Asset Allocation Using Extreme Value Theory

This paper examines asset allocation strategies in an extreme value at risk (VaR) framework in which the risk measure is the p-quantile from the extreme value distribution. The main focus is on the allocation problem faced by an extremely risk-averse institution, such as a central bank. The optimal portfolio in terms of excess return over the risk-free rate per unit of risk is also described.

An example of asset allocation is presented using a 1-year treasury bill and a 5-year zero-coupon bond. The allocation is conducted using different risk measures: duration, standard VaR, the quantile of the empirical distribution, and the quantile of the extreme distribution. An approximation procedure is described for the allocation of N-assets. An example of allocating eight Canadian treasuries and bonds is given (covering the whole Canadian term structure).

The implications of the results on optimal allocation of capital under stressed market conditions are discussed. Some practical issues concerning the use of the results are described, such as who should allocate capital based on extreme values.