Michael Mauboussin: Maximize Your Opportunities With Position Sizing

Yesterday we provided an excerpt from a Stanley Drukenmiller interview in which he discussed the importance of sizing your position in an investment, when you think you’re right. Following on that theme, back in 2006 Michael Mauboussin wrote a great paper titled – Size Matters, in which he also discussed the importance of sizing positions to generate outsized returns saying:

Two portfolio managers with the same list and number of stocks can generate meaningfully different results based on how they allocate the capital among the stocks.

Here’s an excerpt from that paper:

To suppose that safety-first consists in having a small gamble in a large number of different [companies] where I have no information to reach a good judgment, as compared with a substantial stake in a company where one’s information is adequate, strikes me as a travesty of investment policy.

John Maynard Keynes
Letter to F.C. Scott, February 6, 1942

As an investor, maximizing wealth over time requires you to do two things: find situations where you have an analytical edge; and allocate the appropriate amount of capital when you do have an edge. While Wall Street dedicates a substantial percentage of time and effort trying to gain an edge, very few portfolio managers understand how to size their positions to maximize long-term wealth.

A simple example illustrates the point. Assume you can participate in a coin toss game where heads pays $2 and tails costs $1. You start with a $100 bankroll and can play for 40 rounds. What betting strategy will allow you to achieve the greatest probability of the most money at the end of the fortieth round?

We’ll get to the answer in a moment, but let’s consider the obvious extremes: if you bet too little, you won’t take advantage of a clearly positive expected-value opportunity. On the other hand, if you bet everything, you risk losing all of your money. Money management is all about determining the right amount of capital to allocate to an investment opportunity, given the edge and the frequency of such opportunities.

Position size is extremely important in determining equity portfolio returns. Two portfolio managers with the same list and number of stocks can generate meaningfully different results based on how they allocate the capital among the stocks. Great investors don’t stop with finding attractive investment opportunities; they know how to take maximum advantage of the opportunities. As Charlie Munger says, good investing combines patience and aggressive opportunism.

Let’s go back and answer our opening coin-toss question using the Kelly formula. The payoff scheme, a $2 win for a heads and a $1 loss for a tails, suggests 2-to-1 odds. Since we’re dealing with a fair coin, we know the tosses will be 1-to-1. So we recognize something the market doesn’t: heads will show up more often than the payoff scheme suggests.

Solving the formula, edge is $0.50 (expected value, or 50 percent x $2 + 50 percent x -$1) and odds are $2 (the amount you win if you win). The optimal amount to bet is 25 percent of your bankroll in each round. Said differently, betting 25 percent will lead to a greater accumulation of wealth, on average, than any other betting strategy.