Risk-Adjusted Performances of World Equity Indices

This article investigates whether equity indices of twenty-four emerging and twenty-eight developed markets compensate their investors equally after adjusting for total or downside risk, and examines the predictive power of reward-to-risk ratios for expected market returns. We find that when all fifty-two markets are ranked based on their alternative reward-to-risk ratios, almost all of the countries in the top (bottom) quartile are emerging (developed) markets. The pooled means of the reward-to-risk ratios are also significantly higher for emerging markets. Both portfolio and regressions analysis reveal that there is a significantly positive relation between various reward-to-risk metrics and expected market returns.     

Correlation and return dispersion dynamics in Chinese markets

This paper studies the relation between firm-level return dispersions and correlations among Chinese stocks during periods of unusually large upward and downward swings. We analyze individual stock returns across 18 sectors and test if return dispersions and stock correlations show asymmetric patterns for extreme up and down markets. Evidence from studies on U.S. stocks suggests that equity return correlations tend to be much greater on the downside than on the upside and that the degree of comovement gets even stronger during extreme market states. However, in the case of Chinese stock market, we find that higher downside correlations apply to only stocks within the Financial sector. With the exception of Financial stocks, we find that stock correlations are significantly higher during up markets, rather than down markets. Regarding firm-level return dispersions, our findings are consistent with rational asset pricing model predictions. We find that equity return dispersions are significantly higher during periods of large price changes.     

Optimal Number of Stock Holdings in Mutual Fund Portfolios Based on Market Performance

Among the decisions that most mutual fund portfolio managers make is the number of stocks to hold. We posit that there is an optimal number of stocks for each mutual fund, reflecting the trade‐off between diversification benefits versus transactions and monitoring costs. We find a significant quadratic relation between number of stock holdings and risk‐adjusted returns for U.S. equity mutual fund portfolios during 1992–2000. Moreover, we find that changes in the number of stocks held over time are more highly correlated with mutual fund flows than with funds' investment returns.     

Life Insurer Cost of Equity with Asymmetric Risk Factors

This study presents an improved model for estimating life insurer cost of capital with the inclusion of upside and downside risk factors and controlling for life insurer characteristics. Although various asymmetric measures of market risk have been shown to be priced factors for the broader equity market, life insurer realized equity returns include a much larger premium for bearing downside risk, even after controlling for firm characteristics and other measures of risk. Cross‐sectional regression analysis finds a positive (negative) premium for downside (upside) betas, conditional on down and up markets, respectively. Coskewness and cokurtosis are also priced factors.     

Downside Risk in Emerging Markets

This paper investigates the relation between downside risk and expected returns on the aggregate stock market in an international context. Nonparametric and parametric value at risk are used as measures of downside risk to determine the existence of a risk-return trade-off. For emerging markets, fixed effects panel data regressions provide evidence for a significantly positive relationship between monthly expected market returns and downside risk. This result is robust after controlling for aggregate dividend yield and price-to-fundamental ratios. The relationship between expected returns and downside risk is weaker for developed markets and vanishes when control variables are included in the specification.     

Does Idiosyncratic Risk Really Matter?

Goyal and Santa‐Clara (2003) find a significantly positive relation between the equal‐weighted average stock volatility and the value‐weighted portfolio returns on the NYSE/AMEX/Nasdaq stocks for the period of 1963:08 to 1999:12. We show that this result is driven by small stocks traded on the Nasdaq, and is in part due to a liquidity premium. In addition, their result does not hold for the extended sample of 1963:08 to 2001:12 and for the NYSE/AMEX and NYSE stocks. More importantly, we find no evidence of a significant link between the value‐weighted portfolio returns and the median and value‐weighted average stock volatility.     

Risk Interpretation of the CAPM's Beta: Evidence from a New Research Method

This study tests the validity of using the CAPM beta as a risk control in cross‐sectional accounting and finance research. We recognize that high‐risk stocks should experience either very good or very bad returns more frequently compared to low‐risk stocks, that is, high‐risk stocks should cluster in the tails of the cross‐sectional return distribution. Building on this intuition, we test the risk interpretation of the CAPM's beta by examining if high‐beta stocks are more likely than low‐beta stocks to experience either very high or very low returns. Our empirical results indicate that beta is a strong predictor of large positive and large negative returns, which confirms that beta is a valid empirical risk measure and that researchers should use beta as a risk control in empirical tests. Further, we show that because the relation between beta and returns is U‐shaped, that is, high betas predict both very high and very low returns, linear cross‐sectional regression models, for example, Fama–MacBeth regressions, will fail on average to reject the null hypothesis that beta does not capture risk. This result explains why previous studies find no significant cross‐sectional relation between beta and returns.     

THE EFFECT OF SIZE,BOOK-TO-MARKET EQUITY,PRIOR RETURNS,AND BETA ON STOCK RETURNS: JANUARY VERSUS THE REMAINDER OF THE YEAR

Size and book-to-market equity are shown to transcend beta in explaining stock returns. One possible explanation of the book-to-market equity effect is overreaction. We investigate the effect of size, book-to-market equity, prior returns, and beta on stock returns. We find significant reversals in January consistent with overreaction. We find a strong positive relation between returns and prior returns for February through December. Both patterns are distinct from either a size or book-to-market equity effect. Book-to-market equity is significantly related to returns, with some evidence of a stronger effect in January.     

The cost of equity of internet stocks: a downside risk approach

Beta as a measure of risk has been under fire for many years. Although practitioners still widely use the CAPM to estimate the cost of equity of companies, they are aware of its problems and are looking for alternatives. A possible alternative is to estimate the cost of equity based on the semideviation, a well-known and intuitively plausible measure of downside risk. Complementing evidence reported elsewhere about the ability of the semideviation to explain the cross-section of returns in emerging markets and that of industries in emerging markets, this article reports results showing that the semideviation also explains the cross-section of Internet stock returns.     

A novel downside beta and expected stock returns

A number of studies have found that the cross-section of stock returns reflects a risk premium for bearing downside beta; however, existing measures of downside beta have poor power for predicting returns. This paper proposes a novel measure of downside beta, the ES-implied beta, to improve the prediction of the cross-section of asset returns. The ES-implied beta explains stock returns over the same period as well as the widely used downside beta, but improves the prediction for future returns due to its high persistence. In the empirical analysis, the widely used downside beta shows a weak relation with future expected returns, but the ES-implied beta implies a statistically and economically significant risk premium of 0.6% per month and explains 0.6% of the variation in the cross-sectional returns. The effect cannot be explained by traditional cross-sectional effects and is different from the CAPM beta, the downside beta in Ang et al. (2006), coskewness, and cokurtosis.     

Conditional interest rate risk and the cross‐section of excess stock returns

Differences in excess stock returns can be rationalized by their sensitivities to conditional interest rate risk. Value stocks are particularly sensitive to upside movements in interest rate growth, while growth stocks react strongly to downside movements in interest rate growth. Consistent with the basic asset pricing theory, the upside interest rate risk commands a negative premium which is higher than the premium associated with the downside interest rate risk. Upside beta pertains its explanatory power after controlling for exposure to regular unconditional interest rate and various sources of financial and conditional macroeconomic risk.     

Asymmetric Volatility,Skewness, and Downside Risk in Different Asset Classes: Evidence from Futures Markets

This study examines the cross‐sectional variation of futures returns from different asset classes. The monthly returns are positively correlated with downside risk and negatively correlated with coskewness. The asymmetric volatility effect generates negatively skewed returns. Assets with high coskewness and low downside betas provide hedges against market downside risk and offer low returns. The high returns offered by assets with low coskewness and high downside betas are a risk premium for bearing downside risk. The asset pricing model that incorporates downside risk partially explains the futures returns. The results indicate a unified risk perspective to jointly price different asset classes.     

The Role of Beta and Size in the Cross-Section of European Stock Returns

This paper examines the ability of beta and size to explain cross-sectional variation in average returns in 12 European countries. We find that average stock returns are positively related to beta and negatively related to firm size. The beta premium is in part due to the fact that high beta countries outperform low beta countries. Within countries high beta stocks outperform low beta stocks only in January, not in other months. We reject the hypothesis that differences in average returns on size- and beta-sorted portfolios can be explained by market risk and exposure to the excess return of small over large stocks (SMB). Consistent with recent US evidence, we find that after controlling for size, there is no association between average returns and exposure to SMB.     

Why Do Firms Issue Equity after Splitting Stocks?

This paper examines the motivations of firms that conduct seasoned equity offerings (SEOs) after splitting stocks. We find no difference in equity announcement and issue period returns between these firms and other equity‐issuing firms, suggesting that firms do not split stocks to reveal information and reduce adverse selection costs at the subsequent SEO. However, because investors react positively to split announcements, firms that issue equity after splitting stocks sell new shares at a higher price and raise more funds. We also find that firms split stocks to make the subsequent SEO more marketable to individual investors who are attracted to low‐priced shares.     

Downside risk of international stock returns

This paper investigates the downside risk exposure of international stock returns in 14 major industrialized economies around the world. For the period 1975–2010, we find that differences in returns on value and growth portfolios can be rationalized by assets’ reagibilities to market’s downside shocks. International value stocks are particularly sensitive to market’s permanent downside shocks, while international growth stocks are particularly sensitive to market’s temporary downside shocks. In line with recent evidence for the US, risk associated with unfavorable changes in market’s cash-flow innovations carries a premium which is pervasive and statistically significant.     

Delayed Expected Loss Recognition and the Risk Profile of Banks

This paper investigates the extent to which delayed expected loan loss recognition (DELR) is associated with greater vulnerability of banks to three distinct dimensions of risk: (1) stock market liquidity risk, (2) downside tail risk of individual banks, and (3) codependence of downside tail risk among banks. We hypothesize that DELR increases vulnerability to downside risk by creating expected loss overhangs that threaten future capital adequacy and by degrading bank transparency, which increases financing frictions and opportunities for risk‐shifting. We find that DELR is associated with higher correlations between bank‐level illiquidity and both aggregate banking sector illiquidity and market returns (i.e., higher liquidity risks) during recessions, suggesting that high DELR banks as a group may simultaneously face elevated financing frictions and enhanced opportunities for risk‐shifting behavior in crisis periods. With respect to downside risk, we find that during recessions DELR is associated with significantly higher risk of individual banks suffering severe drops in their equity values, where this association is magnified for banks with low capital levels. Consistent with increased systemic risk, we find that DELR is associated with significantly higher codependence between downside risk of individual banks and downside risk of the banking sector. We theorize that downside risk vulnerability at the individual bank level can translate into systemic risk by virtue of DELR creating a common source of risk vulnerability across high DELR banks simultaneously, which leads to risk codependence among banks and systemic effects from banks acting as part of a herd.     

The Equity Premium: Consistent with GDP Growth and Portfolio Insurance

We find that the long‐term equity premium is consistent with both GDP growth and portfolio insurance. We use a supply‐side growth model and demonstrate that the arithmetic average stock market return and the returns on corporate assets and debt depend on GDP per capita growth. The implied equity premium matches the U.S. historical average over 1926–2001. Separately, we find that the equity premium tracks the value of a put option on the S&P 500. Our theory predicts a smaller equity premium in the future, assuming that the recent regime shifts in dividend policies, interest rates, and tax rates are permanent.     

Downside Risk in Practice

Although investors associate risk with negative outcomes and downside fluctuations, modern portfolio theory does not. For investors, volatility per se is not necessarily bad; volatility below a benchmark is. A stock that magnifies the market's fluctuations is not necessarily bad; one that magnifies the market's downside swings is. Even Harry Mar‐kowitz, the father of modern portfolio theory, viewed downside risk as a better way to assess risk than the “mean‐variance” framework that he ultimately proposed and that has since become the standard. This article highlights the shortcomings of traditional measures of risk (the standard deviation and beta), introduces the concept of downside risk, and discusses two measures of it—the “semideviation” and “downside beta.” It also discusses the use of such measures in asset pricing models to estimate required returns on equity. Data from a few well‐known companies are used to illustrate that the cost of equity based on downside risk can be substantially different from that based on the CAPM. The article concludes with a brief discussion of risk‐adjusted returns and a comparison of the traditional method of calculating such returns with both the Sharpe ratio and its counterpart in a downside risk framework, the Sortino ratio. The appendix demonstrates how to calculate these risk measures in Excel.     

Analyst Forecasts and the Cross Section of European Stock Returns

We examine revisions to earnings forecasts by equity analysts and their role in predicting stock returns. We provide evidence that European stocks with net upward revised forecasts earn higher future returns than otherwise similar stocks. This effect is not concentrated in small stocks, stocks with low analyst coverage, or stocks with low book‐to‐market ratios. We find differences in the return continuation patterns of stocks with upward versus downward revisions, namely, bad news travels quickly, but good news travels slowly. This result is consistent with investors' attaching greater significance to poor earnings forecasts, but adopting a wait‐and‐see approach to good news.     

The Value and Risk of Defined Contribution Pension Schemes: International Evidence

We use historical data on investment returns and labor income from 16 countries to quantify the value and risk of defined contribution pension plans, building frequency distributions of pension fund and pension replacement ratios for each country. We show that pension risk is substantial and find that pension fund ratios are lower and less variable than when the correlation between wage growth and investment returns is ignored, typically halving the median pension fund ratio. We also show that an all‐equity fund is the dominant investment strategy across all countries, although sometimes a life‐cycle strategy insures against downside risk.