• No results found

The low volatility anomaly : a look at different bull and bear market states

N/A
N/A
Protected

Academic year: 2021

Share "The low volatility anomaly : a look at different bull and bear market states"

Copied!
26
0
0

Bezig met laden.... (Bekijk nu de volledige tekst)

Hele tekst

(1)

The low volatility anomaly: A look at different

bull and bear market states.

Bachelor Thesis – University of Amsterdam – Economics and Finance –Faculty

of Economics and Business

Nick Rohrbach – 10875549

Nick.rohrbach@student.uva.nl

Supervisor: Liang Zou

16 February 2018

Abstract

The low volatility anomaly has been confirmed in many markets. Low volatility stock portfolios tend to have positive alphas while high volatility stock portfolios tend to have negative alphas. This paper analyzed this volatility effect on the US stock market during different bull and bear market periods. CAPM 1-factor, Fama & French 3-factor and Carhart 4-factor alphas are found by creating quintile portfolios formed by ranking stocks on volatility and doing an OLS-regression. The results found were inconclusive, but differences between the volatility effect were found in the bull market states. Further research is warranted as the effects behind this difference were not investigated and discussed.

(2)

This document is written by Student Nick Rohrbach who declares to take full responsibility for the contents of this document.

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

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

(3)

Table of Contents

Introduction ... 4

Literature review ... 5

Data and methodology ... 9

Results ... 11

Conclusion ... 14

Bibliography ... 16

(4)

Introduction

The purpose of this paper is to investigate if the volatility effect is present during different bull and bear market periods on the US stock market. A bull market period is usually described as a period in which the movement of stock prices has an upward trend and during a bear market period the movement of stock prices has a downward trend (Kole & van Dijk, 2017). The volatility effect, also known as the low volatility anomaly, tells us that low risk, low volatility stocks have significantly higher returns and risk-adjusted returns than high risk, high volatility stocks (Blitz & van Vliet, 2007). Extensive research has been done on the relationship between risk and return in different markets around the world as soon as the CAPM was formed back in 1964 (Sharpe, 1964) (Lintner, 1965a). Different drivers behind the low volatility anomaly were found by for example Baker et al. in 2011. They used behavioural science as a driver behind the effect (Baker, Bradley, & Wurgler, 2011). Another suggestion is that the higher compensation could be attributed to higher factor risk (Clarke, Thorley, & De Silva, 2010). To investigate the reasons behind the effect is not the purpose of this paper. The research is done solely to identify the differences between the volatility effect in different bull and bear market periods by looking at different volatility quintile portfolios formed from all stocks on the S&P 500 between 1990 and 2012. As the research has never been done before on such specific time periods, the results could be subject to different biases that only form during these specific bull and bear market states. First, different bull and bear market periods were formed using the research of Kole and van Dijk (2017) to identify the different periods. Quintile portfolios were formed with a monthly rearrangement based on past 12-month volatility. After the creation of the portfolios, OLS regression was used to find the CAPM 1-factor alpha, the Fama and French 3-factor alpha and the Carhart 4-3-factor alpha. The alphas found give the abnormal excess returns. Besides the alpha, the Sharpe ratio will be displayed for every time period. This gives an indication of the risk adjusted returns (Sharpe, The Sharpe Ratio, 1994). The paper is structured as follows: Section 2 will display the literature review. The literature review is structured approximately in a chronological order. Section 3 shows the data and methodology in which the research is discussed extensively from the collection of the data until the regressions that are done. Section 4 will show all the results, including remarks about the interesting findings. Section 5 is the conclusion in which the results will be discussed. Section 6 is a list of the literature used in and throughout the whole research. Section 7 is the appendix which will show additional findings and results including all regression results.

(5)

Literature review

The capital asset pricing model presented by Sharpe and later extended and clarified by Lintner predicts a positive relation between Beta and expected return. The model imposes that the expected return of an asset is linearly related to the expected return of the market in excess of the risk-free return. (Sharpe, 1964) (Lintner, 1965a) (Lintner, 1965b). The model is subject to certain assumptions that “(1) all investors are single period risk-averse utility of terminal wealth maximizers and can choose among portfolios solely on the basis of mean and variance, (2) there are no taxes or transaction costs, (3) all investors have homogeneous views regarding the parameters of the joint probability distribution of all security returns, and (4) all investors can borrow and lend at a given riskless rate of interest.” (Jensen, Black, & Scholes, 1972, pp. 1-2). The CAPM is as follows:

𝐸(𝑅$) = 𝛽$𝐸(𝑅)) Where the variables are defined as:

𝐸(𝑅$) =*(+,)-+,./0*(1,)

+,./ − 𝑟4,= Expected return on asset i.

𝐸(𝑅)) = Expected excess return on a market portfolio consisting of an investment in every

asset outstanding in proportion to its value. 𝛽$ = 567(8<=(89,89);) = Systematic risk of the asset.

If the expected excess return on the asset is directly proportional and 𝛼$ = 𝐸(𝑅$) − 𝛽$𝐸(𝑅)) the α

on every asset must be 0. (Jensen, Black, & Scholes, 1972)

The work of Miller and Scholes first indicated that the model was not a true representation of the risk and return relation. In particular, they found that the α was not 0 and that the α of an individual asset depends in a systematic way on the β of that asset. They found that beta stocks tend to have positive alphas and high beta stocks tend to have negative alphas. (Miller & Scholes)

Later in 1972 Jensen et all found the same results and with their evidence warranted the rejection of the traditional CAPM. (Jensen, Black, & Scholes, 1972)

This evidence has since been found in multiple studies done on stock markets around the world. For example, Haugen and Heinz (1975) wrote a paper in 1972 that was finally published in 1975 which documented a study over the time period of 1926-1971 on both the stock and bond market that and found that risk (systematic or otherwise) generates extra reward. In fact, they found that lower variance stock portfolios have experienced greater average returns that their riskier counterparts. Haugen and Heinz also introduced the bull-bear market problem, which tells us that timing is critical when testing the relationship between risk and expected return. If the assumption that investors’ expectations are based on averages is violated, a systematic error appears that results in a positive or a negative bias. (Haugen & Heins, 1975)

Two other studies on the stock and bond markets confirming that the beta does not predict returns in both cross section and time series regressions in the 1963-1990 period is done by Fama and French (1992) (1993). Upon expending on the Sharpe-Lintner CAPM they make use of 5 different

(6)

control variables including size, value, unexpected changes in long term interest rates on bonds and a default factor on bonds. A 3-factor cross-section regression model with the first two variables, being SMB to control for size, and HML to control for value showed that these variables add to the explanation of the variation in expected returns besides the beta. This resulted in the following widely used Fama and French 3-factor model:

𝑅$,?− 𝑅4,?= 𝛼$+ 𝛽$,AB𝑅A,?− 𝑅4,?C + 𝛽$,DAE𝑆𝑀𝐵?+ 𝛽$,IAJ𝐻𝑀𝐿?+ 𝜀$,?

Where the variables added to the 1-factor model are defined as:

𝑆𝑀𝐵?= Excess return of small cap stock over big cap stock measured in market capitalization.

𝐻𝑀𝐿?= Excess return of value stock over growth stock measured in book to market ratio.

The SMB and HML proxies are meant to capture the risk-factor in returns related to size and book-to market equity (Fama & French, 1993).

Carhart (1997) later expanded the Fama and French 3-factor model with a 1 year momentum factor after Jegadeesh and Titman found that strategies of buying stocks that performed well in the past and selling stocks that performed poorly in the past lead to significantly higher returns. (Jegadeesh & Titman)

The Carhart model 4-factor model:

𝑅$,?− 𝑅4,?= 𝛼$+ 𝛽$,AB𝑅A,?− 𝑅4,?C + 𝛽$,DAE𝑆𝑀𝐵?+ 𝛽$,IAJ𝐻𝑀𝐿?+ 𝛽$,+8NO8𝑃𝑅1𝑌𝑅?+ 𝜀$,?

Where the variable added to the Fama and French 3-factor model is:

𝑃𝑅1𝑌𝑅?= One-year momentum, defined as “the equal-weight average of firms with the

highest 30% element month returns lagged one month minus the equal weight average of firms with the lowest 30% eleven month returns lagged one month” (Carhart, 1997, p. 61). Carhart found that the 4-factor model noticeably reduces the average pricing errors from both the CAPM and the Fama and French 3-factor model. By comparison, the absolute mean errors from CAPM, 3-factor model and the 4-factor model were respectively 0,35%, 0,31% and 0,14% per month (Carhart, 1997).

In 1994 William F Sharpe elaborated on his earlier research where he created a measure to describe mutual fund performance called the reward to variability ratio. The ratio formed from this research we now call the Sharpe-ratio and is known to “measure the expected return per unit of risk for a zero-investment strategy” (Sharpe, The Sharpe Ratio, 1994, p. 16). It is also known as the risk adjusted return. The Sharpe-ratio:

𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 = 𝑅Z[− 𝑅4 𝜎[

(7)

Where the variables are defined as:

𝑅Z[= Expected return on the portfolio. 𝑅4= Risk-free rate.

𝜎[= Standard deviation of the portfolio.

There are multiple theories explaining the drivers behind the low volatility anomaly. For example, Baker et al. (2011) use behavioural finance to try to explain the anomaly on the US stock market. They argue that investors are not fully rational and a mandate to compare returns to a fixed benchmark discourages arbitrage activity in both low beta, high alpha and high beta, low alpha stocks.

The irrational preference for higher volatility stocks can be derived from 3 biases. The first being called a preference for lotteries. Loss aversion tells us investors usually shy away from volatility because of a fear of realizing a loss, but when probabilities shift towards there being a big chance of losing a small amount of money and a small chance of winning a big amount of money more people take the gamble. Buying a volatile, lower priced stock can be compared to buying a lottery ticket. Kumar (2009) found that some investors show real preference for stocks with lottery-like payoffs. The second bias is called representativeness. When someone is trying to decide where to invest, they think of past great investments. For example, buying Microsoft during the IPO. Investing in speculative new technologies can then be perceived to be the way to success. People ignore the large base rate of failure with these new speculative investments and thus overpay for volatile stocks. The last bias is overconfidence. Some sort of forecasting is used when valuing stocks. When people use forecasting they tend to use a too narrow confidence interval (Fischhoff, Slovic, & Lichtenstein, 1977). Overconfident investors are also more likely to disagree and with that, more likely to agree to disagree. Being overconfident leads these investors to sticking with their original predictions instead of altering their predictions. More uncertainty, for example with more volatile stocks, likely also increases the extent of the disagreement. This is seen as an important part of the demand for volatile stocks (Cornell, The Pricing of Volatility and Skewness: A New Interpretation, 2009).

The second argument Baker et al. believe to be a contributor to the low volatility anomaly is benchmarking. An institutional investment manager usually has an explicit or implicit mandate to maximize the information ratio in his contract without using leverage. The information ratio is as follows:

𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜:𝑅[− 𝑅$ 𝑆[-$ Where the variables are defined as:

𝑅[= Return on the portfolio.

𝑅$ = Return on the index (or benchmark).

(8)

The SEC imposed the rule that all mutual funds have to pick a benchmark and show the benchmarks’ performance versus the funds’ performance in their prospectus. Even though an individual investor should care more about the total risk of a fund than the risk compared to a certain benchmark, it is easier to assess the funds’ performance and risk when comparing to a benchmark. This mandate has a downside as well. Several studies have been done to analyse the implications of a fixed benchmark mandate and the effect it has on stock prices. Research done by Cornell and Roll (2005) concludes that the low-volatility anomaly is less likely to be exploited when institutional investment managers use a benchmark. Similar to the findings by Cornell and Roll, Baker et al present the fact that

investment managers that have a fixed benchmark and no possibility of using leverage are better off exploiting mispriced stocks near market risk (i.e. 𝛽$ = 1). Trying to exploit the mispricing of stocks

deviating further from the market risk will result in a greater tracking error and thus reducing the information ratio.

A study done by Dutt et al. (2013) complements the research of Baker et al. (2011). They state the benchmarking driver of the anomaly provided by Baker et al. should not be as prominent in stock markets outside of the US. For example, emerging markets have a less institutionalized financial industry and benchmarks there generally include less volatile stocks. They find significant evidence of the presence of the low volatility anomaly in multiple markets across the world including

emerging markets. The same evidence was found in the research done on the low volatility anomaly in emerging markets by Van Vliet et al. (2013). Dutt et al. hypothesized that operating performance can be another driver behind the anomaly. They found evidence that firms with less volatile stock do have a stronger future operating performance around the world and that strong operating

performance in the past indicates lower volatility in the future. Stronger operating performance could lead to higher expected stock returns. Besides this, higher operating performance leads to higher cash flows as well. These cash flows can be used to aggressively invest in expansion

opportunities which in turn increases the future expected returns too. The research also shows that controlling for operating performance significantly influences the relationship of volatility and stock returns. This implies that operating performance might be another driver behind the low volatility anomaly.

Another explanation given for the low volatility anomaly is that there is, or are likely pervasive systematic risk factor(s) directly associated with volatility. Clarke et al. (2010) suggested that idiosyncratic and total volatility might be an extra risk factor on the US stock market. They

introduced the factor to the Fama and French 3-factor and Carhart 4-factor model. The VMS-factor is the volatility VMS-factor (Return on volatile minus stable stocks). Their evidence says that the long term historical data shows negative or low effect on return. They found that high idiosyncratic-volatility stock did not yield higher excess return, but that exposure to low idiosyncratic-idiosyncratic-volatility did benefit investors (Li, Sullivan, & Garcia-Feijóo, 2016).

In 2009 Ang et al. found the same evidence of this idiosyncratic- volatility anomaly in both the US stock market and in other stock markets outside the US. Besides this, they found that the effects in markets outside the US are highly correlated with the effect in the US. They found that the abnormal returns created by the idiosyncratic volatility-based portfolios in markets outside the us strongly co-move with the portfolios in the US stock market. The finding of this co-co-movement tells us that the return-predictive capabilities of the idiosyncratic risk is likely due to a pervasive risk factor (Ang, Hodrick, Xing, & Zhang, 2009).

(9)

Later in 2016 Xi et al did research to whether the phenomenon could be attributed to either the mispricing of stocks or to the higher compensation for factor risk. Their research was based on the US stock market. They used an approach where they created different quintile portfolios based on idiosyncratic volatility (IVOL) and used the Fama and French 3 factor model to find the excess returns. Besides this, they created a separate IVOL-factor by subtracting the monthly return on the high-IVOL portfolio from the monthly return on the low-IVOL portfolio. Afterwards they used rolling regressions of the excess returns on the Fama-French model including the IVOL-factor to find the IVOL-factor betas. Their approach “allowed them to separate low-IVOL stocks with high and low loadings on the IVOL factor. If the risk-based explanation for the higher observed returns of low-IVOL stocks is correct, a low-IVOL stock with a low-IVOL factor loading should have a low average return. In contrast, if characteristics rather than factor loadings determine prices, a low- IVOL stock should have a high return regardless of its loading.” (Li, Sullivan, & Garcia-Feijóo, 2016, p. 37) In their results they found significant evidence that market mispricing best explains the link between the low idiosyncratic volatility and the returns. Which according to them can be seen as a compensation for some hidden factor risk (Li, Sullivan, & Garcia-Feijóo, The Low-Volatility Anomaly: Market Evidence on Systematic Risk vs. Mispricing, 2016).

Since the bull-bear market problem was introduced in 1975 by Haugen and Heinz (1975), the low volatility anomaly has been found across the world in multiple time periods. There have been different approaches on how to identify bull and bear market periods. Kole and van Dijk (2017) did research on how to recognize these market states using different approaches. They distinguished between 6 different methods to identify bull and bear markets. The first two methods, being derived from the research of Lunde and Timmermann (2004) and Pagan and Sossounov (2003), are rule based and identify the different market periods through peaks and troughs in a certain market index. The difference between the methods are the criteria being used for selecting the peaks and troughs, where the first relate the criteria to the magnitudes of price changes and the latter relates to the duration of the states. The other four methods are based on the Markov regime switching models. The difference between the Markov switching models and the rule-based models is that the Markov switching models use both the variance and the mean of the different regimes opposite to where the rule-based methods only use the recent price trends. The methods based on the Markov switching models seem to be a better predictor for the bull and bear market states, but the states are less constant and switch more.

Data and methodology

The research goal is to find if abnormal excess returns were found by holding low volatility stock portfolios on the US stock market in different during different bull and bear market periods. The methodology is similar to the method used by Blitz and van Vliet in their research (Blitz & van Vliet, 2007) (Blitz, Pang, & van Vliet, 2013). The data used was comprised of the monthly stock return of all S&P 500 constituents between January 1989 and January 2012. The returns included the dividend pay-out. All return data was gathered from Compustat. The stock returns were only included in the portfolios when they were listed on the S&P500. The first thing that had to be done was to compute the portfolios with a monthly reassignment on low to high 12-month return volatility.

(10)

To compute the 12-month volatility the standard deviation was calculated using the following formula: 𝑆𝑡𝑑 = c∑B𝑅$,− 𝑅ZC e ) 𝑛 Where n = 12 and 𝑅Z is the past 12-month average.

Stock portfolios are formed every month in quintiles of low to high return volatility. To eliminate most of the outliers, the 1,5% least and most volatile stocks were taken out of the sample every month. After forming the portfolios, the average of all the returns that month in the portfolios were calculated to get the monthly portfolio returns.

See graph 1 in the results for the returns that would have been realised for investing 1,00$ in January 1990 for each quintile portfolio. This is given that there were no liquidity constraints and transaction costs to rearrange the portfolio every month.

To find the alphas, which denote the abnormal excess returns, in different time periods, the bull and bear markets were defined first. The framework of Kole and Van dyk (2017) was used to identify the markets. They described 6 different methods of which the rule-based methods gave the most clearly identifiable periods. See table 2 in the appendix for the defined bull and bear market periods. For every quintile portfolio in every period the annualized simple mean, the annualized geometric mean, the annualized standard deviation, the Sharpe ratio and the annualized one, three, and four factor alphas are reported with their corresponding T-statistic. The geometric average is the more important of the two averages as this accounts for the compounding effect in stock returns. To find the 1-factor alpha the Sharpe-Lintner CAPM was used. The monthly quintile portfolio return in excess of the risk-free rate is regressed using a simple OLS-regression on the market risk premium, which is the market return in excess of the risk-free rate. The 1-month T-bill rate was taken from the Federal Reserve database as the risk-free rate. As market-proxy, the total S&P500 portfolio return was used.

The Fama and French 3-factor alpha is found by adding the Size and Value proxies to the CAPM. These proxies for north American markets can be found in the database of Kenneth French. The Carhart 4-factor alpha is subsequently found by adding a momentum factor to the Fama and french 3-factor model. The momentum factor can be found in the same database of Kenneth French. As the momentum factor was only available from January 1991, the 4-factor regression is only done from January 1991 to January 2012.

All regressions are done over the total period of January 1990 to January 2012 and all the bull- and bear market periods in between. All regressions are done using robust standard errors. For all alphas found, the statistical significance is shown in 10%, 5% and 1 % levels. The full regression results can be found in the appendix.

(11)

Results

As seen in graph 1 there is a clear difference in the returns of the quintile portfolios over the total time period with the total return of the lowest volatility quintile portfolio over 20 years being 886,8% and the return of the highest volatility quintile portfolio being 486,0%. Being exposed to more volatility in your portfolio during the total time period certainly did not give any extra return. There are differences in different time periods as can be seen around for example the internet bubble around 2000.

Graph 1:

The main results of the regressions the can be found from table 2 to table 9. Table 2:

Time period 1990 - 2012

Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Q5-Q1 Mean (simple) Excess R 7,142% 7,442% 8,027% 7,838% 9,798% 2,656% Mean (geometric) Excess R 6,677% 6,582% 6,563% 5,572% 4,296% -2,381% Standard deviation (of R) 9,322% 12,649% 16,447% 20,499% 32,063% 22,740%

Sharpe ratio 0,716 0,520 0,399 0,272 0,134 -0,582288401 1-factor Alpha 3,475% 1,869% 0,505% -1,522% -4,164% -7,639% t-statistic 3,1*** 1,98** 0,68 -2,03** -1,86* 3-factor Alpha 3,436% 1,916% 0,266% -1,627% -3,839% -7,275% t-statistic 3,64*** 2,47** 0,41 -2,18** -2,2** 4-factor Alpha 2,904% 1,405% -0,430% -1,495% -2,302% -5,206% t-statistic 2,92*** 1,70* -0,62 -1,94* -1,25

(Statistical significance is shown at the 10%, 5% and 1% levels by *, ** and ***.) 0 1 2 3 4 5 6 7 8 9 10 31/01/ 1990 31/01/ 1991 31/01/ 1992 31/01/ 1993 31/01/ 1994 31/01/ 1995 31/01/ 1996 31/01/ 1997 31/01/ 1998 31/01/ 1999 31/01/ 2000 31/01/ 2001 31/01/ 2002 31/01/ 2003 31/01/ 2004 31/01/ 2005 31/01/ 2006 31/01/ 2007 31/01/ 2008 31/01/ 2009 31/01/ 2010 31/01/ 2011 31/01/ 2012

Total return

(12)

The findings in table 2 over the total 20-year time period are in line of expectation and they confirm all the previously done research. There is clear statistically significant evidence (at 99%) that the lowest volatility quintile portfolio has the highest 1-factor, 3-factor and 4-factor alpha. We can also see that the second lowest volatility quintile portfolio has a statistically positive alpha at 95% for the 1-factor and the 3 factor models and at 90% for the 4-factor model. On the opposite side we can also see that there is statistically significant evidence (at 90% and 95%) that the highest two quintiles have negative 1-factor and 3-factor alphas. The -7,639% difference found in the 1-factor alpha can be seen as the volatility effect as stated by Blitz and van Vliet (2007). We can also see a clear negative relation between the risk adjusted return and volatility. The least volatile portfolio has the highest Sharpe-ratio.

Below in table 3, 5 and 9 we find the regression results of the bear market periods between January 1990 and January 2012. Note that the bear market periods usually lasted a lot shorter than the bull market periods. With monthly stock return data this caused a lot of the results to be insignificant. The Sharpe-ratios during the bear market period (except the period between 01/06/2010 - 31/10/2011) were of no importance as it holds no value with negative returns.

Table 3:

Time period 01/01/1990 - 31/10/1990 (Bear)

Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Q5-Q1 Mean (simple) Excess R -14,411% -23,572% -24,295% -38,254% -45,497% -31,086% Mean (geometric) Excess R -15,065% -24,531% -25,656% -40,170% -48,001% -32,936% Standard deviation (of R) 12,961% 16,509% 19,828% 25,767% 31,142% 18,180%

Sharpe ratio -1,162 -1,486 -1,294 -1,559 -1,541 -0,379105577

1-factor Alpha 4,643% 1,143% 6,129% -4,359% 7,441% 2,797%

t-statistic 0,78 0,51 3,42*** -0,9 -0,95

3-factor Alpha 0,627% -2,851% 0,645% -2,750% 4,496% 3,870%

t-statistic 0,13 -0,83 0,26 -0,48 0,73

The only statistically significant positive alpha we found in the first bear period was the 1-factor alpha in the third volatility quintile portfolio. The 4-factor alphas are omitted in the first period because the momentum-factor was not available until 1991.

Table 5:

Time period 01/09/2000 - 31/10/2002(Bear)

Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Q5-Q1 Mean (simple) Excess R 2,068% 3,119% -1,834% -11,338% -37,990% -40,058% Mean (geometric) Excess R 1,599% 2,259% -3,408% -13,935% -44,829% -46,428% Standard deviation (of R) 9,830% 13,265% 18,196% 24,302% 47,572% 37,742%

Sharpe ratio 0,163 0,170 -0,187 -0,573 -0,942 -1,104990345 1-factor Alpha 6,276% 9,729% 7,532% 0,664% -21,022% -27,298% t-statistic 1,41 2,17** 1,83* 0,22 -1,91* 3-factor Alpha 1,149% 5,017% 1,671% -3,164% -4,403% -5,552% t-statistic 0,41 1,42 0,7 -1,11 -0,65 4-factor Alpha 1,873% 6,108% 2,046% -3,207% -6,378% -8,251% t-statistic 0,83 2,04* 0,83 -1,11 -1,02

(13)

As seen in the second bear period there is a big difference (albeit at 95 and 90% statistical significance) between the 1 factor alphas of quintile 2 and quintile 5 indicating a strong volatility effect in this bear period.

The third bear period does not show any statistically significant results. The results can be found in table 7 of the appendix.

Table 9:

Time period 01/06/2010 - 31/10/2011 (Bear)

Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Q5-Q1 Mean (simple) Excess R 17,244% 18,298% 13,297% 13,991% 13,330% -3,913% Mean (geometric) Excess R 16,818% 17,126% 10,897% 10,314% 6,491% -10,327% Standard deviation (of R) 8,917% 14,778% 21,574% 26,768% 36,833% 27,916%

Sharpe ratio 1,886 1,159 0,505 0,385 0,176 -1,709804938 1-factor Alpha 11,194% 7,436% -1,667% -4,417% -11,060% -22,254% t-statistic 3,21*** 4,38*** -0,71 -1,78* -2,72** 3-factor Alpha 6,808% 5,720% -2,894% -2,732% -6,291% -13,098% t-statistic 1,55* 2,65** -1,08 -0,76 -1,26 4-factor Alpha 6,963% 5,820% -2,471% -2,754% -6,903% -13,866% t-statistic 1,51 2,87** -0,97 -0,73 -1,56

Even though this period is market as a bearmarket period, the market has moved with an upward trend. This explains the positive average returns. The period is marked as a bear period because there was a quick succession of bull and bear market periods which lasted only a few months. Two bear market periods with a short bull market period in between were merged. The volatility effect can clearly be seen in this table as the 1-factor alphas of the first and last quintile are both

statistically significant (at 99% and 95%) positive and negative. The 3-factor alphas in the first quintile and second quintile both show as statistically significant (at 90% and 95%) positive as well. The second quintile also shows a statistically significant positive alpha (at 95%). The Sharpe-ratio declines as well when looking at higher volatility quintile portfolios.

Below in table 4, 6 and 8 and 10 we find the regression results of the bull market periods between January 1990 and January 2012.

Table 4:

Time period 01/11/1990 - 31/08/2000 (Bull)

Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Q5-Q1 Mean (simple) Excess R 9,456% 10,819% 12,985% 15,033% 25,933% 16,477% Mean (geometric) Excess R 9,016% 10,083% 11,894% 13,499% 22,853% 13,837% Standard deviation (of R) 9,073% 11,655% 14,079% 16,545% 22,540% 13,466%

Sharpe ratio 0,994 0,865 0,845 0,816 1,014 0,020193031 1-factor Alpha 1,685% -0,656% -1,456% -2,140% 2,645% 0,960% t-statistic 0,9 -0,49 -1,51 -2,29** 0,81 3-factor Alpha 1,844% -0,283% -1,538% -2,138% 2,185% 0,341% t-statistic 1,33 -0,32 -1,68* -2,28** 1,15 4-factor Alpha 1,473% -0,697% -0,886% -2,254% 2,431% 0,958% t-statistic 0,95 -0,76 -0,88 -2,04** 1,22

(14)

The first bull market period just before the internet bubble shows some interesting results. The fourth quintile volatility portfolio had a statistically significant (at 95%) negative 1, 3 and 4-factor alpha, while the most volatile quintile did not have a negative alpha. It even seems to have a positive alpha (not statistically significant). It appears that holding portfolios with highly volatility stock gave extra reward during this period. The Sharpe-ratio in the highest volatility quintile was the highest as well.

Table 6:

Time period 01/11/2002 - 31/10/2007 (Bull)

Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Q5-Q1 Mean (simple) Excess R 11,586% 12,293% 14,614% 18,407% 22,754% 11,169% Mean (geometric) Excess R 11,426% 11,971% 14,039% 17,235% 19,567% 8,140% Standard deviation (of R) 5,360% 7,673% 10,166% 14,455% 23,849% 18,489%

Sharpe ratio 2,132 1,560 1,381 1,192 0,820 -1,311472084 1-factor Alpha 5,807% 2,901% 1,011% -1,121% -8,085% -13,891% t-statistic 3,47*** 1,89* 0,89 -0,8 -2,62** 3-factor Alpha 4,861% 2,449% 0,980% -1,099% -6,825% -11,686% t-statistic 3,16*** 1,58 0,8 -0,74 -2,29** 4-factor Alpha 4,172% 1,870% 0,525% -0,255% -5,420% -9,592% t-statistic 2,45** 1,03 0,41 -0,59 -1,56

The bull market period before the credit crisis seems to follow the patterns displayed over the total time period of 1990-2012. It also seems to be consistent with research done before by for example Blitz and van Vliet (2007). The 1,3 and 4-factor alphas in the lowest volatility quintile are statistically significant positive (at 99% and 95%) and the 1 and 3-factor alphas in the highest volatility quintile are statistically significant negative (at 95%). The Sharpe-ratio of the lower quintile portfolios are higher too.

The bull market period between 01/04/2009 and 31/05/2010 did not show any statistically significant regression results. The results can be found in table 8 of the appendix.

Conclusion

Looking at the total time period between 1990 and 2012 we see that all the results are consistent with research done before. Over an extended period of time, portfolios with more volatile stocks do tend to give abnormal excess returns in the form of a negative alpha and portfolios with less volatile stocks do tend to give abnormal excess returns in the form of a positive alpha. The reasons behind this volatility effect were not the purpose behind this paper, so whether is can be attributed to mispricing or as a compensation for factor risk is not determined. We also see that the Sharpe-ratio did decline when looking at the higher volatility quintiles. Even though the regression results get a lot less statistically significant when divide the total time period is shorter bull- and bear market periods, we did find some interesting results. For example, during the bull market period from 1991 to 2000 we found that the most volatile quintile portfolio outperformed every other portfolio. Opposite to other research we even found a positive alpha there (not statistically significant).

(15)

Further research is warranted here to find if this alpha can be statistically significant and if it is formed by mispricing due to the internet bubble. Furthermore, we can see that during the second bull period, the housing bubble, the volatility effect is present. The lowest volatility quintile had a statistically significant positive alpha and the highest volatility quintile had a statistically significant negative alpha. We currently do not have an explanation on what made the difference between these two bull market periods and this needs further investigation. During the bear market periods, it is hard to make conclusions from the results as we are lacking in finding statically significant results due to shorter time periods and thus less data points. We still see some evidence of the volatility effect. Especially during the last bearmarket period between 2010 and 2011 we can see a clear volatility effect on the 1-factor regressions. For further research it is advised to take daily returns as this will probably increase the statistical significance of the results. Due to the lack of significance in the regressions, the result is inconclusive if there is a clear difference in the volatility effect during bull and bear market periods. Further research is warranted to investigate the

difference in, and the drivers behind the volatility effect during different bull and bear market time periods.

(16)

Bibliography

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, 1-23.

Baker, M., Bradley, B., & Wurgler, J. (2011). Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly. Financial Analyst Journal, 67(1).

Baker, N. L., & Haugen, R. A. (2012). Low Risk Stocks Outperform within All Observable Markets of the World.

Blitz, D. C., & van Vliet, P. (2007). The Volatility Effect: Lower Risk Without Lower Return. Journal of Portfolio Management, 102-113.

Blitz, D., Pang, J., & van Vliet, P. (2013). The volatility effect in emerging markets. Emerging Markets Review, 16, 31-45.

Body, Kane, & Marcus. (2011). Investments. New York: McGraw-Hill/Irwin.

Carhart, M. M. (1997). On Persistence in Mutual Fund Performance. The Journal of Finance, 57-82. Clarke, R., Thorley, S., & De Silva, H. (2010). Know Your VMS Exposure. Journal of Portfolio

Management, 52-59.

Cornell, B. (2009). The Pricing of Volatility and Skewness: A New Interpretation. Journal of Investing, 27-30.

Cornell, B., & Roll, R. (2005). A Delegated-Agent Asset-Pricing Model. Financial Analysts Journal, 57-69.

Dutt, T. A., & 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, 999-1017.

Fama, E. F., & French, K. R. (1992). The Cross-Section of Expected Stock Returns. Journal of Finance, 427-465.

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds*. Journal of Financial economics, 3-56.

Fischhoff, B., Slovic, P., & Lichtenstein, S. (1977). Knowing with Certainty: The Appropriateness of Extreme Confidence. Journal of Experimental Psychology, 552-564.

Gonzalez, L., Powell, J. G., Shi, J., & Wilson, A. (2005). Two centuries of bull and bear market cycles. International Review of Economics and Finance, 4, 469–486.

Haugen, R. A., & Heins, J. A. (1975). Risk and the Rate of Return on Financial Assets: Some Old Wine in New Bottles. The Journal of Financial and Quantitative Analysis, 775-784.

Jegadeesh, N., & Titman, S. (n.d.). Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.

(17)

Jensen, M. C., Black, F., & Scholes, M. S. (1972). The Capital Asset Pricing Model: Some Empirical Tests.

Kole, E., & van Dijk, D. (2017). How to identify and forcast bull and bear markets. . JOURNAL OF APPLIED ECONOMETRICS, 32, 120-139.

Kumar, A. (2009). Who Gambles in the Stock Market? The Journal of Finance, 1889-1933. Lamy, A. (2016, 05 17). Low-Volatility ETFs at the Popular Table. Retrieved from Morningstar:

http://www.morningstar.com/cover/VideoCenter.aspx?id=754323

Li, X., Sullivan, R. N., & Garcia-Feijóo, L. (2014). The Limits to Arbitrage and the Low-Volatility Anomaly. Financial Analysts Journal, 70(1), 52-63.

Li, X., Sullivan, R. N., & Garcia-Feijóo, L. (2016). The Low-Volatility Anomaly: Market Evidence on Systematic Risk vs. Mispricing. Financial Analysts Journal, 71(1).

Lintner, J. (1965a). Security Prices, Risk, and Maximal Gains From Diversification. Journal of Finance, 587-616.

Lintner, J. (1965b). The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios. The Review of Economics and Statistics, 13-37.

Lunde, A., & Timmermann, A. (2004). Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets. Journal of Business & Economic Statistics, 253-273.

Miller, M. H., & Scholes, M. (n.d.). Rates of Return in Relation to Risk: A Reexamination of Some Recent Findings. Studies in the Theory of Capital Markets. New York: Preager.

Pagan, A. R., & Sossounov, K. A. (2003). A simple framework for analysing bull and bear markets. Journal of Applied Econometrics, 23-46.

Sharpe, W. F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 425-442.

(18)

Appendix

Table 1.

Table 7:

Time period 01/11/2007 - 31/03/2009 (Bear)

Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Q5-Q1 Mean (simple) Excess R -20,961% -27,825% -35,717% -40,304% -53,968% -33,007% Mean (geometric) Excess R -21,695% -29,275% -38,075% -43,192% -58,618% -36,923% Standard deviation (of R) 13,762% 20,009% 26,707% 30,506% 44,199% 30,437%

Sharpe ratio -1,576 -1,463 -1,426 -1,416 -1,326 0,250174217 1-factor Alpha -1,251% 0,882% 1,329% 0,528% -1,458% -0,208% t-statistic -0,37 0,26 0,36 0,15 -0,22 3-factor Alpha -0,369% 1,786% -0,277% 0,774% -1,880% -1,511% t-statistic -0,1 0,4 -0,07 0,22 -0,22 4-factor Alpha -0,710% 1,205% -0,025% 1,577% -2,008% -1,298% t-statistic -0,2 0,27 -0,01 0,46 -0,22 Table 8:

Time period 01/04/2009 - 31/05/2010 (Bull)

Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5 Q5-Q1 Mean (simple) Excess R 22,753% 29,972% 49,250% 60,654% 142,758% 120,004% Mean (geometric) Excess R 22,241% 28,968% 46,945% 56,420% 124,282% 102,041% Standard deviation (of R) 9,568% 13,049% 18,874% 25,060% 46,181% 36,613%

Sharpe ratio 2,325 2,220 2,487 2,251 2,691 0,366688278 1-factor Alpha 6,184% 1,085% 0,739% -4,445% -3,244% -9,428% t-statistic 0,73 0,16 0,28 -0,85 -0,21 3-factor Alpha 5,730% 1,001% 0,348% -4,171% -2,643% -8,373% t-statistic 0,67 0,14 0,13 -0,79 -0,17 4-factor Alpha 5,635% 0,927% 0,325% -4,155% -2,476% -8,111% t-statistic 1,58 0,28 0,16 -0,77 -0,4

(19)
(20)
(21)
(22)
(23)
(24)
(25)
(26)

Referenties

GERELATEERDE DOCUMENTEN

reg GapinTotalReturnsHK4Q recessionHKLag2 CrAvGrHKLag2 RiskAversionHK... reg GapinTotalReturns4Q Recession4Q

Een interessante vraag voor Nederland is dan welke landen en sectoren betrokken zijn bij het vervaardigen van de producten die in ons land worden geconsumeerd. Deze paragraaf laat

'fabel 1 memperlihatkan jum1ah perkiraan produksi, jumlah perusahaan/bengkel yang membuat, jenis traktor yang diproduksi, asa1 desain dan tahap produksinya.. Jenis

Ten minste één bad of douche voor algemeen gebru i k op elke acht kamers die niet van een privé-bad of -douche zijn voorzien, met dien verstande dat per etage een bad of dou- che

The analysis time for a given resolution is a complex function of stationary phase selectivity, column radius, and thickness of the stationary phase film.. Variation of

Moreover, since the factor weights vary over time and the factors have a different level of correlation with the stock returns, a multi-factor model allows for stochastic

It can be concluded that the CSV measures in panel A and panel B do contain information about the subsequent short-term momentum strategy, while the VDAX measure

Figure 7 shows that for this sample period the stocks in the low quintile exhibit a positive and linear relationship between standard deviations and average returns