One of the easiest ways for traders to improve the profitability and reduce the volatility of their systems is to optimize their position sizing algorithm. There are many different ways to break down your system’s optimal position sizing, but one of the most popular is to use the Kelly Criterion.
The Kelly Criterion is most famous for the way that Edward Thorp successfully applied it in his quest to create a strategy that could consistently beat the game of blackjack. Thorp also used the Kelly Criterion in his work with roulette and his hedge fund trading. The Kelly Criterion has also been linked to other famous traders like Warren Buffet and Bill Gross.
Andrew Butler wrote a post for his blog, Butler’s Math, that does a nice job of why you might want to consider implementing the Kelly Criterion in your trading system. He begins by making a few modifications to the Kelly Criterion:
With a few modifications, this basic framework can also be applied to securities selection.
Let us define as
where is our initial capital, is the risk free rate, and is our expected return on a given portfolio of securities. Thorp shows that for large number of “bets”, , the growth function for such a model is defined as
Again, through simple calculus, the optimal occurs when .
Butler generated simulated data for a portfolio of 100 different stocks and ran 100 different simulations using the following three position sizing strategies:
- Kelly Criterion for optimal growth:
- Full betting Strategy: .
- Fractional Kelly Criterion: .
The results show that betting the full Kelly Criterion just barely outperformed the full betting strategy, but the Kelly Criterion has less overall volatility. The Fractional Kelly approach had inferior results, but an even greater reduction in volatility.
Butler made the following additional comments about his results:
- Both the Kelly Criterion strategy and the Full Betting strategy provide comparable final capital at the end of the simulation.
- The Kelly Criterion strategy in fact provides an additional 0.32% net growth.
- Additionally, the volatility of the Kelly Criterion Portfolio is significantly less than that of the Full Betting strategy. This in theory could reduce irrational financial decision making as a more stable growth is observed.
- The Fractional Kelly strategy is the least volatile but also provides the least potential for growth.
As you can see, implementing the Kelly Criterion is not going to suddenly turn a poor system into a profitable one. However, the primary goal of any trader is to avoid the erosion of capital, and using the Kelly Criterion to reduce volatility can do just that.