# Mimicking the Esoteric: The Source of Hedge Fund Returns

The objective of liquid alternatives is replicating hedge fund index returns (and to a lesser extent, their risk). The focus is on the root drivers of returns. There are three principal drivers in the context of hedge funds: public market beta, strategy beta, and uncorrelated return (“alpha”). The difference between the three is critical to reproducing the return stream.

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Public market beta is exposure to traditional assets, including equities and bonds. For US investors, typical indices that measure these returns profiles are the S&P 500 index for US large-capitalization stocks and the FTSE Broad Investment Grade Index for bonds. The price of these exposures is negligible with the advent of zero or near-zero cost ETFs for major stock indices. Beneficially, they are dominant exposure for most strategies in public or private markets.

Strategy betas are alternative factors that may include value and size for equities, carry trades in currencies, yield curve strategies in bonds, and momentum factors in all markets. While not an exhaustive list, they convey the diversity of markets and strategies employed by hedge funds. They are also the second-largest component of the potential return stream. Crucially, these systemic exposures are accessible through focused ETFs at a low cost. This combination is valuable when constructing a hedge fund index.

Alpha or uncorrelated return is a return exposure that is unrelated to the prior two components. In investment theory, this is a measure of the manager's skill with positive values preferred. Complications exist with this factor exposure. Identifying managers with skill in advance of the skill's realization is arduous and compelling research indicates its near impossibility. Even if persistently identifying the manager in advance existed, it may not matter.

Since hedge fund strategies are zero-sum games, the exposure to skill is typically not present in a diversified portfolio as underperformers offset outperformers. This statement does not preclude a narrowly focused fund with a handful of managers from generating alpha. That is most likely the only way possible for an uncorrelated return to express itself in a portfolio. Further, some alpha is the result of the provision of illiquidity, which a liquid alternative forgoes. The expectation is for no meaningful alpha sources because the objective is a diversified portfolio of strategies.

Exhibit 1: Deconstructing Hedge Fund Index Returns with ETFs

This illustration is hypothetical and solely intended for demonstration purposes.

Source: Capital Risk.

Public market and strategy factors dominate hedge fund returns. Analysis of the hedge fund index returns reveals that public and strategy factors explain between 50% and 70% of the variation. At the aggregate level, the value approaches 80%. The analysis uses investable, and low-cost ETFs as the primary vehicle to access the return premium (exhibit 1). The benefits are two-fold. First, the ETFs implement their strategies at low cost. Second, the liquidity of the ETFs minimizes the execution risk. Thus, investible strategies increase accessibility.

The vast expansion in the number of ETFs over the last two decades permits efficient implementation of the well-reasoned rationale for a factor. The linkage between strategy, factor, and ETF is possible through an understanding of the esoteric strategies employed by hedge fund managers, a robust quantitative background, and the theoretical knowledge to link them (exhibit 4). From a practical standpoint, the data supports the theory.

Identifying the factors to represent the exposures of the hedge funds is a laborious task. While dramatic strides in computation efficiency make the job manageable from a data science perspective, they are subject to overfitting and poor out-of-sample performance. Thus, the objective is an a priori economic rationale for the exposure while finding validity in and out of sample. Significantly, a coherent argument in advance avoids the necessity of creating other indices to explain the hedge fund index returns. There is material value in simplicity because it achieves efficient implementation.

Liquid alternatives improve risk management.

The possibility of liquid alternatives exists because of a diversified index removes the alpha component. The remaining public market exposures are available in low-cost ETFs. Advances in computer capacity and data science enable identification of the factor exposures. Thus, there is an ex-ante rationale for liquid alternatives to replicate hedge fund index returns. The benefits enable improved portfolio diversification and risk management.

## Mixing the Ingredients: Detecting the Factor Solution

Every great recipe is contingent on the ingredients and the ingredient’s proportions. Since return premia are time-varying, the mix of factors must also change over time. A hedge fund index's relevant factors will change as the market environment changes, and the managers dynamically adjust their strategies. Factors are not different. The number of relevant factors and their weights will vary over time.

Determining how to adjust the factor exposures over time is the domain of financial theory and statistical analysis. The usual techniques to calculate the factor loadings are regression analysis using data known at that time. The range of possible techniques is limitless. Leaning towards simplicity in model selection helps to reduce the required assumptions. Tangible benefits accrue to this decision, including a ready explanation of the linkages between factors and indices, reduced model risk from parsimony in factor selection, and reduced implementation and transaction costs by focusing on a few factors.

The factor mix is critical.

More significant to the investor is the selection of the appropriate hedge fund benchmark to replicate. All investors have unique objectives for their portfolio due to their varying return requirements and risk profiles. A well-diversified portfolio may only require a completion allocation to hedge fund that directs the investor to the headline index. Another investor may seek exposure to a hedge fund equity value index to broaden their portfolio's equity diversity. Thus, each investor must determine which hedge fund index (and the corresponding factor exposures) benefits their portfolio.

One critical dimension for investors in hedge funds indices is the weighting scheme. Equally weighted indices avoid one strategy's dominance as it becomes widespread, and assets flow into it. The result is the factor exposure changes. Alternately, the high incidence of equity long-short managers implies that equity exposure increases in an equal-weighted index. This outcome may be undesirable when public market equity exposure is nearly costless.

The drawbacks of the index weighting method are less material for the narrower strategy indices (e.g., managed futures or global strategies). This result occurs because the focused indices deploy varying strategies that offer more specific exposures. Even if they share similar factors, the amount of the exposures varies, so their performance is not fungible. Crucially, strategy-level indices provide the investor with the means to tailor the exposures to their needs. The potential benefit is increased diversification of their portfolio.

All hedge fund indices are amendable to replication.

There is not a general rule for an investor on which to hedge fund index to access. Index weighting methods may or may not beneficially influence the return stream depending upon the investor’s portfolio. A broad index provides easy access to the return premium in a diversified manner and best corresponds to transition and completion hedge fund allocations. Specific strategy indices permit the investor to tailor the allocation to their needs. The critical requirement for the investor is that the index or replication strategy demonstrates and continually communicates their return drivers and risk exposures so that the investor can make informed decisions about their portfolio.

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