The downside risk premium of a stock is caused by the shape of the risk-neutral distribution and the Downside Risk Capital Asset Pricing Model (DR-CAPM) is accurately explained by the risk-neutral moments of stocks. Using a set of 179 million equity options, this thesis demonstrates that the risk-neutral variance, risk-neutral skewness and risk-neutral kurtosis determine stocks ex-ante exposure to downside risk and ex-ante returns. A risk-neutral representation of beta and downside beta is derived and it implies that the downside risk premium is a compensation for the non-normality of the underlying return distribution.

Recent evidence suggests that global equity markets are becoming more risky. We find that much of the apparent increase in international variance and covariance of returns can be attributed to systematic variations in global risk premia correlated across markets, rather than to any fundamental change in the risk attributes of these markets. This result has interest both for practitioners and for those interested in modeling global asset prices.

'We decompose total variance into its bad and good components and measure the premia associated with their fluctuations using stock and option data from a large cross-section of firms. The total variance risk premium (VRP) represents the premium paid to insure against fluctuations in bad variance (called bad VRP), net of the premium received to compensate for fluctuations in good variance (called good VRP). Bad VRP provides a direct assessment of the degree to which asset downside risk may become extreme, while good VRP proxies for the degree to which asset upside potential may shrink. We find that bad VRP is important economically; in the cross-section, a one-standard-deviation increase is associated with an increase of up to 13% in annualized expected excess returns. Simultaneously going long on stocks with high bad VRP and short on stocks with low bad VRP yields an annualized risk-adjusted expected excess return of 18%. This result remains significant in double-sort strategies and cross-sectional regressions controlling for a host of firm characteristics and exposures to regular and downside risk factors'--Abstract, p. ii.

We measure "good" and "bad" variance premia that capture risk compensations for the realized variation in positive and negative market returns, respectively. The two variance premium components jointly predict excess returns over the next 1 and 2 years with statistically significant positive (negative) coefficients on the good (bad) component. The R2s reach about 10% for aggregate equity and portfolio returns, and 20% for corporate bond returns. To explain the new empirical evidence, we develop a model that highlights the differential impact of upside and downside risk on equity and variance risk premia.