Optimal Bet Size

This article deals with the question of how much you should bet on a certain trade. It starts with some theoretical thinking, presents the “Kelly criterion,” and some application in real trading.

Let’s say you know, with absolute certainty, that your next trade will make zero profit, then how much would you bet? If you’re a rational person, you bet nothing. Now let’s assume you know, with absolute certainty, that a trade will be a huge winner. How much would you bet now? Right, everything you have. You would also apply leverage to maximize profits. As the two extreme examples show, there is a clear link between how much a rational trader should bet on a given certain outcome.

In a world of uncertainty, you would still be willing to risk more on a trade with a higher expected outcome in comparison to an inferior trade setup. However, the higher the uncertainty, the lower your bet size is, generally speaking.

The “Kelly criterion” is a formula with the aim to maximize the long-run geometrical return of a strategy, or, simply put, a way to make as much money as possible. For example, if your trading strategy has a win rate of 55%, and the payoff structure is symmetrical (win = 1 USD, lose = 1 USD), the calculation of the optimal bet size (in % of your capital) is: (0.55/1)-(1-0.55)/1 = 10 %

Two problems arise in the above mentioned formula. First, the parameters of your strategy are uncertain (even observed parameters may change). Second, the suggested bet size is maximizing the long-run geometrical return, but it is extremely aggressive. Only a few would be able to hold during drawdowns without changing or entirely abandoning their strategy. Most would rather have a proper balance between return, risk, and manageable drawdowns.

I did the simulations of the above mentioned example. 55% win-rate, symmetrical payoff, and, therefore, 10% risk on a certain trade, by making one trade a day for the next 10 years, with a 100.000 USD capital, and 1000 different runs.

The median yearly return of the different runs is 280% and 99% of the different runs have made money after 10 years.

In the chart above I’ve shown you the impact of the “Kelly size” on some key performance figures (1000 runs each).

No surprise is the maximization of the return at 1 Kelly. What is more interesting is the maximization of the Sharpe ratio at approximately 0.5 Kelly. Furthermore, there is no rational reason to bet more than 1 Kelly (because return and risk-adjusted return start falling).

Key points:

  • In general, more promising setups should have more risk than regular ones.
  • The “Kelly criterion” is the optimal bet size to maximize the long-run geometrical return of a certain strategy.
  • It doesn’t make any sense to bet more than the “Kelly criterion” suggests.
  • For most traders, it would make sense to bet much less (because of uncertainty of parameters, emotions, higher risk-adjusted return, manageable drawdowns).
  • A viable solution is to calculate the suggested “Kelly bet size” on your trade history, and then use 1/8 to 1/4 of the suggested size. For example, with a 55 % win-rate and symmetrical payoff, the risk range would be between 1.25-2.5 %.

 

About me

Former hedge fund portfolio manager/trader

15 years of experience in financial markets

✓ Master of Science (MSc) in Business and Economics from the University of Basel

✓ Developed quantitative tools for an asset management