The Risk‐Return Relation in International Stock Markets

We investigate the risk‐return relation in international stock markets using realized variance constructed from MSCI (Morgan Stanley Capital International) daily stock price indices. In contrast with the capital asset pricing model, realized variance by itself provides negligible information about future excess stock market returns; however, we uncover a positive and significant risk‐return tradeoff in many countries after controlling for the (U.S.) consumption‐wealth ratio. U.S. realized variance is also significantly related to future international stock market returns; more importantly, it always subsumes the information content of its local counterparts. Our results indicate that stock market variance is an important determinant of the equity premium.     

Average correlation and stock market returns

If the Roll critique is important, changes in the variance of the stock market may be only weakly related to changes in aggregate risk and subsequent stock market excess returns. However, since individual stock returns share a common sensitivity to true market return shocks, higher aggregate risk can be revealed by higher correlation between stocks. In addition, a change in stock market variance that leaves aggregate risk unchanged can have a zero or even negative effect on the stock market risk premium. We show that the average correlation between daily stock returns predicts subsequent quarterly stock market excess returns. We also show that changes in stock market risk holding average correlation constant can be interpreted as changes in the average variance of individual stocks. Such changes have a negative relation with future stock market excess returns.     

Time‐Varying Risk–Return Trade‐off in the Stock Market

We uncover a strong comovement of the stock market risk–return trade‐off with the consumption–wealth ratio (CAY). The finding reflects time‐varying investment opportunities rather than countercyclical aggregate relative risk aversion. Specifically, the partial risk–return trade‐off is positive and constant when we control for CAY as a proxy for investment opportunities. Moreover, conditional market variance scaled by CAY is negatively priced in the cross‐section of stock returns. Our results are consistent with a limited stock market participation model, in which shareholders require an illiquidity premium that increases with CAY, in addition to the risk premium that is proportional to conditional market variance.     

The Effect of Executive Stock Option Plans on Stockholders and Bondholders

Executive stock option plans have asymmetric payoffs that could induce managers to take on more risk. Evidence from traded call options and stock return data supports this notion. Implicit share price variance, computed from the Black-Scholes option pricing model, and stock return variance increase after the approval of an executive stock option plan. The event is accompanied by a significant positive stock and a negative bond market reaction. This evidence is consistent with the notion that executive stock options may induce a wealth transfer from bondholders to stockholders.     

Time-varying risk The case of the American computer industry

A bivariate GARCH-in-mean model for individual stock returns and the market portfolio is designed to model volatility and to test the conditional Capital Asset Pricing Model versus the conditional Residual Risk Model. We find that a univariate model of volatility for individual stock returns is misspecified. A joint modelling of the market return and the individual stock return shows that a major force driving the conditional variances of individual stocks is the history contained in the market return variance. We find that a conditional residual risk model, where the variance of the individual stock return is used to explain expected returns, is preferred to a conditional CAPM. We propose a partial ordering of securities according to their market risk using first and second order dominance criteria.     

There is a risk-return trade-off after all

This paper studies the intertemporal relation between the conditional mean and the conditional variance of the aggregate stock market return. We introduce a new estimator that forecasts monthly variance with past daily squared returns, the mixed data sampling (or MIDAS) approach. Using MIDAS, we find a significantly positive relation between risk and return in the stock market. This finding is robust in subsamples, to asymmetric specifications of the variance process and to controlling for variables associated with the business cycle. We compare the MIDAS results with tests of the intertemporal capital asset pricing model based on alternative conditional variance specifications and explain the conflicting results in the literature. Finally, we offer new insights about the dynamics of conditional variance.     

ON ESTIMATING STOCK MARKET VOLATILITY: AN EXPLORATORY APPROACH

Traditional methods of estimating market volatility use daily return observations from a stock index to calculate monthly variance. We break with tradition and estimate stock market volatility using the daily, cross-sectional standard deviation of returns for all firms trading on the New York Stock Exchange and the American Stock Exchange. We find a significantly positive relation between risk and return. Market volatility is estimated to be about half the volatility level previously reported. The intraday, cross-sectional market volatility measure provides findings consistent with risk-return theory.     

Is the Market Portfolio a Dynamic Factor? Evidence from Individual Stock Returns

This paper uses a factor model to test whether the market portfolio is a dynamic factor in the sense that individual stock returns contain a premium linked to the conditional risk of the market portfolio. The market conditional risk is based on a decomposition of the market variance into a time-varying trend component and a transitory component. The evidence shows that the conditional market premium is rising when the permanent trend rises relative to the conditional variance. The evidence for individual stock returns supports the notion that the market portfolio is a dynamic factor. Individual stock return autocorrelations are fully explained by the time variation in the market premium. The risk premia attributed to static factors are statistically insignificant.     

The empirical relationship between risk and return: evidence from the UK stock market

Previous studies reach no consensus on the relationship between risk and return using data from one market. We argue that the world market factor should not be ignored in assessing the risk-return relationship in a partially integrated market. Applying a bivariate generalized autoregressive conditional heteroscedasticity in mean (GARCH-M) model to the weekly stock index returns from the UK and the world market, we document a significant positive relationship between stock returns and the variance of returns in the UK stock market after controlling for the covariance of the UK and the world market return. In contrast, conventional univariate GARCH-M models typically fail to detect this relationship. Nonnested hypothesis tests supplemented with other commonly used model selection criteria unambiguously demonstrate that our bivariate GARCH-M model is more likely to be the true model for UK stock market returns than univariate GARCH-M models. Our results have implications for empirical assessments of the risk-return relationship, expected return estimation, and international diversification.     

Time-Varying Variance Risk Premium and the Predictability of Chinese Stock Market Return

A number of studies have shown that the variance risk premium (VRP), defined as the difference between risk-neutral and physical expected variances, has strong predictive power for the excess stock market return, and this predictability peaks at 3- to 6-month prediction horizons. However, little research presents empirical evidences for Chinese stock market due to the absence of option market. Under general equilibrium asset pricing framework, this article estimates time-varying VRP using the Chinese stock market data. We find that the estimated VRP predicts the excess Chinese stock market return, and this forecasting power is stronger at 4- and 5-month horizons, which is consistent with the findings of existing literature.     

What Is the Expected Return on a Stock?

We derive a formula for the expected return on a stock in terms of the risk‐neutral variance of the market and the stock's excess risk‐neutral variance relative to that of the average stock. These quantities can be computed from index and stock option prices; the formula has no free parameters. The theory performs well empirically both in and out of sample. Our results suggest that there is considerably more variation in expected returns, over time and across stocks, than has previously been acknowledged.     

The relationship between risk and expected return in Europe

We employ MIDAS (mixed data sampling) to study the risk–expected return trade-off in several European stock indices. Using MIDAS, we report that in most indices there is a significant positive relationship between risk and expected return. This strongly contrasts with the result we obtain when we employ both symmetric and asymmetric GARCH models for conditional variance. We also find that asymmetric specifications of the variance process within the MIDAS framework improve the relationship between risk and expected return. As an additional application, we analyze the extent to which European stock markets are integrated, which is a particularly relevant issue, especially following the launch of the Euro in January 1999. Finally, we propose a bivariate MIDAS specification to test the pricing significance of the hedging component within an intertemporal risk–return trade-off with multiple European market indices.     

Models for stock returns

Historically, the normal variance model has been used to describe stock return distributions. This model is based on taking the conditional stock return distribution to be normal with its variance itself being a random variable. The form of the actual stock return distribution will depend on the distribution for the variance. In practice, the distributions chosen for the variance appear to be very limited. In this note, we derive a comprehensive collection of formulas for the actual stock return distribution, covering some sixteen flexible families. The corresponding estimation procedures are derived by the method of moments and the method of maximum likelihood. We feel that this work could serve as a useful reference and lead to improved modelling with respect to stock market returns.     

Time-varying risk premia and the cross section of stock returns

This paper develops and estimates a heteroskedastic variant of Campbell’s [Campbell, J., 1993. Intertemporal asset pricing without consumption data. American Economic Review 83, 487–512] ICAPM, in which risk factors include a stock market return and variables forecasting stock market returns or variance. Our main innovation is the use of a new set of predictive variables, which not only have superior forecasting abilities for stock returns and variance, but also are theoretically motivated. In contrast with the early authors, we find that Campbell’s ICAPM performs significantly better than the CAPM. That is, the additional factors account for a substantial portion of the two CAPM-related anomalies, namely, the value premium and the momentum profit.     

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.     

Overconfidence among option traders

The investor overconfidence theory predicts a direct relationship between market‐wide turnover and lagged market return. However, previous research has examined this prediction in the equity market, we focus on trading in the options market. Controlling for stock market cross‐sectional volatility, stock idiosyncratic risk, and option market volatility, we find that option trading turnover is positively related to past stock market return. In addition, call option turnover and call to put ratio are also positively associated with the past stock market return. These findings are consistent with the overconfidence theory. We also find that overconfident investors trade more in the options market than in the equity market. We rule out explanations other than investor overconfidence, such as momentum trading and varying risk preferences, for our findings.     

Forecasting stock-return variance: toward an understanding of stochastic implied volatilities

We examine the behavior of measured variances from the optionsmarket and the underlying stock market. Under the joint hypothesesthat markets are informationally efficient and that option pricesare explained by a particular asset pricing model, forecastsfrom time-series models of the stock return process should nothave predictive content given the market forecast as embodiedin option prices. Both in-sample and out-of-sample tests suggestthat this hypothesis can be rejected. Using simulations, weshow that biases inherent in the procedure we use to imply variancescannot explain this result. Thus, we provide evidence inconsistentwith the orthogonality restrictions of option pricing modelsthat assume that variance risk is unpriced. These results alsohave implications for optimum variance forecast rules.     

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.     

STOCK MARKET PERCEPTION OF INDUSTRIAL FIRM BANKRUPTCY

The objectives of this study are to determine (1) when the stock market first perceives the impending bankruptcy of a potentially bankrupt firm and (2) what firm-specific factors explain the interval between the perception time and the eventual date of bankruptcy (i.e., market lead time). A computational methodology based on the Hillmer-Yu technique is used to determine the month in which a structural change in the mean and variance of monthly stock return occurs for a potentially bankrupt firm. This parametric change month or the “market perception time” is computed for a sample of 47 industrial firms. The range of market lead times cautions against the common assumption of a uniform event period in event studies. The lead time interval (for both the mean and variance of monthly market return) of poteintially bankrupt firms is found to be positively related to the firm's earnings per share at the time of stock market perception of eventual bankruptcy. Neither the firm's asset size nor systematic risk appear to be significant indicators of lead time interval. Also, change in investment at market perception time is positively related to percentage change in the market lead times. This suggests that innovations in the investment variable are a source of new information to the security market in assesing the probability of future bankruptcy of a firm.     

Downside risk and asset pricing

We analyze if the value-weighted stock market portfolio is stochastic dominance (SD) efficient relative to benchmark portfolios formed on size, value, and momentum. In the process, we also develop several methodological improvements to the existing tests for SD efficiency. Interestingly, the market portfolio seems third-order SD (TSD) efficient relative to all benchmark sets. By contrast, the market portfolio is inefficient if we replace the TSD criterion with the traditional mean–variance criterion. Combined these results suggest that the mean–variance inefficiency of the market portfolio is caused by the omission of return moments other than variance. Especially downside risk seems to be important for explaining the high average returns of small/value/winner stocks.