Advances in Financial Machine Learning

CHAPTER 15 Understanding Strategy Risk

15.1 Motivation

As we saw in Chapters 3 and 13, investment strategies are often implemented in terms of positions held until one of two conditions are met: (1) a condition to exit the position with profits (profit-taking), or (2) a condition to exit the position with losses (stop-loss). Even when a strategy does not explicitly declare a stop-loss, there is always an implicit stop-loss limit, at which the investor can no longer finance her position (margin call) or bear the pain caused by an increasing unrealized loss. Because most strategies have (implicitly or explicitly) these two exit conditions, it makes sense to model the distribution of outcomes through a binomial process. This in turn will help us understand what combinations of betting frequency, odds, and payouts are uneconomic. The goal of this chapter is to help you evaluate when a strategy is vulnerable to small changes in any of these variables.

15.2 Symmetric Payouts

Consider a strategy that produces n IID bets per year, where the outcome X_i of a bet i ∈ [1, n] is a profit π > 0 with probability P[X_i = π] = p, and a loss − π with probability P[X_i = −π] = 1 − p. You can think of p as the precision of a binary classifier where a positive means betting on an opportunity, and a negative means passing on an opportunity: True positives are rewarded, false positives are punished, and negatives (whether true or false) have no payout. Since the betting outcomes {X_i}_{i = 1, …, n}