The Cost of Capital for Alternative Investments

This paper studies the cost of capital for alternative investments. We document that the risk profile of the aggregate hedge fund universe can be accurately matched by a simple index put option writing strategy that offers monthly liquidity and complete transparency over its state-contingent payoffs. The contractual nature of the put options in the benchmark portfolio allows us to evaluate appropriate required rates of return as a function of investor risk preferences and the underlying distribution of market returns. This simple framework produces a number of distinct predictions about the cost of capital for alternatives relative to traditional mean-variance analysis. First draft: June 2011 This draft: August 2011 ∗Jurek: Bendheim Center for Finance, Princeton University; [email protected]. Stafford: Harvard Business School; [email protected]. This paper studies the required rate of return for a risk averse investor allocating capital to alternative investments. There are two key aspects to this asset allocation decision that are inconsistent with (present a challenge for) standard decision-making tools. First, the alternative investment exposure is nonlinear with respect to the remainder of the portfolio at the horizon where the investor is able to rebalance the portfolio, making static mean-variance analysis inappropriate. Second, the typical allocation is large relative to the aggregate outstanding share in the economy, such that charging for a small marginal allocation to this risk is a poor approximation to the actual contribution to the portfolio’s overall risk. These two features interact to produce very large required rates of return relative to commonly used models. Investments made by sophisticated individual and institutional investors in private investment companies like hedge funds and private equity funds are referred to as alternative investments. These investments are frequently combined with financial leverage to bear risks that may be unappealing to the typical investor or that require flexibility that public investment funds may not provide. The economic nature of these investments is commonly described as “picking up pennies in front of a steamroller” indicating that it is understood that there is a real possibility of a complete loss of invested capital. Moreover, the aggregate performance of these unappealing positive net supply risks tend to be correlated with aggregate economic conditions, such that losses are more likely when other positive net supply assets are also experiencing losses. As emphasized by Shleifer and Vishny (1997), investors in hedge funds executing risk arbitrage strategies typically do not have the technology and information required to engage in these activities directly and must infer the risks from realized returns. One point of this paper is that even with direct knowledge of the underlying risks the commonly used tools for asset allocation and determining required rates of return are inappropriate for these types of risk. A practical challenge in measuring the risks from realized returns is that the portfolios are not directly observable at any point in time and the risks of any fund are likely to be changing through time because of the manager’s discretion over portfolio composition, financial leverage, and hedging rules. To estimate the aggregate risks of the hedge fund universe, we exploit the 2008 stock market decline to identify an index put writing strategy that matches the aggregate hedge fund drawdown. This put writing strategy matches the risks of the hedge fund universe throughout the sample period (1996-2010) in terms of other drawdown patterns, stock market beta, and time series return volatility. The implied fee on the put writing strategy required to match the cumulative returns on the hedge fund index is 3.6% per year, which corresponds closely with the 2% fixed fee plus 20% profit sharing compensation structure that is common in alternative investments.