Kelly Fraction Calculator for Stock and Bond Investment

This calculator gives you the Kelly fraction for investing in a stock and a risk free compound interest investment that will be referred to as a bond. The assumption is that there are only two possible returns for the stock in a given time period. It's as easy to use as the average mortgage calculator, just fill in the blanks with the necessary figures and you're good to go. The stock price will either increase by a percentage r1 > 0, or decrease by a percentage r2 < 0. The probability of the price increasing is p, and the probability of it decreasing is 1-p. The investment in the bond grows by the percentage rb (the interest rate or bond yield) in each time period.

The fraction of total assets invested in the stock is fs, and the fraction of assets invested in the bond is fb. All assets are completely invested so that fs + fb = 1.

As an example, suppose we have a stock that has an equal chance of doubling in value or decreasing to 1/2 its value. In this case r1 = 1, r2 = -1/2, and p = 1/2. If the risk free bond is yielding 10% then rb = 0.1. The Kelly fraction for the stock investment in this case is fs = 0.305556. This means you should invest about 30% of your assets in the stock and 70% in the bond.

p: = probability of stock going up.
r1: = positive return on the stock in a given time period.
r2: = negative return on the stock in a given time period.
rb: = return on risk free bond in one time period.
fs :

Note:

  • r1 must be positive and r2 must be negative.
  • Getting a negative value for fs means don't buy the stock, or if you prefer, you can "sell short" the stock.