Performance Control and Risk Calibration in the Black–Litterman Model

Abstract

The authors show that risk aversion and prior estimation error input parameters of the Black–Litterman model that are arbitrarily fixed in existing practices should instead be carefully calibrated because they are related to the Sharpe performance ratio and Value at Risk or tail risk of the active portfolio. A related important insight is that these parameters are not entirely exogenous but are connected closely to the portfolio manager’s inputs of subjective expected returns, as well as the degree of confidence over these subjective beliefs. The value of τ is closer to zero if the manager believes the initial estimates based on historical data are accurate compared to the subjective views and closer to one if the manager believes there is a fundamental shift in the market landscape such that past history should not be overly relied upon. The authors also show that in the event of an incorrect view, an unrealistically high Sharpe ratio and excessive risk taking can produce disastrous losses. Unifying parameter calibrations with performance and risk measures, the model is internally consistent and provides a powerful means for practical application.