Motivated by extensive evidence that stock-return correlations are stochastic, we analyze whether the risk of correlation changes (affecting diversification benefits) is priced. We propose a direct and intuitive test by comparing option-implied correlations between stock returns (obtained by combining index option prices with prices of options on all index components) with realized correlations. Our parsimonious model shows that the substantial gap between average implied (39.5% for S&P500 and 46.0% for DJ30) and realized correlations (32.5% and 35.5%, respectively) is direct evidence of a large negative correlation risk premium. Empirical implementation of our model also indicates that the index variance risk premium can be attributed to the high price of correlation risk. Finally, we provide evidence that option-implied correlations have remarkable predictive power for future market returns, which also stays significant after controlling for a number of fundamental market return predictors.

Implied correlation and variance risk premium stand out in predicting market returns. However, while the predictive ability of implied correlation lasts for up to a year, the variance risk premium predicts market returns only for one quarter ahead. Contrary to the accepted view, implied correlation predicts the market return not through a diversification risk (average correlation) channel, but by predicting a concentration of market exposure, which defines the level of non-diversifiable market risk, or systematic diversification. Economy-wide implied correlation built exclusively from option prices of nine sector ETFs and the S&P500 efficiently predicts future market returns and systematic diversification risk in the form of market betas dispersion. Newly developed implied correlations for economic sectors provide industry-related information and are used to extract option-implied risk factors from sector-based covariances.

We use forward-looking information from option prices to estimate option-implied correlations and to construct an option-implied predictor of factor betas. With our implied market betas, we find a monotonically increasing risk-return relation, not detectable with standard rolling-window betas, with the slope close to the market excess return. Our implied betas confirm a risk-return relation consistent with linear factor models, because, when compared to other beta approaches: (i) they are better predictors of realized betas, and (ii) they exhibit smaller and less systematic prediction errors. The predictive power of our betas is not related to known relations between option-implied characteristics and returns.

This paper investigates the question whether option-implied information may enhance the estimation quality of the Capital Asset Pricing Model and its extensions. Following the approach of Buss and Vilkov (2011), we calculate implied stock correlations for the S\&P100 constituents and include these into the Factor model estimations. Even though the models based on risk-neutral inputs show a slightly better performance, we cannot report any distinctive risk-return relation. Explanatory power remains weak for the models, with the exception of the Beta prediction themselves. The analysis across two subperiods reveal distinctive cycle effects. Almost all models perform better after the outset of the financial crisis, which opens the door for in further research in this direction.

We study whether exposure to market-wide correlation shocks affects expected option returns, using data on Samp;P100 index options, options on all components, and stock returns. We present evidence of priced correlation risk based on prices of index and individual variance risk. A trading strategy exploiting priced correlation risk generates a high alpha and is attractive for CRRA investors without frictions. Correlation risk exposure explains the cross-section of index and individual option returns well. The correlation risk premium cannot be exploited with realistic trading frictions, providing a limits to arbitrage interpretation of our yacute;ndings of a high price of correlation risk.

Risk is the main source of uncertainty for investors, debtholders, corporate managers and other stakeholders. For all these actors, it is vital to focus on identifying and managing risk before making decisions. The success of their businesses depends on the relevance of their decisions and consequently, on their ability to manage and deal with the different types of risk. Accordingly, the main objective of this book is to promote scientific research in the different areas of risk management, aiming at being transversal and dealing with different aspects of risk management related to corporate finance as well as market finance. Thus, this book should provide useful insights for academics as well as professionals to better understand and assess the different types of risk.