An exceptional single *company* can have a higher rate of return, though: Amazon has been growing at an average rate of 36% a year since it IPO'd. If you had to pick between being Jeff Bezos and being a typical VC, on purely money grounds, you'd want to be Bezos.
So what is the optimal amount to invest in a stock with positive variance but zero (risk-adjusted) drift?
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Hmm I believe you are right here. I seem to have misunderstood the definition of a martingale. I'm not sure how one would have a positive rate of return.
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Since a martingale's expected value is it's current value
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