Quantifying the Information Content of Investment Decisions in a Multiple Partial Moment Framework: Formal Definition and Applications of Generalized Conditional Risk Attribution
Title:
Quantifying the Information Content of Investment Decisions in a Multiple Partial Moment Framework: Formal Definition and Applications of Generalized Conditional Risk Attribution
Author:
Okuyama, Noriyuki Francis, Gavin
Appeared in:
Journal of behavioral finance
Paging:
Volume 8 (2007) nr. 3 pages 121-137
Year:
2007-08-27
Contents:
Investment decisions are based on a trade-off between profit and loss. This paper aims to measure the effectiveness of active investment decision-making processes by comparing the distributions of positive and negative outcomes against those available to a passive investor. A genuinely skillful active manager should generate outcomes with more attractive loss/gain balances than a passive buy-and-hold strategy. Generalized conditional risk attribution is a method of assessing whether a decision-making process has created this benefit. We initially describe this methodology in the context of passive investing, where no ongoing investment decisions are made. We then compare the returns resulting from a static risk exposure against a symmetric random walk. The partial moments of a distribution describe the balance between losses and gains relative to the risk-free position. Conditional risk attribution can quantify the asymmetry between the upper and lower partial moments. This technique is useful for characterizing the risk of a set of passively managed outcomes measured over a given time period. In assessing active decision-making processes, we illustrate how to normalize partial moments to account for any bias in the historic environment. By rebasing the results to a unit scale, we obtain a general result that we can compare against other time periods for different risk exposures. We use the term “optionality” to define the degree to which active decisions have skillfully improved the balance between gain and loss. A second term, “visibility,” is used to describe the extent to which available returns were captured; it is not related to manager skill. We then move on to generalized conditional risk attribution (GCRA), which offers several advantages over traditional performance measurement methods. Approaches that summarize outcomes using only two parameters, such as the mean and the volatility, implicitly assume returns are symmetric. However, the entire purpose of active management is to create asymmetric distributions to capture gains and avoid losses. Two-parameter models cannot effectively capture this asymmetry. The results of our analysis allow investors to characterize different investing styles. Some managers focus primarily on forecasting the first moment of the distribution, relying on diversification to control risk. Others concentrate on improving the second moment of the distribution, with styles based on volatility. A third style of decision-making explicitly controls the probability of loss (higher moments).
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