Continuous Kelly Trainer: Ship Investor 2
After I made the first Ship Investor game all that time ago, I continued learning about the Kelly criterion, and made a second game in which you can learn to apply the same principles to a more continuous situation. This is closer to real-world financial investing.
This is a more difficult game than the previous one. This time, you’re setting up a portfolio split between two mutual funds, and you want the allocation that maximises growth,
As before, you can compete against a friend by using the “link to this scenario” button. Send your friend a link to ensure they get the exact same market movements you do, then play simultaneously and see who becomes richest in two minutes. In this game, you can also see how you compare against the “optimal non-anticipatory” portfolio, the details of which would be a separate article.
The trick to doing well in this game is picking a constant fraction to keep in either of the funds, and then sticking to it. For example, if you decide to invest 30 % of your wealth in the Malacca fund, then if that fund goes well, that piece of the pie will grow and it might end up containing 34 % of your wealth. The right thing to do then is sell of some of it to bring it back down to 30 %. This is called a constant-fraction rebalanced portfolio.
Which fraction should you pick? You can figure out a fraction that resembles the optimal Kelly investment, but that takes a little more maths (and an estimation of the probability distribution of future outcomes). However, any constant fraction is better than trying to outsmart the market.
A counter-intuitive observation about the rebalanced portfolio is that it can outperform every single of its components!1 This comes with a caveat, and the interested reader should check out aqr on common misconceptions around rebalancing. In other words, even if you had a crystal ball and could see which of the components will give the highest return in the future, you might still end up in a worse place by investing everything into that best-performing component, compared to spreading your investments out and rebalancing.