The magnitude issue
We noted that an investment manager overseeing a $5 billion portfolio who can improve performance by only one-tenth of 1% per year will increase investment earnings by .001 $5 billion $5 million annually. This manager clearly would be worth her salary! Yet we, as observers, probably cannot statistically measure her contribution. A one tenth of 1% contribution would be swamped by the yearly volatility of the market. Remember, the annual standard deviation of the well-diversified S&P 500 index has been approximately 20% per year. Against these fluctuations, a small increase in performance would be hard to detect.
Nevertheless, $5 million remains an extremely valuable improvement in performance. All might agree that stock prices are very close to fair values, and that only managers of large portfolios can earn enough trading profits to make the exploitation of minor mispricing worth the effort. According to this view, the actions of intelligent investment managers are the driving force behind the constant evolution of market prices to fair levels. Rather than ask the qualitative question, Are markets efficient? we ought instead to ask the quantitative question,
How efficient are markets?
The selection bias issue Suppose you discover an investment scheme that could really make money. You have two choices: Either publish your technique in The Wall Street Journal to win fleeting fame or keep your technique secret and use it to earn millions of dollars.
Most investors would choose the latter option, which presents us with a conundrum. Only investors who find that an investment scheme cannot generate abnormal returns will be willing to report their findings to the whole world. Hence, opponents of the efficient market’s view of the world always can use evidence that various techniques do not provide investment rewards as proof that the techniques that do work simply are not being reported to the public.
This is a problem in selection bias; the outcomes we are able to observe have been preselected in favor of failed attempts. Therefore, we cannot fairly evaluate the true ability of portfolio managers to generate winning stock market strategies.
The lucky event issue
In virtually any month, it seems we read an article in The Wall Street Journal about some investor or investment company with a fantastic investment performance over the recent past. Surely the superior records of such investors disprove the efficient market hypothesis.
This conclusion is far from obvious, however. As an analogy to the “contest” among portfolio managers, consider a contest to flip the most heads out of 50 trials using a fair coin. The expected outcome for any person is 50% heads and 50% tails. If 10,000 people, however, compete in this contest, it would not be surprising if at least one or two contestants flipped more than 75% heads. In fact, elementary statistics tells us that the expected number of contestants flipping 75% or more heads would be two. It would be silly, though, to crown these people the head-flipping champions of the world. They are simply the contestants who happened to get lucky on the day of the event (see the nearby box).
The analogy to efficient markets is clear. Under the hypothesis that any stock is fairly priced given all available information, any bet on a stock is simply a coin toss. There is equal likelihood of winning or losing the bet. Yet, if many investors using a variety of schemes make fair bets, statistically speaking, some of those investors will be lucky and win a great majority of bets. For every big winner, there may be many big losers, but we never hear of these managers.
The winners, though, turn up in The Wall Street Journal as the latest stock market gurus;
then they can make a fortune publishing market newsletters. Our point is that after the fact there will have been at least one successful investment scheme. Adoubter will call the results luck; the successful investor will call it skill. The proper test would be to see whether the successful investors can repeat their performance in another period, yet this approach is rarely taken.
With these caveats in mind, we now turn to some of the empirical tests of the efficient market hypothesis.
Read More: Are Markets Efficient?
