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There has been a lot of discussion about luck and whether it is possible to outperform the market without it. I think it would be helpful to understand what “luck” really is. Here is how I think about it. I know that some of you who disagree with me about the possibility of outperforming the market will disagree with me even if what I say makes sense (what Charlie Munger refers to as “first-conclusion bias”), but c'est la vie.

“Lucky” is when you succeed when the probability of succeeding is very low. “Skill” is when the quality of your actions give you a high probability of succeeding. The greater you can increase your probability of succeeding, the more skillful you are.

I don't care what the activity is. In basketball, Michael Jordan's probability of making a free throw is somewhere near 85%. The probability of *me* making a free throw is probably closer to 8.5%. If we had a free throw contest and Jordan won, it would be foolhardy to think that it was because he was luckier than me. If *I* won, however, then most people would agree that I had gotten “lucky,” and I would agree with them.

The more freethrows we take, the more certain we are of discovering each of our probabilities of making the freethrow. If we took 1,000 free throws each, we would have a good idea of our respective probabilities, and our respective probabilities are a reflection of our skill at making freethrows.

This process of determining the probabilities is similar to flipping a coin repeatedly. If you flip a coin a few times, you won't be very confident in your estimate of the probability of the coin landing heads. However, with enough repetitions, you will be very confident that the probability of getting heads is 50%, if it's a fair coin.

Now, if I repeatedly flipped a coin (say 1,000 coin flips), and I got heads about 49.5% of the time, few people would be shocked, and I would be surprised to hear someone say “That was so lucky!” But if you instead got 99.5% heads, most would agree that you got extremely lucky. But this would be under the *assumption* that the coin is fair. We can't be *certain* that the coin is fair. It is always possible that this particular coin has a 99% probability of landing heads, in which case it wouldn't be particularly lucky to get 99.5% heads. The 49.5% figure would be the lucky one.

If I did get 99.5% heads, you could be certain that people would want to examine the coin to see if it's fair. They would examine all of the physical characteristics of the coin to see if anything could be causing it to be unfair. They would look at the weighting and shape. They might even bring in a magician as a consultant to see if I was doing some sort of trick. They would look at the way I was tossing the coin to see if that could affect the outcome. They would check out the surface that the coin was landing on. In the end, they would use reasoning to determine whether the coin was in fact fair, given everything they found out.

Buffett has been beating the market pretty consistently for about 50 years now. It is conceivable that Buffett has been a lucky coin flipper. A large majority of his 50 coin flips have been heads. If the market is efficient, each person is just about as likely to beat the market as they are to underperform it (i.e. it's a fair coin). The probability of getting the percentage of heads that he got out of 50 coin flips isn't particularly small under this assumption.

But, this ignores a very important measure: the deviation of the outcome from the market average. If the market is efficient, then the greater the deviation from the market average, the smaller the probability of that outcome. Investors returns would be clustered around the market average return, with fewer and fewer investors returns as you move away from the mean. The probability of Buffett's coin flips isn't 0.5 X 0.5 X 0.5… Because Buffett's deviations are so far away from the market average, each deviation has a low probability of occurring (much lower than 50%). Multiply each probability, and you get a infinitesimal probability. If the market is efficient, then Buffett is incomprehensibly lucky.

Consider the performance of Buffett's investments partnerships:
`  Year    Partnerships    Dow     +/-  1957           10.4%   -8.4%    18.8%  1958           40.9%   38.5%     2.4%  1959           25.9%   19.9%     6.0%  1960           22.8%   -6.3%    29.1%  1961           45.9%   22.2%    23.7%  1962           13.9%   -7.6%    21.5%  1963           38.7%   20.6%    18.1%  1964           27.8%   18.7%     9.1%  1965           47.2%   14.2%    33.0%  1966           20.4%  -15.6%    36.0%  1967           36.0%   19.0%    17.0%  1968           59.0%    9.0%    50.0%  1969            7.0%  -11.0%    18.0%                                       13 years       2805.0%  156.3%  2648.6%  CAGR           29.5%    7.4%    22.1%`

But what about risk? Surely he must have taken extraordinary risk, right? Think again! His investments provided large “excess” returns, or risk-adjusted returns (using “standard” measures of risk).

Buffet Partnership (1957-1969)
Buffett: Sharpe Measure = 1.74, Treynor Measure = 41.82
DJIA: Sharpe Measure = 0.28, Treynor Measure = 4.45

Berkshire Hathaway (1966-1997)
BRK: Sharpe = 0.9557, Treynor = 0.5507
S&P 500: Sharpe = 0.3702, Treynor = 0.1371
Considering these staggering numbers (and the extremely impressive performance later at Berkshire), it's very possible that he isn't using a fair coin. We need to examine it thoroughly. I (along with thousands of others) have been closely examining the coin that Buffett has been using for several years. I have studied carefully the things he has said and done to see if he is doing something that might affect the probability of his coin flips. And what I have found is that the things he does make a heck of a lot of sense. Buffett is rational and disciplined. He understands probabilities. He understands complex financial and economic concepts better than virtually anyone around. He is obsessively focused on accumulating capital, giving him motivation far beyond the average investor. He is incredibly intelligent and is considered by most to have a near photographic memory. He has a comprehensive and yet fairly simple model that he uses to analyze stocks – shockingly, he looks at a stock purchase as if he were buying a business (which of course he is). Using reasoning, we can understand why the coin he is using is not even close to being fair!

We don't have to stop here. We can collect more evidence. Look at Buffett's “sidekick,” Charlie Munger, who coincidentally is also very “lucky.”

The results for Munger's partnership (Note: I noticed that some of the returns for the Dow are slightly different from the ones listed for Buffett. The differences were much too small to bother investigating).
`  Year    Partnership   DJIA     +/-  1962          30.1%   -7.6%    37.7%  1963          71.7%   20.6%    51.1%  1964          49.7%   18.7%    31.0%  1965           8.4%   14.2%    -5.8%  1966          12.4%  -15.8%    28.2%  1967          56.2%   19.0%    37.2%  1968          40.4%    7.7%    32.7%  1969          28.3%  -11.6%    39.9%  1970          -0.1%    8.7%    -8.8%  1971          25.4%    9.8%    15.6%  1972           8.3%   18.2%    -9.9%  1973         -31.9%  -13.1%   -18.8%  1974         -31.5%  -23.1%    -8.4%  1975          73.2%   44.4%    28.8%                                      14 years      1156.7%   96.2%  1060.5%CAGR            19.8%    4.9%    14.9%Std Dev         33.0%   18.5%    14.5%`

Munger's performance is also pretty amazing. They quite possibly would have beaten Buffett's numbers if they occurred over the same time period. It looks like Munger took slightly more risk, and I don't have risk-adjusted numbers, but his performance is still extraordinary. What kind of coin is Munger flipping? Well, if you have read about Munger, you know that he was also a extremely hard worker, and he is incredibly intelligent. Some people (and this includes Buffett's son) say that he is even more intelligent than Buffett. He is known for understanding complex “mental models” that explain a wide variety of phenomena. He and Buffett got along so great because they think so much alike, but he is also responsible for teaching Buffett that it makes sense to pay up a little more for quality businesses. He is so selective about investments that Buffett calls him “The Abominable No-man.” Once again, it is easy to use reasoning to come to the conclusion that he just might not be using a fair coin.

Need more evidence? Read Buffett's essay, “The Superinvestors of Graham-and-Doddsville.” It's included as an appendix in the latest edition of Benjamin Graham's The Intelligent Investor. In it, Buffett describes several extraordinarily “lucky” coin flippers. In an incredibly lucky coincidence, Buffett worked with a few of them at Graham-Newman, and they all happened to have an value investment philosophy that was derived from one man: Benjamin Graham.

You might also want to check out two papers from Tweedy, Browne Company LLC:
“10 Ways to Beat an Index”
http://www.tweedy.com/library_docs/papers/tenways.pdf
“What Has Worked in Investing”
http://www.tweedy.com/library_docs/papers/what_has_worked_all.pdf

There are numerous other examples of people with exceptional long-term performance who coincidentally have logical approaches to investing that reasonably could be expected to outperform the market. The legendary former mutual fund manager Peter Lynch comes to mind. Lynch was another famous workaholic. His philosophy differs somewhat from the value “flavored” philosophies, but his approach is logical and sensible. He recommends investing in what you know, keeping an eye out for the opportunities that are all around you, and doing your homework. Could his philosophy be an unfair coin compared to investors who are less diligent and less logical? You bet!

So is beating the market the result of luck? Not if you find the right coin.