Manager profile
years in a row beating the market
the winning years
odds for one manager by luck
Year 1Year 40
Fifteen in a row
Grow a legendary fund manager.
Hire 3,000 fund managers who are secretly coins. Each year a coin decides who beats the market. Run forty years and see who the newspapers would call a genius.
Every square is a manager. Heads, they beat the market this year. Tails, they don't.
Why a streak like this is not a miracle
For one manager you picked in advance, fifteen wins in a row by luck is 1 in 32,768. But nobody picks in advance. There are thousands of managers and many fifteen-year windows. Somebody gets the streak. Then the story gets written about that one person.
In our version, 3,000 coins each get forty years. The chance that at least one of them wins fifteen years running is about . The real fund industry had over 6,000 managers.
This happened
Bill Miller ran the Legg Mason Value Trust fund. It beat the S&P 500 every calendar year from 1991 to 2005. Fifteen in a row. Writers quoted odds against it by luck of 1 in 4,096, 1 in 477,000 and 1 in 2.2 billion. One analyst put a fourteen-year streak at 372,529 to 1.
The physicist Leonard Mlodinow did the sum the right way: many managers, forty years, any fifteen-year window. His answer was roughly 3 out of 4. He also pointed out that in 2004 the fund gained just under 12 percent while the average stock gained more than 15 percent. It still counted as a win, because of how the index is weighted.
None of this says Miller had no skill. It says a streak alone cannot show skill, because luck makes streaks like it all the time.
When someone shows you a streak, ask: how many others were trying?
Sources
- Leonard Mlodinow, The Drunkard's Walk: How Randomness Rules Our Lives (Pantheon, 2008), chapter on streaks: Miller's 1991 to 2005 streak, the quoted odds, 1,000 managers give about 3 percent from 1991, forty years give "roughly 3 out of 4".
- The 372,529-to-1 figure for fourteen years: CNNMoney, quoted in Mlodinow. The other odds: The Consilient Observer, Credit Suisse First Boston, 2003.
- The chance in our version is worked out exactly from the coin flips, for 3,000 managers who each get forty years.