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# Heller House: Using The Kelly Criterion For Position Sizing

By Rupert Hargreaves. Originally published at ValueWalk.

The Heller House opportunity fund partnership gained 7.2% during the first quarter, taking gains over the past 12 months to 22% according to the partnership’s first quarter investor letter, a copy of which has been reviewed by ValueWalk. Since inception over six-and-a-half years ago, the hedge fund has gained over 102.65% or 11.33% annualized net of fees and expenses. In the first quarter letter, Marcelo P. Lima, Managing Partner provides an interesting discussion on the concept of position sizing at the partnership and how the team goes about building the portfolio including the use of the Kelly Criterion.

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### Heller House: Using The Kelly Criterion For Position Sizing

The Heller House team is a fan of the Kelly Criterion, a mathematical tool derived by John Kelly a researcher at Bell Labs during the 1950s and popularized by Ed Thorp, the father of quantitative investing.

The Kelly Criterion can be used to determine the optimal bet size in a game where the player has favorable odds. The optimal size refers to the size of the bet that will allow the player to grow his investment at the fastest possible rate (faster than any other bet size) while at the same time controlling risk to avoid ruin.

Put simply, the Kelly Criterion is a simple portfolio allocation tool based on the risk-reward skew.

As Marcelo Lima explains:

“Suppose you identify an investment that you believe is worth \$87. Upon further analysis, you reach the conclusion that in a worst-case scenario, the security could trade down to \$45. You look up the price offered in the market, and the security is offered at \$56. With these potential outcomes, the Kelly Criterion indicates that there is a 26 percent probability of success implied by the \$56 price. In other words, there isn’t much optimism priced into the security.”

In the above scenario, if an investor believes the investment is worth \$87 with high probability, they should take a swing although what Kelly tells us here is that “high probability” means higher than 26%, which isn’t really that high.

The one problem with the Criterion is that it’s highly susceptible to probability assumptions. If you are of an optimistic disposition and believe in the above scenario the chances of the stock reaching \$87 is more than 90%, Kelly will tell you to bet everything on this one opportunity as risk is contained thanks to the limited 20% downside.

There is, however, one big problem with this approach and that’s “unknown unknowns”. Trying to assess the probability of an unknown event, particularly stock prices is almost impossible. That being said, for special situations, where there’s a limited timeframe, the process can be highly valuable. The real usefulness of the Criterion as Lima explains is to “understand the boundaries of probabilities and position sizes implied by securities prices and estimated payouts”. The letter goes on, “the Kelly Criterion is to size positions according to how little downside they have, not how much upside one expects. Ideally, one wants securities that exhibit asymmetric payoffs, with low risk of loss and a high probability of winning big.”

The post Heller House: Using The Kelly Criterion For Position Sizing appeared first on ValueWalk.