Is the market price right? If you believe in efficient markets, your answer will invariably be: Yes, of course, followed by one of the usual justifications: prices incorporate all information, there is no dollar bill on the pavement, naive investors are arbitraged away, etc.

The Efficient Market Theory is the received wisdom that many market participants and professional investors learn at school. Most of them, however, don’t stick it, and act in ways that are plainly inconsistent with efficient markets. Unless they are explicit passive investors, spending their time reproducing indexes (someone’s got to do it), practitioners don’t believe that market prices are always right, and spend their time looking for investment opportunities, following a wild variety of “strategies”. It is a bit like religion: you know what you are supposed to do, but what you do is a different matter.

In a famous passage of the Intelligent Investor, Ben Graham describes Mr. Market:

Imagine that in some private business you own a small share that cost you $1,000. One of your partners, named Mr. Market, is very obliging indeed. Every day he tells you what he thinks your interest is worth and furthermore offers either to buy you out or to sell you an additional interest on that basis. Sometimes his idea of value appears plausible and justified by business developments and prospects as you may know them. Often, on the other hand, Mr. Market lets his enthusiasm or his fears run away with him, and the value he proposes seems to you a little short of silly (p. 204-205).

Mr. Market is like the expert coach in our child footballer story. The coach says that the child is a champion. Mr. Market says that the price is right. In the child footballer story, the father is strongly inclined to believe the coach. His argument runs as follows: I don’t know whether my child is a champion, but the coach says he is, and the coach is an expert: therefore I think it is likely that my child is a champion. This turns out to be a massive mistake, because the prior probability that the child is a champion is only 0.1%, much lower than the seemingly innocuous 50% indifference level. Hence the true probability that the child is a champion, even after the coach’s pronouncement, is less than 2%. The mistake arises from the Prior Indifference Fallacy. Likewise, investors are strongly inclined to believe Mr. Market. Their argument runs as follows: I don’t know whether the price is right, but Mr. Market says it is, and Mr. Market is an expert: therefore I think it is likely that the price is right. This can also be a large mistake, if the prior probability that the price is right is much lower than the 50% indifference level.

In fact, Mr. Market’s mistake is worse. While the coach can legitimately claim some degree of accuracy and therefore justify an update of the Base Rate, Mr. Market is not accurate at all. He is an extreme version of Dr. Doom and our tricky weather forecaster. To maximize his True Positive Rate, Dr. Doom calls a market downturn as often as possible. For the same purpose, the weather forecaster calls a rainy day most of the times. As a result, their TPR is close to 1: Dr. Doom calls most market downturns; the weather forecaster calls most rainy days. Of course, the catch is that they will raise many False Alarms: their False Positive Rate is also close to 1. Hence, their overall accuracy A=50%+(TPR-FPR)/2 remains close to 50%. Mr. Market does worse: to him the price is *always* right. Hence TPR=FPR=1. He is like a coin thrower always calling Head: perfectly inaccurate. Therefore, his pronouncement is totally uninformative: the prior probability that the price is right should remain unaffected by such useless ‘expertise’. However, as long as investors perceive Mr. Market as an expert, they fall prey to the Prior Indifference Fallacy. As they let their prior probability slide to the 50% indifference level, their posterior probability that the price is right in the light of Mr. Market verdict is 50%.

Imagine, for example, that you value a company stock at V=100. Assume that V is normally distributed around 100, with standard deviation σ. For σ=20, there is a 95% probability that V is between 60 and 140. Imagine then that Mr. Market prices the stock at 50. For our purposes, we can say that the price is “right” if it is equal or greater than V. To you, the probability that a price of 50 is right is very low: 0.6% (use the NORM.DIST function on Excel). But to the average investor V=50: under prior indifference, the probability that the market price is right is 50%.

Avoiding prior indifference can therefore give you a crucial advantage. The size of the advantage is proportional to the probability gap between your valuation and the market price. The gap corresponds to Ben Graham’s *Margin of Safety*. Notice that, as shown in the following graph, the gap advantage is non linear. With the price at 50, the gap is almost the full 50%. But at 80 the probability that the price is right is 16% and the gap is reduced to 34%. A higher valuation uncertainty (e.g. σ=30) would further reduce the advantage to 25%.

Hence a 20% discount is considerably less valuable than a 50% discount. This reflects Graham’s emphasis on the need for the Margin of Safety to be sufficiently *ample*. An ample margin of safety is an opportunity that the Intelligent Investor must seize with firm resolve.

As a big fan of both Graham-style value investing and Bayes, I v much enjoyed this….