Excerpt:
First: “A Jane Street intern had what amounted to a professional obligation to take any bet with a positive expected value”? Really? I feel like, if you are a trading intern, you are really there to learn two things. One is, sure, take bets with positive expected value and avoid bets with negative expected value.
But the other is about bet sizing. As a Jane Street intern, you have $100 to bet each day, and your quasi-job is to turn that into as much money as possible. Is betting all of it (or even $98) on a single bet with a 1% edge really optimal?[6]
People have thought about this question! Like, this is very much a central thing that traders and trading firms worry about. The standard starting point is the Kelly criterion, which computes a maximum bet size based on your edge and the size of your bankroll. Given the intern’s bankroll of $100, I think Kelly would tell you to put at most $10 on this bet, depending on what exactly you mean by “this bet.”[7] Betting $98 is too much.
I am being imprecise, and for various reasons you might not expect the interns to stick to Kelly in this situation. But when I read about interns lining up to lose their entire bankroll on bets with 1% edge, I think, “huh, that’s aggressive, what are they teaching those interns?” (I suppose the $100 daily loss limit is the real lesson about position sizing: The interns who wipe out today get to come back and play again tomorrow.)
But I also think about a Twitter argument that Bankman-Fried had with Matt Hollerbach in 2020, in which Bankman-Fried scoffed at the Kelly criterion and said that “I, personally, would do more” than the Kelly amount. “Why? Because ultimately my utility function isn’t really logarithmic. It’s closer to linear.” As he tells Lewis, “he had use for ‘infinity dollars’” — he was going to become a trillionaire and use the money to cure disease and align AI and defeat Trump, sure — so he always wanted to maximize returns.
But as Hollerbach pointed out, this misunderstands why trading firms use the Kelly criterion.[8] Jane Street does not go around taking any bet with a positive expected value. The point of Kelly is not about utility curves; it’s not “having $200 is less than twice as pleasant as having $100, so you should be less willing to take big risks for big rewards.” The point of Kelly is about maximizing your chances of surviving and obtaining long-run returns: It’s “if you bet 50% of your bankroll on 1%-edge bets, you’ll be more likely to win each bet than lose it, but if you keep doing that you will probably lose all your money eventually.” Kelly is about sizing your bets so you can keep playing the game and make the most money possible in the long run. Betting more can make you more money in the short run, but if you keep doing it you will end in ruin.
Author(s): Matt Levine
Publication Date: 4 Oct 2023
Publication Site: Bloomberg