Imagine I gave you the option of picking an envelope from one of two hats. Hat One holds 100 envelopes each containing $920. Hat Two contains 100 envelopes that hold either $751 or $1,016. Which hat would you choose?

Before you pick, you should know how many of the envelopes in Hat Two contain $751 and how many contain $1,016. That way, you can calculate the probability of whether you will come out ahead of the sure $920 in Hat One.

In this case, Hat Two holds 66 envelopes containing $751 and 34 envelopes containing $1,016. Now which hat would you choose? It may be obvious, but let’s do the math:

Hat One: (100 x $920) / 100 = $920
Hat Two: (66 x $751) + (34 x $1,016) / 100 = $841.10

As you can see, you stand to make $841.10 from Hat Two based on probability and should pick the sure $920 from Hat One. Any rational person should pick from Hat One, yet most of us pick from Hat Two when it comes to investing.

Hat One represents an index fund, specifically the Vanguard 500 Index Fund during the years 1984-2009*. Hat Two represents the 136 actively-managed domestic equity funds that were around in 1976 when the Vanguard 500 Index Fund was born and had survived through 2009. The envelopes represent one year’s worth of the average annual compounded return for each group of funds. In the case of the Vanguard 500 Index Fund (Hat One), an investment of $10,000 would have yielded you $920 per year on average over the 25-year time frame.

For the actively-managed funds (Hat Two), two-thirds underperformed the Vanguard 500 Index Fund by an average of 1.69% over the time frame yielding a 7.51% average annual return or $751 per year. The remaining one-third of the actively-managed funds beat the Vanguard 500 Index Fund by 0.96%. That group averaged a 10.16% annual return or $1,016 per year on your $10,000 investment.

As shown above, randomly selecting an actively managed fund would have yielded you an 8.41% annual return versus 9.2% for the Vanguard 500 Index Fund. “But Rob”, you say, “I don’t randomly picks funds. My investment adviser selects them after doing lots of research”. Sorry to bust your bubble, folks, but no one can regularly select the winning one-third of actively-managed funds in advance, and the winners are usually not those that have outperformed in the past.

To make matters worse for the actively-managed funds, the results from this study do not include the actively-managed funds that closed or merged during the 25 years (the vast majority of which were under-performing). The results also do not account for sales loads (commissions). If loads were included, the Vanguard 500 Index would have beaten 88% of the actively-managed funds.

“Fair enough”, you say, “But this is one area of the market and one period of time. Don’t actively managed funds beat index funds in other asset classes like small-cap stocks or corporate bonds?”

Not according to Richard Ferri’s extensively researched book, The Power of Passive Investing. In fact, it shows that about one-third of actively-managed funds outperform their indexes across multiple asset classes and various time periods and that the amount you are compensated on average for randomly selecting a winning actively-managed fund is not enough to compensate you for the higher probability and lower return of selecting an under performing fund.

My advice is to stick to low-cost index funds whenever possible. Choose Hat One.

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*The study used in this post is from The Power of Passive Investing by Richard Ferri.