and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic … the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications …

probability distributions. This paper also explores the theoretical foundations of risk ranking, including proving a key …

Value at Risk has become the standard measure of market risk employed by financial institutions for both internal and … methodologies developed so far give satisfactory solutions. Interpreting Value at Risk as a quantile of future portfolio values … conditional on current information, we propose a new approach to quantile estimation which does not require any of the extreme …

of banks argue that compensation for bearing systematic risk is not part of bank output. We apply these models and find …

place greater weight on downside risk demand additional compensation for holding stocks with high sensitivities to downside … market movements. We show that the cross-section of stock returns reflects a premium for downside risk. Specifically, stocks … that covary strongly with the market when the market declines have high average returns. We estimate that the downside risk …

We propose a new measure of time-varying tail risk that is directly estimable from the cross section of returns. We … exploit firm-level price crashes every month to identify common fluctuations in tail risk across stocks. Our tail measure is … significantly correlated with tail risk measures extracted from S&P 500 index options, but is available for a longer sample since it …