The following post comes to us from Morten Sorensen and Neng Wang, both of the Finance and Economics Division at Columbia Business School, and Jinqiang Yang of Shanghai University of Finance and Economics.

In our recent NBER working paper, Valuing Private Equity, to value PE investments, we develop a model of the asset allocation for an institutional investor (LP). The model captures the main institutional features of PE, including: (1) Inability to trade or rebalance the PE investment, and the resulting long-term illiquidity and unspanned risks; (2) GPs creating value and generating alpha by effectively managing the fund’s portfolio companies; (3) GP compensation, including management fees and performance-based carried interest; and (4) leverage and the pricing of the resulting risky debt. The model delivers tractable expressions for the LP’s asset allocation and provides an analytical characterization of the certainty-equivalent valuation of the PE investment.

An important benchmark is the full-spanning case where the risk of the PE asset is fully spanned by publicly-traded assets. In this full-spanning case, we can value the individual parts of the waterfall compensation structure, and we derive closed-form expressions for the present value of the GP’s compensation, including both management and incentive fees. Our pricing model differs from standard Black-Scholes option pricing, even under full spanning, because our model must allow for the GP’s value-adding skill, which means that the underlying PE asset earns a positive alpha. In contrast, standard Black-Scholes pricing has no room for risk-adjusted excess returns for any security. Quantitatively, we find that the costs of both management fees and incentive fees are large, in present value terms. This finding corroborates the existing findings for PE compensation from Metrick and Yasuda (2010).

The second important contribution is that our model allows us to evaluate the cost of illiquidity of long-term PE investments. When the risk of the PE asset is not fully spanned by the traded assets, the LP’s risk of the PE investments cannot be fully hedged by dynamically trading in the public market. The additional non-spanned risk exposure increases the risk of the LP’s overall portfolio. To evaluate the resulting costs of illiquidity and the GP’s compensation with non-spanned risks, we calculate the alpha that the GP must generate for the LP to break even, in certainty-equivalent terms. This break-even alpha can be interpreted as the LP’s additional cost of capital in addition to the standard CAPM-implied cost of capital, due to the costs of illiquidity and the GP’s compensation. Quantitatively, we find that the cost of illiquidity is substantial. Evaluated in terms of break-even alphas, it is comparable to the total cost of the GP’s compensation, including both management fees and carried interest. Broadly speaking, the LP’s total costs of the PE investment in present-value terms are 50% illiquidity, 25% management fees, and 25% carried interest.

Leverage reduces the break-even alpha. Intuitively, leverage increases the amount of asset managed by the GP, and allows the GP to earn alpha on a greater asset base. Hence, holding management fees fixed, leverage reduces the effective management fee per dollar of PE assets under management by the GP. Additionally, leverage allows better-diversified creditors to bear more of the risk of the underlying PE investment. Both forces cause the break-even alpha to decrease with leverage, which may provide a new justification for the high levels of debt used in PE transactions.

Finally, we use our model to evaluate actual PE performance. The performance of PE funds is typically evaluated in terms of their internal rate of return (IRR) and public-market equivalent (PME). Our model gives break-even values of these two performance measures, and we find that the break-even values implied by our model are reasonably close to the actual reported performance for buyout funds, suggesting that LPs in these funds may just break even, on average, which is consistent with Berk and Green (2004). LPs with lower effective risk aversion and more skilled LPs, who can exploit the performance persistence of PE firms, may still earn economic rents from PE investments.

The full paper is available for download here.