A Delegated-Agent Asset-Pricing Model

Abstract

Asset-pricing theory has traditionally made predictions about risk and return but has been silent on the actual process of investment. Today, most investors delegate major investment decisions to financial professionals. This suggests that the instructions given by investors to their delegated agents and the compensation of those agents might be important determinants of capital market equilibrium. In the extreme, when all investment decisions are delegated, the preferences and beliefs of individuals would be completely superseded by the objective functions of agent/managers. A provocative illustration of the difference between direct and delegated investing is provided based on active asset management relative to a benchmark index, a common objective function in practice. With the growing preponderance of delegated investing, future asset-pricing theory will not only have to describe risk and return but, to be complete, must also be able to explain the observed objective functions used by professional managers. Asset-pricing theory has traditionally made predictions about risk and return but has been silent on the actual process of investment. Many investors today delegate major investment decisions to professionals—investment managers or financial advisors. Thus, the instructions given by investors to their delegated agents and the compensation of those agents may be important determinants of capital market equilibrium. In the extreme case of all investment decisions being delegated, the preferences and beliefs of individuals would be completely superseded by the objective functions of agent/managers. In specifying an objective function for the agent, there is always a trade-off between (1) a complete reflection of the principal's desires and (2) enough clarity and transparency that the principal's objectives can be codified, monitored, and enforced at reasonable cost. To the extent that delegated agents are the predominant investors, it is their objective functions, not investor utility functions, that determine relative asset prices. In other words, the actual portfolios managed by investment professionals on behalf of their clients may differ in fundamental respects from the investment portfolios clients might have selected on their own. In the case of investment management, the objective functions can be empirically observed. To illustrate, we consider a hypothetical capital market where all investors partition their resources between active and passive managers. Passive managers run index funds. Active managers are compared with those passive benchmark indexes; their compensation depends on average excess return performance and (negatively) on the volatility of tracking error. This compensation arrangement is a common objective function in practice but has no grounding in traditional theory. Investors give half their funds to passive managers to manage because the investors are uncertain about the value added by active managers. Active managers respond to their compensation incentives by selecting portfolios that they believe will have higher average returns than their benchmarks but are also highly correlated with their benchmarks (to control tracking error). Usually, such portfolios will not be optimal in the mean–variance sense. Indeed, active managers are aware that other portfolios have higher expected returns and/or lower volatility than the portfolios they select, but they eschew such choices because of the tracking-error risk. Such suboptimal choices are the direct result of delegated investing and the concomitant divergence between manager objective functions and investor utility functions. The resulting capital market equilibrium differs materially from the standard mean–variance capital asset pricing model, even though investors acting alone would have produced the CAPM equilibrium. Delegated investing adds an extra term to the cross-sectional relationship between risk and return. In addition to the familiar beta, the return–risk trade-off depends on the fraction of all funds invested with active managers and the compensation schedules of those managers. Moreover, one of the central implications of the standard CAPM, that the market portfolio of all assets is mean–variance efficient, is no longer true when professional managers are dominant. The market portfolio's composition is also influenced by agent/manager compensation schedules. With the growing preponderance of delegated investing, asset-pricing theory of the future will not only have to describe risk and return but also, to be complete, explain the observed objective functions and the compensation contracts of professional investment managers.

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