11.1 Introduction

The concept of forecasting skill can be modelled in traditional asset pricing frameworks by defining the joint distribution between an investor s forecast of future returns and actual returns themselves. Literature such as Grinold and Kahn (1999) defines the Information Coefficient (IC) to be the correlation between these forecast and actual returns which provides a basis for parameterizing pricing models so that effects of skill can be investigated from various points of view such as equilibrium price determination and comparative statics.

The elementary concept of IC as a single correlation can be readily extended to a multiperiod setting in either discrete or continuous time. In such a situation IC can be defined in various different ways according to the timing of forecasts and the time horizon of the respective realized returns. A natural way to approach this is to consider correlation between a set of forecasts made simultaneously at time zero but in respect of returns realized over a series of contiguous future time periods.

Multi-period IC therefore introduces the possibility that an investor can have differential forecasting skill depending on time horizon. It is quite intuitively plausible, for instance, that a forecaster who excels on a near-term basis might nevertheless deteriorate when predicting longer-term returns (and in the very distant future limit it is unreasonable to expect IC to be significantly non-zero). Similarly, one forecaster may display different profiles of skill over time when predicting returns on different assets: returns on...