Academic journal article The Lahore Journal of Economics

Value-at-Risk and Expected Stock Returns: Evidence from Pakistan

Academic journal article The Lahore Journal of Economics

Value-at-Risk and Expected Stock Returns: Evidence from Pakistan

Article excerpt

(ProQuest: ... denotes formulae omitted.)

1. Introduction

The most important implications of the capital asset pricing model (CAPM) (see Sharpe, 1964; Lintner, 1969; Black, Jensen, & Scholes, 1972) are that (i) the expected return on a risky asset is linearly and positively related to its systematic risk, and (ii) only the asset's beta captures cross-sectional variations in expected stock returns; other variables have no explanatory power. However, the empirical evidence of the last few decades suggests that many alternative risk and nonrisk variables are able to explain average stock returns. These include size (Banz, 1981), the ratio of book equity to market equity (Fama & French, 1992, 1993, 1995, 1996; Stattman, 1980; Rosenberg, Reid, & Lanstein, 1985; Chan, Hamao, & Lakonishok, 1991), the price/earnings ratio (Basu, 1977), leverage (Bhandari, 1988), liquidity (Pastor & Stambaugh, 2003), and value-at-risk (VaR) (Bali & Cakici, 2004; Chen, Chen, & Chen, 2010).

Bali and Cakici (2004) investigate the relationship between portfolios sorted by VaR1 and expected stock returns and find that VaR, size, and liquidity explain the cross-sectional variation in expected returns, while beta and total volatility have almost no explanatory power at the stock level. Furthermore, the strong positive relationship between average returns and VaR is robust for different investment horizons and loss-probability levels.

VaR is a popular measure of risk value among finance practitioners and regulators of banks and financial institutions because it provides a single number with which to quantify the monetary loss associated with a portfolio exposed to market risk with a certain probability. If portfolios sorted by VaR result in higher returns associated with a higher VaR, then this can prove to be extremely valuable information for investors, portfolio managers, and financial analysts who can construct and recommend profitable portfolio strategies accordingly. The Basel II accord on banking supervision also recommends using VaR to measure the market risk exposure of banking assets. It is, therefore, an equally useful measure for market regulators and policymakers, making it important to investigate the asset pricing implications of VaR as a risk factor.

Apart from Bali and Cakici's (2004) pioneering study on the US and a recent study on Taiwan by Chen et al. (2010), there are no empirical studies on this aspect of asset pricing in the context of emerging and developed markets. The major objective of our study is to test whether the maximum likely loss as measured by VaR can explain the cross-sectional and time variations in average returns in Pakistan as an emerging market.

We have selected Pakistan for this analysis because it typifies an emerging market, exhibiting features such as higher returns associated with higher volatility, lower liquidity, a relatively high market concentration, and infrequent trading of many stocks.2 Additionally, given that determining the validity of an economic or financial theory or model requires testing it under different conditions, this study aims to contribute to the literature by testing the relationship between VaR and expected returns accordingly. Our analysis reveals that constructing VaR as the common risk factor enables a better explanation for time variations in average portfolio returns sorted by size and book-to-market factors as compared to the Fama-French common factors.

2. Literature Review

Over the last six decades, downside risk has been studied from the perspective of explaining asset returns. The concept of measuring downside risk dates back to Markowitz (1952) and Roy (1952). Markowitz (1952) provides a quantitative framework for measuring portfolio risk and return. The study utilizes mean returns, variances, and covariances to develop an efficient frontier on which every portfolio maximizes the expected return for a given variance or minimizes the variance for a given expected return. …

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