On Measuring Nonlinear Risk with Scarce Observations

We consider the problem of measuring the risk of a portfolio with scarce observations by linking it to several risk factors. A typical example is measuring the risk of a hedge fund. It is assumed that from the available data one can estimate the joint law of all the factors as well as all the 2-dimensional joint laws of the portfolio's return and increments of each factor. The problem is to recover the conditional mean of the portfolio's return given the values for all factors. We present an analytic computationally feasible solution of this problem for the case when the joint law of factors is a Gaussian copula.A shorter and more practical version of this paper can be found on SSRN under the name, quot;On Measuring Hedge Fund Risk.quot