Advances in Financial Machine Learning

CHAPTER 10 Bet Sizing

10.1 Motivation

There are fascinating parallels between strategy games and investing. Some of the best portfolio managers I have worked with are excellent poker players, perhaps more so than chess players. One reason is bet sizing, for which Texas Hold'em provides a great analogue and training ground. Your ML algorithm can achieve high accuracy, but if you do not size your bets properly, your investment strategy will inevitably lose money. In this chapter we will review a few approaches to size bets from ML predictions.

10.2 Strategy-Independent Bet Sizing Approaches

Consider two strategies on the same instrument. Let m_{i, t} ∈ [ − 1, 1] be the bet size of strategy i at time t, where m_{i, t} = −1 indicates a full short position and m_{i, t} = 1 indicates a full long position. Suppose that one strategy produced a sequence of bet sizes [m_{1, 1}, m_{1, 2}, m_{1, 3}] = [.5, 1, 0], as the market price followed a sequence [p₁, p₂, p₃] = [1, .5, 1.25], where p_t is the price at time t. The other strategy produced a sequence [m_{2, 1}, m_{2, 2}, m_{2, 3}] = [1, .5, 0], as it was forced to reduce its bet size once the market moved against the initial full position. Both strategies produced forecasts that turned out to be correct (the price increased by 25% between p₁ and p₃), however the first strategy made money (0.5) while the second strategy lost money (−.125).

We would prefer to size positions in such way that we reserve some cash for the possibility that the trading signal strengthens ...