Hedge fund return attribution and performance forecasting using the Kalman filter

Abstract

The practice of forecasting is fraught with difficulty: history is replete with examples of wild-ly inaccurate predictions. Nevertheless, attempts to guess future events as accurately as possible form the basis of risk management, economic policy and financial remuneration and rewards. Skilful prediction is, however, a non-trivial exercise, particularly in the fields of finance and economics. Apart from the normal impediment of insufficient historical data to establish the presence and persistence of patterns, prediction accuracy suffers from two additional obstructions. One, opinion and sentiment are often involved, both often (but not always) based on irrational suppositions and two, data are noisy, infrequently sampled, in-consistently recorded and often in short supply. These hindrances, coupled with a multitude of relevant variables (each of which may influence others via multifaceted interactions) can conceal real, but frequently buried, relationships. The capital asset pricing model (CAPM), mean-variance framework is a metric commonly-used to identify investment performance. Quantities generated from the CAPM assume time-invariance of historical data and use rolling-window, ordinary least squares regression methods to forecast future returns. These quantities are of considerable significance to in-vestors and fund managers since all rely on these to establish compensation and rewards for relevant parties. Problems associated with CAPM regression models diminish the signifi-cance of the outputs – sometimes rendering the results irrelevant and the interpretation of the results suspect. The Kalman filter, a variance reduction framework, estimates dynamic CAPM parameters. These time-varying parameters improve predictive accuracy considera-bly compared with ordinary least square (and other) estimates. The institution and advance of hedge funds offers attractive investment possibilities be-cause they engage in investment styles and opportunity sets which – because they are dif-ferent from traditional asset class funds – generate different risk exposures (Fung & Hsieh, 1997 and Agarwal & Naik, 2000). Murguía & Umemoto (2004) showed that hedge funds provide unique investment opportunities and add value because of their ability to invest in different risk exposures, not because of the manager’s ability to add value through stock selection or market timing. Individual hedge fund returns are apportioned into market tim-ing and stock selection components to identify whether fund managers really do generate statistically significant abnormal profits and, if so, which component dominates the return profile. Compelling evidence is produced to support an alternative interpretation for meas-ured return constituents. As far as the author is aware, this work represents the first time the Kalman filter has been used to extract a time series of the CAPM's dynamic variables for determining fund return component magnitudes. The Kalman filter output provided critical insight into the reassessment of the market timing return component