I mostly disagree with this: log isn't linear.
So if you separately have $1b on the side and are considering what to do with $1k, then the growth rates are going to be roughly 0.00005% instead of 50%, and the nonlinear terms are going to be much weaker
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Totally, it’s irrelevant. But given that you are managing this $1k as its own pot, might as well manage it well. If you robotically maximize EV for it, then it will get St. Petersburged and end up at 0 with very high probability
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Imagine you divided your $1b into 1 billion pots of $1 each, managed independently. (A really bad idea!)
The right strategy for each one would be to maximize its own log growth.
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yeah I think this is the exact debate we had yesterday and I disagree strongly.
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Awesome—sounds like we’ve hit on a real disagreement (although I think we have to delineate the question more formally because there are probably some underlying different assumptions around what kind of active management is allowed)
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Is your position that each sub-portfolio manager should always maximize EV(wealth), forever?
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nope!
well, mine is closer to that, but fuck that, let's assume that I like ev(log(wealth)) instead of ev(wealth)
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For instance, assume that there are the following assets in the world:
1) USDC
2) BTC
3) ETH
assume that ETH and BTC both have positive growth rates, and USDC = USD
Say portfolio (a) can only have USD and/or ETH, and portfolio (b) can only have USD and/or BTC
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and finally assume you're trying to maximize ev(log(wealth))
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(to be clear here these are all portfolios you own, not ones you're managing for others)
and, fine, assume that you're not trying to maximze ev(log(wealth)), instead you're trying to construct a strategy which does very well in terms of some set of percentile outcomes
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if all you had was portfolio (a), you'd have X% ETH, (1-x%) USD
if all you had was portfolio (b), you'd have Y% BTC, (1-y%) USD
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since you have both, instead you want w% ETH and v% BTC respectively
I clam that w > x and v > y
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The most important Boolean variable in all of quant finance.
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