In quantitive finance, there are always many thousands of simultaneous bets available. You can be short oil, long Apple and short the Yen all at the same time. If you have a good model of the assets, then that model will tell you that some of these bets have positive expected value.

Being faced with thousands of positive expected value bets sounds like Christmas but today it’s Easter. Positive expect value bets are only necessarily good when they are independent of the other bets you’re holding. This is because there’s a lot of math on your side if you can get your bets to be independent. In particular, the shape of the cumulative distribution function of the Binomial distribution shows how hard it is to lose when you place lots of independent bets. And also, the Kelly Criterion will tell you how much to risk on your independent bets.

Statistical or machine learning models will tend to produce portfolios with some bias.…