The Hidden Risks of Optimizing Bond Portfolios under VaR

Value at risk (VaR) has become a standard measure of portfolio risk over the last decade. It even became one of the corner stones in the Basel II accord about banks' equity requirements. Nevertheless, the practical application of the VaR concept suffers from two problems: how to estimate VaR and how to optimize a portfolio for a given level of VaR? For the first problem, several approaches have been suggested including the historical simulation method. The optimization problem can be tackled using recent advances in heuristic optimization algorithms. However, our application to bond portfolios shows that a solution to the two aforementioned problems gives rise to a third one: the actual VaR of bond portfolios optimized under a VaR constraint might exceed its nominal level to a large extent. Thus, optimizing bond portfolios under a VaR constraint might increase risk. This finding is of relevance not only for investors, but even more so for bank regulation authorities.