The Better-of-Two Strategy for Active Management: Dynamically Combining (and Valuing) Active and Passive Portfolios Through Time

Abstract

The active-versus-passive asset debate falsely forces investors into an all-or-nothing decision between the two. Instead, following Margrabe, we use a “better-of-two” option to:

(1) calculate the value of active management and,

(2) find the optimal weights for an active-plus-passive portfolio that dynamically replicates this option through time.

Using simulations, we found that for an at-the-money exchange option with a 10-year horizon, an investor would pay about 5.5% of the passive portfolio’s value. To replicate this option, the investor would allocate roughly 40% the active asset. We also accounted for borrowing costs, tracking error and active alpha, finding that replication cost and portfolio turnover decrease as time horizon increases and that results are robust to errors in expected volatility. Finally, we replaced hypothetical return distributions with historical mutual fund returns used in 60/40 equity/fixed income portfolios rebalanced monthly. Excess ending wealth distributions using the better-of-two strategy exceeded those of an all-active strategy with better downside protection. These values also came close or, in the case of funds that produced excess return, exceeded the ending value of the all-passive strategy while limiting downside relative risk. Gains from the dynamic option replication portfolio are particularly noticeable during periods when active excess returns are negative. Turnover for long-horizon portfolios is less than 4% per month and our results are statistically significant.