[The third moment of returns is important for asset pricing, but it is hard to measure precisely, particularly at long horizons. This paper proposes a definition of the realized third moment that is computed from high-frequency returns. It provides an unbiased estimate of the true third moment of long-horizon returns, doing for the third moment what realized variance does for the second moment. The methodology is used to demonstrate that the skewness of equity index returns, far from diminishing with horizon, actually increases with horizons up to a year, and its magnitude is economically important.]

[This article analyzes the problem facing an agent who has a long-term commodity supply commitment and who wishes to hedge that commitment using short-maturity commodity futures contracts. As time evolves, the agent has to roll the hedge as old futures contracts mature and new futures contracts are listed. This gives rise to hedge errors. The optimal hedging strategy is characterized in a world where contracts of several different maturities coexist. The strategy is independent both of the agent's risk aversion and, under certain conditions, of beliefs about expected returns from holding futures contracts. The methodology is compared with approaches based on dynamic models of the term structure. It is tested on data from the oil futures market.]

[We develop a new method for measuring moment risk premiums. We find that the skew premium accounts for over 40% of the slope in the implied volatility curve in the S&P 500 market. Skew risk is tightly related to variance risk, in the sense that strategies designed to capture the one and hedge out exposure to the other earn an insignificant risk premium. This provides a new testable restriction for asset pricing models trying to capture, in particular, disaster risk premiums. We base our results on a general trading strategy by replicating contracts that swap implied for realized conditional asset moments.]

The third moment of returns is important for asset pricing, but it is hard to measure precisely, particularly at long horizons. This paper proposes a definition of the realized third moment that is computed from high-frequency returns. It provides an unbiased estimate of the true third moment of long-horizon returns, doing for the third moment what realized variance does for the second moment. The methodology is used to demonstrate that the skewness of equity index returns, far from diminishing with horizon, actually increases with horizons up to a year, and its magnitude is economically important. The Author 2012. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: [email protected]. , Oxford University Press.

This article analyzes the problem facing an agent who has a long-term commodity supply commitment and who wishes to hedge that commitment using short-maturity commodity futures contracts. As time evolves, the agent has to roll the hedge as old futures contracts mature and new futures contracts are listed. This gives rise to hedge errors. The optimal hedging strategy is characterized in a world where contracts of several different maturities coexist. The strategy is independent both of the agent's risk aversion and, under certain conditions, of beliefs about expected returns from holding futures contracts. The methodology is compared with approaches based on dynamic models of the term structure. It is tested on data from the oil futures market.

[In dealership markets disclosure of size and price details of public trades is typically incomplete. We examine whether full and prompt disclosure of public-trade details improves the welfare of a risk-averse investor. We analyze a model of dealership market where a market maker first executes a public trade and then offsets her position by trading with other market makers. We distinguish between quantity risk and price revision risk. We show that if the market maker learns some information about the motive behind public trade, neither regime is unambiguously welfare superior. This is because greater transparency improves quantity risk sharing but worsens price revision risk sharing.]

The paper explores the economic value of being able to span market outcomes through the use of options. We model an economy with a single risky asset. Consumption takes place at one date, corresponding to the horizon of all investors. Options on the consumption good are not redundant securities in the economy because volatility is uncertain. The model enables us to examine the benefits to investors of using options to optimize their investments. Within this model, the gains from the use of options appear to be relatively minor.

This paper characterizes all continuous price processes that are consistent with current option prices. This extends Derman and Kani (1994) , Dupire (1994 , 1997 ), and Rubinstein (1994) , who only consider processes with deterministic volatility. Our characterization implies a volatility forecast that does not require a specific model, only current option prices. We show how arbitrary volatility processes can be adjusted to fit current option prices exactly, just as interest rate processes can be adjusted to fit bond prices exactly. The procedure works with many volatility models, is fast to calibrate, and can price exotic options efficiently using familiar lattice techniques.

Abstract Higher moments of long-horizon returns are important for asset pricing but are hard to measure accurately using standard techniques. We provide theory showing that short-horizon (e.g., daily) returns can be used to construct precise estimates of long-horizon (e.g., annual) moments without making strong assumptions about the data-generating process. Skewness comprises two components: skewness of short-horizon returns and a leverage effect, that is, covariance between variance and lagged returns. We provide similar results for kurtosis. An application to U.S. stock index returns shows that skew is large and negative and attenuates only slowly as one moves from monthly to multiyear horizons.

We develop a new method for measuring moment risk premiums. We find that the skew premium accounts for over 40% of the slope in the implied volatility curve in the S&P 500 market. Skew risk is tightly related to variance risk, in the sense that strategies designed to capture the one and hedge out exposure to the other earn an insignificant risk premium. This provides a new testable restriction for asset pricing models trying to capture, in particular, disaster risk premiums. We base our results on a general trading strategy by replicating contracts that swap implied for realized conditional asset moments.