Evaluating allocations

Abstract

The classical approach to allocation evaluation discussed in the second part of the book assumes known the distribution of the market. In reality, the distribution of the market is not known and can only be estimated with some error. Therefore we need to update the evaluation criteria of a generic allocation in such a way that they account for estimation risk: this is the subject of the present chapter. In Section 8.1 we realize that, since the distribution of the market is not known, an allocation cannot be a simple number. Instead, it is the outcome of a decision, contingent on the specific realization of the available information: the same allocation decision would have outputted different portfolios if the time series of market invariants had assumed different values. In order to evaluate an allocation decision it is important to track its dependence on the available information and stress test its performance in a set of different information scenarios. This is the same approach used to assess the performance of an estimator: the natural equivalent of the estimator's loss in this context is the opportunity cost, a positive quantity that the investor should try to minimize. In Section 8.2 we apply the above evaluation process to the simplest allocation strategy: the prior allocation decision. This is a decision that completely disregards any historical information from the market, as it only relies on the investor's prior beliefs. Such an extreme approach is doomed to yield sub-optimal results. Indeed, in the language of estimators the prior allocation is an extremely biased strategy. Nonetheless, the investor's experience is a key ingredient in allocation problems: a milder version of the prior allocation should somehow enter an optimal allocation decision. In Section 8.3 we evaluate the most intuitive allocation strategy: the sample-based allocation decision. This decision is obtained by substituting the unknown market parameters with their estimated values in the maximization problem that defines the classical optimal allocation. Intuitively, when the estimates are backed by plenty of reliable data the final allocation is close to the truly optimal, yet unattainable, allocation. Nevertheless, if the amount of information is limited and the estimation process is naive, this approach is symmys.com copyrighted material: Attilio Meucci-Risk and Asset Allocation-Springer