Play the Odds When Investing

Probability of active besting passive

Perhaps you’ve heard that low-cost passive index mutual funds tend to perform better than funds in which managers actively pick stocks. By my calculations, however, over any given year, roughly 42 percent of actively managed funds outperform the low-cost index. So buying the index fund seems to be shooting for being only slightly better than average. Yet don’t most of us want to be an A student at the top of the class?

To really understand the odds of beating a low-cost indexed portfolio, I created a Monte Carlo Simulator. This is merely a mathematical model that runs thousands of iterations simulating outcomes. You can see the probabilities on the chart to the right. For the model, I assumed the active fund charged an annual expense ratio of 0.75 percent more than the passively managed fund. A total stock index fund can now be purchased with an expense ratio as low as 0.04 percent, such as the Schwab Broad Market Index Fund (SCHB).

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Looking at one actively managed fund, the odds still aren’t that bad, with even 23 percent beating the index fund over 10 years, and a full 12 percent over a quarter century. When I showed my results to some indexing advocates, it surprised them, as many had told me the odds of any one fund beating the index fund over long periods were under 1 percent.

To see why the odds of one fund beating the index fund are much higher than 1 percent, we can use the once-hot Fidelity Magellan Fund (FMAGX) to illustrate. The Chicago-based investment research company Morningstar indicates that Magellan has significantly underperformed for the past 15 years. But if you look at its performance since inception, it has trounced the index fund. That’s because it was on fire when Peter Lynch ran the fund from 1977 to 1990. It’s been a dog since then, yet it developed such a lead in the earlier years that it can probably continue being a dog for many more decades before it falls behind the index since inception. On a related note, this perfectly illustrates the fact that past performance really isn’t predictive of future performance.

Now, very few mutual fund investors own just one mutual fund. We typically own several and I’ve seen many investors who own several dozen. That has a huge negative impact on the odds. Imagine flipping an unfair coin that had only a 42 percent probability of landing heads. The more times you flip the coin and the more series of coin flips you do, the lower the probability of getting more heads than tails.

The same is true for having many mutual funds over many years. Owning 10 funds over 25 years gives less than a 1 percent chance of beating the low-cost index fund. If you are changing the 10 funds during the period, your odds get even worse.

My advice

We tend to overestimate the odds of our investment success. With a portfolio of 10 or more funds you have a 99 percent probability of failure, so it’s not even a close call that playing a game of high-fee active investing is a loser’s game. Consumers are getting the message these days: Money in index funds now represents over 37 percent of the assets in U.S. stock funds as investors pull funds from active mutual funds.

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Never play an important game if you don’t know the odds. Keeping costs low and diversification high vastly improves your odds of having a larger nest egg to retire on, and that you won’t outlive that nest egg. You earned it, you saved it, so don’t give it away playing a loser’s game.

Chart: Wealth Logic Analysis

Allan RothAllan Roth is the founder of Wealth Logic, an hourly-based financial planning firm in Colorado Springs, Colo. He has taught investing and finance at universities and written for Money magazine, the Wall Street Journal and others. His contributions aren’t meant to convey specific investment advice.



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