Risk Forecast Biases of Optimized Portfolios - A Quantitative Analysis

Sep 20, 2011

Portfolio managers have long suspected that the risk forecast of an optimized portfolio tends to be optimistic. Many have identified the culprit as estimation error in the covariance matrix. Forecasts based on historical asset covariance matrices are particularly sensitive to this error. The bias is reduced dramatically by using a factor model. Even so, factor models still tend to under-forecast the risk of optimized portfolios, especially the risk coming from factors. In this paper, we show how estimation error may lead to under-forecasting the risk of optimized portfolio. The degree of under-forecasting depends on several factors including the investment style of the portfolio as well as the size of the investment universe. These affects have a  mathematical basis. We quantify them and explain why they occur.  Lastly, we review MSCI’s new Optimization Bias Adjustment for reducing this forecasting bias and illustrate its effectiveness on portfolios tilting on commonly used styles.