At the asset allocation level, the focus is on maximizing expected return for a given level of risk. Once an investor has made a decision to invest in equity, the tradeoff focuses on active risk and active return. As one moves from passive management to enhanced indexing to active management, the expected active return and active risk increase.

Investors are more risk averse when facing active risk. To believe that an active return is possible, the investor must believe that there are active managers who can produce it and that the investor will be able to pick those successful managers. Second, an active equity style will also be judged against a passive benchmark. It is difficult to earn alpha and those investors who dont will face pressure from their superiors. Lastly, higher active returns mean more is invested with the high return active manager, and this results in less diversification.

At the asset allocation level, the focus is on maximizing expected return for a given level of risk. Once an investor has made a decision to invest in equity, the tradeoff focuses on active risk and active return. As one moves from passive management to enhanced indexing to active management, the expected active return and active risk increase.

Investors are more risk averse when facing active risk. To believe that an active return is possible, the investor must believe that there are active managers who can produce it and that the investor will be able to pick those successful managers. Second, an active equity style will also be judged against a passive benchmark. It is difficult to earn alpha and those investors who dont will face pressure from their superiors. Lastly, higher active returns mean more is invested with the high return active manager, and this results in less diversification.

The utility function for active return is similar to the utility function for total return. The utility of the active return increases as active return increases, active risk decreases, and as the investors risk aversion to active risk decreases. Risk tolerance is the opposite of risk aversion. Lower risk tolerance would imply lower utility from a risky return.

To calculate the portfolio active risk, it is typically assumed that the correlations between the equity managers active returns are zero. This is not an unreasonable assumption if the managers are following different styles.