قیمت های تعادلی در حضور مدیریت پرتفوی واگذار شده

This paper analyzes the asset pricing implications of commonly used portfolio management contracts linking the compensation of fund managers to the excess return of the managed portfolio over a benchmark portfolio. The contract parameters, the extent of delegation, and equilibrium prices are all determined endogenously within the model we consider. Symmetric (fulcrum) performance fees distort the allocation of managed portfolios in a way that induces a significant and unambiguous positive effect on the prices of the assets included in the benchmark and a negative effect on the Sharpe ratios. Asymmetric performance fees have more complex effects on equilibrium prices and Sharpe ratios, with the signs of these effects fluctuating stochastically over time in response to variations in the funds' excess performance.

In modern economies, a significant share of financial wealth is delegated to professional portfolio managers rather than managed directly by the owners, creating an agency relationship. In the U.S., as of 2004, mutual funds managed assets in excess of $8 trillion, hedge funds managed about $1 trillion, and pension funds more than $12 trillion. In other industrialized countries, the percentage of financial assets managed through portfolio managers is even larger than in the U.S. (see, e.g., Bank for International Settlements, 2003). While the theoretical literature on optimal compensation of portfolio managers in dynamic settings points to contracts that are likely to have very complicated path dependencies,2 the industry practice seems to favor relatively simple compensation schemes that typically include a component that depends linearly on the value of the managed assets plus a component that is linearly or non-linearly related to the excess performance of the managed portfolio over a benchmark. In 1970, the U.S. Congress amended the Investment Advisers Act of 1940 so as to allow contracts with registered investment companies to include performance-based compensation, provided that this compensation is of the “fulcrum” type, that is, provided that it includes penalties for underperforming the chosen benchmark that are symmetric to the bonuses for exceeding it. In 1985, the SEC approved the use of performance-based fees in contracts in which the client has either at least $500,000 under management or a net worth of at least $1 million. Performance-based fees were also approved by the Department of Labor in August 1986 for ERISA-governed pension funds. As of 2004, 50% of U.S. corporate pension funds with assets above $5 billion, 35% of all U.S. pension funds, and 9% of all U.S. mutual funds used performance-based fees.3 Furthermore, Brown, Harlow, and Starks (1996), Chevalier and Ellison (1997), and Sirri and Tufano (1998) show that, even when mutual fund managers do not receive explicit incentive fees, an implicit non-linear performance-based compensation still arises with periodic proportional fees as a result of the fact that the net investment flow into mutual funds varies in a convex fashion as a function of recent performance.4 Given the size of the portfolio management industry, studying the implications of this delegation and of the fee structures commonly used in the industry on equilibrium asset prices appears to be a critical task. The importance of models addressing the implications of agency for asset pricing was emphasized by Allen (2001): “In the standard asset pricing paradigm it is assumed investors directly invest their wealth in markets. While this was an appropriate assumption for the U.S. in the 1950 when individuals directly held over 90% of corporate equities, or even in 1970 when the figure was 68%, it has become increasingly less appropriate as time has progressed […] For actively managed funds, the people that make the ultimate investment decisions are not the owners. If the people making the investment decisions obtain a high reward when things go well and a limited penalty if they go badly they will be willing to pay more than the discounted cash flow for an asset. This is the type of incentive scheme that many financial institutions give to investment managers.” Existing theoretical research on delegated portfolio management has been primarily restricted to partial equilibrium settings and has focused on two main areas. The first examines the agency problem that arises between investors and portfolio managers, studying how compensation contracts should be structured: it includes Bhattacharya and Pfleiderer (1985), Starks (1987), Kihlstrom (1988), Stoughton (1993), Heinkel and Stoughton (1994), Admati and Pfleiderer (1997), Das and Sundaram (2002), Palomino and Prat (2003), Ou-Yang (2003), Larsen (2005), Liu (2005), Dybvig, Farnsworth, and Carpenter (2006), Cadenillas, Cvitanić, and Zapatero (2007), Cvitanić, Wan, and Zhang (2009), and Li and Tiwari (2009). The second examines how commonly observed incentive contracts impact managers' decisions: it includes Grinblatt and Titman (1989), Roll (1992), Carpenter (2000), Chen and Pennacchi (2005), Hugonnier and Kaniel (2010), and Basak, Pavlova, and Shapiro (2007). We complement this literature by considering a different problem. As in the literature on optimal behavior of portfolio managers, we take the parametric class of contracts as exogenously given, motivated by commonly observed fee structures. However, we carry the analysis beyond partial equilibrium by studying how the behavior of portfolio managers affects equilibrium prices when the extent of portfolio delegation and the parameters of the management contract are all determined endogenously. A first step in studying the implications of delegated portfolio management on asset returns was made by Brennan (1993), who considered a static mean–variance economy with two types of investors: individual investors (assumed to be standard mean–variance optimizers) and “agency investors” (assumed to be concerned with the mean and the variance of the difference between the return on their portfolio and the return on a benchmark portfolio). Equilibrium expected returns were shown to be characterized by a two-factor model, with the two factors being the market and the benchmark portfolio. Closely related mean–variance models have appeared in Gómez and Zapatero (2003) and Cornell and Roll (2005).5 To our knowledge, the only general equilibrium analyses of portfolio delegation in dynamic settings are in two recent papers by Kapur and Timmermann (2005) and Arora, Ju, and Ou-Yang (2006). Kapur and Timmermann consider a restricted version of our model with mean–variance preferences, normal returns, and fulcrum performance fees, while Arora, Ju, and Ou-Yang assume CARA utilities and normal dividends and do not endogenize the extent of portfolio delegation: as a result of these assumptions, fulcrum performance fees are optimal in their model.6 More importantly, both papers consider settings with a single risky asset. A key shortcoming of models with a single risky asset (or of static models) is that they are unable to capture the shifting risk incentives of portfolio managers receiving implicit or explicit performance fees (and hence the impact of these incentives on portfolio choices and equilibrium prices), as extensively described in both the theoretical and empirical literature.7 In contrast to the papers mentioned above, we study the asset pricing implications of delegated portfolio management in the context of a dynamic (continuous-time) model with multiple risky assets and endogenous portfolio delegation. Specifically, we consider an economy with a continuum of three types of agents: “active investors,” “fund investors,” and “fund managers.” Active investors, who trade on their own account, choose a dynamic trading strategy so as to maximize the expected utility of the terminal value of their portfolio. Fund investors, who implicitly face higher trading or information costs, invest in equities only through mutual funds: therefore, their investment choices are limited to how much to delegate to fund managers, with the rest of their portfolio being invested in riskless assets. Fund managers, who are assumed not to have any private wealth, select a dynamic trading strategy so as to maximize the expected utility of their compensation. The compensation contracts we consider are restricted to a parametric structure that replicates the contracts typically observed in practice, consisting of a combination of the following components: a flat fee, a proportional fee depending on the total value of the assets under management, and a performance fee depending in a piecewise-linear manner on the differential between the return of the managed portfolio and that of a benchmark portfolio.8 Departing from the traditional formulation of principal-agent problems, we assume that individual fund investors are unable to make “take it or leave it” contract offers to fund managers and thus to extract the entire surplus from the agency relation: instead, we assume that the market for fund investors is competitive, so that individual investors take the fee structure as given when deciding what fraction of their wealth to delegate.9 Similarly, we assume competition on the market for portfolio managers. We analyze in detail the impact on equilibrium price dynamics of commonly observed contracts, with commonly observed contract parameters. However, we also allow contract parameters to be selected in our model so that they are constrained Pareto efficient, i.e., so that there is no other contract within our parametric class that provides both fund investors and fund managers with higher welfares. As shown in Section 6, even when fund investors and fund managers have identical preferences, the principle of preference similarity (Ross, 1973) does not apply in our setting and asymmetric performance contracts Pareto-dominate purely proportional contracts (as well as fulcrum performance contracts): intuitively, convex performance fees are a way to incentivize fund managers to select portfolio strategies having higher overall stock allocations, benefiting fund investors who have direct access to riskless investment opportunities. Because of this incentive role of performance fees, the optimal benchmark typically differs from the market portfolio.10 Portfolio delegation can have a substantial impact on equilibrium prices. With fulcrum fees, the presence of a penalty for underperforming the benchmark portfolio leads risk-averse fund managers to be overinvested in the stocks included in the benchmark portfolio and underinvested in the stocks excluded from this portfolio. The bias of managed portfolios in favor of the stocks included in the benchmark portfolio results in the equilibrium expected returns and Sharpe ratios of these stocks being lower than those of comparable stocks not in the benchmark and in their price/dividend ratios being higher. At the same time, stocks in the benchmark portfolio tend to have higher equilibrium volatilities than those of comparable stocks not in the benchmark: this is due to the fact that, as the price of benchmark stocks starts to rise, the tilt of managed portfolios toward these stocks increases, lowering their equilibrium price/dividend ratios and hence moderating the price increase. Therefore, consistent with empirical evidence, our model implies that, if fund managers are mostly compensated with fulcrum fees, a change in the composition of widely used benchmark portfolios (such as the S&P 500 portfolio) should be accompanied by a permanent increase in the prices and volatilities of the stocks being added to the index and a corresponding permanent decrease in the prices and volatilities of the stocks being dropped from the index. With asymmetric performance fees, the signs of these changes become ambiguous, depending on the current average excess performance of managed portfolios relative to the benchmark. The remainder of the paper is organized as follows. The economic setup is described in Section 2. Section 3 provides a characterization of the optimal investment strategies. Section 4 focuses on the characterization of equilibria. Section 5 provides a detailed calibrated numerical analysis of equilibrium under asymmetric and fulcrum performance fees. Section 6 discusses the optimality of performance contracts in our model. Section 7 concludes. The Appendix contains all the proofs.

We have examined the impact of delegated portfolio management on equilibrium prices within a dynamic general-equilibrium setting in which the parameters of the management contract, the extent of delegated portfolio management, and the returns of both benchmark and non-benchmark securities are all determined endogenously. When fund managers receive performance fees of the fulcrum type, they optimally choose to tilt their portfolios toward stocks that are part of the benchmark: in equilibrium, this results in a significant positive price effect associated with the addition of a stock to the benchmark and a smaller negative price effect associated with a deletion. These implications are consistent with empirical evidence regarding changes in the composition of the S&P 500 index (the most widely used benchmark portfolio). Everything else being the same, we also find that benchmark stocks have lower expected returns, lower Sharpe ratios, and higher volatilities than similar non-benchmark stocks. With asymmetric performance fees, the composition of the portfolios selected by fund managers depends critically on the funds' excess return. As a result, cross-sectional differences between benchmark and non-benchmark stocks can have either sign, depending on the funds' performance relative to the benchmark. Interestingly, the presence of portfolio managers receiving asymmetric performance fees can stabilize prices by decreasing the equilibrium stock volatilities of both benchmark and non-benchmark stocks, although portfolio turnovers are higher with asymmetric fees. Previous literature has typically taken asset returns and the level of delegated portfolio management as given, analyzing managers' portfolio choice decisions and deriving optimal contracts. We have complemented this literature by analyzing the asset pricing implications of a prevalent parametric class of existing contracts, when the level of delegated portfolio management is determined endogenously. We have also demonstrated that when full delegation is not exogenously imposed, performance contracts may be welfare-improving, even when there is no asymmetric information and investors and fund managers have CRRA preferences with the same risk aversion coefficient.