Frank Armstrong

Dunn's Law Revisited

Occasionally even serious financial columns mention Dunn's Law as if it were an accepted economic maxim. It isn't, and it's dangerous to pretend that it might be.

In short, Dunn's law states that when an asset class does well an index fund in that class will usually outperform actively managed funds, but when an asset class does poorly, the actively managed fund will outperform the index. Hogwash!

At first blush, the evidence seems to support the thesis. But, Dunn's law is fuzzythink at its worst. It should be restated like this: When you compare an actively managed fund with the WRONG index, you will get a strange result.

Most discrepancies between active management funds and index performance can easily be explained by the application of Fama-French three factor analysis. For instance, when small funds are doing well, the fund (or index) with the smallest average size company holdings is most likely doing better. Actively managed funds usually do not attempt to trade in the smallest company stocks so they end up with an average company size somewhat larger than the index. Likewise, actively managed funds avoid the deep value companies, so an actively managed fund that calls itself a value fund usually has far less tilt toward value than the appropriate index.

If an index and fund have similar size/value characteristics, most likely the index did about 2% better. Of course, there is always an element of random drift. But as Mark Carhart pointed out in perhaps the most exhaustive study ever done on mutual fund performance, after size and value are taken into account there is very little alpha (manager skill and cunning, or excess performance due to manager) left to explain.

So, really the comparison of active vs. passive will be flawed unless the portfolios have identical weights to the priced risk factors. Dunn's Law compares apples to oranges.

I forgive you if by now you are asking, "Why should I care?" Here is why this really is important:

• Dunn's Law implies that index funds are not as effective during adverse markets as actively managed funds. Not true. Index funds are far more effective than actively managed funds over the entire market cycle. But, to make a fair comparison in good markets and bad, the proper size and value adjustments must be made.
• Even worse, Dunn's Law might lead the innocent and unsuspecting investor into the most grievous sin of market timing. Investors shifting back and forth between index funds and actively managed funds in a vain attempt to chase apparent performance discrepancies that they don't understand are unlikely to generate anything more than huge tax and transaction costs as they decrease their net returns and wonder what went wrong.

Relegate Dunn's Law to the scrap heap with other inane and dangerous ideas. Keep the faith. Markets work just fine without the intervention of active managers in all phases of the investment cycle. Do the right thing: Build your appropriate asset allocation plan, then index. All the time!