Uncovering the Risk-Return Relation in the Stock Market

There is an ongoing debate in the literature about the apparent weak or negative relation between risk (conditional variance) and return (expected returns) in the aggregate stock market. We develop and estimate an empirical model based on the ICAPM to investigate this relation. Our primary innovation is to model and identify empirically the two components of expected returns--the risk component and the component due to the desire to hedge changes in investment opportunities. We also explicitly model the effect of shocks to expected returns on ex post returns and use implied volatility from traded options to increase estimation efficiency. As a result, the coefficient of relative risk aversion is estimated more precisely, and we find it to be positive and reasonable in magnitude. Although volatility risk is priced, as theory dictates, it contributes only a small amount to the time-variation in expected returns. Expected returns are driven primarily by the desire to hedge changes in investment opportunities. It is the omission of this hedge component that is responsible for the contradictory and counter-intuitive results in the existing literature.

Limited Arbitrage and Short Sales Restrictions: Evidence from the Options Markets

In this paper, we investigate empirically the well-known put-call parity no-arbitrage relation in the presence of short sale restrictions. We use a new and comprehensive sample of options on individual stocks in combination with a measure of the cost and difficulty of short selling, specifically the spread between the rate a short-seller earns on the proceeds from the sale relative to the standard rate (the rebate rate spread). We find that violations of put-call parity are asymmetric in the direction of short sales constraints, their magnitudes are strongly related to the rebate rate spread, and they are maintained even in the presence of transactions costs both in the options and equity lending market. These violations appear to be related to both the maturity of the option and the level of valuations in the stock market, consistent with a behavioral finance theory that relies on over-optimistic investors in the stock market and segmentation between the stock and options markets. Moreover, the extent of violations of put-call parity and the rebate rate spread for individual stocks are significant predictors of future stock returns. For example, cumulative abnormal returns, net of borrowing costs, over a 2«-year sample period can exceed 65%.

Uncovering the Risk-Return Relation in the Stock Market

There is an ongoing debate in the literature about the apparent weak or negative relation between risk (conditional variance) and return (expected returns) in the aggregate stock market. We develop and estimate an empirical model based on the ICAPM to investigate this relation. Our primary innovation is to model and identify empirically the two components of expected returns –the risk component and the component due to the desire to hedge changes in investment opportunities. We also explicitly model the effect of shocks to expected returns on ex post returns and use implied volatility from added options to increase estimation efficiency. As a result, the coefficient of relative risk aversion is estimated more precisely, and we find it to be positive and reasonable in magnitude. Although volatility risk is priced, as theory dictates, it contributes only a small amount to the time-variation in expected returns. Expected returns are driven primarily by the desire to hedge changes in investment opportunities. It is the omission of this hedge component that is responsible for the contradictory and counter-intuitive results in the existing literature

Do Asset Prices Reflect Fundamentals? Freshly Squeezed Evidence from the OJ Market

The behavioral finance literature cites the frozen concentrated orange juice (FCOJ) futures market as a prominent example of the failure of prices to reflect fundamentals. This paper reexamines the relation between FCOJ futures returns and fundamentals, focusing primarily on temperature. We show that when theory clearly identifies the fundamental, i.e., at temperatures close to or below freezing, there is a close link between FCOJ prices and that fundamental. Using a simple, theoretically-motivated, nonlinear, state dependent model of the relation between FCOJ returns and temperature, we can explain approximately 50% of the return variation. This is important because while only 4.5% of the days in winter coincide with freezing temperatures, two-thirds of the entire winter return variability occurs on these days. Moreover, when theory suggests no such relation, i.e., at most temperature levels, we show empirically that none exists. The fact that there is no relation the majority of the time is good news for the theory and for market efficiency, not bad news. In terms of residual FCOJ return volatility, we also show that other fundamental information about supply, such as USDA production forecasts and news about Brazil production, generate significant return variation that is consistent with theoretical predictions. The fact that, even in the comparatively simple setting of the FCOJ market, it is easy to erroneously conclude that fundamentals have little explanatory power for returns serves as an important warning to researchers who attempt to interpret the evidence in markets where both fundamentals and their relation to prices are more complex.

Behavioralize This! International Evidence on Autocorrelation Patterns of Stock Index and Futures Returns

This paper investigates the relation between returns on stock indices and their corresponding futures contracts in order to evaluate potential explanations for the pervasive yet anomalous evidence of positive, short-horizon portfolio autocorrelations. Using a simple theoretical framework, we generate empirical implications for both microstructure and behavioral models. These implications are then tested using futures data on 24 contracts across 15 countries. The major findings are (I) return autocorrelations of indices tend to be positive even though their corresponding futures contracts have autocorrelations close to zero, (ii) these autocorrelation differences between spot and futures markets are maintained even under conditions favorable for spot-futures arbitrage, and (iii) these autocorrelation differences are most prevalent during low volume periods. These results point us towards a market microstructure-based explanation for short-horizon autocorrelations and away from explanations based on current popular behavioral models.

An Explanation of the Forward Premium Puzzle: The Long and the Short of It

The forward premium anomaly, i.e., the empirical evidence that exchange rate changes are negatively related to interest rate differentials, is one of the most robust puzzles in financial economics. We add to this literature by recasting the underlying parity relation in terms of cross-country differences between forward interest rates rather than spot interest rates. The differences using spot and maturity-matched forward rates are dramatic. As the maturity of the forward interest rate differential increases, the anomalous sign on the coefficient in the traditional specification is reversed, and the explanatory power increases. We present a simple model of interest rates, inflation, and exchange rates that explains this novel empirical evidence. The model is based on interest rate distortions due to Taylor rules and exchange rate determination involving not just purchasing power parity, but also effects due to real rate differentials and subsequent reversion of the exchange rate to fundamentals. We develop and test additional implications of this model. A key finding is that the effect of current interest rate differentials on exchange rates can be decomposed into two offsetting components, which, if used separately, greatly increase the explanatory power of regression models for exchange rates.hry 2451/25922hry 2451/2592

The Information in Long-Maturity Forward Rates: Implications for Exchange Rates and the Forward Premium Anomaly

The forward premium anomaly is one of the most robust puzzles in financial economics. We recast the underlying parity relation in terms of cross-country differences between forward interest rates rather than spot interest rates with dramatic results. These forward interest rate differentials have statistically and economically significant forecast power for annual exchange rate movements, both in- and out-of-sample, and the signs and magnitudes of the corresponding coefficients are consistent with economic theory. Forward interest rates also forecast future spot interest rates and future inflation. Thus, we attribute much of the forward premium anomaly to the anomalous behavior of shortterm interest rates, not to a breakdown of the link between fundamentals and exchange rates

Stock Market Risk and Return: An Equilibrium Approach

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

Risk and Return: An Equilibrium Approach

This paper develops a regime switching, pure exchange economy which duplicates many of the empirical features of the relation between the expectation and volatility of stock returns. The key features of the model are heteroscedasticity in inflation, regimes which mimic the expansionary and contractionary phases of the economy, and transitions between regimes which depend on the level of inflation. These features result in time-varying and asymmetric cross serial correlations between the conditional moments of returns

Time-Varying Sharpe Ratios and Market Timing

This paper documents predictable time-variation in stock market Sharpe ratios. Predetermined financial variables are used to estimate both the conditional mean and volatility of equity returns, and these moments are combined to estimate the conditional Sharpe ratio. In sample, estimated conditional Sharpe ratios show substantial time-variation that coincides with the variation in ex post Sharpe ratios and with the phases of the business cycle. Generally, Sharpe ratios are low at the peak of the cycle and high at the trough. In out-of-sample analysis, using 10-year rolling regressions, we can identify periods in which the ex post Sharpe ratio is approximately three times larger than it full-sample value. Moreover, relatively nave market-timing strategies that exploit this predictability can generate Sharpe ratios more than 70% larger than a buy-and-hold strategy