Investment Theory and Risk Management, + Website

Methodological Concepts

Seen in this light, risk budgeting is a method for allocating active risk. In times in which valuations in general are falling or stagnant and plans must face funding shortfalls, active risk is a commodity that can be allocated along with the remaining assets in the portfolio.

What does it mean to be confident in a view that a particular manager will generate relatively superior active returns? Budgeting active risk is predicated on ranking relative likelihoods of success among active managers. On an intuitive level, confidence in a view is inversely related to the level of active risk (or just returns volatility). More formally, confidences can be implied using the estimated moments of the returns distribution (sample covariances and mean returns) in conjunction with a set of views concerning relative asset performance (for example, small cap stocks will outperform large cap stocks by 50 basis points). Similarly, a set of views and their respective confidences will produce a set of expected returns that reflect a mix of sample information (covariances and mean returns) and prior information (views and associated confidences). Black and Litterman (1992) describe these expected returns as the mean of the posterior distribution in a Bayesian setup in which sample information is mixed with prior information in an optimal way. We cover this topic in more detail further on. This so-called Black-Litterman model was refined further in He and Litterman (1999); more ...