How to Value Active Versus Passive Management: Using Options to Choose 'Better-of-Two'
50 Pages Posted: 29 Jun 2020
Date Written: June 3, 2020
The active-versus-passive portfolio debate falsely forces investors into an all-or-nothing decision between the two. Instead, using a well-known option approach, we show (1) how to value active management and (2) replicate that option through time using a dynamic mix of active and passive portfolios. First, we show how the investor earns the “better-of-two” returns by buying a passive portfolio and simultaneously purchasing an option to exchange, on a certain date, the results of the passive portfolio for the results of an active portfolio. The investor gets a minimum payoff equal to the passive portfolio’s return minus the cost of the option plus the opportunity to receive the active portfolio’s return if it finishes in the money. In a more practical vein, we then show how investors and fiduciaries can replicate this option over time through an optimal dynamic mix of the active and passive portfolios. In our base case, an at-the-money option 10 years from expiration would be worth (i.e., cost) about 5.5% of passive portfolio’s value and could be replicated with roughly a 40/60 mix of active and passive assets. Then, to add realism, we show the effects of introducing borrowing costs, tracking error and alpha on the distribution of returns and replication costs of a dynamic allocation strategy. Finally, we simulate returns from the dynamic replication strategy using historical mutual fund returns within 60/40 stock/bond portfolios. We find that the dynamic replication outcomes, using both hypothetical return distributions and actual mutual fund returns, are close to or better than those of similar allocations involving static all-passive and all-active portfolios. We find that gains are particularly noticeable during periods when active excess returns are negative. Turnover for long-horizon portfolios is less than 4% per month.
Keywords: active management, passive management, option value, exchange option, fiduciary responsibility, dynamic replication, portfolio allocation
JEL Classification: G00, G10, G11, G12
Suggested Citation: Suggested Citation