Market Risk Analysis Volume IV: Value-at-Risk Models

IV.6

Risk Model Risk

IV.6.1 INTRODUCTION

Portfolio risk is a measure of the uncertainty in the distribution of portfolio returns, and a risk model is a statistical model for generating such a distribution. A risk model actually contains three types of statistical models, for the

(a)portfolio's risk factor mapping,

(b)multivariate distribution of risk factor returns, and

(c)resolution method.

The choice of resolution method depends on the risk metric that we apply to the risk model. In this chapter we shall be focusing on VaR models, so the choice of resolution method is between using different analytic, historical or Monte Carlo VaR models.

The choices made in each of (i)–(iii) above are interlinked. For instance, if the risk factor mapping is a linear model of risk factor returns and these returns are assumed to be i.i.d. multivariate normal, then the resolution method for estimating VaR is analytic. This is because historical simulation uses an empirical distribution, not an i.i.d. normal one, and under the i.i.d. normal assumption there is no point in using Monte Carlo simulation because it only introduces sampling error into the exact solution, which may be obtained using an analytic formula.

Of course, the distribution of portfolio returns has an expected value, and if the risk model is also used to forecast this expected value then we could call the model a returns model as well. What we call the model depends on the context. For instance, fund managers normally call their ...