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The Kelly Criterion
Kelly Criterion was developed by John Kelly at Bell Labs. It has been proven to maximize the portfolio growth over time compared to any other strategy.
It is rumored that Warren Buffett and Bill Gross use Kelly Criterion or some modified version of it.
This is how it works:
Assume,
– f is the fraction of the current capital you have available to invest
– b is the odds of winning (if you succeed, the value of your investment increases from 1 to 1 + b)
– a is the odds of losing (value decreases from 1 to 1 – a)
– p is the probability of winning, and,
– q is the probability of losing, or 1 – p
Then, you should invest
f = p/a – q/b of your portfolio in this stock.
Over time, this will theoretically give you the best growth in your portfolio possible.
What You Should Know if You Wish to Use the Kelly Criterion
There are several considerations if you want to use the Kelly Criterion
- You need to have a long track record and well-established process to properly estimate the probability of winning. The probability of winning here is primarily a function of how your investments tend to perform over time. Do you make winning investments 75% of the time? Then p for you is 0.75
- The portfolio using Kelly Criterion can be VERY concentrated and volatile. For example, if p = 0.75 and your odds of losing is 50% and odds of winning is 50% (very common, value is halved in the worst case or doubled in the best case), Kelly Criterion asks you to invest 0.75/0.5 – 0.25/0.5 = 1 or your entire portfolio in this stock. This makes sense because 3 out of 4 times you will double your investment. In practice, this can be a nightmare for someone who is no able to tolerate this much volatility
- While mathematically, using Kelly Criterion means your portfolio will never go to zero, the volatility will be unnerving
- Investors who do use Kelly Criterion tend to use ½ – Kelly. This means using half of the fraction the Kelly Criterion recommends. This is not as good as full Kelly, but it makes the portfolio more stable without sacrificing too much in the long-term returns.
See: Risk Premia Meaning
At Value Stock Guide, we evaluated these 2 methods and chose to use the Volatility based Risk Premia Parity Method for position sizing and risk control. Premium members participate in this portfolio sizing and risk control process.
NOTE: Originally Kelly Criterion was designed to be used in a game of chance, but this can be adopted to investing in stocks. Ed Thorpe is one of the premier examples of an investor with great success both in the casinos and in the stock market. I wholly recommend William Poundstone’s book The Fortune’s Formula for more background and a great explanation of how this all works (Amazon affiliate link).