The Cost of Constraints: Risk Management, Agency Theory and Asset Prices

Traditional academic literature has relied on so-called “limits to arbitrage” theories to explain why investment managers are unable to eliminate the effects of investor “irrational” preferences (either the asset-pricing anomalies or the behavioral finance literature) on asset pricing.  We demonstrate, however, that investment managers may not eliminate the observed asset-pricing anomalies because they may contribute to their existence.  We show that if managers face constraints such as a “tracking-error constraint,” coupled with the need to hold liquidity to meet redemptions or to actively-manage investments, they optimally hold higher-volatility securities in their portfolios.  Investment constraints, such as tracking-error constraints, however, reduce the principal-agent problems inherent in delegated asset management and serve as effective risk-control tools.  Liquidity reserves allow managers to meet redemptions or redeploy risks efficiently.  We prove that investment managers will combine a portfolio of active risks (a so-called “alpha portfolio”) for a given level of liquidity with a hedging portfolio designed to control tracking error.  As the demand for either liquidity or active management increases presumably because of confidence in alpha, the cost of maintaining the tracking-error constraint increases in that the investment managers must finance these demands by selling more lower-volatility securities and holding more higher volatility securities.  With more demand for the “alpha” portfolio, managers are forced to buy more of the tracking-error control portfolio.  Investment managers and their investors are willing to hold inefficient portfolios and to give up returns, if necessary, to control the tracking-error of their portfolios.  Given the liquidity and tracking-error constraints, investment managers concentrate more of their holdings in higher volatility (higher beta) securities.  And, we show that it is optimal for investors to limit their manager’s use of leverage, which implies that leverage has a different cost other than the cost of borrowing exceeding the return from lending.   Empirically, we show that active investment managers, such as mutual funds, hold portfolios that concentrate in higher volatility securities.  Moreover, when they change their holdings of their “alpha” portfolios (reduce or increase their tracking error by choice), the relative prices of higher volatility stocks change according to the predictions of the model.  That is, if investment managers move closer to a market portfolio, the prices of lower-volatility stocks rise more than the prices of higher-volatility stocks given changes in the prices of other market factors.