Performance Control and Risk Calibration in the Black-Litterman Model

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 as they are related to 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 0 if the manager believes the initial estimates based on historical data is accurate compared to the subjective views, and closer to 1 if the manager believes there is a fundamental shift in the market landscape such that past history should not be overly relied upon. We also show that in the event of an incorrect view, an unrealistically high Sharpe ratio and taking too much risk can produce disastrous losses. By unifying parameter calibrations with performance and risk measures, the model is internally consistent and provides a powerful means for practical application