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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(I’m noooot I am trying to maximize my actual wealth)
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ok this is not relevant here but I will work with it anyway