The validity of modern portfolio theory has been and will continue to be an important research issue. The tradeoff between risk and expected return, which can be viewed as a “No free lunch” principle, asserts that over the long run it is not possible to achieve exceptional returns without accepting commensurably substantial risks. Any standard equilibrium model of asset pricing justifies this relationship. The well- known capital asset pricing model (CAPM) of Sharpe (1964), Linter (1965), and Black (1972) has, for decades, been the major framework for analyzing the cross sectional variation in expected asset returns. The main implication of the theory is that: (a) the expected return on a security is a positive linear function of its market β and (b) the market β itself suffices to describe the cross-section of expected returns.
Unfortunately, theory and practice do not always match. Fama and French (1992) drew two negative conclusions regarding CAPM, namely: (a) when one allows for variations in CAPM market βs that are unrelated to size, the univariate relationship between β and the average return for 1941-1990 is weak, and (b) β does not suffice to explain the average return. Fama and French further find no cross-sectional mean-beta relationship after controlling for size and the ratio of book-to-market equity. The evidence shows that the market return should not be the only relevant risk factor in the economy, and additional factors are required to explain the expected returns.
Several alternative risk factors have consequently been employed in the literature, for example, the size effect of Banz (1981). He finds that the market value of equity (ME) provides a prominent explanation of the cross-section of average returns provided by market beta. Variables such as the book-to-market equity ratio (BE/ME) (Fama and French, 1992, 1993, 1995, 1996; Stattman, 1980; Rosenberg, Reid, and Lanstein, 1985), the price/earnings ratio (Basu, 1977), leverage (Bhandari, 1998), and
Value-at-Risk (Bali and Cakici, 2004) all have significant explanatory power for explaining average expected returns.
In particular, the concept and use of Value-at-Risk (henceforth VaR) is relatively recent and is designed to summarize the predicted maximum loss (or worst loss) over a target horizon within a given confidence interval (Jorion, 2000). Extreme price movements are rare, but they can bring serious results to some corporations, leading to disastrous consequences for a country’s financial markets. For instance, the New York stock market crashed in October 1987, and then, one decade later, the Asian stock market crashed in 1997. Besides, the Enron scandal has also caused the Dow Jones Industrial Average (DJIA) to drop sharply. These crises have harmed thousands of companies and much of the value of their stocks has been wiped out within a short period of time. Therefore, to a risk manager, a good measure of market risk is more than necessary. VaR was first used by major financial firms in the late 1980’s to measure the risks of their trading portfolios. Since then, the use of VaR has exploded, with J.P. Morgan’s attempt to establish a market standard through its release of the RiskMetricsTM system in 1994.
VaR is now not only widely used by financial institutions, non-financial corporations, and institutional investors, but has also become a common language for communication with regard to aggregate risk taking, both within an organization and outside it (for example, with analysts, regulators, and shareholders). Even regulators have become interested in VaR. For example, the Basle Committee on Banking Supervision (Basle Committee, 1996) permits banks to calculate their capital requirements for market risk using their own proprietary VaR models, while the Securities and Exchange Commission (SEC, 1997) requires that U.S. companies disclose quantitative measures of market risks, with VaR listed as one of three possible market risk disclosure measures.
In a normal world, the standard deviation of the portfolio returns is a good risk measure, and efficient portfolios are the ones generating the best mean-variance profiles. Modeling portfolio risk with traditional standard deviation measures implies that investors are concerned only with the average variation in individual stock returns, and they are not allowed to treat the negative and positive tails of the return distribution separately. However, statistical data exhibit fat-tailed and asymmetric distributions for market returns. The fat tail represents the extent to which the portfolio’s value can be affected by large jumps in market prices. The empirical evidence also indicates that the minimum-variance portfolios are far from being the most efficient ones with respect to the relevant risk measures. During the last few decades we can see that the most popular and traditional measure of risk has been volatility. The main problem with volatility, however, is that it does not take into consideration the direction of an investment’s movement － a stock can be volatile because it suddenly jumps higher. However, investors are not distressed by gains! By assuming that investors care about the likelihood of a really big loss, VaR answers the question, “What is my worst-case scenario?”
Traditional models treat all uncertainty as risk, regardless of the direction it takes.
As many people have shown, that is a problem if returns are not symmetrical – investors worry about their losses “to the left” of the average, but they do not worry about their gains “to the right” of the average. If investors are more averse to the risk of losses on the downside than to the gains on the upside, investors ought to demand greater compensation for holding stocks with greater downside risk. In particular, many authors, including Campbell, et al. (2001), find that market volatility increases in bear markets and recessions. Moreover, Duffee (1995) finds that idiosyncratic volatility decreases in down-markets. Both of these effects cause the conditional beta to have little asymmetry across the downside and the upside. To
sum up, this paper measures VaR in terms of a company’s market value at risk.
Hence the VaR is related to the company’s stock price and it thus reflects the shareholders’ perception of risk. The reason for considering VaR is that it is an easy-to-understand summary measure of downside risk. The downside focus separates the loss from the upside potential － only the former truly constitutes risk and only negative surprises to the stock market represent potential litigation threats.
Furthermore, the concept of VaR is easily grasped and hence easily communicated.
Surprisingly, despite its wide acceptance among practitioners, academics, and regulators, VaR has so far only been considered to be a risk factor in Bali and Cakici’s (2004) study. Therefore, this research aims to supplement our understanding of the measurement of risk and to provide some emerging market evidence while the only related study focuses mainly on mature markets. The Taiwan stock market is also unique for its tight short-sale constraints and a 7% daily price change limit.
An important contribution of this paper is that it tests whether the maximum likely loss measured by VaR plays a key role in explaining expected returns in Taiwan. The central motivation behind this paper is that it also provides an analysis in terms of examining the cross-sectional variation among beta, firm size, the book-to-market ratio (BE/ME) and Value-at-Risk (VaR) at the firm level. The remainder of this paper is organized as follows. Section 2 reviews the literature.
Section 3 describes the dataset and variable definitions. Section 4 contains the methodology and models. Section 5 presents the empirical results of our analysis.
Section 6 summarizes and concludes our findings.