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. For example, a machine learning algorithm might teach itself that buying US technology stocks is a good idea. But that’s not good because Apple, Google and Facebook are all exposed to many of the same risks. They move together. They are not independent bets.

To find the independent bets, you might need to create independent (orthogonal) models. Two accurate models with high correlation are not as useful two less accurate, but uncorrelated ones. Correlated models will tend to produce portfolios with similar risk exposures. Even if you bet on many models, the lack of diversity means you’re only repeating the same bets. Taking independent bets from many independent models let’s you reduce risk and hence volatility in your portfolio’s because all the mathematics around independent bets now apply to yours.

Adapted from:
https://blog.numer.ai/2016/03/04/Introducing-Originality

See also:
https://en.wikipedia.org/wiki/Binomial_distribution#Cumulative_distribution_function https://en.wikipedia.org/wiki/Kelly_criterion
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