Position sizing is an interesting topic because it affects all investors. Yet, I would be willing to bet very few investors spend a significant amount of time on the subject.
Even the most prominent investors are split on how they should manage their portfolio and weight allocation toward the best ideas. Warren Buffett (Trades, Portfolio) is clearly not afraid to run a highly concentrated portfolio with 57% of Berkshire Hathaway’s (BRK.A, Financial) (BRK.B, Financial) equity portfolio devoted to just four positions -- Apple (AAPL, Financial), Coca-Cola (KO, Financial), Wells Fargo (WFC, Financial) and Kraft Heinz (KHC, Financial). Meanwhile, Seth Klarman (Trades, Portfolio)'s top seven positions account for 57% of his equity portfolio, and David Tepper (Trades, Portfolio) has 10 positions accounting for 57% of his equity portfolio.
Every investor is different
Portfolio construction really does vary from investor to investor. And with so much research showing the benefits of diversification, it is questionable if investors should have any sort of concentration in their portfolio at all.
That said, those investors who are comfortable with their own research process and a concentrated portfolio have to deal with deciding what percentage of the portfolio each position is worth. Allocating the most money to the highest conviction positions is one answer, but how do you decide which of your positions has the highest conviction?
One solution is the Kelly criterion.
Kelly criterion
The Kelly criterion is a formula used to determine the optimal size of a series of bets. Initially designed to be used to beat the house at gambling, the criterion gives investors some insight into how much they should bet on each stock position considering the potential payoff and likelihood the payoff will be realized. The criterion also acts as a risk management device because it controls position size to avoid total loss. There are two basic components to the Kelly criterion: 1) the win probability, or the probability that any given trade you make will make a positive return, and 2) win-loss ratio, or the total positive trade amounts divided by the total negative trade amounts. You can see the formula here.
For example, if your research process turns up a stock that you believe is worth $87 but is currently trading at $56, you want to buy the security but are not sure how much of your portfolio you should devote to the position. Further research leads you to conclude the total potential downside for this stock is $45. You believe there is a high probability (greater than 26%) the stock will hit $87 before its $45. Putting these assumptions into the Kelly criterion, the formula gives you a 26% probability of success on the $56 price.
The one problem with all of this is the Kelly criterion makes a number of assumptions and, as any experienced investor will tell you, in the real world these assumptions often count for nothing. Even if you believe the security may not trade lower than $45, the average investor is only able to access a certain amount of information about any particular company. There may be nasty surprises hiding in the woodwork, which you only find out about when it is too late.
Risk-reward
While the functions of the Kelly criterion are limited, the one thing the formula is useful for is to understand the boundaries of probabilities and position sizes implied by securities' prices and estimated payouts. By trying to compute expected downside for the security in question, you can allocate according to how little downside each stock has, not how much upside you expect it to produce.
With this approach, you should be able to select and build a portfolio of stocks with asymmetric payoffs. While this is the desire of most investors, putting it into practice is another thing entirely. The Kelly criterion should help meet this goal with little effort.
Disclosure: The author owns no stock mentioned.
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