Model uncertainty and portfolio management

Asset management is difficult because you do not know a lot of things about assets. You have to infer risk and volatility from past behavior, and this may lead to systematic biases. For example, if you actively manage a portfolio to reduce price volatility, you will select stocks that have had low volatility in the past. But the fact that you thus sampled from the tail of the distribution of volatilities makes it very likely that you are underestimating the true volatility of your portfolio.

Peter Shepard makes this important point and devises a measure of risk that takes this kind of bias into account, which is a second order risk. Most interestingly, the bias adjustment depends only on the number of stocks and the number of periods used in the estimation. And it performs remarkably well in simulations.