known factor structure. There, the bias in optimization can be reduced dramatically by using a covariance matrix based on a … portfolios, the bias in factor-model forecasts is less than previously thought. Lastly, we discuss the role of constraints in … mitigating risk forecasting bias …

We develop the analytical second-order bias of a Value-at-Risk estimator based on an ARCH(1) volatility specification … when the parameters are estimated by the method of quasi maximum likelihood. We show that the bias results from two sources …