Probabilities and the Efficient Market Hypothesis

An article in the Globe and Mail got us interested in a book entitled Zombie Economics: How Dead Ideas Still Walk Among Us by John Quiggin. (Click here for article) We currently have the book on order from Amazon and will report back once we have read it in full.

In the meantime, we thought we might do a few blogs on the efficient market hypothesis and this one is based on a single line from the Globe and Mail article that suggests the EMH must be false because:

"Nothing in the hypothesis can explain the frequent bubbles and busts, strange stock valuations or the inconvenient truth that some shrewd investors do outperform the market." (emphasis added)

A little experiment. If you flip a fair coin, what do you believe the likelihood of it coming up 'heads' 10 times in a row? If it did, would you suggest that the coin wasn't balanced properly? Most people would. Now, however, lets start with 1024 people and ask them all to flip a coin. Those that come up tails must leave, and those that come up heads can stay. After the first toss, we should have about 512 people left. Repeat a second time and about 256 people should be left. On each successive toss, about half will be tails and half will be heads. After three tosses 128 people are left, then 64, 32, 16, 8, 4, 2 and finally, after ten rounds, only one person is left. That person just tossed 10 consecutive heads. (The probablility of doing that is one in 1024)

Lets do the experiment again with 1024 "shrewd investors" who build a portfolio by choosing any 59 stocks in the TSX 60. The one stock they don't hold is chosen by throwing a dart at the list. If the stock they omit underperforms the TSX then their portfolio will outperform the market. The omitted stock is chosen at random and thus has a probability of beating the index of approximately one half. After one year, those investors that beat the index can stay, they rest leave. At the beginning of each year, the survivors choose a new portfolio in the same manner. By the same logic as the coin game, after 10 years one of those "shrewd investors" beat the index 10 years in a row ... by throwing a dart.

According to the Chartered Financial Analyst Website, there are currently 90,113 individuals that hold the CFA designation. These are the people that manage portfolios and are well trained in what they do. If they all build portfolios in the game above, 88 will beat the market 10 years in a row, and one will be expected to beat the index for 16 consecutive years.

The existance of investors that outperform the market is not a sufficient reason to dismiss the efficient market hypothesis. As just shown, even with efficient markets, given a big enough pool, it is possible to beat the market entirely by luck.

Next time we look at the meaning of "beating the market".