A Multi-factor model for the Risk Management of Portfolios

A b stra c t We propose a methodology for modelling the value at risk of a complex portfolio, based on an extension of the Ho, Stapleton and Subrahmanyam technique. We model the variance-covariance structure of up to seven variables. These could represent four country indices and three exchange rates, for example. In addition, the e®ect of an arbitrary number of orthogonal factors can be analysed. The system is illustrated by estimating the value at risk for a portfolio of international stocks where the factors are stock market indices and exchange rates, a portfolio of international bonds where the factors are interest rates as well as exchange rates, and a portfolio of interest rate derivatives in di®erent currencies. In this last case, we model a two-factor term structure of interest rates in each of the currencies, valuing the derivatives at a future date using these term structures and the Black model. The model is applied for di®erent ¯neness of the binomial density and computational accuracy and e±ciency are estimated.