Bet Sizing at the Frontier

Investing at the Edge of Knowledge, Part 4 · Start with Part 1 “He who acts in N plays to make his mean log of wealth as big as it can be made will, with odds that go to one as N soars, beat me who acts to meet my own tastes for risk.” That’s Paul Samuelson, writing in one-syllable words. The title of his 1979 paper: “Why We Should Not Make Mean Log of Wealth Big Though Years to Act Are Long.” Published in the Journal of Banking & Finance, a journal not typically known for its prose style. The playfulness of the writing masks the seriousness of the dispute underneath: a disagreement about the foundations of position sizing that remains unresolved half a century later. In Part 3 I described how to assess whether the other side of a trade knows something you don’t. But even if you’re confident you’re in Box D or Box F (shared uncertainty or shared ignorance, where neither side has an information edge), you still need to decide how much capital to commit. And in a UU world, the most…