Low Volatility Anomaly Osama Abdetawab

Low-Volatility Anomaly

Low-Volatility Anomaly

Author: Osama Abdeltawab

9490 Alvierweg 16 Osama.abdeltawab@uni.li

130212

Seminar paper

University of Liechtenstein

Graduate School

Programme: Master in Banking and Financial Management

Course: Advanced Research Methods in Finance

Module: Empirical Finance

Assessor: Dr. Georg Peter

Supervisor: Prof. Dr. Marco J. Menichetti

Working period: 27.09.2013 to 31.12.2013

Date of submission: 31.12.2013

Low-Volatility Anomaly

2

TABLE OF CONTENTS

1 INTRODUCTION 3

2 A LITERATURE REVIEW 4

3 DATA AND METHODOLOGY 5

4 EMPIRICAL RESULTS 6

5 CONCLUSION 8

REFERENCE LIST 9

Low-Volatility Anomaly

3

1 Introduction and Motivation

Some theoretical models explain the relation between risk and return, such as the Capital Asset Pricing

Model (CAPM) which proves that the expected return of a security or a portfolio depends on the

risk-free rate and risk premium of the asset. Additionally, Modern Portfolio Theory (MPT) is the

theory that seeks to maximize the expected return of the portfolio for a given risk. Consequently, the

high-volatility is connected with higher future return and the low-volatility is connected with lower

future return.1

According to some analysts, investors choose the high volatility portfolio with high beta to achieve a

high expected return. However, some investors choose the low volatility portfolio with low beta to

achieve a higher risk–adjusted return. The main reason of this behavior is that the investor cannot

achieve a high expected return by investing in high volatility stocks, so the investor tends to

trade in low-volatility stocks. Generally risk-averse investors who have a long-term investment

horizon prefer to choose a low- risk strategy for acceptable performance levels.2

In this paper, we seek to understand the behavior for low-volatility anomaly by examining the

behavior of the investors that choose a high volatility portfolio with high beta and ignore the portfolio

with lower risk. An irrational preference for high volatility portfolio is the main reason for investors to

trade in high volatility stocks or risky portfolios due to the representativeness bias and over-confidence

bias.3 High volatility stocks are costly to trade in both position buy and short especially for stocks of

small firms, because the borrowing cost is very high and the number of shares that are available for

borrowing are not enough for all investors.4 The relation between the future return and risk is a

positive relationship but with the concept of the Low volatility anomaly, the relation between risk and

return is flat or negative which leads us to seek ways to resolve such conflict between financial

theories.5

In addition, an investor who has a long-term investment objective can outperform the market by

keeping mixes of financial assets. In other words, investors have probabilities to achieve high return

by exploiting anomalies strategies. Low volatility products expand the options available to equity

investors. Even better; some of them give investors cheap access to important investment anomalies.

Although low-volatility investments are likely to be used during expansionary market environments,

they are expected to achieve a high performance during declines and protect against large drawdown.

1 Yamada & Uesaki , 2009, p.2. 2 Yamada & Uesaki, 2009, p.11. 3 Baker, Bradley & Wurgler, 2010,p.5. 4 Baker, Bradley & Wurgler, 2010,p.8. 5 Vliet, Blitz & Grient, 2011,p.5.

Low-Volatility Anomaly

4

2 Literature Review

Most of the previous studies in this domain tried to explain that both systematic risk and unsystematic

risk are equal to the total risk. Systematic risk refers to the market risk which we can’t mitigate with

diversification of financial products. For example the Capital Asset Pricing Model (CAPM) is used to

measure and calculate the systematic risk. The sensitivity of return to risk depends on some factors

that decide the performance. The most common of these factors are market, a momentum factor based

on the work of Carhart (1997), the size and the value based on the work of Fama and French

(1992, 1993).6 The Capital Asset Pricing Model (CAPM) and Modern Portfolio Theory (MPT) state

that the relation between risk and return is positive. However, this relation is not simple in reality.7

There are several arguments presenting different explanations of the Low-Volatility Anomaly. For

example, Black (1993) argues that investors choose low volatility products in case they face leverage

restriction. Blitz and Vliet (2007), Falkenstein (2010) and Baker, Bradley and Wurgler (2011) state

that investors with a relative return perspective do not support low volatility stocks even if they have

high Sharpe ratio.8 Also Siri and Tufano (1998) explained that fund managers seek to invest in high

volatility stocks and ignore investing in low-volatility stocks, which lead to the flattened relationship

between risk and return. Barberis and Huang (2008) state that it can be negative relation between risk

and return if we invest in stocks as gambling in lotteries, which has an effect on the stock price and

makes the stock overpriced. 9

Furthermore Ang, Hodrick, Xing, and Zhang (2006) find that stocks with a high-volatility achieve

lower future returns, as the main reason to invest in high-risk products is to hedge. 10 Baker, Bradley,

and Wurgler (2011) find that the behavioural explanation is the best way to describe the low-volatility

anomaly. Therefore investing in high-volatility products without objective, just for speculation or

gambling will increase the price of the stock as bubble and decrease the future return.11

6 Li-Lan & Feifei, 2013, p.3. 7 Yamada & Uesaki , 2009, p.2. 8 Vliet, Blitz & Grient, 2011,pp.13-14. 9 Barberis & Huang, 2008,p. 33. 10 Li-Lan & Feifei, 2013, p.3. 11 Baker, Bradley & Wurgler, 2010,p.5.

Low-Volatility Anomaly

5

3 Data and Methodology

Data

To assess the empirical validity of Low-Volatility Anomaly, we chose Standard & Poor's 500 because

it is one of the most commonly used benchmarks for the overall US stock market. We selected 30

stocks randomly from dataset of S&P 500 with a sample period of 20 years for the 1993 through 2013

period. Then we computed the returns of 30 stocks based on monthly returns and estimated the

standard deviation of monthly returns for each stock based on rolling 5 years window.

Methodology

In order to test the relationship between stocks returns and the previous month’s standard deviations,

we applied a two stage Fama-Macbeth regression to price how much return we expect to receive for a

Particular Beta. We assumed we have 30 stocks returns over 20 years with a particular stock’s excess

return in a particular time denoted . We would like to test whether the m factors , and

explain our stocks returns and the premia awarded to exposure to each factor. To do so, we must run a

two-stage regression. The first stage involves a set of regression equal in number to the number of our

sample. The second stage is a set of regressions equal in number to the number of time periods. The

first stage regressions are a set of time series regression of each stock on the factors.

We ran a cross-sectional regression between stocks returns and the previous month’s standard

deviations for each stock separately to calculate the parameters (Alpha ( ) and Beta ( ) of the model.

Now, we know to what extent each stock’s return is affected by each factor. Next, we will test whether

or not the time-series mean of coefficients is statistically significant different from zero. So we can

state our hypothesis, which is as follows:

The null hypothesis notes that our coefficients (Alpha ( ) and Beta ( ) are equal to zero,

states that there is no significant relationship between stocks returns and the previous

month’s standard deviations. In addition, the alternative hypothesis notes that our coefficients

(Alpha ( ) and Beta ( ) are not equal to zero, states that there is significant relationship between

Null Hypothesis

Alternative Hypothesis

Low-Volatility Anomaly

6

stocks returns and the previous month’s standard deviations. If we don’t reject the null hypothesis ),

this does not necessarily mean that the null hypothesis is true, it only suggests that there is not

sufficient evidence against in favour of . Rejecting the null hypothesis then, suggests that the

alternative hypothesis may be true.

4 Empirical Results

Based on our sample, we couldn’t find positive relationship between stocks returns and the previous

month’s standard deviations which can support the Capital Asset Pricing Model (CAPM). And we

couldn’t find negative relationship between stocks returns and the previous month’s standard

deviations which can support the Low-Volatility Anomaly. We can support our result by statistical

tests, which is as follows:

Exhibit (1)

Coefficients Mean 95% confidence interval p-value t-statistic

Alpha (α) -0.1339467 -1.2195262 to 0.9516327 0.8079 -0.2435

Beta (β) 0.1040446 -0.04600003 to 0.25408933 0.1729 1.3683

Table (1) shows that p-value of Alpha (α) 0.8079 is larger than the actual significance level (5%) of

our test, so we can’t reject the null hypothesis ) and confirms that there is no relationship between

stocks returns and the previous month’s standard deviations. In additional, the p-value of

Beta (β) 0.1729 is larger than the actual significance level (5%) of our test, so we can’t reject the null

hypothesis ) and confirms that there is no relationship between stocks returns and the previous

month’s standard deviations.

We can support our result by t-statistic, Table (1) shows that t-statistic of Alpha (α) -0.2435 is lower

than the critical value (1.96) of our test, so we can’t reject the null hypothesis ) and confirms that

there is no relationship between stocks returns and the previous month’s standard deviations.

Furthermore, t-statistic of Beta (β) 1.3683 is lower than the critical value (1.96) of our test, so we can’t

reject the null hypothesis ) and confirms that there is no relationship between stocks returns and the

previous month’s standard deviations.

Afterwards, we created three portfolios with low, medium and high volatility stocks based on our

sample which is 30 stocks. Each portfolio will cover a maximum of 10 stocks. Then we computed a

time series of monthly returns for each portfolio of the three groups by calculating the weighted

average of next month’s returns. We can provide a descriptive statistic of the time-series of returns for

each of the three volatility portfolios which is as follows:

Low-Volatility Anomaly

7

Exhibit (2)

Low Portfolio Med Portfolio High Portfolio

nobs 180 180 180

Nas 0 0 0

Minimum -25.196012 -35.392793 -35.594055

Maximum 24.707609 24.655112 29.26647

1. Quartile -1.375935 -2.043676 -2.297949

3. Quartile 3.510044 4.866799 5.002555

Mean 0.56099 0.823101 1.155686

Median 1.242904 1.673981 1.816925

Sum 100.978246 148.158184 208.023484

SE Mean 0.424156 0.502859 0.568108

LCL Mean -0.275999 -0.169193 0.034636

UCL Mean 1.39798 1.815395 2.276736

Variance 32.383509 45.516019 58.094307

Stdev 5.690651 6.746556 7.621962

Skewness -0.765326 -0.962803 -0.528061

Kurtosis 6.131932 5.688747 3.695875

It can be seen that high volatility portfolio had the highest median (Median=1.816925), on the other

hand the low volatility portfolio had the lowest median (Median=1.242904). Additionally, the high

volatility portfolio had the highest standard deviation which indicates that the data points are spread

out over a large range of values and high variation (SD=7.621962), on the other hand the low volatility

portfolio had the lowest standard deviation which indicates that the data points tend to be very close to

the median and low dispersion (SD=5.690651).

Table (2) shows that, the skewness of the three volatility portfolios is lower than zero which is

negatively skewed, so there are more negative values which indicates that the the degree and the

direction of asymmetry are skewed to the left. We can conclude that a risk-averse investor does not

like negative skewness. It can be seen that the kurtosis of the three volatility portfolios is high than 3

which is positive excess kurtosis (leptokurtic distribution). In case of a positive skewness, it is possible

to have a high excess kurtosis and to have no future extreme negative returns. The extreme returns will

only be positive. This is only possible when the skewness is positive. As soon as the skewness is nega-

tive, the impact of a high excess kurtosis affects the extreme negative returns.

-60 -50 -40 -30 -20 -10

0 10 20 30 40 50 60

1

7

13

19

25

31

37

43

49

55

61

67

73

79

85

91

97

10

3

10

9

11

5

12

1

12

7

13

3

13

9

14

5

15

1

15

7

16

3

16

9

17

5

Exhibit (3) Analysis of Volatility Portfolios

low volatility portfolio Med volatility portfolio High volatility portfolio

Low-Volatility Anomaly

8

5 Conclusion

In theory, the positive relationship between stocks returns and the previous month’s standards

deviations can be supported by traditional models, for example, the Capital Asset Pricing Model

(CAPM) and the Modern Portfolio Theory (MPT).The main reason for those theories is the fact that a

rational investor would only accept a higher level of risk if it is offset by a higher degree of return. In

contrast, the negative relationship between stocks returns and the previous month’s standards

deviations can be supported by the Low-volatility Anomaly. On the other hand, there are many

empirical evidences suggest that the relationship between risk and return is flat or negative.

In the final analysis, we conclude that there is no relationship between stocks returns and the previous

month’s standards deviations to support the traditional models or the Low-Volatility Anomaly based

on our sample of 30 stocks. If we tried to run a cross-sectional regression between stocks returns and

the previous month’s standard deviations for many times and calculate our parameters (Alpha ( ) and

Beta ( ) of the model again, we could find a positive or negative relationship between stocks returns

and the previous month’s standards deviations.

Low-Volatility Anomaly

9

Reference List

Baker, M., Bradley, B., &Wurgler, J. (2010). Benchmarks as Limits to Arbitrage:Understanding the

Low Volatility Anomaly. NYU Working Paper No. 2451/29593. Retrieved from SSRN:

http://ssrn.com/abstract=1585031

Barberis, N., & Huang, M. (2008). Stocks as Lotteries: The Implications of Probability Weighting for

Security prices. American Economic Review, 98(5), 2066-2100. doi: 10.1257/aer.98.5.2066

Hsu, L. C., Kudoh , H., & Yamada, T. (2013). When Sell-Side Analysts Meet High-Volatility Stocks:

An Alternative Explanation for the Low-Volatility Puzzle. Journal of Investment Management, 11(2),

28-46. doi:10.2139/ssrn.2061824

Li-Lan, K., & Feifei, L. (2013). An Investor’s Low Volatility Strategy. The Journal of Index Investing,

3(4), 8-22. doi:10.3905/jii.2013.3.4.008

Vliet,P., Blitz, D., & Grient, B. (2011). Is the Relation between Volatility and Expected Stock Returns

Positive, Flat or Negative?. Retrieved from SSRN: http://ssrn.com/abstract=1881503

Yamada, T., & Uesaki, I. (2009). Low Volatility Strategy in Global Equity Markets. Retrieved from

http://www.saa.or.jp/english/publications/yamade_uesaki.pdf