Using the Black and Litterman framework for stress test analysis in asset management

In the classic Black and Litterman approach, it is possible, using reverse engineering, to obtain the expected asset equilibrium returns implied by the weights of the market portfolio, that is, the benchmark. However, given that analysts may have different views on some of the expected returns implied by the benchmark weights, it is possible to obtain the posterior distribution by combining analysts’ views and prior market information. In this article, we propose a methodology for the stress test analysis of a current managed portfolio, in which two different shock types are combined. More precisely: we shock a set of factors that affect asset returns, imposing the analysts’ views on any variation from the expected levels; and we assume that a mixture of normal distributions describe the presence of hectic periods and quiet periods. The asset correlation breakdown effect is well known – that is, ‘… joint distributions estimated over periods without panics will misestimate the degree of correlation between asset returns during panics’ (Alan Greenspan, 1999). To this end, we introduce a number of macroeconomic factors that affect asset returns, such as volatilities, interest rates, oil price and so on. At this stage, a multi-factor analysis is not carried out, although we include the information in the covariance matrix. We assume that a mixture of normal distributions is well suited to describing and representing the presence of high- and low-volatility periods, taking into account extreme movements in the market. We derive the conditional moments of the posterior distribution by combining views on factors and market information.