The Cost of Capital for Alternative Investments

• Published date: 01 October 2015
• Date: 01 October 2015
• Author: ERIK STAFFORD,JAKUB W. JUREK
• DOI: http://doi.org/10.1111/jofi.12269

THE JOURNAL OF FINANCE •VOL. LXX, NO. 5 •OCTOBER 2015

The Cost of Capital for Alternative Investments

JAKUB W. JUREK and ERIK STAFFORD∗

ABSTRACT

Traditional risk factor models indicate that hedge funds capture pre-fee alphas of 6%

to 10% per annum over the period from 1996 to 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.

LINEAR FACTOR REGRESSIONS (e.g., Capital Asset Pricing Model (CAPM), Fama–

French three-factor model, Fung–Hsieh nine-factor model, and conditional

variations thereof) indicate that hedge funds deliver statistically significant

alphas (Sharpe (1964), Lintner (1965), 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 inef-

ficiency, that is dramatically different from other areas of investment manage-

ment (Fama and French (2010)), and suggest that hedge fund returns cannot

be replicated by portfolios combining traditional risk factors. Another inter-

pretation 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.

∗Jurek is at Bendheim Center for Finance, Princeton University and NBER. Stafford is at

Harvard Business School. We thank Joshua Coval, Ken French, Samuel Hanson, Campbell Har-

vey (Editor), Jonathan Lewellen, Andrew Lo (discussant), Burton Malkiel, Robert Merton, Gideon

Ozik (discussant), Andr´

e Perold, David Sraer, Jeremy Stein, Marti Subrahmanyam (discussant),

Jules van Binsbergen (discussant), Russell Wermers (discussant), and seminar participants at

Dartmouth College, Harvard Business School, Imperial College, Bocconi University, USI Lugano,

Princeton University, Spring 2013 Q-Group Seminar, 2013 CEAR Workshop on Institutional In-

vestors, the 2012 NBER Asset Pricing Summer Institute, the 2011 NYU Five-Star Conference, the

4th NYSE Liffe Hedge Fund Research Conference, and the BYU Red Rock Finance Conference for

helpful comments and discussions.

DOI: 10.1111/jofi.12269

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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.1For example,

as of June 2010, 40% of the aggregated Ivy League endowment assets were

allocated to nontraditional assets (Lerner, Schoar, and Wang (2008)). From this

perspective, the high excess returns of alternatives may simply reflect fair com-

pensation demanded by specialized investors, rather than unearned returns,

or “alpha.”

We focus on the possibility that, in aggregate, hedge fund investors spe-

cialize 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 in-

vestors 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 op-

tion writing strategies designed to satisfy exchange margin requirements, as

emphasized by Santa-Clara and Saretto (2009).2Specifically, we contrast the

hedge fund index returns with two put-writing portfolios with different down-

side 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

1As of the end of 2010, the total assets under management held by hedge funds stood at roughly

$2 trillion (source: HFRI), in comparison to a combined global equity market capitalization of $57

trillion (source: World Federation of Exchanges) and a combined global bond market capitalization

of $54 trillion, excluding the value of government bonds (source: TheCityUK, “Bond Markets 2011”).

2Our methodology for constructing put-writing strategy returns improves on several nonlinear

risk factors proposed in the hedge fund literature. For example, we consider a wide range of option

moneyness levels and leverage magnitudes, whereas Agarwal and Naik (2004) only use options

that are 1% out-of-the-money. Fung and Hsieh (2004) construct factors based on the theoretical

returns to lookback straddle portfolios, that are designed to capture long exposure to volatility.

Instead, our focus is on strategies that are short volatility. The extreme volatility of the lookback

straddle factors also suggests that—in order to ensure feasibility—short exposures would place

severe margin requirements on the investor.

The Cost of Capital for Alternative Investments 2187

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Feasible Linear Replicating Portfolio

Actual

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Feasible Nonlinear Replicating Portfolio

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Figure 1. Replicating the risks and returns of the HFRI Fund Weighted Composite In-

dex. The top panels plot the cumulative value of $1 invested in the HFRI Fund WeightedComposite

Index (pre-fees; “Actual”), along with various replicating strategies. The left-hand panel shows the

cumulative return based on the fitted values from three common factor models (CAPM, Fama–

French/Carhart, Fung–Hsieh) exclusive of the estimated intercept (feasible linear replication).

The middle panel repeats the plot based on the fitted factor models, but returns are cumulated

inclusive of the estimated intercept (infeasible linear replication). The right-hand panel plots the

returns to the two put-writing strategies (feasible nonlinear replication). Relative to the [Z=−1,

L=2] put-writing strategy, the [Z=−2, L=4] strategy applies a higher amount of leverage

to options that are written further out of the money. The bottom panels plot the corresponding

monthly drawdown series for the hedge fund index and the replicating strategies.

intercept and unit slope coefficient when the index excess returns are regressed

onto the strategy excess returns.

Figure 1plots the value of $1 invested in the aggregate hedge fund index

(pre-fees), along with various replicating strategies. The left-hand panel shows

the cumulative return based on the fitted values from three common factor

models exclusive of the estimated intercept (feasible linear replications), the

middle panel repeats the plot but inclusive of the estimated intercept (infea-

sible linear replication), and the right-hand panel plots the returns to the two

put-writing strategies (feasible nonlinear replication). The performance of the

aggregate hedge fund index is impressive, accumulating wealth much more

quickly than the risk-matched common factors predict would be fair. Popular

common factor models explain most of the time series variation, but miss most

of the mean, identifying this as alpha. The graph also shows that the com-

mon factors beyond the market factor explain little of the overall pattern, so

much of our analysis emphasizes the market factor. On the other hand, simple