Risk-Taking & Bet Sizing

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During their recent episode of the VALUE: After Hours Podcast, Taylor, Brewster, and Carlisle discussed Risk-Taking & Bet Sizing. Here’s an excerpt from the episode:

Bill: I had said about Buffett back, I don’t know what letter, what meeting he said it but he said that he and Charlie would bet substantial amounts on a coin flip if the odds are right. And somebody said to me, “Well, what would you bet on a coin flip?” And my response was, “I don’t think that that’s an easy question to answer because given my situation now, I don’t have enough money that I can just mess around and lose it on a 50-50 bet.

So, no matter how good the odds are, I wouldn’t press that much of my net worth into it. But I mean, the way that I run my portfolio is somewhat concentrated. So, I guess I put a fair amount, but I think the odds are better than 50-50. But as I got wealthier, I think I’d be more willing to bet more on those types because if I lost, my quality of life doesn’t actually step change down. We’ve sort of talked about this before. I try to size bets, like my Qurate bet or that one on I asked my wife, “How much can I lose before you resent me for the rest of our lives?” That was how I sized it.

Tobias: That’s the best sizing discussion I’ve ever heard. [laughs]

Jake: That’s the risk department chiming in on.

Bill: Yeah, that’s right. I’m not trying to do some hero call for some BS reputation when it’s going to cost me my family. So, that’s how I think about sizing things.

Jake: What would you call that like Wife-far or something like that?

Bill: Yeah, it’s a little bit– that’s right.

Tobias: Can I throw some– like Kelly. The Kelly criterion for a 50-50 bet with a one to one payoff would advise you to bet zero. So, if you’re 50-50, you need to be getting better prospects than that, but that’s the outer limit of how much you should bet that gives you the optimal geometric growth in wealth if you’re doing that. But there’s clearly some– there’s a distinction between what kind of you need to survive and what is the portion of your wealth that you should be applying Kelly to, that’s the way I think about it a little bit. You can Kelly bet on the portion that is wealth and the pot that is working capital is not Kelly bettable. So, I always make that distinction.

And then, it’s the outer limit, you’ve got to remember that and so your calculation’s necessarily going to be fuzzy. So, you probably should be sizing down to fractional Kelly for those reasons. And you’re not doing it in sequence, you’re doing it in parallel, so you size down again. And that’s sort of the way I think about. Kelly– there would be no circumstance–

Jake: [crosstalk] –rent money.

Tobias: Yeah. There’d be no circumstances where I’d be Kelly sizing into something. I’d always be some fraction of Kelly.

Bill: Yeah, that makes sense. The nice thing about equities too is, if you’re right on the business and you believe you can own it forever, the right tail gets the expected payout is theoretically infinite. It’s clearly not infinite, but it can really skew your expected value at that and from what I’ve seen, the right tail is a lot longer and priced a lot higher than I ever imagined it would be.

Tobias: I think it’s interesting that you would bet more as you get more wealthy because the criticism of Kelly is that you get to a point where it doesn’t make sense to be Kelly betting, if you’ve covered your [unintelligible [00:06:56] for the rest of your life for everything that you want to do, it doesn’t make sense at that point to Kelly bet because all you can do is reduce your quality of life. Do you know what I mean? If you win, then–

Jake: I’d assume that there isn’t some step change to the level of wealth up there that maybe you’re aspiring to–

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