## Wednesday, August 8, 2012

### Investing Outperformance is Necessarily Rare

Unlike the fictional Lake Wobegon where “all the children are above average,” in the real world we can’t all be above average. If one investor gets above-average returns, there must be some other investor whose returns are below average. Because of a compounding effect, there actually have to be many below-average investors to compensate for one above-average investor.

Consider two investors, A and B, who each start with \$10,000 to invest. Suppose that after 40 years, they have an average of \$250,000. Their average compound return per year works out to 8.4%. If investor A ends up with \$475,000, then investor B must end up with only \$25,000 to make the average \$250,000. But look at their individual compound average yearly returns:

Investor A: 10.1% (1.6% above average)
Investor B: 2.3% (5.6% below average)

So, what has happened here? If A and B exactly balance each other out to give the correct average portfolio size, why is B’s yearly return so far below average, while A’s return is not much above average? This is a compounding effect. Investor A ended up with 1.9 times the average portfolio size, but investor B ended up with a portfolio 10 times smaller than average. This difference between 1.9 and 10 leads to the +1.6% and -5.6% figures.

Let’s look at this from another point of view. Suppose that a group of investors each start with the same portfolio size and invest for 40 years. Suppose that outperformers make 10% per year above the average return, and underperformers make 10% per year below the average return. How many underperformers does it take to compensate for one outperformer? The answer is 45!

In a more extreme example, if Warren Buffett has outperformed the average by \$40 billion, it would take a million investors each underperforming by \$40,000 to compensate. So, we see that investing outperformance is necessarily rare and that there have to be many who underperform for each high flyer. Of course, none of this applies in Lake Wobegon.

#### 4 comments:

1. Michael, I tried to recreate your calculations using FV() from Excel and could not get the same numbers. Close, but not the same.

I like your conclusion: on the long term success in attempting to outperform the market is much less likely than not.

2. @AnatoliN: I rounded all percentages to the nearest tenth of a percent. Another thing to consider is that in this context the difference between 20% return and 10% return is not 10%, but is (1.2/1.1)-1=9.1%. Perhaps one of these two things accounts for the differences you see.

3. This is really mind blowing. Seems more plausible that someone who compounds at a 2% better than market averages would be offset by someone who compounds at 2% worse than market averages.

I guess that applies for each individual year, but when compounding over a long period, the (theoretical) loser lags further and further behind. Very interesting.

4. @Gene: That's right. Over time the winner's portfolio grow and there are more dollars attracting the higher return.