The case for convex risk measures and scenario-dependent correlation matrices to replace VaR, C-VaR and covariance simulations for safer risk control of portfolios

Abstract

Value at risk (VaR) is the most popular risk measure and is enshrined in various regulations. It postulates that portfolio losses are less than some prescribed amount most of the time. Therefore a loss of $ 10 million is the same as a loss of $ 5 billion. C-VaR tries to correct this by linearly penalizing the loss so a loss of $ 20 million is twice as damaging as that of $ 10 million with the same probability. This is an improvement but is not enough of a penalty to force investment portfolios to be structured to avoid these losses. The author has used convex risk measures since 1974 in various asset–liability management (ALM) models such as the Russell Yasuda Kasai and the Vienna InnoALM. They penalize losses at a much greater rate than linear rate so that double or triple losses are more than two or three times as undesirable. Also scenario-dependent correlation matrices are very important in model applications because ordinary average correlations tend to work when you do not need them and fail by giving misleading results when you need them. For example, in stock market crash situations, bonds and stocks are no longer positively correlated. Adding these two features to stochastic asset–liability planning models is a big step towards improving risk control and performance.