If you're looking at a marginal benefit, you definitely don't want to be maximising the log of that benefit.
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Of course not. But again, I am not talking about maximization of subjective enjoyment. I am talking about managing a portfolio in order to maximize wealth
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The model doesn't assume that the portfolio is all of your wealth, but it does assume that it never interacts with the rest of your wealth. More realistic in some cases (like a Roth IRA) than others
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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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you are working for a VC fund - do you actually want your early stage investments to manage their resources according to Kelly, or do you want them to go big or go home, accepting the odds that >50% of them fail?
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Different scenario!! We are able to exit at some point and reinvest the returns from each investment into new investments
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uh if you can never exit at any point then what's the point of an investment doing well? you'll never get the money!
and if you eventually pool all the money together at the end, 's point still stands even if you can't reinvest it
The game ends infinity years from now. We count up the total value of my pots and compare it to the total value of your pots.
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great so say that there is 1 startup S which has a 25% chance of 10x'ing and a 75% of busting
the optimal strategy according to your metric is not to invest
if instead there are 100 uncorrelated startups each with the same distribution the optimal strategy is to invest in each
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