Portfolio Backtesting

1. Introduction

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1.1          Portfolio backtesting comes in two main (related) forms:

(a)    Backtesting the return generating potential of a particular investment strategy, and

(b)   Backtesting the forecasting ability of a risk model.

1.2          In either case,  backtesting can be thought of as a short-hand way of seeking working out whether some sort of forecasting approach might work in the future without actually having to wait for the future to arrive. In (a) we are forecasting, in effect, the first moment of the distribution, i.e. the mean drift of the relative return that might arise were we to follow a particular investment strategy. In (b) we are forecasting, in effect, second and higher moments, by testing the spread of returns that should have arisen in the past were the model to be accurate versus the spread of returns that actually did arise.

1.3          The aim of this and the following pages is to explore this topic further and to comment on the range of tools that can be used for such exercises. They build on material on backtesting (of risk models) contained in Kemp (2009). These tools need to be slightly more sophisticated than we might first expect, because in the past we would not have had the same amount of information as we have now.

1.4          We focus principally in these pages on backtesting risk models, because in some sense it is a more general mathematical problem than one focusing mainly on the first moment of the distribution, and because it also intimately relates to calibration, a topic that is explored in some detail in Kemp (2009).

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