Conversation

SBF
@SBF_FTX
Replying to
@SBF_FTX
3) Let’s say you were offered a coin flip. 75% it comes up heads, 25% it comes up tails; 1:1 payout. How much would you risk?
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SBF
@SBF_FTX
4) There are a number of ways to approach this question, but to start: what do you want, in the first place? What’s your utility function?
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SBF
@SBF_FTX
5) In other words--how cool would it be to make $10,000? How about $1,000,000--is that 100 times as good? For most people the answer is ‘no, it’s more like 10 times as good’. This is because of decreasing marginal utility of money.
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SBF
@SBF_FTX
6) For the median US household, making another $10k helps them move to a more comfortable house, buy a newer car, and eat out more--not nearly the utility that you can get for $10k in the developing world, but still something.
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SBF
@SBF_FTX
7) But the 100th time you win $10k, it’s worth less. You’ve already bought a new car and moved to a fancier house. You could buy a few more new cars, but honestly who’s going to drive them? There are things you can do with it, but generally it’s just worth less.
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SBF
@SBF_FTX
8) One reasonable utility function here is U = log(W): approximating your happiness as logarithmic in your wealth. That would mean going from $10k to $100k is worth about as much as going from $100k to $1m, which feels…. reasonable? (this is what the Kelly Criteria assumes)
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SBF
@SBF_FTX
9) So, if you have $100k, Kelly would suggest you risk half of it ($50k). This is a lot! But also 75% odds are good.
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SBF
@SBF_FTX
10) What about a wackier bet? How about you only win 10% of the time, but if you do you get paid out 10,000x your bet size? (For now, let’s assume you only get to do this bet once.)
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SBF
@SBF_FTX
11) Kelly suggests you only bet $10k: you’ll almost certainly lose. And if you kept doing this much more than $10k at a time, you’d probably blow out. That this bet is great expected value; you win 1,000x your bet size, way better than the first one! It’s just very risky.
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Zack
@attmgromov
Replying to
@SBF_FTX
and
@SBF_Alameda
My bad.. it should be 999.1/10000 which is close to 10% bet. So it’s pretty conservative? But in practice traders use fractional Kelly, if they use the criterion at all.. does it mean Kelly is also quite aggressive?!
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SBF
@SBF_FTX
Replying to
@attmgromov
I think it means either: 1) traders bet too small 2) traders subconsciously realize that they probabilities they give are overconfident and that in fact many of their bets might be negative EV
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