### Kelly Criterion based strategies for value investing

Kelly criterion is a very simple formula that returns a percentage value for the size of bets as edge divided by odds. It essentially tells you the best bet size for you to realize maximum returns after n rounds. The original formula is suitable for betting and gambling scenarios. Variations of the criterion have been applied successfully in many areas including as a money management sytem. Below is a look at the use and limitations of the criterion for money management:

Stock Selection

Applying Kelly criterion to stock selection boils down to coming up with estimates for Payoff (P), Win% (W), and Loss% (L) in the expanded form of the Kelly criterion:

(P*W - L)/P.

Value investors can attempt to estimate the edge using Fundamental Analysis - given that the vast majority of the money invested in the stock market goes into blind indexing schemes and unproven stock selection methods, fundamental analysis can result in an edge, as studying company reports including Annual Reports (10K) and Quarterly Reports (10Q) can unearth misconceptions in the marketplace that can result in a significant margin-of-safety. For example, say a company XYZ is trading at \$30 and you have come up with an average Fair Value Estimate (FVE) of \$50.  The Payoff (P) in this scenario is 50/30 = 1.67. The probability of winning (W) is an estimate that you have to come up with based on how confident you are on your fundamental analysis. In our example, if we take the estimate as 0.5, the formula becomes:

(1.67 * 0.5 – 0.5)/1.67 = 16.67%.

The value indicates that to maximize returns after n bets, one should invest one-sixth of the money in XYZ. On the other hand, if the FVE is \$25 and your confidence in the analysis is the same (0.5), the formula yields -10%. So, one should not invest in XYZ.

The main benefit of using Kelly criterion for stock selection is that it forces investors to think in terms of payoff probabilities thereby allowing them to shy away from high-risk or low-reward opportunities. One disadvantage with the criterion is that the idea with the formula is optimizing returns when doing sequential bets, as in a gambling situation. But, value investing involves selection of multiple companies at a time and as such there is a mismatch – the formula has limited scientific value for stock selection and so investors should also look at other methods to arrive at their final stock selection decision.

Diversification:

One of the classic value investor dilemmas is coming up with a number for how many stocks one should optimally own in the portfolio. Kelly criterion can be used to come up with a value for this number, if you know your average edge and odds of winning – just plug-in these values into the formula to get a percentage rate.

Coming up with your average edge and odds of winning is easier said than done. One approach is to look at your historic trades to derive these numbers, based on your past behavior. The obvious assumption is that future behavior will parallel the average of your past behaviors. Below is a look at the steps to come up with this number:

1. Calculate your historic payoff (P): From the list of your previous trades, sum up all dividends, interest, and total value of your stock sales. Divide this value by the sum of your cost basis of all your trades.
2. Calculate your historic winning probability (W): From the list of your previous trades, divide the number of trades that yielded a positive return including dividends by the total number of trades.
3. Apply the numbers to the formula (P*W - L)/P to come up with a percentage value. For example, if the criterion returns 2%, then you should take 50 different positions at 2% each.

The criterion looks at your historic performance to come up with an optimal value on how much your diversification should be. The main advantage with this formula is that you can come up with an absolute number for the number of stocks you should own. There are however many limitations to the approach:

1. Although the criterion yields an absolute number, the fact that the size of each position should be the same is a limitation. It is highly unlikely that you have the same conviction on all your stock picks.
2. The criterion assumes your historic behavior can be projected into the future. In the real world, this is not true – investors either get better at stock picking over a period of time or they give up and outsource money management.

The criterion can return a zero or negative value, if your historic returns have been poor. In this scenario, the criterion is useful only as a warning that a change in investment approach is necessary.