The Cost Of Capital For Alternative Investments via Wiley Online Library
Jakub W. Jurek and Erik Stafford
Traditional risk factor models indicate that hedge funds capture pre-fee alphas of 6% to 10% per annum over the period from 1996-2012. At the same time, the hedge fund return series is not reliably distinguishable from the returns of mechanical S&P 500 put writing strategies. We show that the high excess returns to hedge funds and put writing are consistent with an equilibrium in which a small subset of investors specialize in bearing downside market risks. Required rates of return in such an equilibrium can dramatically exceed those suggested by traditional models, affecting inference about the attractiveness of these investments.
The Cost Of Capital For Alternative Investments – Introduction
Linear factor regressions (e.g., CAPM, Fama-French three-factor model, Fung-Hsieh nine-factor model, and conditional variations thereof) indicate that hedge funds deliver statistically significant alphas (Fama and French (1993), Agarwal and Naik (2004), Fung and Hsieh (2004), Hasanhodzic and Lo (2007)). Over the period from January 1996 to June 2012, pre-fee alpha estimates for diversified hedge fund indices range from 6% to 10% per annum, and thus even after deducting fees, investors appear to earn large abnormal returns relative to commonly used risk models. These estimates indicate a degree of market inefficiency, which is dramatically different from other areas of investment management (Fama and French (2010)), and suggest that hedge fund returns cannot be replicated by portfolios combining traditional risk factors. Another interpretation of these results is that the proposed risk models fail to identify, or accurately measure, an important dimension of risk that hedge fund investors specialize in bearing. In this paper, we explore this explanation, focusing on downside market risks and their implications for cost of capital computations when the asset market equilibrium may involve investor specialization.
Merton (1987) explores a simple one-factor equilibrium model in which agents only trade subsets of assets, and demonstrates that linear factor pricing fails in this setting. In particular, assets that are borne by specialized investors appear to earn positive abnormal returns relative to the market portfolio. Equivalently, the equilibrium required rate of the return on these “specialized investments” exceeds the required rate of return implicit in linear factor regressions. We argue that a similar type of equilibrium may help rationalize the returns to alternative investments (and also index put-writing strategies). In practice, while alternatives comprise a modest 2% share of the global wealth portfolio, most investors hold none of these investments, leaving a few investors with large allocations relative to the aggregate supply.1 For example, as of June 2010, 40% of the aggregated Ivy League endowment assets were allocated to non-traditional assets (Lerner, Schoar, and Wang (2008)). From this perspective, the high excess returns of alternatives may simply reflect fair compensation demanded by specialized investors, rather than unearned returns, or “alpha.”
We focus on the possibility that, in aggregate, hedge fund investors specialize in bearing downside market risks. These risks concentrate losses in highly adverse economic states, and are known to receive high equilibrium risk compensation. Importantly, the additional compensation demanded by investors that specialize in bearing these risks is likely to be large relative to that prevailing in the absence of segmentation, as these assets magnify the negative skewness of aggregate (market) shocks. While evidence of nonlinear systematic risk exposures resembling those of index put-writing is provided by Mitchell and Pulvino (2001) for risk arbitrage and Agarwal and Naik (2004) for a large number of equity-oriented strategies, the literature – aside from Lo (2001) – has been comparatively silent on nonlinear replicating strategies. We fill this gap by constructing the returns to a range of S&P 500 equity index option writing strategies designed to satisfy exchange margin requirements, as emphasized by Santa-Clara and Saretto (2009).2 Specifically, we contrast the hedge fund index returns with two put-writing portfolios with different downside risk exposures, as measured by how far the put option is out-of-the-money and how much leverage is applied to the portfolio. Each of these strategies provides an unbiased proxy for pre-fee hedge fund returns, delivering a zero intercept and unit slope coefficient when the index excess returns are regressed onto the strategy excess returns.
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