Valuing Active Managers, Fees, and Fund Discounts

We use risk-neutral valuation to value a portfolio and decompose the value into the components accruing to its stakeholders—service providers, portfolio managers, and the owners. The analysis incorporates managers' expected performance and contract-renewal issues. It provides a paradigm for valuing active portfolio management. A managed portfolio's economic value is shown to differ from its net asset value. The article provides an improved foundation for computing fair closed-end fund discounts and a partial explanation of equilibrium in the markets for open- and closed-end mutual funds. The article implies that changes in closed-end fund discounts are the analog of open-end fund inflows. It also shows that closed-end fund discounts are relatively sensitive to small changes in anticipated fund performance. We use risk-neutral valuation to value a portfolio and decompose the value into the components accruing to its stakeholders—service providers, portfolio managers, and the owner. The work extends an earlier model for valuing investment management fees. In particular, the analysis incorporates the portfolio manager's expected performance, allows the portfolio's value to change over time, takes account of management fees paid from the fund and from external sources, and incorporates the portfolio's distributions (e.g., yield) and expenses (e.g., nonmanagement fees).We also provide a paradigm for valuing active portfolio management. Active management's value to the manager is the difference between the fee structure's value obtained by assuming the manager's true talent minus the value obtained by assuming no talent. Active management's value to the client is the difference between the value of the client's interest obtained by assuming the manager's true talent minus the value obtained by assuming no talent. Active management's total value is the sum of its value to the manager, the client, and the other stakeholders. Active management's value can be positive, zero, or negative, depending on the manager's talent.A by-product of the analysis is a partial explanation of equilibrium in the market for open- and closed-end mutual funds. For closed-end funds, the fund's economic value reflects the marginal shareholder's expected performance. Because the number of shares outstanding is fixed and investors are heterogeneous, the marginal shareholder's expected performance generally will not imply an economic value equal to the fund's net asset value. Thus, closed-end funds will sell at discounts or premiums to NAV. For open-end funds, generally, the economic value may seem not to be NAV, and hence not the market price of the stock, but equilibrium in the open-end fund market requires only that the marginal shareholder's computation of economic value yield NAV. If the existing marginal shareholder's expected performance implies an economic value above NAV, then contributions will continue until the new marginal shareholder's expected performance implies an economic value equal to NAV. If the existing marginal shareholder's expected performance implies an economic value below NAV, then redemptions will occur until the performance expected by the new marginal shareholder implies an economic value equal to NAV. Thus, an open-end fund's size is determined by the distribution of the fund's expected performance among investors. The implication is that as long as investors' performance expectations are positively correlated with measures of past performance, a positive relationship will exist between past performance and open-end fund (relative) net inflows. Indeed, researchers have documented empirically a positive relationship between past performance and open-end fund (relative) net inflows. The analysis also implies that changes in closed-end fund discounts are the analog of open-end fund inflows.As we demonstrate, closed-end fund discounts are relatively sensitive to small changes in anticipated fund performance. Thus, contrary to the literature, the existence of discounts and the fact that they are volatile does not imply inefficiency in the closed-end fund market.We have elsewhere presented empirical support for the model described here. In this article, we present evidence consistent with the theory to explain how the initial public offering of an equity closed-end fund can sell at a premium when existing funds sell at a discount and why the initial IPO premiums decay after the IPO. Tests on (1) the relationship between relative-premium changes and investment performance following IPOs, (2) relative-premium mean reversion following management changes, and (3) net redemptions following closed-end fund open endings for funds trading at pre-open-ending announcement discounts strongly support the theory.