Using Black & Litterman framework for stress testing analysis in asset management

In the classical Black and Litterman approach, by using reverse engineering, it is possible to obtain the expected assets equilibrium returns implied in the weights of the market portfolio, i.e. the benchmark. However, analysts may have different views on some of the expected returns implied in the benchmark’s weights and it is possible to obtain the posterior distribution by combining analysts’ views and prior market information. In this paper we propose a methodology for a stress test analysis of the current managed portfolio, where two different shock types are combined. More precisely: 1. we shock a set of factors which affect asset returns, imposing the analysts’ views on their variation from the expected level; 2. we assume that a mixture of normal distributions can describe the presence of hectic periods and quiet period. The asset correlation breakdown effect is well known i.e., “.. joint distributions estimated over periods without panics will misestimate the degree of correlation between asset returns during panics. “ (Alan Greenspan). For this purpose, we introduce a number of macroeconomic factors which affect asset returns such as volatilities, interest rates, oil price etc. , At this stage, we do not perform a multi factor analysis, but we include the information in the covariance matrix. We assume that a mixture of normal distributions can describe the presence of high volatility periods 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.