Comment of the Day: Investingidiocy: How Leveraged Should Your Stock Market Investments Have Been? http://www.bradford-delong.com/2017/07/here-we-have-robert-shillers-stock-market-index-data-since-1871-the-cumulative-real-return-from-investing-in-the-sp-compos.html#comment-6a00e551f08003883401b7c908de51970b: "So... Optimal Kelly. Right?..."
This is what happens (or would have happened). That's the baseline for discussing what one should have done (and what one should do). But it doesn't lead to any immediate conclusions, as issues are complex...
As I understand it, the Kelly Risk Criterion https://en.wikipedia.org/wiki/Kelly_criterion has a legitimate claim if your portfoio is all of your wealth, if the bets are independent, and if you have a constant degree of relative risk aversion of 1: log utility, in which equal proportion increases in your wealth generate equal steps toward eudaemonia. If you have other resources (or obligations), if the bets are not independent, or if you have a different utility function than log and thus a different degree of relative risk aversion, you should not be doing Kelly but should be doing something else.
Do note that, with monthly rebalancing, the β=4 portfolio loses 100% of its wealth between August and October 1929; that the β=3 portfolio loses 99.9% of its wealth between August 1929 and May 1932; that the β=2 portfolio loses 98% of its wealth between August 1929 and May 1932; and that the β=1 portfolio loses 75% of its wealth between August 1929 and May 1932. Any argument that the portfolio that maximizes the Kelly criterion has a β between 2 and 3 relies very heavily on an assumption that we have seen the worst: that 1929-1932 is as bad as it can possibly get.
And do note that returns are definitely not independent across time. Any positive return that is generated by an increase in valuation ratios rather than an increase in smoothed earnings is highly likely to be substantially reversed over the next decade: