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By Michael Rawson, CFA

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 (NYSEARCA:SPY) and total stock market funds such as Vanguard Total Stock Market ETF (NYSEARCA:VTI) and iShares Russell 1000 Index (NYSEARCA: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.

Keeping an Eye on Risk
The certainty equivalent return adjusts for the cross section dispersion in performance among funds. In layman's terms, this adjustment is a penalty for risk. This is similar in concept to the Morningstar Risk Adjusted Return measure, which penalizes a fund's return for each unit of risk (volatility). However, the Morningstar Risk Adjusted Return is a time series measure that reduces a fund return by its historical risk. The more volatile a fund has been, the lower will be its Morningstar Risk adjusted Return. As an example, the 10-year annualized return for Vanguard 500 Index Admiral (VFIAX) was 6.32% while its Morningstar Risk Adjusted Return was 1.80%. That large discrepancy was due to the relatively large 16% standard deviation in stocks. For comparison, PIMCO Total Return Institutional (PTTRX) has a 10-year return of 7.10% and a Morningstar Risk Adjusted Return of 5.02%. These returns were much closer because the standard deviation of returns was only 4%. Bond returns are typically much less volatile than stocks.

Much like we applied the certainty equivalent concept to fund returns, we can also apply it to Morningstar Risk Adjusted Returns. When we do this, we find the certainty equivalent Morningstar Risk Adjusted Return for active funds is negative 0.04%, while for passive funds, it is 1.38%. Here again, we see that the advantage for passive funds is even larger when we penalize risk.

The above results include only funds that completed the 10-year period. One way to adjust for this survivorship bias is to assign a return for funds that drop out of the study. That way, at least their initial results will be included. The return we choose to assign is the return of the S&P 500 Index. If anything, this approach should favor these funds because the S&P 500 has proved to be a difficult proxy to beat. Under this approach, our list of actively managed funds grew from 682 to 1,316 and the list of passive funds grew from 169 to 287. The median return for the active fund was 5.58%, while the median passive fund was 6.06%. That spread widens if we look at certainty equivalents to 5.09% for active and 6.00% for passive.

Another potential flaw in the above analysis is that it does not account for the fact that investors do not choose funds at random but tend to pick better-performing funds. We can account for both of these factors by looking at asset-weighted returns. The asset-weighted active return over the past 10 years is 5.41%, while the asset-weighted passive return is 6.38%.

Stay in Your Zone
While we are advocates of both passive and active strategies, we think passive makes a great deal of sense for certain investors. If you are a hands-off investor who doesn't have the time to devote to manager and security research, indexing is a good way to go. Also, if you've already decided to be an active advocate, don't fool yourself. Some people are good at choosing active managers (I can think of several of my peers), but others are not. Utilizing all the data we provide in fund reports and constructing indexed-based comparisons to your historical performance can help you decide how skilled you really are. Finally, whichever approach you use, be sure that you are willing to stick with it through the tough times. Any strategy is going to have periods of relative underperformance that can last for years.

Disclosure: Morningstar licenses its indexes to certain ETF and ETN providers, including BlackRock, Invesco, Merrill Lynch, Northern Trust, and Scottrade for use in exchange-traded funds and notes. These ETFs and ETNs are not sponsored, issued, or sold by Morningstar. Morningstar does not make any representation regarding the advisability of investing in ETFs or ETNs that are based on Morningstar indexes.

Source: Taking Risk Into Account In The Active Vs. Passive Debate