Hedge Fund Replication: A Model Combination Approach

Michael S. O’Doherty

University of Missouri at Columbia – Department of Finance

Eugene Savin

University of Iowa – Henry B. Tippie College of Business – Department of Economics

Ashish Tiwari

University of Iowa

Abstract:

Recent years have seen increased demand from institutional investors for passive replication products that track the performance of hedge fund strategies. These “clones” offer the diversification benefits of hedge-fund-like investments, while simultaneously providing superior fee structures, scalability, transparency, and liquidity. We find that, in practice, linear replication methods routinely suffer from poor tracking performance and high turnover. To address these concerns, we propose a model combination approach to index replication that effectively pools information from a diverse set of pre-specified factor models. Compared to existing approaches, the pooled clone strategies yield consistently lower tracking errors, generate less severe portfolio drawdowns, and require substantially smaller trading volume. The pooled hedge fund clones also provide economic benefits in a portfolio allocation context.

Hedge Fund Replication: A Model Combination Approach – Introduction

In recent years there has been a growing interest in alternative assets, including hedge funds, on the part of institutional investors. Some of the characteristic features of hedge funds, however, including the lack of transparency, illiquidity, high leverage, and the typical 2 plus 20 incentive fee structure, are not very appealing from the perspective of such investors. For example, in an effort to reduce complexity and costs in its investment program, the California Public Employees’ Retirement System (CALPERS) recently decided to shed its entire $4 billion investment in 24 hedge funds and six hedge funds-of-funds.1

As a result there is a robust demand for hedge fund replication strategies that seek to \clone” hedge-fund-like returns by investing in liquid instruments such as futures contracts. A popular approach to hedge fund replication involves estimating a target fund’s factor exposures via Sharpe’s (1992) asset-class factor model framework (e.g., Hasanhodzic and Lo (2007)) and using the estimated coefficients to determine clone portfolio weights. Briefly, the factor-based replication strategy relies on estimating long/short positions in a set of pre-specified asset-class indices with a view to minimizing the tracking error of the clone strategy. This conventional approach to replication thus involves the identification of a \best fit” factor model.

While this framework is intuitively appealing, the existing literature has identified several practical problems with the implementation of linear factor clones. First, given the inherent flexibility of hedge funds in terms of asset-class exposure and choice of markets in which to operate, it is difficult to identify an appropriate set of factors to include in the replication model. Parsimony is also a first-order concern, as models with a large number of factors often suffer from estimation error, overfitting, and poor out-of-sample performance. Second, to capture any dynamics in the underlying hedge fund investment strategies, factor clones are typically estimated using a rolling window of prior fund returns with investment positions updated on a monthly basis. The resulting coefficient estimates often suggest a high level of portfolio turnover, making cloning costly to implement in practice. Third, the existing literature (see, e.g., Hasanhodzic and Lo (2007), Amenc, Martellini, Meyfredi, and Ziemann (2010), and Bollen and Fisher (2013)) largely finds that factorbased replication products for individual hedge funds and hedge fund indexes tend to underperform their target portfolios.

Motivated by these concerns, we propose a novel replication approach that relies on combining or pooling a set of diverse factor models to clone hedge fund index returns. The optimal combination of factor models is determined via a decision-theoretic framework. This method employs the log score criterion, which has a long history as a decision tool.2 Our application is motivated by the notion that, given data limitations and the flexibility of hedge funds’ strategies, there is no single \best fit” model that fully characterizes index returns. We argue that a more reasonable way to proceed is to start with a pre-specified set of potential factor models for a given index. While each of the individual models is likely to generate errors in index replication, an optimal combination of these models helps to diversify individual tracking errors and leads to better out-of-sample performance.

Hedge Fund Replication

 

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