Investing is a continual education and from time to time we like to highlight concepts on refining investment process. Today we present a piece on position sizing utilizing the Kelly Growth Criterion. The following is a guest post from Kyle Mowery, who founded GrizzlyRock Capital in 2011 as a long / short manager investing in corporate debt and equity securities.

He can be reached at kyle@grizzlyrockcapital.com or at. Position Sizing Utilizing the Kelly Growth Criterion One of the more vexing tasks for investment allocators is position sizing. Regardless whether allocators select investment managers or individual securities, optimal position sizing is paramount to portfolio success.

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Small allocations to prescient investments minimize their impact while large allocations to poorly performing investments leads to underperformance. Some allocators elect to equal-weight investments given uncertainty regarding which investments will perform best. This strategy creates a basket of attractive investments that should profit regardless of which investments in the basket succeed. This method benefits from simplicity and recognizes the future is inherently uncertain. Drawbacks of the strategy include underweighting exceptional investments and overweighting marginal ideas.

Another strategy is to allocate large amounts of capital to the investment ideas with the most potential. This methodology suggests investors should invest proportionally according to their ex-ante return expectations. The advantage of this methodology is matching prospective return to investment size.

However, this strategy breaks down when allocators are incorrect about future investment return or risk prospects. Investment allocators determine their methodology through a combination of portfolio mandate, risk tolerance, and confidence level in investment assessments. While the various approaches implemented are directionally helpful, most are mathematically sub-optimal. There is a better way - the Kelly Growth Criterion. Kelly Growth Criterion The Kelly Growth Criterion is a simple formula that determines mathematically optimal allocations to maximize long-term portfolio performance given each investment’s probability of success (“edge”) compared to the amount gained or lost (“odds”).

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The formula assumes a bimodal outcome of success (“base case”) or failure (“stress case”) over a single time period. The formula’s power lies in considering both the chance of success and payoff offered. For example the formula would urge a large investment if you had a significant edge given reasonable odds or exceptional odds payoff offsetting a moderate chance of success. Ok, How Can the Formula be Applied to Investing? When applied to investing, the Kelly Growth Criterion formula has six inputs.

First is simply portfolio size. Second is the amount of capital the portfolio will risk in the pursuit of gain. This amount is also called the maximum tolerable drawdown. For a venture capital group this number will be high while a conservative pension plan would be willing to risk much less. Portfolio size and maximum tolerable drawdown remain constant for each portfolio analyzed regardless of specific investment opportunities. Next comes four factors regarding the investment itself: the probability of gain in a base case, probability of loss in a stress case, percent of projected gain in the base case, and percent of projected loss in the stress case.