The generalization of this is a martingale. https://en.wikipedia.org/wiki/Martingale_(probability_theory) … Your expected value at the next time step is the same as your present value, but your variance grows over time as you keep reinvesting your winnings. In the long run, you get rich...or go broke.
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A martingale can have a positive expected rate of return but a zero "drift" term (modeled as a geometric Brownian motion, e^(mu*t + sigma W_t), martingales have mu=0.)
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The Kelly Criterion https://en.wikipedia.org/wiki/Kelly_criterion … would say that to maximize your long-run growth, you should not invest in martingales at all -- after all, they have no long-run tendency to grow!
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So do the portfolios of VCs have a positive exponential growth rate? i.e. do they have a systematic tendency to grow, or are they just exponentials of random walks? (which only make money on average because you exclude those which go broke).
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You can't know for sure, but you can do quick-and-dirty Z-tests to see if the firm's long-run IRR is outside a 95% confidence interval away from zero. My data is very incomplete but so far it looks like some firms meet this criterion and some don't.
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But I just made up the 95% confidence interval; investors are not necessarily foolish for investing in VCs that "can't reject the null hypothesis", especially if they invest in a diverse set of VCs that together have a mean growth rate >0.
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The basic overall conclusion is that VC’s as a class make about the same return you’d expect to compensate for their level of risk. This average includes a mix of VC track records, from “no better than coin flipping” to “way above-market returns.”
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Replying to @s_r_constantin
Interesting. Do you have a sense of how useful it is as part of a portfolio – how uncorrelated it is to other asset classes?
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No clue, except that VC dips lower in recessions and soars higher in booms than the stock market, so "pretty correlated with stocks". (Don't have numbers offhand, sorry.)
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