The role of exchange rates in intertemporal risk–return relations

This paper investigates the significance of an intertemporal relation between expected returns on countries’ stock market portfolios and their risk exposures to the world market portfolio. We find that the intertemporal risk–return relation differs significantly under different currency denominations. The slope coefficient is the largest at around seven when the returns are denominated in Japanese yen, moderate at about five when the returns are denominated in the Canadian or US dollars, and the smallest at around three when the returns are denominated in pound or euro and its predecessors. The ranking of the risk–return coefficients across different currency denominations remains the same when we replace country equity indices with global industry portfolios in estimating the intertemporal relations, when we change the return frequency from monthly to daily, and when we consider different specifications for the conditional covariance process.     

The empirical risk–return relation: A factor analysis approach

Existing empirical literature on the risk–return relation uses relatively small amount of conditioning information to model the conditional mean and conditional volatility of excess stock market returns. We use dynamic factor analysis for large data sets, to summarize a large amount of economic information by few estimated factors, and find that three new factors—termed “volatility,” “risk premium,” and “real” factors—contain important information about one-quarter-ahead excess returns and volatility not contained in commonly used predictor variables. Our specifications predict 16–20% of the one-quarter-ahead variation in excess stock market returns, and exhibit stable and statistically significant out-of-sample forecasting power. We also find a positive conditional risk–return correlation.     

Time-varying moments, idiosyncratic risk, and an application to hot-issue IPO aftermarket returns

This paper proposes time-varying idiosyncratic risk as a component driving conditional abnormal returns and outlines a corresponding Engle et al. [Econometrica 55 (1987) 391] ARCH-M market model. An application is given to initial public offering (IPO) aftermarket stock returns, where a positive relation between idiosyncratic risk and returns is consistent with young issues’ equity as a contingent claim on firm assets. The empirical results for an illustrative sample of German Neuer Markt stocks traded during the first two years after initial listing indicate pronounced skewness as well as a positive relation between conditional idiosyncratic risk and expected returns. Conditioning aftermarket performance on risk yields much lower levels of abnormal return significance than a standard approach.     

The relationship between stock returns and volatility in international stock markets

This study examines the relationship between expected stock returns and volatility in the 12 largest international stock markets during January 1980 to December 2001. Consistent with most previous studies, we find a positive but insignificant relationship during the sample period for the majority of the markets based on parametric EGARCH-M models. However, using a flexible semiparametric specification of conditional variance, we find evidence of a significant negative relationship between expected returns and volatility in 6 out of the 12 markets. The results lend some support to the recent claim [Bekaert, G., Wu, G., 2000. Asymmetric volatility and risk in equity markets. Review of Financial Studies 13, 1–42; Whitelaw, R., 2000. Stock market risk and return: an empirical equilibrium approach. Review of Financial Studies 13, 521–547] that stock market returns are negatively correlated with stock market volatility.     

Risk,return, and dividends

Using only the definition of returns, together with a transversality assumption, we demonstrate that given a dividend process, any one of three variables—expected return, return volatility, and the price–dividend ratio—completely determines the other two. By parameterizing only one of these processes, common empirical specifications place strong, and sometimes counter-factual, restrictions on the dynamics of the other variables. Our findings lend insight into the nature of the risk–return relation and the predictability of stock returns.     

Sensitivity of Multivariate Tests of the Capital Asset-Pricing Model to the Return Measurement Interval

The capital asset-pricing model's (CAPM) primary empirical implication is a positively sloped linear relation between a security's expected rate of return and its relative risk (beta). Recent research indicates that inferences about the risk-return relation are sensitive to the choice of the return measurement interval. We perform multivariate tests of the Sharpe-Lintner CAPM using monthly and annual returns on market-value-ranked portfolios. The CAPM is rejected using monthly returns, a result consistent with previous research. In contrast, we fail to reject the CAPM when annual holding period returns are used.     

Asset pricing: A tale of two days

We show that asset prices behave very differently on days when important macroeconomic news is scheduled for announcement. In addition to significantly higher average returns for risky assets on announcement days, return patterns are much easier to reconcile with standard asset pricing theories, both cross-sectionally and over time. On such days, stock market beta is strongly related to average returns. This positive relation holds for individual stocks, for various test portfolios, and even for bonds and currencies, suggesting that beta is after all an important measure of systematic risk. Furthermore, a robust risk–return trade-off exists on announcement days. Expected variance is positively related to future aggregated quarterly announcement day returns, but not to aggregated non-announcement day returns. We explore the implications of our findings in the context of various asset pricing models.     

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.     

Idiosyncratic risk and the cross-section of stock returns: Merton (1987) meets Miller (1977)

Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predicts that idiosyncratic risk should be priced when investors hold sub-optimally diversified portfolios, and cross-sectional stock returns should be positively related to their idiosyncratic risk. However, the literature generally finds a negative relationship between returns and idiosyncratic risk, which is more consistent with Miller's [1977. Risk, uncertainty, and divergence of opinion. Journal of Finance 32, 1151–1168] analysis of asset pricing under short-sale constraints. We examine the cross-sectional effects of idiosyncratic risk while explicitly recognizing the confounding effects that dispersion of beliefs and short-sale constraints produce in the Merton framework. We find strong support for Merton's [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] model among stocks that have low levels of investor recognition and for which short selling is limited. For these stocks, the relation between idiosyncratic risk and expected returns is positive, as predicted by Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510].     

Comment on “Optimal portfolio selection in a value-at-risk framework”

This comment discusses some errors in [Journal of Banking and Finance 25 (2001) 1789]. Given the portfolio rate of return is normally distributed, the following can be inferred. First, taking expected portfolio return rate as the benchmark of value-at-risk (VaR), the risk–return ratio collapses to a multiple of the Sharpe index. However, using risk-free rate as the benchmark, then above inference does not hold. Second, whether the benchmark of VaR is expected portfolio return rate or the risk-free rate, the optimal asset allocations for maximizing the risk–return ratio and Sharpe index are identical.     

The risk return tradeoff in the long run: 1836–2003

Previous studies typically find a statistically insignificant relation between the market risk premium and its expected volatility. Further, several of these studies estimate a negative risk return tradeoff, contrary to the predictions of mainstream theory. Using simulations, I demonstrate that even 100 years of data constitute a small sample that may easily lead to this finding even though the true risk return tradeoff is positive. Small-sample inference is plagued by the fact that conditional volatility has almost no explanatory power for realized returns. Using the nearly two century history of U.S. equity market returns from Schwert [1990. Indexes of United States stock prices from 1802 to 1987. Journal of Business 63, 399–426], I estimate a positive and statistically significant risk return tradeoff. Finally, exploratory analysis suggests a role for a time-varying relation linked to the changing nature of the U.S. economy.     

Accounting Returns Revisited: Evidence of their Usefulness in Estimating Economic Returns

Accounting information is used for measuring firm performance in various financial applications—a practice supported by empirical studies demonstrating the value relevance of accounting numbers, but disputed by theoretical papers arguing that a firm's accounting rate of return (ARR) serves poorly as a proxy for its internal rate of return (IRR). We derive a new model of the ARR–IRR relation, and describe how the conservatism of GAAP constrains a firm's IRR to fall in a range bounded by its historical growth rate and ARR. Using cross-sectional data, we demonstrate that economic returns can be estimated from accounting numbers for many firms. We link empirical results to underlying economic theory, and thus contribute to understanding why accounting information is value relevant.     

The current account and stock returns

In this paper, I use stock return data to test an intertemporal model of the current account. I find that the model performs well in three countries: the U.K., Canada, and Japan. Hall [Hall, R.E., 1978. Stochastic implication of the life cycle-permanent income hypothesis: theory and evidence. J. Polit. Econ. 86 (6), 971–987] points out that because stock price predicts the future state of the economy, it predicts consumption. Assuming that consumption depends on permanent income, my empirical finding indicates that a representative agent smoothes consumption based on stock market information. In other words, stock market returns yield information about permanent income.     

Prospect theory and the risk-return paradox: some recent evidence

There is extensive evidence indicating a negative risk–return relation when a firm’s performance is measured based on accounting measures such as return on asset (ROA) and return on equity (ROE). Previous studies show that the risk-return paradox can be explained by the prospect theory, which predicts that managers’ risk attitudes are different for firms of different performances. However, those studies mostly use earlier data from the COMPUSTAT database, which suffers from a survivorship bias. Failure to account for delisting firms may understate the risk–return relation. We reexamine the mixture of risk-seeking and risk-averse behaviors based on an updated 20-year sample period that is free from the survivorship problem. Interestingly, our results show stronger and robust evidence supporting the prospect theory during the period from 1984 to 2003.     

Estimating the Intertemporal Risk–Return Tradeoff Using the Implied Cost of Capital

We argue that the implied cost of capital (ICC), computed using earnings forecasts, is useful in capturing time variation in expected stock returns. First, we show theoretically that ICC is perfectly correlated with the conditional expected stock return under plausible conditions. Second, our simulations show that ICC is helpful in detecting an intertemporal risk–return relation, even when earnings forecasts are poor. Finally, in empirical analysis, we construct the time series of ICC for the G–7 countries. We find a positive relation between the conditional mean and variance of stock returns, at both the country level and the world market level.     

Idiosyncratic risk and the cross-section of expected stock returns

Theories such as Merton [1987. A simple model of capital market equilibrium with incomplete information. Journal of Finance 42, 483–510] predict a positive relation between idiosyncratic risk and expected return when investors do not diversify their portfolio. Ang, Hodrick, Xing, and Zhang [2006. The cross-section of volatility and expected returns. Journal of Finance 61, 259–299], however, find that monthly stock returns are negatively related to the one-month lagged idiosyncratic volatilities. I show that idiosyncratic volatilities are time-varying and thus, their findings should not be used to imply the relation between idiosyncratic risk and expected return. Using the exponential GARCH models to estimate expected idiosyncratic volatilities, I find a significantly positive relation between the estimated conditional idiosyncratic volatilities and expected returns. Further evidence suggests that Ang et al.'s findings are largely explained by the return reversal of a subset of small stocks with high idiosyncratic volatilities.     

On the relation between expected returns and implied cost of capital

We examine the relation between implied cost of capital and expected returns under an assumption that expected returns are stochastic, a property supported by theory and empirical evidence. We demonstrate that implied cost of capital differs from expected return, on average, by a function encompassing volatilities of, as well as correlation between, expected returns and cash flows, growth in cash flows, and leverage. These results provide alternative explanations for findings from empirical studies employing implied cost of capital on the magnitude of the market risk premium; predictability of future returns; and the relations between cost of capital and a host of firm characteristics, such as growth, leverage, idiosyncratic risk and the firm’s information environment.     

Asset Pricing and Expected Inflation

This paper provides an equilibrium model in which expected real returns on common stocks are negatively related to expected inflation and money growth. It is shown that the fall in real wealth associated with an increase in expected inflation decreases the real rate of interest and the expected real rate of return of the market portfolio. The expected real rate of return of the market portfolio falls less, for a given increase in expected inflation, when the increase in expected inflation is caused by an increase in money growth rather than by a worsening of the investment opportunity set. The model has empirical implications for the effect of a change in expected inflation on the cross-sectional distribution of asset returns and can help to understand why assets whose return covaries positively with expected inflation may have lower expected returns. The model also agrees with explanations advanced by Fama [5] and Geske and Roll [10] for the negative relation between stock returns and inflation.     

The alpha factor asset pricing model: A parable

Recent empirical studies use the returns of attribute-sorted portfolios of common stocks as if they represent risk factors in an asset pricing model. If the attributes are chosen following an empirically observed relation to the cross-section of stock returns, such portfolios will appear to be useful risk factors, even when the attributes are completely unrelated to risk. We illustrate this result using a parable and argue that the moral of the story is important in practice.     

Commercial Real Estate Return Performance: A Cross-Country Analysis

This paper investigates the return performance of publicly traded real estate companies. The analysis spans the 1984–1999 time period and includes return data on over 600 companies in 28 countries. The return data reveal a substantial amount of variation in mean real estate returns and standard deviations across countries. Moreover, standard Treynor ratios, which scale country excess returns by the estimated beta on the world wealth portfolio, also reveal substantial variation across countries in excess real estate returns per unit of systematic risk. However, when we estimate Jensens alphas using both single and multifactor specifications, we detect little evidence of abnormal, risk-adjusted returns at the country level. We do, however, find evidence of a strong world-wide factor in international real estate returns. Furthermore, even after controlling for the effects of world-wide systematic risk, an orthogonalized country-specific factor is highly significant. This suggests that real estate securities may provide international diversification opportunities.