The low volatility effect in the U.S. explained by the Fama-French five-factor model

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The low volatility effect in the U.S.

explained by the Fama-French five-factor

model

Name: Bram de Waal

Student number: 11063807

Programme: Economie en Bedrijfskunde Track: Finance and Organization Supervisor: Esther Eiling

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Abstract:

In this thesis the low volatility effect in the U.S. has been researched for the period 1964-2017. This anomaly has been proven by the CAPM and Fama-French three-factor model in earlier research, however, not yet for the Fama-French five-factor model.

The first research question is as follows: can the low volatility effect be explained by the Fama-French five-factor model in the U.S. for the period 1964-2017? The results have shown that the low volatility effect is still observable with the five-factor model, though the effect has diminished significantly compared to the three-factor model. Similar conclusions were drawn for the portfolios sorted on both volatility and size. Furthermore, for the double sorted analysis the low volatility effect has been noticeably stronger for the portfolios with low market equities and vice-versa for the high market equity portfolios.

The second research question has tested the persistence of the volatility anomaly for the period 1991-2017. The low volatility effect has appeared to be consistent in the

subsample analysis for all three models. Despite this fact the results have been more difficult to interpret. The alphas and low-high volatility spreads in the CAPM and three-factor model have shown an increase for the second period unlike the five-factor model where a decrease has been ascertained.

To conclude, the results in this thesis have proven the existence of the low volatility effect with the Fama-French five-factor model, although the effect is significantly weaker when compared to the other two models and when compared to portfolios with big stocks as opposed to small stocks.

Statement of Originality:

This document is written by Student Bram de Waal who declares to take full responsibility for the contents of this document.

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

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

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1 Introduction

In this thesis the low volatility effect in the U.S. will be discussed. This effect shows that stocks with low volatility have a higher risk-adjusted return compared to stocks with high volatility (Blitz & van Vliet, 2007). Although the existence of this effect has been shown by multiple papers, the research has been done mainly with older models. Therefore, this topic caught my interest whether the effect is still present with a newer model like the Fama-French five-factor model. Furthermore, little research been done on this topic that is recent, so it is possible that the low volatility effect has diminished or even fully disappeared over time. As a result, this research is also interesting for investors, who might want to take this effect into account when allocating assets.

Over the last 10 years investing in low minimum volatility indices and exchange traded funds (ETF) has increased. Investors try to profit from this anomaly by buying these ETFs, which increases the demand and should eventually cause this anomaly to be traded away. Malkiel (2014) states that several low volatility ETFs that have been created were not able to outperform their capitalization-weighted benchmarks. Furthermore, Malkiel argues that investors should be wary for these kinds of ETFs which try to beat the market portfolio. To sum up, the low volatility effect has been proven by numerous studies but it remains a difficult task for investors to benefit from this knowledge (Malkiel, 2014).

The main purpose of this thesis is to do research to be able to answer my research question; can the low volatility effect be explained by the Fama-French five-factor model in the U.S. for the period 1964-2017? To answer this question the results of the low volatility effect will be compared with the CAPM and Fama-French five and three-factor model. A set of portfolios that are sorted on their variance of daily returns and size will be analyzed for all three models. The hypothesis will test whether the alphas and low-high volatility spreads of the Fama-French five-factor model are significantly higher compared to the three-factor model. The results in this thesis regarding the first research question show evidently that the low volatility effect can be explained by the five-factor model only to a lesser extent

compared to the three-factor model.

There is a probability that the high volatility deciles contain mostly small stocks which would mean that the alphas can be explained by both a volatility and size effect. Therefore, the same regressions have been executed for portfolios that have been sorted on volatility

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and size to be able to analyze if the main results are biased because of the size effect. My second research question is as follows: is the low volatility effect still present in the period 1991-2017 in the U.S.? For this research question the subsample double sorted portfolios will be used and analyzed by the CAPM and Fama-French five and three-factor model. The results of the sub-period regressions will be compared with each other and to the full period regressions and tested for any significant differences. The outcome of these regressions show the persistence of the low volatility effect for the period 1991-2017 for all three models. However, the alteration of the effect is not as unambiguous because the low volatility effect increases in the second period for the CAPM and the three-factor model in contrast to the five-factor model where the effect decreases.

In this thesis an empirical approach will be applied. The data that is being used can be retrieved from Ken French’s website (“Kenneth R. French - Data Library,” n.d.). The data that is used for the portfolios include stocks from the NYSE, AMEX and NASDAQ. The portfolios are sorted monthly on their variance of the daily returns. For the estimation of the variance the 60 days lagged returns are used (“Kenneth R. French - Detail for Portfolios Formed on Earnings/Price,” n.d.). The monthly Fama-French five and three factors have been used.

For both research questions the ordinary least squares regression will be applied to test for significance. Although this research will focus mainly on the Fama-French models the results for the CAPM will also be included as this can give useful insights for this thesis. Furthermore, the alpha or the abnormal return will be the key variable for both research questions and will indicate how well the model works. For the execution of the regressions robust standard errors have been used, this is to make sure that the heteroscedastic standard errors of the OLS method are unbiased.

In the next chapter related literature will be discussed to clarify the added value of this thesis and to give an overview of this topic in the current literature. At the end of this chapter a logical hypothesis will follow from the discussed literature. Subsequently the third chapter will contain summary statistics and a more elaborate look to the methodology. In the fourth chapter the decile portfolio and double sorted portfolio results will be discussed and analyzed. The same methodology will be applied to the subsample data. Finally, in the last chapter a conclusion will be provided based on my findings and an answer to my research questions will be formulated. In the discussion section the shortcomings of this thesis and possible further research will be addressed.

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2 Literature review

In this chapter the relevant literature will be discussed and a broad overview of the topic will be given. Furthermore, the added value of this thesis and differences with existing literature will be highlighted. Finally, at the end of this chapter a hypothesis will follow based on earlier work or a logical extrapolation of the discussed literature.

The volatility effect is an effect that has been proven in the existing literature. Blitz and van Vliet (2007) have shown that the Fama-French corrected alphas are higher for the low risk portfolios. This contradicts the classic risk-reward assumption, which means that an investor is only prepared to buy a riskier stock if the reward is higher as well. This anomaly where the risk-reward relation is flat or even negative turned out to be both globally as well as for the separate regions U.S., Europe and Japan significant. Another research looks at this effect in emerging markets and the results are consistent with the results for developed markets. Furthermore Blitz and van Vliet (2013) found that there is no significant correlation between the volatility effect of the two markets which makes a common-factor explanation unlikely.

In another research the volatility effect has been studied across 23 developed markets with similar results and conclusions to the previous mentioned papers (Ang, Hodrick, Xing, & Zhang, 2009). However, a key difference for this thesis is that I will look whether the results are still consistent with the Fama-French five-factor model and compare them with the results of the Fama-French three-factor model. Most of the research that has been done about this topic use the CAPM or Fama-French three-factor model.

According to Dutt and Humphery-Jenner (2013) a partial explanation for this anomaly is that low volatility stocks have higher operating returns which increases the expected return of these stocks. However, only if these operating returns are unexpected it causes investors to drive up the price of these low volatility stocks.

Because the Fama-French model is of great importance for this thesis the factors of the model will be thoroughly discussed. Starting with the Fama-French three-factor model which exists out of the market beta, the size factor and the value factor. The five-factor model is based on the three-factor model but with two new factors added to it. The first factor 𝑅𝑀𝑊𝑡 is the profitability factor and represents: “the difference between the returns on diversified portfolios of stocks with robust and weak profitability” (Fama & French, 2015,

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p. 3). The other factor is the investment factor 𝐶𝑀𝐴𝑡 which represents: “the difference between the returns on diversified portfolios of the stocks of low and high investment firms” (Fama & French, 2015, p. 3). However, the opinion about the five-factor model is still

inconclusive and not as respected as the three-factor model. Blitz, Hanauer, Vidojevic, & van Vliet (2016) argue it is unclear why Fama and French added these two specific factors and why they didn’t add other factors such as the momentum factor which is a more established factor in the asset pricing literature compared to the two added factors. Another concern is that the market beta factor which is also included in the three-factor model assumes that a higher market beta results in a higher expected return. This assumption contradicts the previously mentioned literature which have proven the existence of a low market beta and volatility effect. At last Blitz et al. think that although the five-factor model is a step in the right direction it will not settle the asset pricing debate and they expect more models and factors to appear in the future that are capable of explaining more anomalies (Blitz et al., 2016).

To answer my second research question I will execute a subperiod analysis from 1964 to 1991 and 1991 to 2017. The period has been divided into two equal subperiods to test whether the effect changes significantly over time. A similar methodology was applied for the subperiod analysis by Blitz and van Vliet (2007). Their results show that the effect does not diminish over time, moreover the spread of the alphas of their most recent period 1996-2005 turns out to be larger.

2.1 Hypotheses

The literature has shown that the empirical relation between risk and (excess)return is negative instead of a positive relation what asset pricing theories would suggest. However the five-factor model is not as proven as the low volatility effect in the existing literature, therefore I want to test this relative new model on a in the meantime well recognized anomaly in the asset pricing world.

I do expect to be able to clearly see the low volatility effect for the period 1964-2017 in the U.S. with the five-factor model as this model is still very similar to the three-factor model which has proven to show a low volatility effect. However, in Blitz and van Vliet (2007) their research they compare the CAPM-alphas with the Fama-French adjusted alphas and find that globally and regionally the spread between the first and last decile is smaller for the Fama-French adjusted alphas. Therefore, I expect the spread between the deciles to

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For my second research question I will test if the low volatility is still present for the period 1991-2017. In other research, where similar methods have been applied, the low volatility spread appeared to be larger for their most recent period (Blitz & van Vliet, 2007). Although only the CAPM was used for this subsample analysis the conclusions are in line with my expectations namely, I still expect stocks with a low volatility to have a higher risk-adjusted return. Furthermore, I expect the magnitude of the low volatility effect in the recent period to be lower. The reason for this being that the existence of this volatility anomaly has become a generally known phenomenon, therefore you would expect investors to take this into account when allocating assets. I do not expect there to be major

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3 Data and Methodology

In this chapter the data sources that have been used for this thesis will be discussed and the methodology for this research. A closer look will be given to what kind of estimation

procedures have been used and which statistical tests have been used.

3.1 Data

Both the portfolio data and the Fama-French factors were retrieved from Kenneth R. French’s data library. The portfolios are divided into value weighted deciles and contain monthly returns from 1964-2017 formed monthly on the variance of daily returns using NYSE breakpoints. For the calculation of the variance 60 days of lagged returns are used. The exchanges that have been used to construct the portfolios are: NYSE, AMEX and NASDAQ (“Kenneth R. French - Detail for Portfolios Formed on Earnings/Price,” n.d.).

For the Fama-French factors two datasets have been downloaded one for the three-factor model and the other for the five-three-factor model. Because the returns are monthly both Fama-French factor datasets are monthly as well. The one-month treasury bill return will be used as the risk-free rate. The factors that will be used are: the excess market return, the size factor, the value factor, the profitability factor and the investment factor.

Table 1: Summary statistics decile portfolios

Low D2 D3 D4 D5 D6 D7 D8 D9 High Observations 648 648 648 648 648 648 648 648 648 648 Mean 0,469 0,592 0,608 0,586 0,625 0,730 0,750 0,765 0,571 0,014 Std. Dev. 3,260 3,815 4,196 4,652 4,913 5,477 5,927 6,634 7,445 8,811 Min -14,58 -18,13 -21,54 -22,57 -24,92 -25,17 -30,74 -29,77 -31,94 -34,5 Max 11,97 14,69 14,88 15,56 17,81 21,58 23,79 28,3 24,33 33,89

From the 6480 observations none have been removed. The summary statistics in table 1 show an expected increase in the average return and standard deviation for the higher deciles. The only odd-looking results are the average returns for the 9th_{and 10}th_{decile for} which you would expect a higher average return compared to the other deciles since the risk does increase. Even though this captures the essence of the volatility puzzle it is nonetheless a remarkable low average return. On the other hand the minimum and maximum values are

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in line with the expectations regarding the increase in volatility of the deciles. The data that has been used for the double sorted regressions has also been retrieved from ken French’s website, 25 portfolios have been downloaded for the period 1964-2017 (“Kenneth R. French - Detail for 25 Portfolios Formed on Size and

Book-to-Market,” n.d.). These portfolios have been divided into quintiles and are formed monthly on their market equity and variance of daily returns. Just like the portfolios sorted on variance the value weighted returns have been used. In table 2 the same volatility anomaly can be detected especially if we look at the smaller stocks. The low volatility effect seems to weaken as the market equity of the firms increase. For the big firms a higher standard deviation gives a higher average return as opposed to the small firms where the highest volatility quintile yields a negative average return.

Table 2: Means quintile portfolios

SMALL 2 3 4 BIG LOW 1.035 0.920 0.771 0.703 0.444 (4.055) (4.009) (3.655) (3.673) (3.388) 2 1.171 1.043 0.847 0.770 0.560 (5.638) (5.213) (4.750) (4.422) (3.962) 3 1.076 1.046 0.963 0.790 0.537 (6.463) (5.864) (5.327) (5.047) (4.416) 4 0.791 0.923 0.888 0.767 0.476 (7.499) (6.755) (6.145) (5.708) (5.031) HIGH -0.153 0.298 0.440 0.489 0.485 (9.207) (8.713) (8.014) (7.584) (6.645)

Robust standard deviation given between brackets.

Furthermore, this table shows a clear relation between size and volatility, namely that as the size increases the volatility of the quintiles decrease. For the subsample summary statistics similar conclusions can be drawn with the riskiest portfolios having the highest standard deviation and the lowest average return of their size quintile.

3.2 Methodology

This research will be a quantitative research, this type of research is commonly used for asset pricing. The applied models are the CAPM, Fama-French three and five factor model.

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An ordinal least squares regression will be executed which will predict the best linear relation between the factors and the portfolios. The three models are as follows: 𝑅_𝑖 − 𝑅_𝑓= 𝛼_𝑖+ 𝛽_𝑖(𝑅_𝑚− 𝑅_𝑓) + 𝜀_𝑖

𝑅_𝑖 − 𝑅_𝑓= 𝛼_𝑖+ 𝛽_𝑖(𝑅_𝑚− 𝑅_𝑓) + 𝑠_𝑖𝑆𝑀𝐵 + ℎ_𝑖𝐻𝑀𝐿 + 𝜀_𝑖

𝑅_𝑖 − 𝑅_𝑓= 𝛼_𝑖+ 𝛽_𝑖(𝑅_𝑚− 𝑅_𝑓) + 𝑠_𝑖𝑆𝑀𝐵 + ℎ_𝑖𝐻𝑀𝐿 + 𝑟_𝑖𝑅𝑀𝑊 + 𝑐_𝑖𝐶𝑀𝐴 + 𝜀_𝑖

𝑅𝑖 is the return of stock i and 𝑅𝑓 is the risk-free rate. The constant in this model is 𝛼𝑖, this represents the abnormal returns and should be zero if the model works well. A high alpha signifies that the factors in the model are not able to explain the portfolio returns well. 𝑅_𝑚− 𝑅_𝑓, SMB, HML, RMW and CMA are the five factors that try to explain the returns of the portfolios sorted on volatility.

The used data has been imported from excel to stata. For the linear regressions robust standard errors have been used to make sure that if the standard errors are heteroscedastic they are unbiased. For the double sorted analysis the same linear

regressions have been executed for the 25 portfolios sorted on size and volatility. The same methodology has been applied to the subperiod analysis for the first 324 observations and for the other 324 observations.

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4 Results

In this section the results that have been found will be interpreted. First the results of the full sample will be discussed and subsequently the results that are double sorted on size and volatility.

4.1 Full sample results

The obtained results can be found in the two tables below. Like the observations from the summary statistics the two Sharpe ratios of the two riskiest deciles are unusual low. Especially the high volatility decile in table 3 which has an alpha of -92.9% could be

considered as an outlier or the data for this portfolio could be deficient, therefore the results for this decile will be interpreted with caution.

Table 3: Fama-French three-factor regression

Low D2 D3 D4 D5 D6 D7 D8 D9 High Low-High

Market Beta 0.67*** 0.85*** 0.94*** 1.05*** 1.09*** 1.19*** 1.24*** 1.32*** 1.40*** 1.42*** -0.75

(31.85) (49.68) (57.06) (55.89) (54.46) (53.62) (50.11) (47.38) (40.15) (27.09)

Alpha 7.8% 12.5%** 11.3%* 0.7% 1.5% 5.8% 1.5% -1.9% -28.4%*** -92.9%*** 100.7%***

(1.10) (2.18) (1.92) (0.12) (0.24) (0.82) (0.20) (-0.22) (-2.74) (-6.40)

*** denotes significance at 1 percent, ** at 5 percent, * at 10 percent. Robust standard errors are calculated throughout the analysis. T-value given between brackets.

As shown in table 2 all the market betas are significant at 1 percent and are

monotonically increasing. This is a logical consequence from the portfolios being sorted on their volatility as the market beta of these deciles reflect their sensitivity compared to the market. However, most of the alphas are not significantly different from zero and there is not as clear of a trend as there is for the market betas. Nevertheless, the low volatility effect can be observed if the three most and least riskiest deciles are compared. The first three deciles all show positive risk-adjusted returns as opposed to the last three deciles showing all negative risk-adjusted returns. Furthermore, the spread between the highest and lowest decile is 100.7% which suggests that portfolios with low volatility outperform high volatility portfolios. Because the alpha of the first decile is not significant and the alpha for the tenth decile is remarkably high the same conclusions can be drawn if we look at the spread between the second and ninth decile which equals 40.9%.

The market betas for the five-factor model are very similar to those of the three-factor model with the same characteristics as stated before except for the tenth decile not

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monotonically increasing. However, this exception does not impact the interpretation of the results and can therefore be ignored.

Table 4: Fama-French five-factor regression

Low D2 D3 D4 D5 D6 D7 D8 D9 High Low-High

Market beta 0.71*** 0.89*** 0.98*** 1.08*** 1.11*** 1.19*** 1.24*** 1.28*** 1.34*** 1.28*** -0.57

(35.28) (59.61) (62.69) (64.67) (64.73) (55.16) (51.64) (46.86) (39.66) (28.70)

Alpha -4.8% -2.9% -2.9% -12.9%** -8.9% 0.01% -0.67% 6.03% -13.0% -46.1%*** 41.3%***

(-0.69) (-0.52) (-0.50) (-2.19) (-1.47) (0.00) (-0.09) (0.69) (-1.30) (-3.37)

*** denotes significance at 1 percent, ** at 5 percent, * at 10 percent. Robust standard errors are calculated throughout the analysis. T-value given between brackets.

Something that stands out in table 3 are the many negative alphas compared to the three-factor model. Although most of the alphas are not significantly different from zero a low volatility effect can still be observed. The spread between the most and least risky decile equals 41.3% which still suggests a negative relationship between risk and return. Though if we compare the spread between the two models a drastic reduction is observed. This presumption is verified if the alphas of the first and last three deciles are compared. Both models show the existence of the low volatility effect which corresponds with the related literature. However, there is a clear difference in to what extent the effect is present in both models.

The spread of the alphas for the five-factor model is noticeably smaller compared to the three-factor model. The reduction in the spread between the highest and lowest decile is 59.4% which can be attributed to the profitability and investment factor. Other research that looks at the CAPM and the Fama-French three-factor model also concluded that the addition of two new factors, the value and size factor, led to a smaller low-high decile spread (Blitz & van Vliet, 2007).

4.2 Double sorted results

Table 5 shows the same relations as concluded before with the means of the portfolios. Smaller stocks yield a higher risk-adjusted return with low volatility and a significant lower return with high volatility compared to big stocks. This effect is well noticeable if we look at the high-low spread that monotonically decreases as the market equity of the firms increase.

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Table 5: CAPM alphas

SMALL 2 3 4 BIG S-B LOW 66.22%*** 52.83%*** 40.91%*** 34.90%*** 11.45% 54.77%*** 2 62.27%*** 51.57%*** 34.70%*** 30.19%*** 13.54%* 48.72%*** 3 43.86%*** 43.92%*** 39.67%*** 23.89%*** 4.43% 39.43%*** 4 5.70% 21.20%* 22.85%** 13.49% -9.47% 15.16%*** HIGH -97.79%*** -58.51%*** -40.13%*** -32.99%*** -24.49%** -73.31%*** H-L -164.01%*** -111.34%*** -81.03%*** -67.89%*** -35.94%***

*** denotes significance at 1 percent, ** at 5 percent, * at 10 percent. Robust standard errors are calculated throughout the analysis.

These results are conform with the results found in the before mentioned section, namely that there is a clear low volatility effect observable.

Table 6: Fama-French three-factor alphas

SMALL 2 3 4 BIG S-B LOW 39.07%*** 28.50%*** 21.24%*** 18.88%** 7.32% 31.75%*** 2 29.02%*** 22.36%*** 11.41%* 14.61%* 13.69%** 15.33%*** 3 10.54% 16.68%** 18.10%** 8.82% 4.63% 5.90%*** 4 -25.39%*** -2.17% 1.64% 1.07% -6.96% -18.43%*** HIGH -128.21%*** -70.87%*** -43.57%*** -31.42%*** -14.76% -113.45%*** H-L -167.28%*** -99.37%*** -64.80%*** -50.31%*** -22.08%***

The alphas for the Fama-French three factor model are noticeably lower compared to the CAPM alphas, the same applies for the H-L and S-B spreads with the small H-L and high S-B as exceptions (-167.28% & -113.45%).

Table 7: Fama-French five-factor alphas

SMALL 2 3 4 BIG S-B LOW 29.34%*** 15.32%** 6.27% 3.92% -4.06% 33.40%*** 2 16.90%** 5.56% -2.65% -2.29% -3.66% 20.56%*** 3 5.24% 2.43% 1.74% -9.44% -7.60% 12.83%*** 4 -16.48% -13.79%* -13.68%* -10.34% -10.13%* -6.34%*** HIGH -88.70%*** -44.49%*** -20.75%** -7.66% 10.69% -99.38%*** H-L -118.04%*** -59.81%*** -27.02%*** -11.58%*** 14.75%***

For the five-factor model the alphas are lower compared to the three-factor model which is to be expected as the new model does a better job explaining the portfolio returns and therefore showing lower risk-adjusted returns. In all three models the low volatility anomaly is present, however to a lesser extent as new factors are added to the CAPM. There is one

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odd looking alpha which is the high-big alpha (10.69%) which contradicts the other results that have been found, however this can be ignored since it is not significant and the only result that suggests that there is no low volatility effect. Because most of the five-factor alphas are non-significant the betas must be able to explain the portfolio returns.

In table 8 this presumption is verified, with most of the betas being significant at 1 percent. There are no odd-looking results for the market beta, as concluded in the previous results the market beta increases monotonically as the volatility increases. For the size factor similar conclusions can be drawn, namely that it increases as the volatility increases. A negative relation can be detected for the size factor and the market equity quintiles, this is a logical outcome as the size factor (SMB) controls for small firms outperforming the market in the long-run. For the value factor (HML) the relation is not as obvious although this factor is better at explaining the returns for smaller firms especially if we look at the quintile for the big firms there are a lot of low insignificant results. The profitability factor (RMW) is most of the time significant and is therefore a valuable addition to the five-factor model. The same can be said for the investment factor (CMA) if we look at the high market equity and high volatility quintiles.

4.3 Subperiod analysis

In this subsection the low volatility effect will be tested for its consistency over time for the periods 1964-1991 and 1991-2017 and if the effect diminishes or increases. The results for the three models will be compared to see if there are any differences with the full sample regressions.

If we look at table 9 the CAPM results show that every volatility spread has increased for the period 1991-2017 except for the second size quintile. However, the size spreads seem to have decreased over time. This suggests that investors do not take the low volatility into account yet but do take the size factor into account. Still the CAPM results should be interpreted carefully as we can observe more significant alphas for the subsample analysis compared to the Fama-French models. Though similar conclusions for the three-factor model can be drawn. The volatility spreads have increased for the three highest market equity quintiles and the size spreads have decreased in table 9B compared to table 9A with exception of the third volatility quintile (13.71%).

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Something that stands out immediately are the smaller volatility spreads in table 11B compared to the other subsample volatility spreads. Furthermore, the big-high portfolio in table 11B has an alpha of 15.18% which is unusual high considering this portfolio has a negative alpha for all the other subsample regressions. A consistent observation that holds for both periods and for every model is the difference in volatility spread for small and big stocks. These results emphasize the sensitivity of small firms to the volatility anomaly in a portfolio. The low volatility effect is certainly less prominent in the five-factor model

compared to the three-factor model and even more so if we compare the high-low spread of the first period with the second.

Although it is hard to distinguish a clear pattern based on the subsample results as most of the alphas for the CAPM and three-factor model are higher for the second period in contrast to the five-factor model for which most of the alphas have decreased over time. With regards to the high-low and small-big spreads the same can be concluded. A possible explanation for this could be that the two added factors in the five-factor model are a more recent phenomenon and therefore not being able to explain the returns as well in the first subperiod compared to the second subperiod.

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5 Conclusion

In this thesis the low volatility effect has been researched. This anomaly has been examined based on the Fama-French three and five-factor model. A clear low volatility effect has been observed for the results that were sorted on volatility and divided into deciles. The alphas in the five-factor model are lower and the spread significantly smaller, furthermore the same pattern has been found when the CAPM and three-factor model are compared. This raises the question whether the low volatility effect will eventually disappear if more factors get added to the five-factor model or that the effect decreases over time as investors start taking the effect into account. The answer to my first research question is yes, the low volatility effect can be explained by the Fama-French five-factor model in the U.S. for the period 1964-2017. However, the low volatility anomaly is much weaker when compared to the three-factor model.

The results of the double sorted portfolios match the results that have been found for the portfolios only sorted on volatility. Both the spread and alpha have decreased as more factors have been added to the CAPM. Another effect that is clearly distinguishable is the size effect. The low volatility effect is much stronger for portfolios with low market equities, this is applicable for all three models. Most of the betas in the five-factor model are significant at 1 percent which explains the many insignificant alphas. It can be determined that the five-factor model does a better job at explaining the portfolio returns compared to the three-factor model.

The results that have been found for the subsample analysis are not as coherent as the previously mentioned results. All the high-low volatility spreads for the CAPM have become greater over time. For the three-factor model the high-low spreads have increased for the three quintiles with the highest market equity. It could be stated based on these two models for the subsample period regressions that the low volatility effect has increased. However, this does not only contradict our hypothesis but also the results that have been found for the factor model. As opposed to the CAPM and three-factor model the five-factor high-low spreads for the period 1991-2017 have mostly decreased compared to the first period. Although it is hard to draw conclusions from this contrast a possible explanation could be the addition of the profitability and investment factor to the five-factor model.

Finally, to return to my second research question which is formulated as follows: is the low volatility effect still present in the period 1991-2017? It can be concluded that the

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low volatility effect is still present for this period with regards to all three models. Yet the results for the subsample analysis are slightly ambiguous concerning the change of the effect.

A shortcoming of this thesis is that there are a couple of doubtful results which do not make a lot of sense. For example, the extreme low average excess return of the highest decile or the incredible high negative alphas of the riskiest decile for both the three and five-factor model. Moreover, the high-big alpha in table 11B is a remarkable result as well despite being insignificant. However, I do think that the drawn conclusions are sustainable despite these several peculiar results.

My suggestion with respect to further research would be to analyze the low volatility effect based on an even more sophisticated model. Moreover, a paper that researches a model with a low volatility factor would be extremely interesting. Blitz e.a. (2016) question whether the CAPM should be used as the basis for an asset pricing model as the addition of a low-high volatility factor to the CAPM would cause the model to be internally inconsistent.

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6 References

Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2009). High idiosyncratic volatility and low returns: International and further U.S. evidence. Journal of Financial Economics, 91(1), 1–23. https://doi.org/10.1016/j.jfineco.2007.12.005

Blitz, D. C., & Vliet, P. van. (2007). The Volatility Effect. The Journal of Portfolio Management,

34(1), 102–113. https://doi.org/10.3905/jpm.2007.698039

Blitz, D., Hanauer, M. X., Vidojevic, M., & van Vliet, P. (2016). Five Concerns with the

Five-Factor Model (SSRN Scholarly Paper No. ID 2862317). Rochester, NY: Social Science Research

Network. Retrieved from https://papers.ssrn.com/abstract=2862317

Blitz, D., Pang, J., & van Vliet, P. (2013). The volatility effect in emerging markets. Emerging

Markets Review, 16, 31–45. https://doi.org/10.1016/j.ememar.2013.02.004

Dutt, T., & Humphery-Jenner, M. (2013). Stock return volatility, operating performance and stock returns: International evidence on drivers of the ‘low volatility’ anomaly. Journal of

Banking & Finance, 37(3), 999–1017. https://doi.org/10.1016/j.jbankfin.2012.11.001

Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial

Economics, 116(1), 1–22. https://doi.org/10.1016/j.jfineco.2014.10.010

Kenneth R. French - Data Library. (n.d.). Retrieved May 24, 2018, from http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

Kenneth R. French - Detail for 25 Portfolios Formed on Size and Book-to-Market. (n.d.). Retrieved June 18, 2018, from

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/tw_5_ports_me_VA R.html

Kenneth R. French - Detail for Portfolios Formed on Earnings/Price. (n.d.). Retrieved May 24, 2018, from

http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_port_form_VA R.html

Malkiel, B. G. (2014). Is Smart Beta Really Smart? The Journal of Portfolio Management,

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Appendix

Table 8: Betas Fama-French five-factor model

SMALLLoVAR ME1VAR2 ME1VAR3 ME1VAR4 SMALLHiVAR

MktRF 0.687*** 0.984*** 1.094*** 1.175*** 1.176***

SMB 0.654*** 0.930*** 1.055*** 1.192*** 1.371***

HML 0.362*** 0.402*** 0.372*** 0.325*** 0.282**

RMW 0.272*** 0.346*** 0.193** -0.107 -0.828***

CMA 0.057 0.055 -0.016 -0.208* -0.470**

ME2VAR1 ME2VAR2 ME2VAR3 ME2VAR4 ME2VAR5

MktRF 0.755*** 0.995*** 1.106*** 1.246*** 1.331***

SMB 0.546*** 0.745*** 0.830*** 0.951*** 1.132***

HML 0.305*** 0.353*** 0.306*** 0.207*** -0.053

RMW 0.321*** 0.427*** 0.395*** 0.367*** -0.518***

CMA 0.144*** 0.141*** 0.067 -0.020 -0.369***

MktRF 0.752*** 0.977*** 1.083*** 1.221*** 1.305***

SMB 0.298*** 0.475*** 0.564*** 0.697*** 0.842***

HML 0.278*** 0.358*** 0.289*** 0.220*** -0.153**

RMW 0.335*** 0.379*** 0.447*** 0.413*** -0.441***

CMA 0.193*** 0.064 0.064 0.076 -0.335***

MktRF 0.775*** 0.972*** 1.120*** 1.218*** 1.322***

SMB 0.088*** 0.188*** 0.243*** 0.308*** 0.517***

HML 0.279*** 0.251*** 0.231*** 0.166*** -0.168***

RMW 0.325*** 0.392*** 0.442*** 0.292*** -0.508***

CMA 0.193*** 0.168*** 0.150** 0.067 -0.281***

BIGLoVAR ME5VAR2 ME5VAR3 ME5VAR4 BIGHiVAR

MktRF 0.755*** 0.936*** 1.026*** 1.134*** 1.236***

SMB -0.246*** -0.227*** -0.156*** -0.177*** 0.012

HML 0.107*** 0.033 0.044 0.011 -0.042

RMW 0.189*** 0.374*** 0.283*** 0.066* -0.447***

CMA 0.235*** 0.206*** 0.103** 0.027 -0.514***

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Table 9: CAPM subsample alphas Panel A: 1964-1991 SMALL 2 3 4 BIG S-B LOW 60.30%*** 45.63%*** 29.12%*** 29.05%*** -0.29% 60.60%*** 2 68.93%*** 58.83%*** 38.80%*** 27.34%*** 5.80% 63.13%*** 3 48.77%** 53.72%*** 55.72%*** 27.66%*** 4.67% 44.10%*** 4 2.54% 26.56% 22.67%* 23.90%** -11.12% 13.66%*** HIGH -103.45%*** -77.08%*** -35.29%* -33.58%** -21.03%* -82.42%*** H-L -163.75%*** -122.71%*** -64.41%*** -62.63%*** -20.74%*** Panel B: 1991-2017 SMALL 2 3 4 BIG S-B LOW 75.80%*** 64.51%*** 57.39%*** 47.35%*** 27.71%** 48.09%*** 2 61.79%*** 49.62%*** 34.23%** 38.19%*** 24.34%** 37.45%*** 3 43.42%** 39.10%** 27.31%* 24.47%* 6.06% 37.36%*** 4 8.94% 21.51% 27.34% 5.94% -8.50% 17.44%*** HIGH -99.02%*** -46.40%* -49.88%** -38.82%* -33.75%** -65.27%*** H-L -174.82%*** -110.91%*** -107.27%*** -86.17%*** -61.46%***

Table 10: Fama-French three-factor subsample alphas Panel A: 1964-1991 SMALL 2 3 4 BIG S-B LOW 32.01%*** 19.76%*** 5.96% 7.52% -6.97% 38.97%*** 2 36.41%*** 30.38%*** 16.06%** 11.40% 10.54% 25.87%*** 3 13.24%* 30.22%*** 37.70%*** 18.56%** 12.16%* 1.08% 4 -33.30%*** 10.68% 6.51% 18.77%** 0.43% -33.73%*** HIGH -147.77%*** -90.96%*** -40.23%*** -32.79%*** -8.56% -139.21%*** H-L -179.77%*** -110.72%*** -46.20%*** -40.32%*** -1.59% Panel B: 1991-2017 SMALL 2 3 4 BIG S-B LOW 53.17%*** 43.92%*** 41.91%*** 36.11%*** 24.89%*** 28.28%*** 2 33.08%*** 24.16%** 14.13% 25.03%** 22.03%** 11.05%*** 3 16.23% 13.80% 7.33% 8.55% 2.52% 13.71%*** 4 -14.74% -2.18% 6.60% -8.21% -10.96% -3.78% HIGH -117.26%*** -56.11%*** -51.53%*** -36.84%** -26.42%* -90.84%*** H-L -170.43%*** -100.03%*** -93.43%*** -72.95%*** -51.31%***

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Table 11: Fama-French five-factor subsample alphas Panel A: 1964-1991 SMALL 2 3 4 BIG S-B LOW 27.36%*** 11.49% -0.03% 12.53% -5.48% 32.84%*** 2 36.91%*** 24.11%*** 14.39%* 14.98% 0.29% 36.62%*** 3 17.83%** 25.36%*** 34.41%*** 19.19%** 11.21% 6.62%*** 4 -22.20%*** 16.16%* 8.35% 27.02%*** -1.00% -21.20%*** HIGH -124.35%*** -72.48%*** -19.65% -16.74% -1.57% -122.77%*** H-L -151.70%*** -83.97%*** -19.62%*** -29.26%*** 3.91% Panel B: 1991-2017 SMALL 2 3 4 BIG S-B LOW 41.60%*** 24.71%*** 17.92%** 10.81% 7.58% 34.02%*** 2 20.33%* 0.55% -8.96% -3.44% -4.66% 24.99%*** 3 12.17% -4.55% -19.67%* -20.71%* -17.27%** 29.44%*** 4 0.71% -16.71% -19.02%* -27.36%** -12.20% 12.92%*** HIGH -53.43%* -20.81% -21.78% -4.66% 15.18% -68.60%*** H-L -95.03%*** -45.52%*** -39.70%*** -15.47%*** 7.60%***

The low volatility effect in the U.S. explained by the Fama-French five-factor model