Empirical evidence that expected stock returns are weakly related to volatility at the market level appears to contradict the intuition that risk and return are positively related. We investigate this issue in a general equilibrium exchange economy characterized by a regime-switching consumption process with time-varying transition probabilities between regimes. When estimated using consumption data, the model generates a complex, nonlinear and time-varying relation between expected returns and volatility, duplicating the salient features of the risk/return trade-off in the data. The results emphasize the importance of time-varying investment opportunities and highlight the perils of relying on intuition from static models.

Recent empirical evidence suggests that expected stock returns are weakly, or even negatively, related to the volatility of stock returns at the market level, and that this relation varies substantially over time. This evidence contradicts the apparently reliable intuition that risk and return are positively related and that stock market volatility is a good proxy for risk. This paper investigates the relation between volatility and expected returns in a general equilibrium, exchange economy. A relatively simple model, estimated using aggregate consumption data, is able to duplicate the salient features of the observed expected return/volatility relation. The key features of the model are the existence of two regimes with different consumption growth processes and time-varying correlations between stock returns and the marginal rate of substitution; thus inducing variability in the short-run relation between expected returns and volatility and a weakening of the long-run relation. These results highlight the perils of relying on intuition from static models. They also have important implications for the empirical modeling of returns.

This article investigates empirically the comovements of the conditional mean and volatility of stock returns. It extends the results in the literature by demonstrating the role of the commercial paper—Treasury yield spread in predicting time variation in volatility. The conditional mean and volatility exhibit an asymmetric relation, which contrasts with the contemporaneous relation that has been tested previously. The volatility leads the expected return, and this time series relation is documented using offset correlations, short‐horizon contemporaneous correlations, and a vector autoregression. These results bring into question the value of modeling expected returns as a constant function of conditional volatility.

This article investigates empirically the comovements of the conditional mean and volatility of stock returns. It extends the results in the literature by demonstrating the role of the commercial paper-Treasury yield spread in predicting time variation in volatility. The conditional mean and volatility exhibit an asymmetric relation, which contrasts with the contemporaneous relation that has been tested previously. The volatility leads the expected return, and this time-series relation is documented using offset correlations, short-horizon contemporaneous correlations, and a vector autoregression. These results bring into question the value of modeling expected returns as a constant function of conditional volatility.

We introduce a new hybrid measure of stock return tail covariance risk, motivated by the underdiversified portfolio holdings of individual investors, and investigate its cross-sectional predictive power. Our key innovation is that this covariance is measured across the left tail states of the individual stock return distribution, and not across those of the market return as in standard systematic risk measures. We document a positive and significant relation between hybrid tail covariance risk (H-TCR) and expected stock returns, with an annualized premium of 9%, in contrast to the insignificant or negative results for purely stock-specific or systematic tail risk measures.

[In Japan, almost identical government bonds can trade at large price differentials. Motivated by this phenomenon, we examine the issue of the value of liquidity in markets for riskless securities. We develop a model of an issuer of bonds, a market maker, and heterogeneous investors trading in an incomplete market. We show not only that divergent prices for similar securities can be sustained in a rational expectations equilibrium, but also that this divergence may be optimal from the perspective of the issuer. Price segmentation is possible because agents have a desire to trade, but short-sale restrictions limit their trading strategies and prevent them from forcing bond prices to be equal. Restricting the form of market making to exclude price competition and unregulated profit maximization is also necessary to sustain price segmentation. The optimality of segmentation from the issuer's standpoint arises because of the issuer's ability to charge for the liquidity services provided to the investors.]

In Japan, almost identical government bonds can trade at large price differentials. Motivated by this phenomenon, we examine the issue of the value of liquidity in markets for riskless securities. We develop a model of an issuer of bonds, a market maker, and heterogeneous investors trading in an incomplete market. We show not only that divergent prices for similar securities can be sustained in a rational expectations equilibrium, but also that this divergence may be optimal from the perspective of the issuer. Price segmentation is possible because agents have a desire to trade, but short-sale restrictions limit their trading strategies and prevent them from forcing bond prices to be equal. Restricting the form of market making to exclude price competition and unregulated profit maximization is also necessary to sustain price segmentation. The optimality of segmentation from the issuer's standpoint arises because of the issuer's ability to charge for the liquidity services provided to the investors.

[The prevailing view in finance is that the evidence for long-horizon stock return predictability is significantly stronger than that for short horizons. We show that for persistent regressors, a characteristic of most of the predictive variables used in the literature, the estimators are almost perfectly correlated across horizons under the null hypothesis of no predictability. For the persistence levels of dividend yields, the analytical correlation is 99% between the 1- and 2-year horizon estimators and 94% between the 1- and 5-year horizons. Common sampling error across equations leads to ordinary least squares coefficient estimates and R²s that are roughly proportional to the horizon under the null hypothesis. This is the precise pattern found in the data. We perform joint tests across horizons for a variety of explanatory variables and provide an alternative view of the existing evidence.]

We propose a new approach to modeling bond risk and risk premia, inspired by the equity risk-return literature, which does not impose the tight restrictions found in models that generate closed-form bond prices. We estimate the joint dynamics of the volatility and Sharpe ratio of principal-component bond-factor portfolios as functions of yield curve variables and VIX. We uncover an important second factor in risk premia and document a complex time-varying relation between the price and quantity of interest rate risk inconsistent with the frameworks in existing studies. Exploiting this predictability in dynamic portfolio choice appears to enhance portfolio performance. Abstract We propose a new approach to modeling bond risk and risk premia, inspired by the equity risk-return literature, which does not impose the tight restrictions found in models that generate closed-form bond prices. We estimate the joint dynamics of the volatility and Sharpe ratio of principal-component bond-factor portfolios as functions of yield curve variables and VIX. We uncover an important second factor in risk premia and document a complex time-varying relation between the price and quantity of interest rate risk inconsistent with the frameworks in existing studies. Exploiting this predictability in dynamic portfolio choice appears to enhance portfolio performance.