Art of risking everything

In my last post about my resuming my blog, I asked for suggestions on the scope and nature of the blog. Several comments requested me to write about the books that I have been reading recently, and I have embraced this idea. The caveat is that these would not be book reviews, but would be my reflections on what I took away from the book. Moreover, they would be highly opinionated, and would largely be about finance even if the book is not about finance.

Today’s book is On the Edge: The Art of Risking Everything¹ by Nate Silver, author of The Signal and the Noise and famous mostly for founding the election forecasting site FiveThirtyEight. This book is not about finance at all, and I had great difficulty wading through four uninteresting chapters about gambling and poker before getting to the relatively small bit of finance in the middle. The finance portion is mainly about venture capital and cryptocurrency.

Underlying all the disparate chapters in the book is the broader theme about attitude towards risk, and this is of great interest to any finance professional. Nate Silver begins by distinguishing between the “river” and the “village”, where the people in the river are given to analytical and abstract thinking and are competitive and risk tolerant (This is a bit of an oversimplification because Silver mentions a few other cognitive and personality traits also). The difficulty with this characterization is that in finance, attitude towards risk is not binary (risk averse versus risk tolerant), but encompasses a broad spectrum of risk aversion coefficients. The theoretical range of the Arrow-Pratt measure of relative risk aversion² is from negative infinity to positive infinity, but for most people, it probably lies between 1 and 10. Therefore, a finance professional would quite likely regard a risk aversion coefficient of around unity as being quite risk tolerant, though technically any risk aversion coefficient greater than zero signifies risk aversion. Zero represents risk neutrality and negative coefficients signify risk seeking.

At certain points in the book, Silver seems to imply that somebody with a risk aversion coefficient of unity or even somewhat higher belongs in the “river”. For example, twice he says that most gamblers regard the Kelly criterion³ as being too aggressive and prefer bets of only quarter to half of the Kelly bet size. The Kelly criterion corresponds to a risk aversion coefficient of exactly unity, and so this implies that most gamblers have risk aversion coefficients significantly above unity. At other points in the book, Silver seems to suggest that people in the river seek out any positive expected value opportunities which suggest risk neutrality (a coefficient of zero) if not risk seeking. Of course, Pratt showed that a rational person would take at least a tiny slice of any positive expected value opportunity. This is because risk aversion (which is a second order phenomenon) can be ignored for infinitesimal bets. Perhaps, this is what Silver means, but, in that case, the logic applies only to highly divisible bets.

At times, I got the feeling that all expected utility maximizers are in Silver’s “river”, and only people confirming to prospect theory or behavioural finance are in his “village”, but Silver mentions prospect theory only in a footnote and in the glossary, and he does not describe this as a “village” trait. He does emphasize that “river” people perform Bayesian calculations, and the distortion of probabilities in prospect theory would perhaps not be “riverine”. What I do not understand after reading the whole book is whether a highly rational expected utility maximizer with a risk aversion coefficient of 25 belongs in the “river” or not. The problem is that while Silver praises river people for “decoupling” (keeping different aspects of a problem separate), he works throughout with a tight coupling of the cognitive and personality traits of the “river” people.

Silver cheerfully admits to being a “river” person, and often suggests that the “river” is winning. But there is some ambiguity about what it means for the “river” to win. Does it mean that the “river” people collectively win, or that the typical or average “river” person wins? This distinction is illustrated by Silver’s discussion of the Kelly criterion on pages 396-400 (if you do not have the book in front of you, Brad Delong’s blog post which Silver cites in an end note provides a very similar treatment). Mathematically, the Kelly criterion maximizes long run wealth. The intuition is that when you have positive expected value investment opportunities, you definitely want to bet on them (recall Pratt’s result that the optimal bet size is never zero), but if you bet too much, you may be ruined and then you lose the opportunity to make more positive value bets in future. Long run optimization must therefore ensure long run survival to allow wealth to compound over those long horizons, and this leads to an optimal size of the bet.

Imagine three groups of people: (a) the “village” whose inhabitants do not participate in risky assets at all because of behavioural reasons or infinite risk aversion, (b) the Kelly “river” filled with venture capitalists who bet the optimal fraction of their wealth at each round on various risky (positive expected value) ventures, and (c) the risk neutral “river” comprising risk neutral founders who bet their entire wealth on their respective risky (positive expected value) ventures. Note that this is my analogy, and Silver does not use this interpretation during the discussion on Kelly. Most inhabitants of the Kelly “river” will outperform the “village” handsomely because Kelly ensures high returns with negligible chance of being ruined. But the risk neutral “river” will outperform both of the others on average. Almost everybody here would be ruined, but the one person who managed to survive would make so much money that the average wealth of the risk neutral “river” will be far higher than even the Kelly “river”. (For simplicity, I assume that the different ventures are independent.)

If you care more about the group rather than yourself, then the risk neutral “river” is possibly optimal in the sense that collectively this group is better off than the others. But the “river” people were supposed to be competitive and not collectivist and socialistic. So it is not clear whether this is the “river” at all. Brad Delong’s blog post uses the multiple universes interpretation of quantum physics to suggest that even if you are ruined in this universe, there is a parallel you in some other universe who has made it big. I think that this is closer to theology than to finance.

Silver’s book does have a long discussion about venture capitalists and founders and seems to suggest that the venture capitalists have to be rational, while the founders have to be irrational to willingly accept large probability of ruin. I do not agree because as Broughman and Wansley⁴ have pointed out, risk sharing between the VC and the founder can ensure that founders do well even when the venture fails. Recall Adam Neumann making a fortune even as WeWork went bust.

At the end of the book, I was left with the impression that Silver wants to self identify not with cold blooded rational calculators, but with daring risk takers, and this tendency colours a great deal of the discussion in the book. This attitude is best captured in the last of his thirteen habits of successful risk-takers: “13. Successful risk-takers are not driven by money. They live on the edge because it’s their way of life.” Nevertheless, by ignoring his personal preferences, I could learn many interesting things from the book, and some of these ideas are useful in finance as well. The “river” and the “village” are I think a useful way of thinking about classical and behavioural finance even if that was not what Silver had in mind at all.

Notes and references:

Posted at 1:36 pm IST on Wed, 30 Oct 2024         permanent link

Categories: behavioural finance, interesting books, risk management

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