The Kelly Criteria are actually relatively simple in their design. There are two components that make up the basis of the formula. The first is the probability that your transaction will produce a profitable return. This is called the win probability. The second is the total dollar amount of transactions with positive returns divided by total amount of transactions with negative returns. This is called the win/loss ratio.
The actual Kelly Formula utilizes both of these criteria in its calculations. The formula gives the investor the Kelly Percentage – or what percentage the transaction should take up in your portfolio. Let’s start with formula itself.
Kelly % = W - [(1 - W)/R]
W represents the win probability and R represents the win/loss ratio. To get the numbers required to populate the equation, the following steps are required.
1. Collect data on your previous 50 trades.
2. Calculate the winning probability by dividing positive return transactions by negative return transactions.
3. Calculate the win/loss ratio by dividing the total gains from your positive return transactions by the total losses of your negative return transactions.
4. Plug these numbers into the formula and the Kelly percentage represents the percentage that this transaction should amount to in your portfolio.
Some Thoughts on the Formula
It’s far beyond the purview of this article to comprehensively address the pros and cons of the formula. However, at the Nintai Charitable Trust we employ the Kelly Formula as a piece in an integrated capital deployment strategy. Simply put, it plays a very diminished role in our capital allocation decisions. Over the course of our investment management career we’ve had many individuals ask why we don’t use the formula to a greater degree in our portfolio selection.
The short answer is I believe the formula gives an investor a partial – and wholly incomplete – picture of the capital allocation process. The idea of your largest position being dictated by a formulaic approach is compelling. In games of chance it is even more so. Allowing your allocation of capital to be decided by such an approach alone gives away the great advantage one has as an investment manager.
Whist versus Bridge
Anybody who plays whist and bridge knows there is a vast difference in the role of luck between them. In bridge, partners communicate with each other through a detailed bidding process that discusses both strength of their hands and their preferred suit. In whist, players communicate about points but cannot disclose anything about their preferred suit. I bring this up because the Kelly Formula is similar to whist. One can get a pretty good sense of how much to invest but the context of what to invest in – industry, strength of management, balance sheet strength – is not part of the investment decision process.
“The Odds” versus Compounding
One of the real dangers in the investing world is Wall Street’s penchant for creating formulas that back-test amazingly. The Street also loves to use formulas to make it appear their recommendations are based on sophisticated data-driven models. We see a little bit of this in Wall Street’s approach to the Kelly Formula. At the Nintai Charitable Trust we are happy to rely less on mathematical formulas to calculate capital allocation and more on managers who are extraordinary allocators of capital. Put more simply, we rely less on short-term bets on portfolio position size and more on long term compounding.
A Working Example
In February 2015 two stocks reached Nintai’s buy price and I began the standard process of double checking our numbers and deciding on capital allocation. The two stocks were Paychex (PAYX) and SEI Investments (SEIC). While the Kelly Formula gave a recommendation based solely on win probability and win/loss ratio, looking at our forecasts (such as free cash flow growth, future return on capital, margin expansion/contraction, etc.) I came to a diametrically opposing view on how much to allocate to each position. For instance the Kelly Formula took no account of the impact of interest rates on Paychex “float” and their long-term impact on gross and net margins. In addition, the formula failed to reflect the growing disparity between active and index based investing (indexing creates larger margins for SEI based on trading volumes). In the end, each position was allocated capital on a blend of valuation, market trends, financial strength, and yes, the Kelly Formula.
Much like the whist versus bridge comparison, the ability to layer on additional data can provide investors with a vastly different view on capital allocation. While the Kelly Formula can certainly play a role in your investment decisions, I generally like to include multiple sources of data when making decisions on position sizing. The ability to understand major market drivers (such as competition, technology innovation, etc.) is a critical component to getting a broader view on capital allocation. The Kelly Formula is a useful tool to have in your investment toolbox. Used by itself, it’s a formula for short-term volatility and potentially long-term underperformance.
1 For those real junkies the original work can be found here: https://www.princeton.edu/~wbialek/rome/refs/kelly_56.pdf