Do banks underestimate VaR diversification?

In this paper we study empirically the diversification effect in banks’ aggregated Value-at-Risk (VaR). Using actual data from the six largest Canadian commercial banks and five leading US commercial banks, we estimate the benchmark VaR based on individual VaRs for each risk factor and an historical correlation matrix, and then compare the benchmark with the aggregated VaR disclosed by the bank. Our main result is that the diversification effect reported by Canadian banks tends to be smaller than the one estimated by our correlation model over the period from 1999 to 2006. For the US banks, there is no supportive evidence for the underestimation of VaR diversification; however, there are very interesting results among different banks.