Threshold Distortion: Skill and Luck

You can find and exploit skill among mutual fund managers. This picks up from where More on Threshold Distortion leaves off.
More on Threshold Distortion

Here are the differences between the average of the top 30 mutual funds and the average of all funds during each 5-year selection period.

Starting in 1970: initial period: 6.90%
Starting in 1975: initial period: 15.26%
Starting in 1980: initial period: 7.68%
Starting in 1985: initial period: 5.68%
Starting in 1990: initial period: 9.55%

The median of these numbers is 7.68%. The thresholds are typically in the neighborhood of 7% to 8%. Since the numbers listed above are averages above a threshold, each of the thresholds must be lower than the number listed above.

I would expect very few funds to exceed the threshold by much.

We have measured the skill level as being 3% to 4%. The skill plus random luck has caused the top 30 funds to exceed the threshold. Because the top 30 are selected from many funds (in the neighborhood of 300 to 3000 or more), we can assume that all 30 of the selected funds are lucky at the time of selection.

This tells us that each fund in the top 30 satisfies the following approximation: skill + luck = 7% to 8%. Since skill is 3% to 4%, the random component: luck = 4%. What is more, the probability associated with this level of luck = 4% must be very high. Otherwise, the distribution of fund returns would be distinctive.

Figure 5.5 on page 125 of John Bogle’s Common Sense on Mutual Funds shows that these findings are consistent with the probability distribution of mutual fund returns.

We can expect luck to subtract from skill at times. Because skill and luck turned out to be almost the same, we can expect the top 30 fund prices to fall back to the average of all funds every now and then. We will have buying opportunities.

In my procedure, I have followed the standard approach of statistics in handling randomness. I established a null hypothesis that (normalized) mutual fund prices are random in each sample. This is consistent with the notion that five years is sufficient for the stock prices to revert to the mean. I avoided a null hypothesis that mutual fund price changes are random. That would be contrary to the evidence that the stock market reverts to the mean.

We see mean reversion in the way that the stock market’s standard deviation decreases. It falls much more rapidly than the square root of the number of years. Prices cannot vary freely. They are drawn in. They are related to earnings.

As for the amount of time required, see pages 174 and 175 of Peter Bernstein’s Against the Gods. He refers to a study indicating that buying the three-year winners would have resulted in underperforming the market by 5.0% three years later. Buying the three-year losers would have outperformed the market by 19.6% three years later.

Five years should be enough.

In a similar vein, on pages 176 and 177, Peter Bernstein offers this advice to investors who are constantly switching managers: “[T]he wisest strategy is to dismiss the manager with the best recent track record and to transfer one’s assets to the manager who has been doing the worst; this strategy is no different from selling stocks that have risen furthest and buying stocks that have fallen furthest. If that contrarian strategy is hard to follow, there is another way to accomplish the same thing. Go ahead and follow your natural instincts. Fire the lagging manager and add to the holdings of the winning manager, but wait two years before doing it.”

I strongly disagree with his advice to invest in the worst manager. I have seen studies that prove that some managers have a special talent for losing money. His recommendation to wait for two years gets my attention. It suggests that he has seen confirming evidence that there will be bargains after a short delay.

Have fun.

John Walter Russell
July 6, 2005