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Taking Risk into Account in the Active vs. Passive Debate

Why a risk-averse investor is even more likely to use a passive fund.

Michael Rawson, CFA, 08/29/2012

How much would you pay for an investment that has a 50% probability to pay $1,000,000 and a 50% probability to pay nothing if you could enter the investment only one time?

While the expected value of this payoff is $500,000, most people would not pay anywhere near that amount to enter this investment. The probability of the zero payoff is just too high. The more risk averse you are, the less you would be willing to pay. Let's say that you would be willing to pay $200,000 to enter this investment. In economic utility theory, this amount is known as the certainty equivalent. We can apply this same concept to the active versus passive debate.

It's Mostly About Fees
While on average, active management underperforms passive management by their fees, this says nothing about the return distribution of active management. Let's take a look at the performance of broadly diversified index funds in the U.S. large-blend category. Virtually by definition, their returns tend to cluster near the category average on an annual basis. The chances of greatly out- or underperforming are muted. Conversely, actively managed funds offer the possibility for greater deviations from the benchmark--for better or worse.

For investors seeking returns more in line with the category average, indexing is a logical way to proceed. The numbers back it up. 

When analyzing the performance of active management, we are faced with the dilemma of what to do with funds that do not survive the period of study. If we ignore them, our analysis will suffer from survivorship bias, which will overstate the true performance of actively managed funds because it is the weaker funds that are more likely to close. If we include them, we have to make some assumptions about the theoretical behavior of these funds had they survived.

We can approach this problem in several ways. First, we can analyze performance of only the surviving funds, realizing that these results will have survivorship bias. Second, we can asset weight the returns, which tends to diminish the effects of funds that close since these funds are typically small. Finally, we can substitute index fund performance for the periods after an actively managed fund closes. This assumes that when a fund closes, the investor reinvests their proceeds into an index fund.

We can get some idea of the return distribution of actively managed funds by looking at those funds that survived the 10-year period. The median of 682 actively managed funds in the large-blend category returned 5.64% over 10 years, while the median of 169 index funds returned 5.97%. That 0.33% difference amounts to $548 on a $10,000 investment over 10 years.

While the differential in average returns is not huge, the spread of possible outcomes is much wider for active funds than it was for index funds. The bottom 5% of active funds returned 3.21% while the top 95% returned 8.18%. Because the study included all index funds in the large-blend category, including ETFs such as SPDR S&P 500 SPY and total stock market funds such as Vanguard Total Stock Market ETF VTI and iShares Russell 1000 Index IWB, there was also some spread in performance of index funds. The bottom 5% of index funds returned 5.00% while the top 95% returned 7.01%. If we assume an average degree of risk aversion we can compute a certainty equivalent for active returns of 5.06% and for passive returns of 5.89%. In other words, the degree to which passive funds beat active is even larger once risk aversion and the greater spread of outcomes of active funds is factored in.

Michael Rawson, CFA is an ETF Analyst with Morningstar.
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