TIME VARIATIONS IN RISK PREMIA,VOLATILITY, AND REWARD-TO-VOLATILITY

In this paper I relate the risk premia in the stock and bond markets to the conditional volatility of returns and time-varying reward-to-volatility variables. I find that the relation between the expected returns on the stocks and bonds and the volatility of returns is time varying. I provide an approach for evaluating the relative importance of the time-varying volatility of returns and reward-to-volatility variables to explain the predictability of risk premia for stock and bond returns. I show that changing reward-to-volatility variables explain more predictable variation in the risk premia for stocks and bonds than changing volatility of returns.     

News Arrival, Jump Dynamics, and Volatility Components for Individual Stock Returns

This paper models components of the return distribution, which are assumed to be directed by a latent news process. The conditional variance of returns is a combination of jumps and smoothly changing components. A heterogeneous Poisson process with a time‐varying conditional intensity parameter governs the likelihood of jumps. Unlike typical jump models with stochastic volatility, previous realizations of both jump and normal innovations can feed back asymmetrically into expected volatility. This model improves forecasts of volatility, particularly after large changes in stock returns. We provide empirical evidence of the impact and feedback effects of jump versus normal return innovations, leverage effects, and the time‐series dynamics of jump clustering.     

The Determinants of Conditional Autocorrelation in Stock Returns

We investigate whether return volatility, trading volume, return asymmetry, business cycles, and day‐of‐the‐week are potential determinants of conditional autocorrelation in stock returns. Our primary focus is on the role of feedback trading and the interplay of return volatility. We present empirical evidence using conditional autocorrelation estimates generated from multivariate generalized autoregressive conditional heteroskedasticity (M‐GARCH) models for individual U.S. stock and index data. In addition to return volatility, we find that trading volume and market returns are important in explaining the time‐varying patterns of return autocorrelation.     

STOCK RETURNS AND VOLATILITY ON CHINA'S STOCK MARKETS

We examine time‐series features of stock returns and volatility, as well as the relation between return and volatility in four of China's stock exchanges. Variance ratio tests reject the hypothesis that stock returns follow a random walk. We find evidence of long memory of returns. Application of GARCH and EGARCH models provides strong evidence of time‐varying volatility and shows volatility is highly persistent and predictable. The results of GARCH‐M do not show any relation between expected returns and expected risk. Daily trading volume used as a proxy for information arrival time has no significant explanatory power for the conditional volatility of daily returns. JEL classification: G15     

Can Time‐Varying Risk of Rare Disasters Explain Aggregate Stock Market Volatility?

Why is the equity premium so high, and why are stocks so volatile? Why are stock returns in excess of government bill rates predictable? This paper proposes an answer to these questions based on a time‐varying probability of a consumption disaster. In the model, aggregate consumption follows a normal distribution with low volatility most of the time, but with some probability of a consumption realization far out in the left tail. The possibility of this poor outcome substantially increases the equity premium, while time‐variation in the probability of this outcome drives high stock market volatility and excess return predictability.     

Volatility‐Managed Portfolios

Managed portfolios that take less risk when volatility is high produce large alphas, increase Sharpe ratios, and produce large utility gains for mean‐variance investors. We document this for the market, value, momentum, profitability, return on equity, investment, and betting‐against‐beta factors, as well as the currency carry trade. Volatility timing increases Sharpe ratios because changes in volatility are not offset by proportional changes in expected returns. Our strategy is contrary to conventional wisdom because it takes relatively less risk in recessions. This rules out typical risk‐based explanations and is a challenge to structural models of time‐varying expected returns.     

Corporate Bond Returns and Volatility

Recent literature emphasizes the relation of stock volatility to corporate bond yields. We demonstrate that during 1996–2005 corporate bond excess return volatility is directly related to contemporaneous corporate bond excess returns. In fact, the decompositions of aggregate bond volatility have a higher contemporaneous correlation with bond yields in comparison to idiosyncratic stock risk. Additionally, bond volatility and idiosyncratic risk are significant predictors of corporate three‐month and six‐month ahead bond excess returns. We also find that corporate bond volatility contains both slow moving and time‐varying components.     

Carry

We apply the concept of carry, which has been studied almost exclusively in currency markets, to any asset. A security’s expected return is decomposed into its “carry,” an ex-ante and model-free characteristic, and its expected price appreciation. Carry predicts returns cross-sectionally and in time series for a host of different asset classes, including global equities, global bonds, commodities, US Treasuries, credit, and options. Carry is not explained by known predictors of returns from these asset classes, and it captures many of these predictors, providing a unifying framework for return predictability. We reject a generalized version of Uncovered Interest Parity and the Expectations Hypothesis in favor of models with varying risk premia, in which carry strategies are commonly exposed to global recession, liquidity, and volatility risks, though none fully explains carry’s premium.     

Idiosyncratic Risk Matters!

This paper takes a new look at the predictability of stock market returns with risk measures. We find a significant positive relation between average stock variance (largely idiosyncratic) and the return on the market. In contrast, the variance of the market has no forecasting power for the market return. These relations persist after we control for macroeconomic variables known to forecast the stock market. The evidence is consistent with models of time‐varying risk premia based on background risk and investor heterogeneity. Alternatively, our findings can be justified by the option value of equity in the capital structure of the firms.     

Can tail risk explain size,book‐to‐market,momentum, and idiosyncratic volatility anomalies?

We examine the impact of tail risk on the return dynamics of size, book‐to‐market ratio, momentum and idiosyncratic volatility sorted portfolios. Our time‐series analyses document significant portfolio return exposures to aggregate tail risk. In particular, portfolios that contain small, value, high idiosyncratic volatility and low momentum stocks exhibit negative and statistically significant tail risk betas. Our cross‐sectional analyses at the individual stock level suggest that tail risk helps in explaining the four pricing anomalies, particularly size and idiosyncratic volatility anomalies.     

Modelling Time‐Variation in the Stock Return‐Dividend Yield Predictive Equation

Using data for forty markets, this paper examines the nature and possible causes of time‐variation within the stock return‐dividend yield predictive regression. The results in this paper show that there is significant time‐variation in the predictive equation for returns and that such variation is linked to economic and market factors. Furthermore, the strength and nature of those links are themselves time‐varying. The inclusion of this time‐variation in the predictive equation increases the predictive power compared to the standard constant parameter predictive model. Evidence is also reported for time‐varying dividend growth predictability. Long‐horizon predictability is also examined with evidence reported that the nature of the factors affecting time‐varying predictability changes with horizon. The results here, while directly contributing to the returns predictability debate, in particular regarding its existence and source, may also inform the discussion that links time‐varying expected returns (and risk premium) to economic factors.     

Risk and return: Long-run relations,fractional cointegration,and return predictability

Univariate dependencies in market volatility, both objective and risk neutral, are best described by long-memory fractionally integrated processes. Meanwhile, the ex post difference, or the variance swap payoff reflecting the reward for bearing volatility risk, displays far less persistent dynamics. Using intraday data for the Standard & Poor's 500 and the volatility index (VIX), coupled with frequency domain methods, we separate the series into various components. We find that the coherence between volatility and the volatility-risk reward is the strongest at long-run frequencies. Our results are consistent with generalized long-run risk models and help explain why classical efforts of establishing a naïve return-volatility relation fail. We also estimate a fractionally cointegrated vector autoregression (CFVAR). The model-implied long-run equilibrium relation between the two variance variables results in nontrivial return predictability over interdaily and monthly horizons, supporting the idea that the cointegrating relation between the two variance measures proxies for the economic uncertainty rewarded by the market.     

Dynamic analysis of stock return volatility in an integrated international capital market

This paper examines the dynamic behavior of the stock return volatility for Canada, Japan, Germany, and the United Kingdom. The evidence indicates that international stock return volatility is mainly influenced by the U.S. stock return volatility and the exchange rate volatility, supporting the international capital market integration hypothesis. There seems to be some correlation between stock return volatility and macroeconomic volatility, but the effect is relatively weaker. In addition to the economic fundamentals, the noise component is found to be time varying, confirming the AR(MA)CH specifications in the stock return models.     

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

We model consumption and dividend growth rates as containing (1) a small long‐run predictable component, and (2) fluctuating economic uncertainty (consumption volatility). These dynamics, for which we provide empirical support, in conjunction with Epstein and Zin's (1989) preferences, can explain key asset markets phenomena. In our economy, financial markets dislike economic uncertainty and better long‐run growth prospects raise equity prices. The model can justify the equity premium, the risk‐free rate, and the volatility of the market return, risk‐free rate, and the price–dividend ratio. As in the data, dividend yields predict returns and the volatility of returns is time‐varying.     

Stock Returns and Volatility: Pricing the Short‐Run and Long‐Run Components of Market Risk

We explore the cross‐sectional pricing of volatility risk by decomposing equity market volatility into short‐ and long‐run components. Our finding that prices of risk are negative and significant for both volatility components implies that investors pay for insurance against increases in volatility, even if those increases have little persistence. The short‐run component captures market skewness risk, which we interpret as a measure of the tightness of financial constraints. The long‐run component relates to business cycle risk. Furthermore, a three‐factor pricing model with the market return and the two volatility components compares favorably to benchmark models.     

VARIANCE,RETURN, AND HIGH-LOW PRICE SPREADS

We report three new findings that rely upon the high-low price range as an estimate of stock return variance. The predictability of variance is associated with persistence in high prices and with correlated shocks to high and low prices. Excess stock returns are positively related to anticipated variance and inversely related to unanticipated variance. Lagged squared residuals in GARCH(1,1) models have no incremental explanatory power in the presence of forecasts of conditional volatility generated from high-low price spread models.     

Local Trends in Price‐to‐Dividend Ratios—Assessment,Predictive Value,and Determinants

Persistent variations of the log price‐to‐dividend ratio (PD) and their economic determinants have attracted a lively discussion in the literature. We suggest a gradually time‐varying state process to govern the persistence of the PD. The adopted state‐space approach offers favorable model diagnostics and finds particular support in out‐of‐sample stock return prediction. We show that this slowly evolving mean process is jointly shaped by the consumption risk, the demographic structure, and the proportion of firms with traditional dividend payout policy during the past 60 years. In particular, the volatility of consumption growth plays the dominant role.     

The Economic Value of Volatility Timing

Numerous studies report that standard volatility models have low explanatory power, leading some researchers to question whether these models have economic value. We examine this question by using conditional mean-variance analysis to assess the value of volatility timing to short-horizon investors. We find that the volatility timing strategies outperform the unconditionally efficient static portfolios that have the same target expected return and volatility. This finding is robust to estimation risk and transaction costs.     

Modelling conditional heteroscedasticity and jumps in Australian short-term interest rates

The present paper explores a class of jump–diffusion models for the Australian short‐term interest rate. The proposed general model incorporates linear mean‐reverting drift, time‐varying volatility in the form of LEVELS (sensitivity of the volatility to the levels of the short‐rates) and generalized autoregressive conditional heteroscedasticity (GARCH), as well as jumps, to match the salient features of the short‐rate dynamics. Maximum likelihood estimation reveals that pure diffusion models that ignore the jump factor are mis‐specified in the sense that they imply a spuriously high speed of mean‐reversion in the level of short‐rate changes as well as a spuriously high degree of persistence in volatility. Once the jump factor is incorporated, the jump models that can also capture the GARCH‐induced volatility produce reasonable estimates of the speed of mean reversion. The introduction of the jump factor also yields reasonable estimates of the GARCH parameters. Overall, the LEVELS–GARCH–JUMP model fits the data best.     

Bond risk premia and realized jump risk

We find that augmenting a regression of excess bond returns on the term structure of forward rates with an estimate of the mean realized jump size almost doubles the R² of the forecasting regression. The return predictability from augmenting with the jump mean easily dominates that offered by augmenting with options-implied volatility and realized volatility from high-frequency data. In out-of-sample forecasting exercises, inclusion of the jump mean can reduce the root mean square prediction error by up to 40%. The incremental return predictability captured by the realized jump mean largely accounts for the countercyclical movements in bond risk premia. This result is consistent with the setting of an incomplete market in which the conditional distribution of excess bond returns is affected by a jump risk factor that does not lie in the span of the term structure of yields.