One of the more interesting aspects of our practice at Springwater is that we occasionally find our “investment mood” at odds with that of our prospective clients.

So it is context of managing (prospective) client expectations that we share with you below the contents of an email we sent to our clients in May 2007, a few short months before the market peak that preceded the 2008/09 market correction.

On a recent flight, I decided to bring with me a book that I hadn’t read in a while – to counter-act the effects of Fortune, Money, Kiplinger’s and the other “personal finance” publications that try to convince readers (like you and me) that their stock and fund-picking really works.

The book is “Fooled by Randomness” by Nassim Nicholas Taleb (published 2001 by Texere LLC) – one of my favorites.

As a firm believer in asset allocation and diversification, and a skeptic of the claims of active managers, two short stories in the book really resonated with me. I have shared them with you below. As the stock market chugs along through one of its longest bull markets in history, some food for thought:

Story 1 – “The Mysterious Letter”

You get an anonymous letter on January 2nd informing you that the market will go up during the month. It proves to be true, but you disregard it owing to the well-known January effect (stocks have gone up historically during January). Then you receive another one on February 1st telling you that the market will go down. Again, it proves to be true. Then you get another letter on March 1st – same story. By July you are intrigued by the prescience of the anonymous person and you are asked to invest in a special offshore fund. You pour all your savings into it. Two months later, your money is gone. You go spill your tears on your neighbor’s shoulder and he tells you that he remembers that he received two such mysterious letters. But the mailings stopped at the second letter. He recalls that the first one was correct in its prediction, the other incorrect.

What happened? The trick is as follows. The con operator pulls 10,000 names out of a phone book. He mails a bullish letter to one half of the sample, a bearish one to the other half. The following month he selects the names of the persons to whom he mailed the letter whose prediction turned out to be right; that is, 5,000 names. The next month he does the same with the remaining 2,500 names, until the list narrows down to 500 people. Of these there will be 200 victims. An investment in a few thousand dollars worth of postage stamps will turn into several million.

Story 2 – “Nobody Has to Be Competent”

We create a cohort [a cohort is a group of persons sharing a demographic or statistical characteristic] that is composed exclusively of incompetent [investment] managers. We will define an incompetent manager as someone who has a negative expected return, the equivalent of the odds being stacked against him. We instruct the Monte Carlo generator [a statistical program that makes random selections from a data set] now to draw from an urn. The urn has 100 balls, 45 black and 55 red. By drawing with replacement [after a ball is drawn, it is returned to the urn], the ratio of red to black balls will remain the same. If we draw a black ball, the manager will earn $10,000. If we draw a red ball, he will lose $10,000. The manager is thus expected to earn $10,000 with 45% probability, and lose $10,000 with 55% probability. On average, the manager will lose $1,000 each round – but only on average.

At the end of the first year, we still expect to have 4,500 managers turning a profit (45% of them); the second, 45% of that number, 2,205. The third, 911; the fourth, 410; the fifth, 184. Let us give the surviving managers names and dress them in business suits. True, they represent less than 2% of the original cohort. But they will get attention. Nobody will mention the other 98%. What can we conclude?

The first counterintuitive point is that a population entirely composed of bad managers will produce a small amount of great track records. As a matter of fact, assuming the manager shows up unsolicited at your door, it will be practically impossible to figure out whether he is good or bad. The results would not markedly change, even if the population were comprised entirely of managers who are expected in the long run to lose money. Why? Because owing to volatility, some of them will make money. We can see here that volatility actually helps bad investment decisions.

The second counterintuitive point is that the expectation of the maximum of track records, with which we are concerned, depends more on the size of the initial sample, than on the individual odds per manager. In other words the number of managers with great track records in a given market depends far more on the number of people who started in the investment business (in place of going to dental school), rather than on their ability to produce profits. It also depends on the volatility.