Jakub W. Jurek

Princeton University – Bendheim Center for Finance; National Bureau of Economic Research (NBER)

Erik Stafford

Harvard Business School – Finance Unit

May 2013

This paper develops a simple method for calculating the cost of capital for alternative investments. Ex ante cost of capital estimates are central to the efficient allocation of capital, and generally depend on the composition of the investor’s total portfolio and the payoff profile of the new investment relative to the remainder of the portfolio. In the context of alternative investments, these allocations (1) constitute a large share of the investor’s total portfolio and (2) have nonlinear payoffs relative to the remainder of the portfolio at horizons that permit rebalancing. We find that these two features interact to produce very large required rates of return relative to commonly used benchmarking techniques, including those developed recently to address the nonlinear payoffs of alternative investments.

Merton (1987) develops a model of capital market equilibrium with incomplete information in which investors must be informed about an investment before they allocate any capital to it. This creates specialization in investing and leads some investors to hold highly concentrated portfolios in equilibrium. As a result, the equilibrium required rate of the return on these investments exceeds what would be required in a frictionless model. An important class of real world decisions to which this applies are alternative investments. Conditional on investing in alternatives, allocations are typically large relative to the equilibrium supply of these risks, in order to amortize the fixed costs associated with expanding the traditional investment universe to include alternatives. For example, as of June 2010, the Ivy League endowments had 40% of their combined assets allocated to non-traditional assets (Lerner, et al. (2008)), whereas the share of alternatives in the global wealth portfolio was closer to 2%.1 This paper argues that the wedge between the proper cost of capital and that implied by a frictionless model is likely to be particularly large here due to the non-linearity of the payoff profile relative to the remainder of the portfolio. Taking observed portfolio allocations as given, we study the role concentrated allocations play in the cost of capital for alternative investments.

To the extent that the real world equilibrium is affected by market frictions that lead some investors to hold highly concentrated portfolios, these consequences must be explicitly handled in cost of capital estimates, but typically are not. For example, traditional cost of capital computations are heavily reliant on linear factor models, which implicitly assume that: (a) investors trade in frictionless markets, and thus hold efficient portfolios; and (b) asset returns are well described by the considered set of traded factors. Merton (1987) highlights the theoretical and empirical challenges posed by the first assumption when the equilibrium is one where a small subset of investors hold relatively large shares of a particular risk, as appears to be the case for alternative investments.

The linear factor model approach relies on the notion that all agents agree on the required rate of return for a marginal deviation from their efficient portfolios, but this will generally not be true when market frictions cause some investors to hold concentrated portfolios. Ignoring these issues altogether, the focus of the empirical literature has been on expanding the factor set (e.g. by adding non-linear factors) in an attempt to describe the downside risk exposure of alternatives. Nonlinear factors have been included in an ad hoc way, such that they often do not represent feasible investments, and are unlikely to capture the specific nonlinear risk profile of hedge funds. Moreover, this does little to correct for the problems due to return smoothing or asset illiquidity (Asness, et al. (2001), Getmansky, et al. (2004)). We remedy these shortcomings, and produce cost of capital estimates for alternatives reflecting the economic reality of the concentrated portfolio to which they belong.

H/T Alpha Architect

See full “The Cost of Capital for Alternative Investments” in PDF format here via SSRN