Abstract

In this article, we present explorative methods for measuring investment risk. While the underlying concepts are purely quantitative, the way results are visualized and interpreted is rather qualitative but nevertheless rigorous. The methods are in particular well suited for the task of evaluating the performance of investment risk models that are used in the investment decision process of an asset manager, where the time horizon is months and not days. Such a model cannot be subjected to rigorous statistical tests as the amount of time required to achieve significance would be far too long. The explorative methods described in this chapter, however, provide immediate results as they visualize the dynamics of risk behaviour in real time , allowing direct comparison with what the risk model anticipated at the same time. The chapter begins with a brief discussion of in-sample tests versus out-of-sample tests used in investment risk measurement and how these might be utilized in model validation. We then introduce the underlying concepts of cumulative variance and covariance. We outline an approach of viewing risk over time that does not enforce a pre-determined fixed time horizon and apply it in various examples. These examples cover general risk measures like beta, total and active risk that can be applied for either single securities or portfolios. Additional risk measures that are standardized by the risk forecast are then applied to evaluate risk model out-of-sample performance. Finally, we discuss some criteria for judging the quality...