So this is what is behind the latest posts.

Think of the Inspector as an investor, who believes he has found a pearl – a stock with a high probability of a large appreciation. Think of Margot as the pearl: the probability that she is innocent is the probability that the stock will have a large return. Think of the Court as Mr. Market, who believes the current stock price is right. Mr. Market believes that Margot is a pebble – a stock with a normal, low probability of a large appreciation.

For example, let’s say the current stock price is 50. Mr. Market thinks the price is right: the stock is worth 50. Assume value is normally distributed around 50, with standard deviation 20. Then, according to Mr. Market, there is an 11% probability of a return higher than 50% (the area to the right of the value distribution at 75). The investor, on the other hand, values the stock at 100. Assuming the same distribution, centred at 100, the probability of a return higher than 50% is 89%. The two probabilities are very close to the Base Rates we assumed for Margot’s innocence according to the Court (10%) and to the Inspector (90%).

Let’s call a return higher than 50% an ‘obscene’ return. Of course the threshold is arbitrary: an obscene return is difficult to define, but you know it when you see it. So we call a pearl a stock with a 90% probability of an obscene return, and a pebble a stock with a 10% probability of an obscene return. 10% is a reasonably conservative estimate for the Base Rate of obscene annual returns. For example, out of about 3,000 US stocks with a market cap above 100 million, 434 (14%) had a return above 50% in 2012. This turns out to be the 10-year average:

Source: Factset

(As the sample is made up of today’s 3,000 stocks, this is not entirely correct. But I guess it is about right. And yes, there were 41 stocks that went up more than 50% in 2008. The largest company was Dollar Tree (DLTR), +61%).

Mr. Market calls every stock a pebble. To him the price is always right: there is no such a thing as a pearl. He is like a coin thrower always calling Head, or like a weather forecaster always calling rain. His calls are totally uninformative: TPR=FPR=1, hence LR=1, A=0.5 and PP=BR. Therefore, the probability that a stock will have an obscene return, in the light of Mr. Market’s call, does not budge from the 10% Base Rate. Notice that Mr. Market is right 90% of the times: 9 out of 10 stocks will not have an obscene return. But his risk intelligence is perfectly worthless.

The investor, on the other hand, thinks he has found a pearl. Let’s not get into how he did it. The question we ask is: how can he be sure that he is not making a mistake? The investor is like the Inspector, who believes that Margot is very likely innocent. Despite the high probability, both would like to be 100% certain. The Inspector would love to have full proof evidence of Margot’s innocence. But, as we have seen, if he tries to prove her innocence he may end up with imperfect evidence. If he succeeds, fine: she is definitely innocent. But if he doesn’t, he will continue to believe she is quite likely innocent. Hence the best way for the Inspector to be sure about Margot is to try to gather conclusive evidence – positive (Smoking Gun) or negative (Strangler Tie) – that proves her guilty. A Smoking Gun has the additional advantage of avoiding a Blackstonian Inspector’s most dreaded mistake: a False Positive – a wrongful conviction. If Margot is innocent, there is no way that she will open the door. Therefore, if she opens the door, she is certainly guilty. Her conviction cannot be a mistake. But if she does not open the door, in the eyes of the Inspector she is almost certainly innocent. The Inspector can never be perfectly certain: there is always a chance that he is making a mistake. But a small risk of a wrongful acquittal is a small price to pay for the certainty of avoiding a wrongful conviction.

Likewise, the investor would love to have full proof evidence that the stock will earn an obscene return. But if he tries to prove it, he may end up with imperfect evidence. If he succeeds, fine: he will believe the stock is certainly a boon. But if he doesn’t, he will continue to believe that, while not a pearl, the stock still has quite a high chance of an obscene return. Hence the best way for the investor to be sure about the stock is to try to gather conclusive evidence – a Smoking Gun or a Strangler Tie – that proves that it will not earn an obscene return.

Here, however, is a crucial difference. As any investor who has experienced the wreckage of his strongest convictions can easily attest, in matters of investing there is no such a thing as truly conclusive evidence: nothing is certain. Certainty in investment can never be expressed as: There is no way that something or other will or will not happen. There is always a way. The only thing an investor can be sure about is his conclusive decisions: ‘convict’ the stock, i.e. decline its purchase, or ‘acquit’ it, i.e. go ahead and buy it. So, for example, a Smoking Gun can be expressed as: if I see such and such evidence, there is no way that I will buy the stock. The decision does not guarantee against a False Positive, i.e. a ‘wrongful conviction’: the rejected stock may well turn out to be a missed opportunity. But passing on the purchase certainly avoids a False Negative: trivially, no purchase implies no wrongful purchase.

But that’s just fine. Unlike the Blackstonian Inspector, the investor’s most dreaded mistake is not a False Positive: it is a False Negative – a ‘wrongful acquittal’, leading to a bad investment. Perhaps it is not as extreme as: Better ten missed opportunities than one bad investment (or, as Warren Buffett would put it, better ten strikes than one wrong swing), but there is little doubt that Rule no. 1: Never Lose Money is the Blackstone Principle of Intelligent Investing.

A Blackstonian investor’s main aim is to avoid value traps: pebbles resembling pearls. He is not just concerned about ending on the left tail of the value distribution: if value is truly centred at 100, the risk of a negative return is miniscule. The real risk is that the valuation itself is wrong: if value is much lower than 100, the probability of an obscene return is much lower than 90%. Instead of a treasurable pearl, the stock may turn out to be a treacherous pebble. Against such a risk, the Blackstone Principle is upheld by the other side of the Smoking Gun, which can be expressed as: if I don’t see such and such evidence, I get more convinced – possibly almost certain – that the stock will earn an obscene return, and will therefore buy it. The investor will never be perfectly certain: he knows he can’t avoid bad investments and missed opportunities and he is bound to see plenty of both. But focusing on proving ‘guilt’ rather than ‘innocence’ can help him to minimize them.

The Margin of Safety derives not from how similar the stock is to a pearl, but from how different it is from a pebble. Or, as Seth Klarman puts it:

There is nothing inherent in a security or business that alone makes it an attractive investment. Investment opportunity is a function of price, which is established in the marketplace. Whereas some investors are company- or concept-driven, anxious to invest in a particular industry, technology, or fad without special concern for price, a value investor is purposefully driven by price (Margin of Safety, p. 215).

Or, as Charlie Munger – quoting the German mathematician Carl Jacobi – likes to put it: Invert, always invert.

(This post was a tough nut to crack. In the process of writing it, I made substantial changes to Is the market price right? and eliminated a post published on 10 November 2012, entitled Sizing the Margin of Safety, which was confusing and partially wrong. That’s why I like writing: it straightens my thinking).