Applications of quantitative methods in managing hedge funds: Compensation competition and replication

Fei Pan, Purdue University

Abstract

This dissertation discusses two applications of quantitative methods in managing hedge funds (HFs): investigating the impact of competition on hedge fund managers' compensation and replicating hedge fund index returns. ^ The first part of the dissertation explains how competition for capital impacts HF managers' compensation through both theoretical and empirical analyses. Being the open-ended and largely unregulated private investment vehicles, HFs have sharply grown in the last decade. However, because HF managers are not required to publicly report active information on their operations and performance, investors face a high risk in fund selection, gambling on HF managers' skills and performance. HF managers' compensation contracts have become one signal of their skills in investors' fund selection. Before late 2007, since new assets continuously flowed into the HF industry, HF managers lacked competition and had bargaining power to make the take-it-or-leave-it offers to investors regarding their compensations. However, after late 2007, due to the financial crisis, lots of assets have flown out of the HF industry, forcing HFs managers, especially the new entrants, to compete for capital. Managers' compensation contracts have experienced corresponding changes. In this paper, we formulate a signaling game model to investigate the impact of competition among HF managers on their compensation contracts under an information asymmetry structure. Different from the pervious papers in which competition discussions are absent, we show that when competition level is above a threshold, HF managers are less willing to use a high-water mark to signal their skill types in attracting investment. These theoretical findings are further validated by an empirical study, in which 1,840 funds over the period of 1991 to 2008 are included. In particular, our analysis shows that when the net asset flow is negative, the proportion of managers using HWM decreases as the competition increases while the incentive fees also decrease. Meanwhile, we also find that onshore funds and small funds are less likely to use HWM to compete with offshore funds and large funds, respectively. In addition, the minimum investment requirement is not a significant factor in deciding whether to adopt a HWM in a compensation contract.^ The second part of this dissertation discusses a new approach of replicating hedge fund index returns. There has been great interest in creating portfolios using common liquid instruments to replicate hedge fund returns. In a recent article, Hasanhodzic and Lo (2007) demonstrate that a factor-based approach based on a linear regression model with 5 tradable risk factors can adequately replicate monthly returns of 1,610 hedge funds in 1986 to 2005. We propose a learning-based linear replication algorithm to enhance the linear model. Results show that our approach can improve the replicating capability of linear replicator, especially for some nonlinear and dynamic strategies, e.g., Event-driven and Emerging Markets. The annualized root mean squared error is improved by 40% and 34%, respectively. The new method can automatically detect the market changes and separate return points into different polyhedral regions, even high dimensions (multiple risk factors). By using 12 major strategy indexes' monthly returns compiled by 7 data vendors from their inception date until December 2008, we examine our method with six common risk factors and find that our algorithm can improve explanatory of hedge fund index returns. The performance of our new replicator is also tested by cloning out-of-sample monthly returns through using five out of these six factors.^

Degree

Ph.D.

Advisors

Kwei Tang, Purdue University.

Subject Area

Business Administration, Management

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