INVESTMENT SIZE FOR A PORTFOLIO

As a reformed quant, I have spent much time thinking about position sizing, risk/reward, and portfolio allocation. In independent trials with perfect knowledge of outcomes, you can use the Kelly formula to determine the optimal betting size (the amount to bet on each investment to maximize wealth). The formula to be to maximize capital would then be: K = (P*W-L)/P where K = optimal fraction of total amount to invest W = Probability of Winning L = Probability of Losing P = Payoff

Unfortunately, we don’t know exact probabilities or even probability density functions, we have multiple investments simultaneously, and the results often show correlation (they are not truly independent of one another). Enter Markowitz’s portfolio theory, where we end up doing mean-variance optimization with expected returns, expected variances, and correlation as our inputs. (You can add on different objective functions, but this seems like overkill). Also, to further compound the issue, when investing in traditional search funds, you are really buying options on future investments where you don’t know the underlying.
My question is to serial investors like ^[redacted]‌, ^[redacted]‌ and others: How much of your portfolio do you allocate to each investment? Thanks in advance.



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