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What Are the Odds of an Active Portfolio Outperforming?

There's an overwhelming body of evidence demonstrating that the odds against successfully choosing a mutual fund that will outperform its appropriate risk-adjusted benchmark are sufficiently high that it's not prudent to try. For example, the study "How Well Have Taxable Investors Been Served in the 1980s and 1990s?" found:
  • The average fund underperformed its benchmark by 1.75 percent per annum before taxes and by 2.58 percent on an after-tax basis.
  • Just 22 percent of the funds beat their benchmark on a pretax basis. The average outperformance was 1.4 percent, with the average underperformance being 2.6 percent. However, on an after-tax basis, just 14 percent of the funds outperformed. The average after-tax outperformance was 1.3 percent, while the average after-tax underperformance was 3.2 percent. Thus, the risk-adjusted odds against outperformance are about 17:1.
However, even these abysmal odds don't present an accurate picture of the odds of success. Let's see why that's the case.

Since diversification of risk across asset classes is an important part of a prudent investment plan, many investors build portfolios of funds to get exposure to several asset classes, such as:

  • Domestic large-cap
  • Domestic small-cap
  • Domestic small-cap value
  • Domestic large-cap value
  • International large-cap
  • International small-cap
  • International small-cap value
  • International large-cap value
  • Real estate
  • Emerging markets
An active investor would choose 10 funds, hiring the very best fund in each asset class. The question isn't about the odds of each fund generating alpha. Instead, the question is: What are the odds the portfolio will generate alpha?

Thanks to Jim Davis of Dimensional Fund Advisors, we can estimate the odds of a portfolio of 10 equally-weighted actively managed funds, rebalanced annually, successfully generating alpha. To simplify the math, we need make several assumptions. (Please note that no real funds were used in these calculations, though the assumptions used are realistic unless otherwise noted.)

  • All funds have the same true alpha of negative 0.8 percent per year. This seems like a conservative estimate, based on the evidence from studies on performance of actively managed mutual funds. (The after-tax alpha would be much more negative.)
  • The standard deviation of each fund's annual alpha is 5 percent.
  • Alphas are uncorrelated across funds and across years. (Though this probably isn't realistic, as funds that follow similar strategies will probably have positively correlated alphas.)
  • The normal distribution is a reasonable approximation for the distribution of fund alphas.
Based on these assumptions, here are the probabilities of a portfolio having a positive average alpha over various horizons:

To see how sensitive the data is to the assumptions, we now assume that the standard deviation of annual alpha is 7 percent. (We would also get similar sensitivity if we changed the true alpha instead of the standard deviation.) The results are:

Now consider the following. The aforementioned study found that just 22 percent of the funds in the study outperformed their appropriate risk-adjustment benchmark on a pretax basis over the 1980s and 1990s. However the tables above show that the odds of a portfolio of actively managed funds doing so are even lower, and the tables reflect odds only for a 10-year period. For taxable investors, the story gets even worse as just 14 percent of funds outperformed in the 80s and 90s. The odds of a portfolio of actively managed funds generating positive after-tax alpha over the long term are surely much, much worse.

And the odds would get even worse as we increased the number of funds to add other asset classes (such as fixed income or commodities).

It's also important to remember that most investors have investment horizons longer than 10 years. And the longer we extend the investment horizon, the worse the odds of success for active management.

The conclusion we can draw is that active management is the triumph of hype, hope and marketing over wisdom and experience. Choosing passively managed funds to implement your investment plan is the winning strategy -- the one most likely to allow you to achieve your goals.

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