stocks or avoid losing stocks. To grasp the idea of how return dispersion affects the opportunities for active management I provide an illustrative example. Consider two market scenarios; in both scenarios, there are three stocks with monthly returns, together they represent the entire market and are captured in an equally weighted index. Scenario 1: Stock 1 exhibits a return of 10%, stock 2 a return of -3% and stock 3 a return of 8%. Combined the market return is 5%. Scenario 2: Stock 1 exhibits a return of 5.5%, stock 2 a return of 4.5% and stock 3 a return of 5%. Again,
combined the return on the market is equal to 5%. Even though in both scenarios investors are benchmarked against the 5% market return, there is a much larger deviation between individual stock returns and the market return in scenario 1 than in scenario 2. Therefore, due to the high level of return dispersion, scenario 1 clearly provides investment managers a larger opportunity to distinguish themselves from the market index.
A recent study from Reibnitz (2015) shows that more active managers tend to outperform their less active counterparties during periods of high return dispersion. Furthermore, Stivers and Sun (2010) show how the level of return dispersion affects value and momentum premia included in the standard multi-factor benchmark model. Although these studies indicate how return dispersion affects the performance of active management, nothing is known yet about how the level of return dispersion affects the performance of more passive specific investment strategies captured in an index.
Due to the bad performance of the market-cap weighted market index2 and the skepticism
surrounding the merit of active management, investors turned to alternative index
1 See for example: Malkiel (2005), Fama and French (2010) and Petajisto (2013).
2 Market-cap weighted indices tend to perform badly because they overweight overpriced stocks (Arnott, Hsu
concepts3. Generally speaking, index investing is considered as ‘’passive investment’’.
However, as Ranaldo and Haeberle (2008) indicate, this stigma is not justified. Many indices use dynamic stock selection and rebalancing rules which make them active management forms in disguise4. Common alternative index concepts include value- and growth investing.
Several issuers of Exchange traded funds (ETFs) set op funds with solely the goal to track a value- or growth stock oriented index5. Besides the popularity of tracking value and growth
indices; a large amount of assets is contributed to tracking a minimum volatility index. Blackrock currently manages a minimum volatility oriented ETF with 13 billion dollar assets under management. When looking at assets under management of ETF’s; value-, growth- and minimum volatility indices are by far the most popular equity index to track. Given the popularity of each of these strategies, it is interesting to observe how the level of return dispersion affects the returns of a value-, growth- and minimum volatility strategy.
As indicated there is a limited amount of knowledge about how the level of return dispersion affects the performance of other, more passive, investment strategies, such as value-,
growth- and minimum volatility investing. Therefore, the aim of this paper is to answer the following research question: How does the level of return dispersion affect the returns of a value-, growth- and minimum volatility investment strategy.
I contribute to the current literature by exploring the relationship between return dispersion and a set of very popular investment strategies, whereas the current literature mainly focusses on the relationship between return dispersion and managers’ performance. Additionally, I show that not only the level of return dispersion matters but also the
associated state of the market, i.e. are we in an upward or downward market. Whereas the current literature treats return dispersion as a homogenous variable.
This study examines the effect of return dispersion in different states of the market on the performance of several investment strategies. I investigate the effect of return dispersion on the performance of the strategies using monthly strategy returns from 1988 to 2016. MSCI provides indices reflecting the performance of each of the strategies scrutinized in this
3 See Scherer (2011)
4 Do note that the costs associated to these active management forms in disguise are much lower than the
costs associated with actual active management
5 For example: the two largest issuers of ETF’s Blackrock and Vanguard both have ETF’s tracking a value- and
paper. Therefore, the returns of the MSCI indices will serve as a proxy for the performance of the strategies. A multi-factor model, including dummies that indicate the level of return dispersion and the associated state of the market, is used to investigate the effect of return dispersion on the strategy’s performance. The return dispersion variable measures the difference between the market performance and S&P 500 constitutes, in line with Reibnitz (2015).
I show that the effect of high return dispersion on the performance of each of our investment strategies is very limited. Return dispersion only seems to impact the
performance of the minimum volatility strategy. However, this result is very dependent on both the time-frame and return dispersion measure used. Return dispersion does not affect the performance of both a value- and growth strategy. This result shows to be very robust employing different time frames and different return dispersion measures. Lastly, there is no significant difference between the effect of return dispersion on the returns of a value and growth-oriented investment strategy. Again, this result shows to be very robust.
2. Literature review
The concept of active investment and different investment strategies has been subject to plenty of previous research. More recently the subject of return dispersion is used to explain the performance of active fund managers. In this section, I give an overview of the relevant literature on the performance of active management and different the investment
strategies. Additionally, I display papers that explain the concept of return dispersion and its impact on the return of actively managed portfolios. Lastly, I try to connect the current research on both different strategies and cross-sectional volatility to formulate specific hypothesis for this thesis.
2.1 Active fund management
Many studies (Cheng, Jegadeesh and Wermers (2000); Wermers (2003); Fama and French (2010); Malkiel (2003); Malkiel (2005); Petajisto (2013)) find that on average active investors tend to perform worse than the market index. Different authors voice different explanations why on average active managers do not outperform the index. Malkiel (2005) argues that overall active management is a zero-sum game. This implies that whenever one active manager makes a profit another should bear this loss. Malkiel (2015), Fama and French (2010) and Petajisto (2013) all argue that active managers on average underperform the index because of the high costs associated with active management. Active investors on average perform approximately equal to the benchmark index before fees. However, given the high fees for active management, they tend to perform worse than the index.
model. They try to distinguish skill from luck by using a bootstrap method to simulate possible returns. They show that there are some managers who indeed possess the skill to cover the costs associated with active management. However, the return created is hardly better than the return of an efficiently managed passive fund. Even though this thesis uses indices, a strategy widely considered as inactive, as indication for the return of each strategy. It is not inappropriate to compare these indices to an active strategy. As mentioned Ranaldo and Haeberle (2008) argue that commonly used indices are an active management form in disguise. The selection and rebalancing rules make the indices highly dynamic which significantly biases its performance.
2.2. Value and growth stocks
A substantial literature suggest that stocks associated with a high book-to-market ratio, also known as value stocks, have on average a higher return than stocks with a low book-to-market ratio, also known as growth stocks (See for instance: (Fama and French (1992); Fama and French (1995); Lakonishok, Shleifer, and Vishny (1994); Piotroski (2000); Capaul, Rowley, and Sharpe (1993); Haugen and Baker (1996)). Although there is a consensus regarding the fact that value stocks appear to outperform growth stocks there is much debate about the economic reasoning behind this performance difference. Fama and French (1996) argue that stocks with a higher book-to-market ratio are easier subject to financial distress. Therefore, the higher return is a compensation for a higher level of systematic risk. Opposed to Fama and French, Lakonishok et al. (1994) argue that the high returns associated with value stocks compared to growth stocks are generated by investors who incorrectly expect future
performance based on previous growth. They argue that investors are too optimistic about firms that recently performed well and too pessimistic about firms that recently performed poorly. LaPorta, Lakonhishok, Schleifer and Vishny (1997) provide additional empirical evidence in support of this argumentation. They show that during periods of earning
announcements value stocks exhibit positive announcement returns, whereas growth stocks do not. From which they argue that investors are overly pessimistic about future
performance prospects of value firms and overly optimistic about the future performance prospects of growth firms. Furthermore, they argue that these systematic errors in
additionally argue that the price of growth stocks gets pushed upwards by naïve investors, consequently, returns are lower. Daniel and Titman (1997) show that the premium
associated with value stocks is not caused by a higher distress factor. Which suggests that the high returns for high book-to-market stocks cannot be viewed as a compensation for risk, as suggested by Fama and French. Furthermore, Chan and Lakonishok (2004) argue that if the value stock is riskier it should underperform relative to a growth strategy during undesirable states of the world. They identify undesirable states of the world as months when the overall stock market did poorly. Chan and Lakonishok show that value stocks outperform growth stocks when the market return was negative. Whenever the market earned a positive return the value portfolio at least matched the performance of the growth portfolio. Gulen, Xing and Zhang (2011) also find evidence for the countercyclical premium associated with a value-growth strategy, they use a Markov-switching model to show strong countercyclical variation in the value-growth premium.
Although it is not essential for our analysis to show the key driver of the return premium for value stocks, it is valuable to understand when value and growth stock tend to perform well. Identifying the countercyclical nature of the value premium allows us to form hypothesis about the relationship between value- and growth stocks and the level of return dispersion.
2.3 Minimum volatility investing
The opportunity of investing in a minimum volatility strategy, based on the low beta anomaly, is first discovered by Haugen and Heins (1972). Haugen and Heins conclude that: “Over the long run, stock portfolios with lesser variance in monthly returns have
experienced greater average returns than their “riskier” counterparts” (P.26). The concept that lower variance yields higher returns is against the initial idea of the capital asset pricing model (CAPM) initially proposed by Sharpe (1964) and Lintner (1965) following the
weights, subject to several diversification criteria, for 1000 U.S. stocks that would have minimized volatility in the preceding twenty-four months. When created they hold every portfolio for one-quarter before rebalancing based on the new preceding twenty-four-month period. Haugen and Baker show that their low volatility portfolio exhibits larger returns than the Wilshire 5000 benchmark index. Additionally, they show that during the entire period their low volatility portfolio entailed smaller variation than the benchmark index. Overall Haugen and Baker conclude that over the 1972-1989 time-period they employed, there existed investment opportunities to build equity portfolios with equal or greater return but lower volatility than the cap-weighted portfolios. Following their initial analysis, Baker and Haugen (2012) repeated their analysis employing a much broader
investment universe and a new time-frame. Baker and Haugen show that, between 1990 and 2011, in the entire investment universe considered and in each individual country, a low volatility portfolio exhibits larger returns than a high volatility portfolio6, while showing
smaller variances. Baker and Haugen argue that the existence of the low volatility anomaly originates from the nature of manager compensation and agency issues between both professional investment managers within an organization and between professionals and their clients7. Besides Baker and Haugen there are numerous people who find similar results.
Chan et al. (1999), Schwartz (2000), Jagannathan and Ma (2003) and Clarke et al. (2006) all find higher returns and lower realized risk for minimum volatility portfolios compared to a cap-weighted benchmark in the U.S. stock market. Blitz and Van Vliet (2007) find an annual return difference of 12% between low- and high volatility portfolios after controlling for momentum and value premiums. Ang, Hodrick, Xing and Zhang wrote two papers. First, in 2006, they find abnormally low returns in high volatility portfolios. Second, in 2009, they show that stocks with past high idiosyncratic volatility have low future returns in 23 developed markets. Carvalho, Xiao and Moulon (2012) show that in world markets a minimum volatility portfolio achieves the highest Sharpe ratio.
Scherer (2011) illustrates that a minimum volatility portfolio tends to outperform a cap-weighted benchmark in bear markets whereas it tends to underperform the cap-cap-weighted
6They use a technique similar to the technique in Haugen and Baker (1991) to construct these portfolios.
benchmark in bull markets. The economic reasoning behind this result is fairly logic. As a minimum volatility portfolio per definition is subject to smaller changes in value it will suffer less when the market is in a downturn, or a bear market, thereby outperforming the
benchmark. However, when the market is in an upturn or a bull market, the minimum volatility portfolio experiences less upward volatility, thereby underperforming the benchmark.
As with the growth and value strategies knowing the regimes in which the strategy performs well allows us to formulate an economic based logical hypothesis regarding the effect of return dispersion on the performance of the minimum volatility strategy.
2.3 Return dispersion and portfolio returns
Several papers (Gorman, Sapra and Weigand (2010); Ratner, Meric and Meric (2006); Pojarliev and Levich (2008); Ankrim and Ding (2002); De Silva, Sapra and Thorley (2001)) study the relationship between the level of return dispersion and portfolio returns. Gorman et al. (2010) argue that some level of return dispersion is required to provide active
higher during economic regressions, implying that return dispersion tends to be countercyclical.
De Silva et al. (2001) show that the variation in mutual fund performance in the 1991-2001 period was exceptionally large. They argue that this is directly attributable to the wide return dispersion in stocks and not attributable to a sudden increase in managerial talent. De Silva et al. compute the alpha and the corrected alpha, which corrects for the level of return dispersion in the market, for the 25 largest actively managed U.S. equity mutual funds. They show that the average annual alpha earned by a mutual fund can change by up to 2% when correcting for the level of return dispersion in the market8. They argue that the level of
return dispersion in a certain period should be included in a performance evaluation. Earning 10% in a market with low dispersion should be considered as a bigger achievement than earning 10% in a market with high dispersion.
Grant and Satchell (2016) provide a theoretical decomposition of cross-sectional dispersion in stock returns. They identify several scenarios in which expected dispersion is shown to be high. The dispersion between stock returns is expected to be high when the variation between stock returns is high, when the average stock variance is high and when the correlation between stock is relatively low. As concluded by Gorman et al. (2010) the ability to predict high return dispersion has implications for the optimal behavior of active equity investors.
Reibnitz (2015) investigates whether the most active fund managers also tend to perform best in periods of high return dispersion. She shows that return dispersion is persistent over periods. This implies that managers should be able to anticipate on periods with increased potential for active management. She finds that high dispersion indeed significantly
influences fund performances. Furthermore, she concludes that in periods of high dispersion the alpha produced by the most active funds significantly exceeds alpha produced in other months. Additionally, the difference between the performance of the most and least active fund is most substantial in periods of high dispersion.
8 De Silva et al. (2001) argue that performances in years with higher return dispersion should have lower
Stivers and Sun (2010) investigate the impact of return dispersion on the value- and
momentum premium. They argue that since both the value premium and return dispersion are countercyclical that return dispersion should lead to a higher value premium.
Additionally, they argue, that since the momentum premium is pro-cyclical9, they expect a
lower momentum premium when return dispersion is high. Over a 1962-2005 sample, Stivers and Sun indeed find a value premium that is positively related to the level of return dispersion and a momentum premium that is negatively related to the level of return dispersion. Hence given the result of Stivers and Sun we expect our value strategy indicator to perform better during periods of high return dispersion in a downturn market.
2.4 Summary
There is no literature regarding the effect of return dispersion on the performance of value, growth and minimum volatility investing. However, there is a wide variety of literature on the performance of active strategies during periods of high return dispersion and a variety of literature on the performance of the specific strategies during different periods in time. As mentioned above, Gorman et al. (2010) show that return dispersion is highest in bear markets or downturn markets. Moreover, Chan and Lakonishok (2004) and Stivers (2003) show that in general value stocks tend to outperform growth stocks in declining markets. Which makes economic sense as the return of value stocks is more based on fundamentally sound analysis whereas growth returns are based on expected future growth10. Therefore,
one could expect that value stocks tend to perform better in periods of high return
dispersion. Scherer (2011) similarly shows that minimum volatility investing performs best, compared to the market index, in bear markets. Which also is economically speaking logical, minimum variance stocks should show both fewer peaks and troughs. Therefore, we also expect the minimum volatility strategy to produce relatively higher returns in periods of high return dispersion.
Although a combination of literature on separate topics allows us to formulate different hypothesis the lack of empirical evidence makes giving a pronounced certain expectation difficult. Even though Stivers and Sun (2010) show a positive relationship between return dispersion and the value premium, this is based on the notion that both tend to be
3.Methodology
To evaluate the effect of return dispersion on the performance of each index strategy we compare the returns earned on the index with a benchmark model. To directly observe the effect of return dispersion we include dummy variables in our benchmark model. The dummy variables indicate the presence of high or low return dispersion and the associated state of the market. We use the standard Fama-French three-factor model extended with the Carhart (1997) momentum factor as the benchmark model. The initial regression for each index strategy is a standard Ordinary Least Squares (OLS) regression:
𝑟𝑖𝑡− 𝑟𝑓𝑡 = 𝛽𝑖𝑡(𝑀𝑅𝑃𝑡) + ℎ𝑖𝑡(𝐻𝑀𝐿𝑡) + 𝑠𝑖𝑡(𝑆𝑀𝐵𝑡) + 𝑚𝑖𝑡(𝑀𝑂𝑀𝑡)
+ 𝛾1𝑖𝑡(𝐻𝐷𝐷𝑡) + 𝛾2𝑖𝑡(𝐻𝐷𝑈𝑡) + 𝛾3𝑖𝑡(𝐿𝐷𝐷𝑡) + 𝛾4𝑖𝑡(𝐿𝐷𝑈𝑡) + 𝜀𝑖𝑡
(1)
Where ri represents the monthly return of index strategy i, rf represents the risk-free rate,
MRP represents the market risk premium, HML, SMB, and MOM represent the value
premium, small stock premium and momentum premium all available on the Kenneth French’s website11. HDD indicates high return dispersion while in a downward market, HDU
indicates high return dispersion in an upward market, LDD represents low return dispersion in a downward market and lastly LDU represents low return dispersion in an upward market,
εt represents the error term of our regression.
Return dispersion is set to be high when the level of return dispersion in period t exceeds the average level of return dispersion during the entire sample period. Consequently, return dispersion is set to be low when the return dispersion in period t is below the average level of return dispersion. The cutoff point of the average is relatively arbitrary. Moreover,
Reibnitz (2015) shows that active investors tend to significantly outperform their benchmark only in the highest quintile of return dispersion (highest 20%), therefore as robustness test, or additional check, the analysis is also performed using dummies with higher cutoff points (i.e. highest 20%). Expected is that the effects are more pronounced when using higher cutoff values. As previously mentioned, the performance of the different strategies tends to be related to the cycle of the entire market, i.e. value stocks tend to outperform growth stocks in bearish markets and a minimum volatility strategy also strives in a bearish market.
Therefore, we deem it appropriate to make a distinction between the effect of return dispersion on these strategies both in upward markets (or bullish) and downward markets (or bearish). An upward market is considered as the monthly return in period t of the S&P 500 exceeding its average monthly return over the entire period. Consequently, a downward market is considered as the monthly return in period t of the S&P 500 being beneath its average monthly return over the entire period12.
Equation 1 measures the performance of each of the strategies during the same period the return dispersion is present. To assess the ability of managers to use these strategies after they observe dispersion (e.g. have an active response to the presence of high return dispersion) we also run the regression using lagged dispersion dummies. Where the lag represents high or low return dispersion in either an upward or downward market in the previous month. Formally this is expressed as:
𝑟𝑖𝑡− 𝑟𝑓𝑡 = 𝛽𝑖𝑡(𝑀𝑅𝑃𝑡) + ℎ𝑖𝑡(𝐻𝑀𝐿𝑡) + 𝑠𝑖𝑡(𝑆𝑀𝐵𝑡) + 𝑚𝑖𝑡(𝑀𝑂𝑀𝑡) + 𝛾1𝑖𝑡(𝐻𝐷𝐷𝑡−1)
+ 𝛾2𝑖𝑡(𝐻𝐷𝑈𝑡−1) + 𝛾3𝑖𝑡(𝐿𝐷𝐷𝑡−1) + 𝛾4𝑖𝑡(𝐿𝐷𝑈𝑡−1) + 𝜀𝑖𝑡 (2)
Positive coefficient parameters for either of the dummy variables implies that investors can gain by switching to the particular strategy after they observe the state of the market associated to the dummy with the positive coefficient.
As indicated the initial regression for each index strategy is an OLS regression. However, financial data often suffers from volatility clustering; the amplitude of stock returns varies over time13. Estimations that show to have inconsistent variance over time suffer from
AutoRegressive Conditional Heteroskedasticity (ARCH) effects, which results in unreliable standard errors and thereby miscalculated t-statistics. Therefore, each regression is tested for ARCH effects, whenever ARCH effects are present the model is estimated using
Generalized ARCH (GARCH) variance estimators. GARCH variance estimators were first introduced by Engle and Bollerslev (1986). A GARCH model does not only model the
12 The dummy variable high dispersion down (HDD) receives a 1 if the period is identified as high return
dispersion and a declining, i.e. below average, market return. Consequently, the dummy variable high dispersion up (HDU) receives a 1 if the period is identified as high return dispersion and an upward, i.e. above average, market return. Vice versa low dispersion down (LDD) receives a 1 if the period is identified as low return dispersion and a below average market return, and low dispersion up (LDU) receives a 1 when the period has low return dispersion and an above average market return.
relationship between coefficients but also models the variance. The use of the GARCH variance estimator makes our estimated standard errors reliable, which consequently makes the t-statistics interpretable
Given previous research, we identify several expectations regarding the effect of return dispersion. First, given the countercyclical performance of the minimum volatility strategy, we would expect a positive relationship between high return dispersion in downward markets and the performance of the minimum volatility strategy. Vice versa we would expect a negative relationship between high return dispersion in upward markets and the performance of the minimum volatility strategy14. Second Stivers and Sun (2010)
show that periods of high return dispersion lead to positive payoffs for a value-growth strategy. The positive payoffs are caused by the countercyclical nature of both the performance of a value-growth strategy and the level of return dispersion in the market. Given that our dummy variable HDD is countercyclical by construction (it is contingent on poor market performance) and HDU is pro-cyclical by construction (it is contingent on good market performance) we make a distinction between the effect of high return dispersion in both states of the market. Therefore, we expect a higher effect of high return dispersion in downward markets on the return of value stocks than of growth stocks. Vice versa we expect a higher effect of high return dispersion in upward markets on the return of growth stocks than of value stocks15. Third, to test how applicable the strategies are for investment
managers we test the performance of a certain strategy in the period after return dispersion took place. Given the current lack of research on this subject, the hypothesis is the same for each strategy. We test whether both high return dispersion in upward and downward market has an effect different from zero on the returns of each strategy in the subsequent period16.
3.1 Computation of return dispersion
14 In terms of symbols we would expect: γ1mv > 0 and γ2mv < 0. Where the mv subscript indicates that the gamma
coefficients are the result of regressing equation 1 with the minimum volatility strategy returns as dependent variable.
15 In terms of symbols: γ1v – γ1g > 0 and γ2v – γ2g < 0, where the v and g subscript indicate the results from
equation 1 using returns of the value and growth strategy as dependent variable.
16 In terms of symbols: γ1i ≠ 0 and γ2i ≠ 0
, where both coefficients are calculated using equation 2. The i subscript
Return dispersion (RD) measures the degree of variation in individual stock returns in a given investment period. In line with Reibnitz (2015), we consider the level of return dispersion in the American stock market. Following Reibnitz (2015) and Stivers and Sun (2010), return dispersion is measured based on equal weighting of returns and is computed as:
𝑅𝐷𝑡 = √ 1
𝑛 − 1∑(𝑟𝑖𝑡− 𝑟𝑚𝑡)2
𝑛 𝑖=1
(3)
Where RDt represents the monthly return dispersion in period t, n represents the amount of stocks included in the market, rit represents the monthly return of stock i in period t and rmt represents the equally weighted average monthly return of the S&P 500.
As indicated by Reibnitz (2015), an equally weighted dispersion measure may not fully represent the dispersion in the universe applicable to most investors17. Therefore, we also
compute the level of return dispersion when assuming value weighted return dispersion. The value weighted return dispersion should be a more realistic representation of the investment opportunities in the market. The value weighted level of return dispersion is equal to:
𝑅𝐷𝑡 = √∑ 𝜔𝑖𝑡∗ (𝑟𝑖𝑡− 𝑟𝑚𝑡)2 𝑛
𝑖=1
(4)
Where ωit represents the weight, based on market value, of the individual stock at time t. And rmt represents the market cap weighted average monthly return on the S&P 500 at time t.
The weights of individual stocks are computed as follows: 𝜔𝑖𝑡 = #𝑖𝑡∗ 𝑃𝑖𝑡
∑𝑛𝑖=1#𝑖𝑡∗ 𝑃𝑖𝑡
(5)
17 For example: large dispersion caused by small stocks might not be fully exploitable because of potential price
Where #it represents the number of shares outstanding for firm i during period t and Pit represents the price of one share of company i during period t18.
4. Data
This chapter first describes the sources of dependent and independent variables used in the empirical analysis. Additionally, summary statistics of the variables and interaction between the variables are displayed and interpreted. Given the data availability, the main analysis includes a time-span of 1988-2016, for the investment strategies investing in small stocks the time-span is shorter given the limited availability of return data.
4.1 Data sources
The dependent variables are the monthly returns on multiple investment strategies. For each strategy, the return of the US index following that certain strategy is used. Monthly data on the performance of the value, growth and minimum volatility strategies for both normal sized and small sized stocks is obtained from www.msci.com20. Table 4.1 gives an
overview of all the indices used, how they are referred to in this paper, their official name and the associated MSCI index code.
Table 4.1: Indices used within this study
Referred to as Official MSCI Index name
MSCI-index code
Value normal USA VALUE 105826
Value small USA SMALL VALUE 655133
Growth normal USA GROWTH 105825
Growth small USA SMALL GROWTH 655238
Minimum Volatility
normal USA MINIMUM VOLATILITY (USD) 139133
Minimum Volatility small
USA SMALL CAP MINIMUM VOLATILITY
(USD) 706550
18 The Compustat database does not have prices available for each period. When prices are not available they
report the bid-ask average. Whenever this is the case, the bid-ask average is used to compute the market value.
19 To be precise: https://www.msci.com/end-of-day-data-search, for a thorough explanation of the
composition of these indices check:
For each strategy, the monthly gross return, i.e. including dividends and before taxes, is included. For both the value and growth strategy for normal stocks monthly data is available from 1970 till 2016, however, the minimum volatility strategy has monthly data available from 1988 till 2016. Therefore, to prevent inappropriate comparisons for strategies investing in larger stocks, the main timespan considered is 1988-2016. For the equivalent strategies but in smaller cap stocks data is available from 1994 onwards for growth and value
strategies and from 2001 and onwards for the minimum volatility strategy. Again, to prevent inappropriate comparisons the effect of return dispersion on the small-cap strategies are estimated using the period 2001-2016. Note that the large discrepancy between time-frames restricts us from observing a potential size effect (i.e. comparing the effect of return dispersion on normal sized value stock and small sized value stocks requires adapting the time-frame used for normal sized value stocks).
The HDD, HDU, LDD and LDU parameters described in the methodology section are manually created using data on American stock constitutes. In line with Reibnitz (2015) the CRSP/Compustat Merged Database is used to obtain data on the return of S&P 500
constitutes. The CRSP database is also used to compute market values of the independent stocks included in the market to obtain value weighted return dispersion parameters. The control variables included in our regression to create a benchmark, the market risk premium, the value premium, the small-stock premium and the momentum premium, are all obtained from Kenneth French’s website21. For each premium, the monthly values are taken
considering US firms only.
4.2 Levels of return dispersion
Figure 4.1 and figure 4.2 below represents the levels of return dispersion and their average both employing a value weighted and equal weighted approach.
Figure 4.1: Time series plot value weighted return dispersion
As observable in figure 4.1 there are two distinct waves of periods with high return
dispersion, although every period in which the return dispersion is above the average level is considered as a period with high return dispersion. Clearly observable is the period from 1999 to 2002, which coincides with the tech-bubble during. And the second period from late 2008 to 2009, during which the US subprime mortgage market crisis turned into an
international banking crisis with the collapse of Lehman Brothers.
Figure 4.2: Time series plot equally weighted return dispersion
Figure 4.2 illustrates the level of return dispersion using the equal weighting technique described in the methodology section. In general, the equal weighted dispersion is much higher than the value weighted return dispersion. This indicates that small stocks, who receive a higher weight in the equal weighting approach, tend to diverge more from the overall market than larger stocks do. This difference becomes very noticeable in the early 1990’s. During this period, the return dispersion based on value weighting is moderate and fluctuates around the average level, whereas the equal weighting approach shows several months of very high return dispersion. Given that we treat above average dispersion as a homogenous group22 the main concern is whether both approaches identify the same
periods as periods with high return dispersion. Panel A in the appendix provides an overview of the number of periods identified as high return dispersion within each year for both strategies, overall 246 months out of 343 total months are labeled the same, implying that approximately 72% of the months are valued a certain way independent of the measure used. Given this relatively large difference, the effect of return dispersion is estimated using both measures. Table 4.2 represents the number of months each method identifies as high dispersion in downward markets and high dispersion in upward markets, as well as low dispersion in both upward- and downward markets.
Table 4.2: Number of HDD, HDU, LDD and LDU parameters
Method:
Value weighted
Equal weighted
High dispersion down 54 58
High dispersion up 61 83
Low dispersion down 97 93
Low dispersion up 131 109
Total 343 343
Table 4.2 illustrates that both methods identify approximately the same amount of
downward markets with high return dispersion. Nevertheless, the equal weighting approach identifies much more months of high return dispersion in upward markets. This implies that mainly in upward markets small stocks’ performance tends to deviate from the markets’
22 The period receives the label high dispersion whenever the level exceeds the average and is not dependent
performance23. Consequently, we also observe that the value weighted dispersion measure
identifies more periods of low dispersion while in an upward market.
4.3 Dependent variables
Table 4.3 below represents the descriptive statistics for the monthly returns of each of the index used.
Table 4.3: Descriptive statistics monthly returns of each index strategy
Time-period: Full sample (1975-2016)
Index24: Minimum Volatility Small Minimum Volatility normal Growth normal Value normal Value small Growth small S&P 500 Mean 0.009 0.009 0.009 0.010 0.009 0.008 0.008 Median 0.017 0.012 0.011 0.013 0.016 0.017 0.010 Maximum 0.089 0.094 0.139 0.135 0.177 0.206 0.132 Minimum -0.182 -0.157 -0.250 -0.226 -0.228 -0.266 -0.218 Std. Dev. 0.039 0.033 0.048 0.042 0.049 0.064 0.043 Skewness -1.171 -0.764 -0.665 -0.832 -0.866 -0.701 -0.535 Kurtosis 6.030 5.158 5.277 6.214 5.827 4.934 5.027 Observations 189 345 506 506 273 273 504 Data availability: 2001-2016 1988-2016 1975-2016 1975-2016 1994-2016 1994-2016 1975-2016
Table 4.3 shows that the returns of all strategies are negatively skewed and have fat, or leptokurtic, tails25. This implies that the return distribution is not exactly normal, negative
returns are more likely to appear. Additionally, large deviations from the mean appear more often than in normally distributed data. We also observe the that is associated with value stocks have higher mean returns than growth stocks. Further, we observe that the minimum volatility strategies have the lowest standard deviations. The tables in Appendix B illustrate the movement of the strategies during different 5-year time periods. We observe both the negative skewness and leptokurtic tails for each of the 5 year periods.
23 Note that we cannot say whether these small stocks perform better or worse than the market, given that
return dispersion just measures the distance from the overall market performance.
24 For the official names of these indices see table 4.1, the reported names in table 4.2 are in the first column of
table 4.1 under the header: ‘referred to as’.
25 The presence of leptokurtic tails in stock returns is shown by Kendall (1952) and Moore (1962) and is now
4.3 Explanatory variables
Table 4.3 below represents the descriptive statistics for the explanatory variables employing our most used timeframe 1988-2016.
Table 4.4: Descriptive statistics explanatory variables
Time period: 1988-2016
Variable: MRP RF HML SMB MOM HDD HDU LDD LDU
Mean 0.007 0.003 0.002 0.001 0.006 0.157 0.178 0.283 0.382 Median 0.012 0.003 0.000 0.001 0.006 0 0 0 0 Maximum 0.114 0.008 0.129 0.221 0.184 1 1 1 1 Minimum -0.172 0.000 -0.113 -0.172 -0.346 0 0 0 0 Std. Dev. 0.042 0.002 0.030 0.032 0.048 0.365 0.383 0.451 0.487 Skewness -0.640 0.246 0.171 0.781 -1.570 1.881 1.685 0.965 0.486 Kurtosis 4.213 1.917 5.734 11.734 14.494 4.539 3.839 1.930 1.236 Observations 343 343 343 343 343 343 343 343 343
Note: HDD, HDU, LDD and LDU represent the dummy variables used in the regression, not initial values of return dispersion.
From Table 4.4 we observe that on average investors receive a monthly premium of 70 basis points for investing in the equity market. Value stocks receive on average a 20-basis points premium over growth stocks. However, this premium fluctuates substantially with a standard deviation of 3% per month. On average small stocks earn a premium of 10 basis points over big stocks, again this premium fluctuation is large with peaks of a 22.1%
Table 4.4: Correlation matrix explanatory variables
Correlation MRP RF HML SMB MOM HDD HDU LDD LDU
MRP 1 RF -0.020 1 HML -0.178 0.001 1 SMB 0.217 -0.105 -0.276 1 MOM -0.245 0.113 -0.194 0.051 1 HDD -0.545 0.007 0.146 -0.058 0.193 1 HDU 0.460 0.060 -0.148 0.099 -0.219 -0.201 1 LDD -0.402 -0.035 0.035 -0.097 0.018 -0.271 -0.292 1 LDU 0.419 -0.020 -0.026 0.055 0.011 -0.340 -0.366 -0.494 1
5 Results
5.1 Strategy performance and high return dispersion
The results of our regression from Equation 1, the excess return of each strategy including dummies for high dispersion in the upward and downward market and low dispersion in an upward and downward market, are represented below in Table 5.1. Table 5.1 only includes the regression for the normally sized benchmark strategies. Table 5.2 represents the same regression from Equation 1 but for small sized benchmark strategies. The reason for this split is explained in the data section.
Table 5.1: Regression equation 1 normal sized benchmark strategies, period 1988-2016.
Strategy: Growth Minimum Volatility Value
Bi T-stat Bi T-stat Bi T-stat
MRP 1.044 58.329*** 0.819 43.146*** 0.942 64.142*** HML -0.262 -13.981*** 0.155 8.267*** 0.272 17.353*** SMB -0.131 -7.392*** -0.222 -12.984*** -0.183 -10.560*** MOM 0.042 3.173*** 0.028 1.784* -0.048 -4.237*** HDD 0.000 -0.135 0.004 2.624*** -0.001 -0.500 HDU -0.001 -0.900 -0.004 -2.501** 0.000 -0.442 LDD 0.000 -0.278 0.000 0.350 -0.002 -2.130** LDU -0.001 -1.247 0.000 0.288 0.000 0.520 R2 0.944 0.882 0.953
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level
From Table 5.1 we observe several features. First, in line with Fama and French (1993), the growth stocks have a negative relationship with the value premium whereas the value stock has a positive relationship with the value premium. The minimum volatility strategy tends to be value stock oriented given its positive and statistically significant coefficient for the value premium. Additionally, we observe that especially growth stocks tend to perform
coefficient of 0.004 for high return dispersion in downward markets and a negative coefficient of 0.004 of high return dispersion in upward markets. Implying that during periods of high return dispersion the monthly returns of the minimum volatility strategy are 0.4% higher (lower) when in a downward (upward) market. The results from Table 5.1 allow us the accept our first hypothesis, the minimum volatility strategy tends to perform better during periods of high return dispersion in a downward market, and tends to perform worse in a period of high return dispersion in an upward market. Or: the relationship between return dispersion and the return on minimum volatility investing is countercyclical. This result is in line with expectations based on previous literature, as for example, Scherer (2011) showed that minimum volatility strategies tend to perform better in bear markets. It, however, gives a new insight to the current literature in the sense that the state of the market combined with the presence of high return dispersion significantly impacts the performance of the minimum volatility strategy. Note that we can say this result is not purely driven by the performance of the overall market, the dummy variables indicating the same state of the market, but with low return dispersion, have coefficients equal to zero and are highly insignificant.
Lastly, we observe that the presence of high return dispersion does not significantly affect the returns of the value investment strategy. The coefficients for both dummy parameters indicating high return dispersion are close to zero and statistically insignificant. We do observe that the value strategy has lower monthly returns, equal to 0.2%, during periods of low return dispersion in downward markets.
Table 5.2 below represents the results from equation 1 but now for the benchmark strategies investing in small-cap stocks. Data for small stock benchmark strategies is
available from 2001 to 2016, therefore this is the time-frame considered for these strategies. Contrary to the normal sized indices we observe an insignificant effect of high return
frame for both regressions. Both options are evaluated later in the chapter. Additionally, we observe that, contrary to the normal sized minimum volatility strategy, the small sized minimum volatility strategy performs better during periods of low return dispersion in downward markets. During periods of low return dispersion in downward markets the small sized minimum volatility earns monthly returns 0.4% higher than the four-factor benchmark model.
Further, we observe that periods of high return dispersion in a downward market
significantly affects the returns of small growth stocks. During these periods, small growth stocks earn lower monthly returns equal to approximately 60 basis points. The effect of high return dispersion on the returns of a value stock oriented strategy is independent of the size of the stocks considered. High return dispersion has no significant effect on the returns of both the small and normal sized value strategies.
Table 5.2: Regression equation 1 small sized benchmark strategies, period 2001-2016.
Strategy: Growth Minimum Volatility Value
Bi T-stat Bi T-stat Bi T-stat
MRP 1.087 33.750*** 0.776 20.690*** 1.006 33.905*** HML -0.075 -2.159** 0.142 3.943*** 0.339 11.060*** SMB 0.709 27.056*** 0.457 10.761*** 0.549 16.894*** MOM 0.020 0.987 0.088 3.561*** -0.026 -1.658* HDD -0.006 -2.855*** 0.001 0.451 -0.001 -0.478 HDU -0.003 -1.190 0.002 0.613 -0.002 -0.729 LDD 0.001 0.720 0.004 1.745* 0.001 0.764 LDU -0.001 -0.653 0.001 0.370 -0.002 -1.769* R2 0.968 0.885 0.965
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level
5.2 Can investors benefit from strategy switching after observing high return dispersion
Table 5.3: Regression equation 2 normal sized benchmark strategies, period 1988-2016
Strategy: Growth Minimum Volatility Value
Bi T-stat Bi T-stat Bi T-stat
MRP 1.038 84.707*** 0.786 55.790*** 0.956 86.239*** HML -0.261 -13.665*** 0.156 8.058*** 0.270 16.437*** SMB -0.134 -7.215*** -0.218 -12.020*** -0.183 -10.034*** MOM 0.043 3.377*** 0.033 2.180** -0.047 -4.076*** HDDt-1 -0.001 -1.291 -0.001 -1.051 -0.002 -2.235** HDUt-1 0.001 0.657 0.001 0.441 -0.003 -2.861*** LDDt-1 0.000 0.236 0.002 1.726* 0.000 -0.655 LDUt-1 -0.001 -1.946* 0.000 -0.533 0.000 0.140 R2 0.944 0.881 0.954
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level
Table 5.3 shows that for both the growth and minimum volatility strategy the coefficients associated with high return dispersion in the previous month are close to zero and
statistically insignificant. Implying that for these strategies high return dispersion in period 0 is not a good predictor of returns in period 1. Opposed to the positive effect of return dispersion in a downward market in the current period, the lagged version has no impact on the performance of the minimum volatility strategy. Implying that investors could reap positive returns due to high return dispersion in downturn markets from being invested in a minimum volatility strategy, but only if they are already invested. Switching to the minimum volatility strategy yields no additional returns. We do observe that there are small effects from low return dispersion in period 0 on the returns of both a growth strategy and a minimum volatility strategy in period 1.
The returns of value stocks are significantly impacted by the presence of high return dispersion in the previous period. When return dispersion is high and the market is in a downturn (upturn) the value strategy earns 0.2% (0.3%) less in the subsequent period. Implying that investors should not switch to a value-oriented strategy after they observe high return dispersion in the current period26. Overall, we reject our third hypothesis for
both the growth- and minimum volatility strategy; there is no impact of high return dispersion on the returns in the subsequent period. We do accept our third hypothesis for
the value strategy; there is a significant negative impact of high return dispersion on the returns in the subsequent period.
Table 5.4 indicates the effect of high return dispersion in previous months on the different strategies considering small stocks only. Again, as above the effect on small stock returns are computed using a small sample and should, therefore, be compared with caution. From Table 5.4 we observe that both the performance of small growth and value stocks is
independent of return dispersion in the previous period. Both show negative coefficients for high return dispersion in a downward market and positive coefficients for high dispersion in an upward market. Yet, neither of these coefficients are statistically different from zero. Further, we observe that return dispersion in a downward market causes significantly lower returns, equal to 40 basis points, for a small minimum volatility strategy in the subsequent period. This is somewhat contrary to the results of Reibnitz (2015) who shows that in the subsequent month after a period of high return dispersion active strategies tend to outperform less active strategies. Yet, we observe that the most active strategy included, based on the measure of R2, exhibits the worst performance in the subsequent period. We
also observe that small growth stocks perform badly after a period where return dispersion is low and the market in a downturn. Contrary to the minimum volatility strategy who performs significantly better after periods where the market is in a downturn but dispersion is low. Overall Table 5.4 confirms the general message of Table 5.3; high return dispersion is not a good predictor of returns in the subsequent period.
Table 5.4: Regression equation 2 small sized benchmark strategies, period 2001-2016
Strategy: Growth Minimum Volatility Value
Bi T-stat Bi T-stat Bi T-stat
MRP 1.089 53.450*** 0.756 36.696*** 0.985 57.777*** HML -0.080 -2.494** 0.124 3.352*** 0.344 10.888*** SMB 0.696 28.041*** 0.455 11.262*** 0.543 16.464*** MOM 0.032 1.626 0.087 3.546*** -0.024 -1.474 HDDt-1 -0.003 -1.371 -0.004 -1.707* -0.002 -1.182 HDUt-1 0.000 0.017 0.004 1.305 0.002 0.571 LDDt-1 -0.003 -2.926*** 0.004 2.526** -0.001 -0.546 LDUt-1 0.001 1.142 0.002 1.305 -0.001 -1.345 R2 0.967 0.885 0.966
5.3 Return dispersion and the value premium
Stivers and Sun (2010) indicate that they expect a higher value premium during periods of high return dispersion. This is caused by the fact that both the level return dispersion and the returns of a long-value short-growth strategy tend to be countercyclical27. Therefore, we
examine whether employing a value-growth strategy for both normal size and small stocks produces significant premiums caused by the presence of high return dispersion both in the current period and in the previous period. As indicated in the methodology section, we would expect a positive value premium for high return dispersion in a downward market, and a negative value premium for high return dispersion in an upward market. Table 5.5 measures the difference between the estimated coefficients for a value- and a growth strategy. The significance of this differences is tested calculating the z-score, a method explained by Clogg et al. (1995) and Cohen (1983). The z-scores compares coefficients assuming unequal variances and is computed as:
𝑧 = 𝛾𝑣− 𝛾𝑔 √𝑠𝑣2+ 𝑠𝑔2
(6) where γv represents the coefficient for the value strategy, γg the coefficient for the growth strategy, sv the standard deviation of the value strategy and sg the standard deviation of the growth strategy. All coefficients and standard deviations are obtained running regressions associated with equation 1 and 2. For the small size strategies, the differences are based on the 2001-2016 period, for the normal size strategies the differences are based on the 1988-2016 period.
Table 5.5: Return dispersion and a value-growth strategy:
Size: Normal Small
Value-Growth Z-score Value-Growth Z-score
HDD 0.000 -0.317 0.005 1.551 HDU 0.001 0.622 0.001 0.254 LDD -0.001 -1.876* 0.000 -0.112 LDU 0.001 1.784* -0.001 -0.664 HDDt-1 -0.001 -0.595 0.001 0.501 HDUt-1 -0.003 -2.201** 0.002 0.555 LDDt-1 -0.001 -0.639 0.003 2.426** LDUt-1 0.001 1.375 -0.002 -2.603***
27 Countercyclical in the sense that levels of return dispersion are high when market returns are low and vice
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level.
Table 5.5 shows that there are very small insignificant differences between the effect of high return dispersion on a value strategy and a growth strategy. For both the small and normal sized strategy the difference between the effect of high return dispersion on returns in the current period is statistically insignificant. Thereby we reject our second hypothesis; there is no significant difference between the effect of high return dispersion on the returns of growth and value stocks. There are a few possible explanations for the insignificant
differences between the effect of high return dispersion on the return of value and growth strategies. First, it could be the case that high return dispersion simply does not affect the returns of these relatively passive investment strategies. If so it is logical to observe no statistical differences between the effect of high return dispersion on the returns of value- and growth investing. Second, Stivers and Sun (2010) indicate that there should be a value premium associated with high return dispersion, given that we employ a four-factor model extended with our dummy variables to explain the returns of each strategy, this value premium could already be captured by our control variables28. Table 4.4, in the data
chapter, illustrates the correlation matrix of our explanatory variables. From Table 4.4 we clearly observe a positive correlation between the value premium and high return dispersion in downward markets, and a negative correlation between high return dispersion in upward markets. Additionally, we observe that this correlation is much smaller for our dummy variables indicating both low dispersion in downward and low dispersion in an upward market. Suggesting that some of the value premium associated with high return dispersion could be included in a basic four-factor benchmark model. Table 5.6 below illustrates the different effect of high return dispersion on the returns of a value- and a growth strategy when the HML factor is excluded from equation 1 and equation 2. Or, Table 5.6 allows us to observe whether any potential effect of high return dispersion is already included in the value premium initiated by Fama and French. Table 5.6 indicates that excluding HML from our regression only reduces the difference of the impact of high return dispersion on the return of a value- and a growth strategy. Thereby rejecting the possibility that the effect of high return dispersion is already included in the HML parameter. Which leaves us to believe
that high return dispersion does not have a significant impact on the difference in returns of value- and growth strategies.
Table 5.6: Return dispersion and a value-growth strategy, excluding HML:
Size: Normal Small
Value-Growth Z-score Value-Growth Z-score
HDD -0.001 -0.488 0.004 0.967 HDU 0.000 -0.275 0.001 0.245 LDD 0.000 0.011 0.001 0.347 LDU 0.003 1.826* 0.000 -0.202 HDDt-1 -0.003 -1.251 0.000 -0.013 HDUt-1 -0.002 -1.079 0.003 0.777 LDDt-1 -0.001 -0.609 0.002 1.209 LDUt-1 0.003 3.063*** -0.001 -0.423
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level. Z-scores are calculated following equation 6.
5.4 Robustness checks
This paragraph employs a variety of checks to observe how our results change when several changes to the construction of our return dispersion variable are made. Further, it checks whether the results are consistent over time, i.e. if we split the entire time-period into blocks of 5 years do we get similar results.
5.4.1 Equal weighted dispersion dummy’s
Like the value weighted approach, this section presents the returns of each strategy using the equal weighted return dispersion dummies for that period. This section also presents the returns for each strategy using the return dispersion dummies for the previous period.
Table 5.7: Equal weighted regression equation 1 normal sized benchmark strategies, period 1988-2016
Strategy: Growth Minimum Volatility Value
Bi T-stat Bi T-stat Bi T-stat
LDU -0.001 -0.962 0.000 -0.021 0.001 0.762
R2 0.943 0.881 0.954
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level
There are some noteworthy differences between the value weighted return dispersion effects from table 5.1 and the equal weighted return dispersion effects from table 5.7. First, is the sudden insignificance of the minimum volatility strategy. Using value weights confirms our hypothesis of a countercyclical effect for the minimum volatility effect. Whereas the equal weighted approach finds strictly statistically insignificant effects. Second, we observe that using an equally weighted approach finds negative significant effects of high return dispersion in upward markets on the return of a growth investing strategy, whereas a value weighted approach finds strictly insignificant impacts. We do however still observe that high levels of return dispersion do not affect the returns of a value-oriented investment strategy, as the coefficients are still insignificant. Table 5.8 below represents the similar regression but for small-cap stocks.
Table 5.8: Equal weighted regression equation 1 small sized benchmark strategies, period 2001-2016
Strategy: Growth Minimum Volatility Value
Bi T-stat Bi T-stat Bi T-stat
MRP 1.099 36.478*** 0.768 21.503*** 1.008 40.545*** HML -0.070 -2.139* 0.150 3.932*** 0.345 10.997*** SMB 0.706 25.587*** 0.479 11.255*** 0.555 17.347*** MOM 0.021 1.057 0.065 2.324** -0.029 -1.761* HDD -0.007 -2.062** -0.002 -0.463 -0.002 -0.693 HDU -0.003 -0.654 -0.005 -1.387 -0.003 -1.019 LDD 0.001 0.697 0.004 2.257** 0.001 0.764 LDU -0.002 -1.127 0.002 1.005 -0.002 -1.899* R2 0.967 0.889 0.966
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level
Table 5.8 does not change the conclusion initially drawn from table 5.2 As with value
significant alpha in periods of low return dispersion while the market is in a downturn. And the small value strategy earns significant negative returns during periods of low return dispersion when the market is in an upturn. Hence the results for small-cap investment strategies are very robust independent of the return dispersion measure used.
Table 5.9 and 5.10 below represent the regression of equation 2 using equally weighted return dispersion parameters.
Table 5.9: Equal weighted regression equation 2 normal sized benchmark strategies, period 1988-2016
Strategy: Growth Minimum Volatility Value
Bi T-stat Bi T-stat Bi T-stat
MRP 1.036 86.294*** 0.787 57.950*** 0.960 100.541*** HML -0.260 -13.861*** 0.159 8.261*** 0.269 16.618*** SMB -0.134 -7.225*** -0.217 -12.214*** -0.184 -10.166*** MOM 0.042 3.338*** 0.033 2.172** -0.044 -3.804*** HDDt-1 -0.001 -0.727 0.000 0.339 -0.001 -0.945 HDUt-1 0.000 -0.151 0.000 0.023 -0.002 -1.857* LDDt-1 0.000 0.175 0.001 1.027 -0.001 -1.343 LDUt-1 -0.001 -1.469 0.000 -0.294 0.000 0.191 R2 0.944 0.881 0.953
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level
Table 5.10: Equal weighted regression equation 2 small sized benchmark strategies, period 2001-2016
Strategy: Growth Minimum Volatility Value
Bi T-stat Bi T-stat Bi T-stat
MRP 1.083 57.500*** 0.759 34.575*** 0.983 56.169*** HML -0.082 -2.623** 0.147 4.181*** 0.339 11.148*** SMB 0.702 27.920*** 0.463 11.159*** 0.546 16.832*** MOM 0.035 2.097** 0.088 3.436*** -0.016 -0.977 HDDt-1 0.000 0.197 0.004 1.351 0.003 1.153 HDUt-1 0.003 1.106 0.004 0.856 0.001 0.416 LDDt-1 -0.003 -3.438*** 0.001 0.810 -0.001 -1.326 LDUt-1 0.001 0.902 0.002 1.027 -0.001 -1.258 R2 0.965 0.885 0.966
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level
Table 5.10 illustrates some minor differences from table 5.4. In Table 5.4 we observe a significant negative impact of high return dispersion in downward markets on the return of the minimum volatility strategy in the subsequent month. Using equally weighted return dispersion indicates no significant impact of high return dispersion on either of the strategies returns in the subsequent month.
Table 5.11 represents the effect of equal-weighted return dispersion variables on the performance of a value – growth strategy.
Table 5.11: Equal weighted return dispersion and a value-growth strategy.
Size: Normal Small
Value-Growth Z-score Value-Growth Z-score
HDD -0.001 -0.845 0.005 1.090 HDU 0.001 0.980 0.000 0.080 LDD -0.001 -1.149 0.000 -0.025 LDU 0.001 1.218 -0.001 -0.415 HDDt-1 0.000 -0.149 0.002 0.632 HDUt-1 -0.001 -1.211 -0.001 -0.396 LDDt-1 -0.001 -1.065 0.002 1.446 LDUt-1 0.001 1.178 -0.002 -1.525
Table 5.11 confirms the results initially drawn from Table 5.5. There is no significant difference between the effect of high return dispersion on the returns of a value-strategy and a growth strategy. Table 5.11 even indicates that there are no differences independent of both the level of return dispersion and the state of the market. This implies that all differences between the returns of value and growth stocks are already captured by the four-factor benchmark model.
Overall the effect of return dispersion on the performance of each of the strategies are relatively robust. Although there are some minor differences between the use of a value weighted return dispersion measure and an equally weighted return dispersion measure, in general, both indicate a very small insignificant effect of high return dispersion on the returns of each of the strategies.
4.2 Stricter return dispersion criteria
For the initial analysis, it is assumed that return dispersion is high in a certain month whenever the return dispersion of that month is higher than the average return dispersion over the entire period. This cutoff point is somewhat arbitrary, especially since Reibnitz (2015) finds the largest effects of return dispersion are present in the highest quintile of return dispersion. Therefore, this section illustrates how our initial results would alter when we identify high-return dispersion in a certain period as the level of return dispersion in that period exceeding the 80% percentile level over the entire period29. Table 5.12 illustrates the
same regression as in Table 5.1 with the only difference being the strictness of when we define a high level of return dispersion.
Table 5.12: Regression equation 1 normal sized benchmark strategies 80% cutoff point, period 1988-2016
Strategy: Growth Minimum Volatility Value
Bi T-stat Bi T-stat Bi T-stat
MRP 1.047 69.740*** 0.800 44.610*** 0.944 87.723*** HML -0.262 -14.136*** 0.149 7.827*** 0.269 17.265*** SMB -0.131 -7.254*** -0.223 -12.793*** -0.186 -10.784*** MOM 0.041 3.213*** 0.033 2.145** -0.047 -4.334*** HDD 0.000 -0.069 0.000 -0.071 0.000 0.104 HDU -0.001 -0.888 -0.005 -2.004** -0.003 -1.952*
LDD 0.000 0.126 0.001 0.641 -0.002 -2.673***
LDU -0.001 -1.536 0.001 0.667 0.000 0.622
R2 0.944 0.884 0.954
*** denotes significant at a 1% significance level. ** denotes significant at a 5% significance level. * denotes significant at a 10% significance level
From our initial regression, we concluded that there mainly is an effect of return dispersion in both upward and downward markets on the performance of the minimum volatility strategy. In line with Reibnitz (2015), we would expect larger effects when return dispersion is higher. However, we observe that the effects on the growth strategy is still small and statistically insignificant. However, value stocks now perform worse in periods where return dispersion is high and the market is in an upturn. Moreover, we observe that the minimum volatility strategy is not affected by the presence of high return dispersion in downward markets anymore. Although the initial difference seems odd there are some explanations. First, Reibnitz (2015) shows that the effect of return dispersion is largest when return dispersion is highest, but mainly for the most active funds. Given that we use indices as proxies for the returns of our strategies, our strategies are relatively inactive30. Therefore,
the fact that our strategies are not affected by the higher level of return dispersion would support Reibnitz’s argument of manager selection skill in periods of high return dispersion. Second, there might be a high degree of heterogeneity within each strategy group during periods of very high return dispersion. If an entire group, e.g. all value stocks, would perform better during a period of very high return dispersion, the level of return dispersion would, per definition, be smaller31. Appendix C illustrates the equivalents of tables 5.2, 5.3, 5.4 and
5.5 but with the stricter dummies applied. The general message is the same as for Table 5.12, the effect of the stricter dummy tends to be smaller than the initial effect. The only noteworthy difference is observable in Appendix C.4. Appendix C.4 illustrates that small growth stocks earn a significant premium over small value stocks in periods of high return dispersion when the market is in an upturn. Whereas the initial results indicate no premium at all.
30 The inactiveness is also observable from the relatively high levels of R2
31 Return dispersion indicates the difference in performance among stocks, if a large group of stocks tend to
5.4.3 Time-period splits
This section presents the effect of high return dispersion in different periods of time. Each time periods consists of 60-months (or 5-year). Ideally, we would observe similar coefficients and significance for each period of 5 years. If not the effect high return dispersion has on the different strategies is not constant over time and therefore not robust. For each of the regressions made (for each strategy both small and normal sized a regression with return dispersion in the current period and a regression with return dispersion in the previous month), a split is provided in the appendix. The main point, whether there is a consistent value premium over time or whether there is a consistent size premium over time is presented in the main text. Table 5.13 presented below, confirms our initial conclusions drawn from Table 5.5. There is no significant value premium associated with high return dispersion in the current period. Except for the 1993-1998 time-period, all the coefficients indicating the difference between the effect of high return dispersion on the returns of a value-oriented strategy and growth oriented strategy are statistically insignificant. We do observe several periods during which growth stocks significantly outperform value stocks in the period after high return dispersion in an upward market is observed. This is in line with the results from Table 5.5, from which we concluded that on average growth stocks
outperform value stocks in the subsequent period after high return dispersion in downward markets. Table 5.14 represents the difference between the effect of return dispersion on the returns of the normal sized strategies and the small sized strategies. From Table 5.14 we observe that there is no consistent size premium over time. Although there are some
significant differences between the effect of high return dispersion on the returns of normal sized and small sized strategies, these differences are highly time dependent. Additionally, the differences mainly occur between the small sized and normal sized growth strategy. Given that the differences do not occur at the other strategies it is hard to label these differences as a size premium32.
32 A size premium should be observable between all normal and small sized stocks independent of the
