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Position Sizing Using the Kelly Criterion

by | Feb 15, 2021 | Portfolio Management

Position Sizing Using the Kelly Criterion

I am often asked by members and prospective members on position sizing which is a critical element to trading success. A separate discussion will be needed for emphasizing the importance of sizing positions according to your confidence level and risk management is vital for every single trade. It is impossible for me to advise a position size as every investor has his/her own risk parameters and return objectives. Furthermore, different strategies and timeframe tend to dictate different optimal allocations so it is also important to adapt across different portfolios that utilize specific strategies. I was recently reading one of the Market Wizard books that discussed the Kelly Criterion, which is the best “universal” way to decide on optimal portfolio allocations to trades.

Background

The Kelly criterion is a mathematical formula relating to the long-term growth of capital developed by John L. Kelly, Jr. The formula was developed by Kelly while working at AT&T’s Bell Laboratories. The formula is currently used by gamblers and investors for risk and money management purposes, to determine what percentage of their bankroll/capital should be used in each bet/trade to maximize long-term growth.

The Formula for the Kelly Criterion Is

Kelly % = W/A – (1 – W)/B, where W is the win probability, B is the profit in the event of a win, and A is the potential loss.

There are two key components to the formula for the Kelly criterion: the winning probability factor and the win/loss ratio. The winning probability is the probability a trade will have a positive return. The win/loss ratio is equal to the total positive trade amounts, divided by the total negative trading amounts. The result of the formula will tell investors what percentage of their total capital that they should apply to each investment.

Investors can look back at historical results to be able to calculate win rate on trades and the win/loss ratio on trades.

For a free online calculator, one can use

https://dqydj.com/kelly-criterion-bet-calculator/

The further I read on the strategy made me comfortable taking whatever number the calculator gives and dividing it by 1/2 for a more optimal number to be used in the stock market, as opposed to gambling.

I have a historical win-rate of around 75% which is very high but also have a common flaw of letting my losers stick around longer and taking off my winners too soon. The calculator gave me a number of 10% and then taking 1/2 of that I get 5% as the optimal portfolio allocation per trade which makes a lot of sense. I typically am risking closer to 1-3% on trades and my Gain to Pain ratios and other metrics indicate I should be sizing higher as well.

I feel a good compromise is taking the resultant number, in this case 5%, and making that the max allocation to utilize on the highest confidence plays and scaling down by 1% for less confident plays giving a 1%-5% range on trade allocations. In an ideal World patience would result in only taking the 5% trades but that is not realistic/practical with my active style, but very well could be for a less active trader. The formula is consistent with the value investing concept of a margin of safety and leads to concentrated portfolios in which the dominant ideas have the greatest edge and smallest downside.

A deeper mathematical view can be found in this University of Washington Paper:

“The Kelly Criterion and the Stock Market”

An even more in depth paper:

“Practical Implementation of the Kelly Criterion: Optimal Growth Rate, Number of Trades, and Rebalancing Frequency for Equity Portfolios”