Book-review: Fortune’s Formula by William Poundstone

I read about Fortune’s Formula somewhere and put it on my reading list because I am greatly interested in the topic of Position Sizing which the book is about and more specifically about the Kelly Formula.

I see a great deal of parallels between gambling, poker and investing, thus it did not come as a surprise to me that the book is about all three topics. The book is about the kelly criterion or kelly formula which basically helps calculating the optimal betting or position size within a portfolio context if you are interested in optimizing long-term geometric mean returns.

For understanding / discussing the topic it is much easier to think in bets (with clear outcomes) instead of investing in financial markets.

The underlying message is easy to comprehend wihtout higher math. We investors are usually interested in compound returns, i.e. we do not take out any profits from last year but we reinvest our profits, thus in the long-term we (hope to) invest a growing amount of capital. After n years of compounding our yearly returns we have an amount of Cn units of money for each initial money unit with Cn = (1+r1) x (1+r2) … (1+rn). As fundamental math tells us, anything times zero is zero which lies at the heart of the kelly criterion.

Kelly’s framework differs strongly from the common mean-variance framework (Markowitz) known to every finance student. The difference is that the mean-variance framework is (usually) used for one-period optimization-problems while the kelly framework tackles multi-period problems and the difference in considered risk-metrics.

Let’s imagine a very uncommong game of roulette. We double our bet in every instance, except if the ball hits zero, in this case we lose our bet. Within a mean variance approach such a ‘situation’ (or bet) looks very attractive. Not so within the Kelly approach, since if we bet all our capital many times in succession we will ultimately hit ‘zero’ and lose everything. It turns out, many discussed hedge fund managers did (blow up – to use the common expression).

The book is a chain of chapters discussing various characters, many of them can be ascribed to more than one of the following categories: scientists (in the field of information theory, economics, mathematics, …), gamblers (often professional), investors (especially in the widest sense), hedge fund managers showing spectacular performance track records for a certain period, but often gone broke eventually (like Eifuku)

The important lesson is, that one can lose favourable bets more often than ‘should’ be the case (on average). I believe in the common notion that the stock market is (overall) a favourable bet (on average), but outcomes are not the average and the range of outcomes is very wide and potentially (sometimes) wider than imagined.

For fundamental long-term investors the general lessons are important to understand, but practical implementation is difficult. We do not know the real probability distribution for an investment outcomes. Additionally, most investors hold much more than one stock in their portfolio (which would resemble playing at various roulett tables at the same time and allocating the entire capital after each periodic gamble wihtin aboves example – with very favourable effects).

Many topics from the book were already known to me, and I guess you will like Fortune’s Formula if you know and enjoyed some of the following pieces


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