Decision theorists claim that an ordinal measure of risk may be sufficient for an agent to make a rational choice under uncertainty. We propose a measure of financial risk, namely the Varying Cross-sectional Risk (VCR), that is based on a ranking of returns. VCR is defined as the probability of...

Under the squared error loss, the optimal forecast is the conditional mean, and the one-step forecast error is a martingale difference (MD). The one-step forecast error forms the conditional moment condition obtained from the loss derivative with respect to the forecast. Similarly, under a...