Private equity represents one of the major asset classes within alternative investments, which has exhibited tremendous growth over the past few decades. Private equity funds, typically organized as limited partnerships, are professionally managed pools of capital that make leveraged corporate equity investments. Many pension funds, endowments, and other institutional investors act as limited partners and provide the majority of the investment capital in these private equity funds. Private equity fund manager compensation, which consists of a combination of annual fees and a carried interest in the fund, has attracted increased scrutiny in recent years. Regulators have requested that public pension funds that invest heavily in private equity funds report all the fees they have paid, but many large pension funds have not performed this calculation and thus may have unknowingly paid excessive fees. Private equity fees can be significant, typically absorbing approximately 6% annually of the value invested.

The models will enable limited partners to value the carried interest and quantify expected total manager compensation, which will take on increased importance during boom periods. The models will enable limited partners to negotiate a fund manager compensation structure that exhibits a proper balance between fixed compensation and variable compensation.

The authors’ models will also be useful to limited partners, who can use them to more effectively negotiate fund manager compensation. During periods of popularity for private equity funds, total private equity fund manager compensation increases because of higher management fees and a shift in compensation from carried interest (variable compensation) to fees (fixed compensation).

The authors develop option pricing models for valuing private equity carried interest under reasonable assumptions. The carried interest is represented as a single call option or a pair of call options, depending on whether the carried interest includes a preferred rate of return with a catch-up feature. The three alternative structures for valuing the carried interest are the following:

• Structure 1. No hurdle rate of return and no catch-up provision
• Structure 2. Hurdle rate of return and no catch-up provision
• Structure 3. Hurdle rate of return and a catch-up provision

The value of a private equity carried interest depends on eight parameters, which include the spot price of the underlying asset, the expected rate of return and volatility of the return on the fund’s levered equity investment portfolio, and the discount for lack of marketability to capture the cost of illiquidity. 

The authors quantify the sensitivity of the private equity carried interest value to important value drivers. The value of a private equity carried interest is sensitive to, among other things, the limited partners’ preferred return, the fraction of fees rebated to investors, and the cost of illiquidity. Assuming Structure 3, the authors conduct sensitivity analyses for these different variables. For example, they note that the carried interest value decreases as the preferred return increases. Assuming an 8% preferred return and Structure 3, the carried interest value increases by 63% relative to Structure 2, which will likely incentivize the fund manager (i.e., general partner) to increase portfolio alpha. 

Alternative investments, including the private equity asset class, continue to be appealing for institutional investors because of, among other things, their diversification benefits and higher absolute returns. In private equity, the general partner’s contingent carried interest is designed to align the economic interests of the fund manager and limited partners. The models presented should be useful to private equity institutional investors that can effectively seek the optimal balance between annual fund manager compensation and the carried interest.