Kelly Criterion Calculator

The Kelly Criterion is a mathematical formula that can be applied to your investment strategy to determine the optimal amount of money to allocate to each investment. Originally developed for gambling, it has been adapted for the financial world to maximize the growth rate of your investment portfolio over the long term.

Result:

Here's a step-by-step guide on how it works and how to use it:

1. Understanding the Variables:
   • p (Probability of Increase): This is the likelihood that your investment will increase in value. For instance, if you believe there's a 60% chance that a stock will go up, you would input 0.6.
   • q (Probability of Decrease): This is the likelihood that your investment will decrease in value. Typically, q is the complement of p, meaning q = 1 - p.
   • a (Fraction Lost): This represents the percentage of your investment you would lose if the investment's value decreases. For example, if you could lose 10% of your investment's value, you would input 0.1.
   • b (Fraction Gained): This is the percentage of your investment you would gain if the investment's value increases. If you expect to gain 10% on the investment, your input would be 0.1.
2. The Formula:

   The general Kelly Criterion formula for investment is:

   f* = (p/a) - (q/b)

   where f* is the fraction of your total available capital that you should invest. A positive value of f* indicates a potentially profitable investment, while a negative value suggests that you should avoid it.

3. How to Apply It:
   • First, evaluate the investment opportunity to estimate p, a, and b. It's crucial to be as accurate as possible in these estimates, though keep in mind that all investments carry uncertainty.
   • Input these values into the calculator.
   • The calculator will output the value of f*, which is the proportion of your assets you might consider allocating to this investment.
4. Interpreting the Results:
   • If f* is a small positive number, it suggests a conservative investment. You might allocate this fraction of your portfolio to the investment.
   • If f* is close to 1, the investment is predicted to be highly profitable, and you could allocate almost all of your capital to it.
   • If f* exceeds 1, this suggests using leverage (borrowing money to invest), but be cautious—this increases the potential risk significantly.
   • If f* is negative, you should not invest, as the expected outcome is a loss.
5. Practical Example:

   Imagine you have assessed an investment and concluded:

   • There is a 55% chance the investment will increase in value (p = 0.55).
   • There is a 45% chance it will decrease (q = 0.45).
   • You could gain 10% if it increases (b = 0.1).
   • You could lose 10% if it decreases (a = 0.1).

   Entering these values into the Kelly Criterion formula would give you the optimal fraction of your portfolio to invest in this opportunity.

6. Caveats and Considerations:

   The Kelly Criterion assumes that you have accurate probabilities and outcome values, which is rarely the case in investments. It also doesn't account for the investor's risk tolerance—some may not be comfortable investing the full Kelly fraction.

   Remember, the Kelly Criterion is a tool to guide your investment decisions, not a guarantee. Always consider the broader context of your financial situation and risk tolerance before following its suggestions.