Beta Anomaly and Comparative Analysis of Beta Arbitrage Strategies

Abstract

Over a long period of time, stocks with low beta have consistently outperformed their high beta counterparts across developed and emerging markets alike. We explore the presence of low beta anomaly and its robustness after controlling for size, value and momentum factors in the Indian stock markets. We have chosen the universe of past and present constituent stocks of the Nifty 500 index in our study for the period 2001 to 2014. We study relative risk-adjusted performance and portfolio characteristics of three different zero-cost, long-short beta arbitrage strategies including beta neutral and negative net beta version of strategies. We find all the beta arbitrage strategies deliver superior risk adjusted performance in the Indian markets, though of different magnitude, with a clear tilt away from the value factor and towards the momentum factor. However, we don’t find any tilt towards size factor. Our study provides the framework for choosing an implementable beta arbitrage strategy consistent with the investor’s investment objective.

JEL classification: G11, G12, G14, G15

Introduction

An investment strategy based on investing in a portfolio that consists of low risk, stable stocks that consistently outperforms a matching portfolio of high risk, volatile stocks as well as market portfolio on risk adjusted basis. This phenomenon is widely known as risk anomaly or volatility puzzle.

In this study, we explore the presence of low beta anomaly and its robustness, after controlling for size, value and momentum factors, in the Indian stock markets. We have chosen the past and present constituent stocks of the Nifty 500 index for our study over a period 2001 to 2014.

We answer the following questions with respect to the Indian equity markets:

  1. Does beta anomaly exist after removing small and illiquid stocks from the universe?
  2. Does beta anomaly remain robust after controlling for size, value and momentum factors?
  3. What are the alternative ways of implementing beta arbitrage strategies and how to compare different beta arbitrage strategies?

We establish the following: (a) Beta anomaly is robust even after eliminating small and illiquid stocks from the universe. (b) Beta anomaly is robust after controlling for size, value and momentum factors, and is not proxy for any other factors. (c) We compare relative attractiveness of alternative beta arbitrage strategies and we find that all beta arbitrage strategies deliver different magnitudes of superior risk-adjusted performance in Indian markets with a clear tilt away from the value factor and towards the momentum factor. We don’t find any tilt towards size factor. (d) While all strategies offer superior risk-adjusted performance, they have very different ex-post beta and therefore, choice of strategy is a function of the investment objective.

This study highlights key differences in characteristics of alternative beta arbitrage strategies and it provides a simple framework for choosing an implementable beta arbitrage strategy consistent with the investment objective.

Risk anomaly is one of the strongest anomalies. It has remained largely unexplored by researchers and under-exploited by practitioners till the dawn of the twenty first century. This anomaly is against the very spirit of a strictly positive relationship between risk and return depicted by classical asset pricing theories like the capital asset pricing model (CAPM). According to CAPM, systematic risk as measured by beta is the sole driver of the expected return. In the CAPM world, market portfolio is the portfolio with the highest Sharpe ratio, which implies excess return per unit of risk. Rational investors must hold a combination of market portfolio and long/short position in risk-free asset to meet their unique risk preferences. Risk-averse investors de-lever their holding in the market portfolio by investing a fraction of their capital in the market portfolio and remaining capital in risk-free assets. On the contrary, investors with a higher risk appetite use leverage – by borrowing money to increase expected returns on the market portfolio. In the imperfect real world outside the CAPM framework, various categories of investors including retail investors, mutual funds and pension funds may not have unconstrained access to leverage. Such investors tend to exhibit preference for high beta security in anticipation to earn higher expected returns compared to the market portfolio.

Early evidence of low risk anomaly and flatter security market line for US stocks can be traced back to the early 1970s. Black (1972) and Black, Jensen and Scholes (1972) first highlight that the security market line is much flatter than predicted by CAPM, because of the borrowing restrictions resulting in low beta stocks having a positive and higher alpha. Haugen and Heins (1975) were among the first to show that stocks with low volatility of historical returns tend to outperform those with higher volatility. However, during hay days of market efficiency and CAPM, these results were dubbed as a data mining exercise or an aberration.

Subsequently after a long gap, research on risk anomaly has picked up and since the beginning of the twenty first century, many researchers have explored low risk anomaly using various approaches. Studies differ mainly on two counts – choice of risk measure and method of portfolio construction approach. While popular risk measures include idiosyncratic volatility, standard deviation and beta, two popular portfolio construction approaches are portfolio construction based on ranking stocks using a risk measure and constructing a minimum variance portfolio using modern portfolio theory Markowitz (1952) framework. More recent literature is focused on finding rational and behavioral explanations to explain the risk anomaly or to explain it away. Ang, Hodrick, Xing and Zhang ((2006), (2009)) use idiosyncratic volatility calculated as standard deviation of residuals of daily stock returns regressed upon proxies for market, size, value and momentum factors as defined by Fama and French (1992) and Carhart (1997). They report an inverse relationship between idiosyncratic risk and expected returns across global markets. Clarke, De Silva and Thorley (2006) report that minimum variance portfolio in US markets provides comparable or better-than-market returns with 25% reduction in volatility. Blitz and Vliet (2007) find that volatility effect is stronger than beta effect. They further establish that volatility effect is a distinct effect and is by no means disguised in other classic effects such as size, value and momentum.

Baker and Haugen (2012), Blitz and Vliet (2007), and Blitz, Pang and Vliet (2013) demonstrate that risk anomaly is a global phenomenon. Baker, Bradley and Wurgler (2011) use beta as well as volatility sorting, using only large cap stocks in US market and demonstrate that low beta-high alpha and high beta-low alpha phenomenon persists even in large cap stocks. They offer a series of explanations, rational as well as behavioural, to explain persistence of such anomaly. They argue that institutional investors’ mandate to focus on beating a benchmark, coupled with borrowing and short-selling restrictions, hinders their ability to exploit a low beta, high alpha opportunity. As a result, they take exposure to high beta, low alpha stocks.

Moreover, behavioural biases such as preference for lottery, overconfidence and representativeness cause investors to chase high beta stocks. This leads to price increase in high beta stocks leading to lower returns in the subsequent periods. Bali and Cakici (2008) argue that the negative relationship shown by Ang, Hodrick, Xing and Zhang (2006) between idiosyncratic volatility and expected return is due to small, illiquid stocks only. If these small stocks are excluded from the sample, a puzzling negative relationship between idiosyncratic volatility and expected returns turns insignificant. Bali, Cakici and Whitelaw (2011) create a variable to capture lottery-like payoff and show that an inverted risk-return relationship between idiosyncratic risk and expected return is due to investors’ preference for lottery-like payoffs. They also demonstrate that such inverted relationship between risk and return cannot be explained by skewness in distribution of returns. Fu (2009) argues that an inverted relationship between idiosyncratic risk and expected return is due to short term reversals. In line with Black (1993), Frazzini and Pedersen (2010), and Hong and Sraer (2012) also attribute an anomalous flat-to-negative relationship between risk and return to borrowing restrictions and short selling constraints. Brennan (1993), Karceski (2002), Falkenstein (2009), Blitz, Pang and Vliet (2013) and Baker and Haugen (2012) argue that there is an agency problem associated with delegated portfolio management and also argue that the call option-like fund manager’s compensation structure tilts their preference towards high risk stocks. Clarke, De Silva and Thorley (2010) construct an additional factor based on idiosyncratic volatility ‘volatile-minus-stable (VMS)’ after controlling size effect and show that VMS is an important factor in explaining a cross-section of security returns.

While there are several strands of research emerging on this exquisite anomaly of markets, we extend the strand of beta arbitrage based investment strategy. Black, Jensen and Scholes (1972) and Black (1993) first provide a framework and evidence on how unconstrained investors can exploit a flatter-than-expected security market line. More recently, Frazzini and Pedersen (2014), in their seminal work, extend the scope of beta arbitrage by constructing betting against beta (BAB) portfolios across several asset classes and markets. They report large and significant risk-adjusted returns. By design, ‘betting against beta’ portfolios are market neutral on ex-ante basis because of active use of levering of low beta portfolios and de-levering of high beta portfolios. Asness, Frazzini and Pedersen (2014) demonstrate that betting against beta strategies are not merely industry bets as suspected by many. They establish it by constructing industry neutral BAB factor.

The rest of the paper is organized as follows. Section 2 discusses data and methodology, Section 3 discusses results and Section 4 offers the conclusion.

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