Enter the current market price, face value, and interest rate. Click calculate to display the 1,3,6, and 12 month default probabilities. The risk free rates used in the calculation can be changed in the table. Background information is below.

Bond Parameters Default Probabilities
Market price : 1 mo : %
Face value : 3 mo : %
Interest rate % : 6 mo : %
12 mo : %

Risk Free Interest Rates
Values from U.S. Treasury yield curve of
1 month3 month6 month12 month
% % % %

Bond default probabilities can be extracted from a bond's market price. A bond with a high probability of default will sell for less than a comparable bond with a lower probability. The lower price results in a higher yield that compensates for the default risk. The probability of default can be estimated by comparing the bond's yield with the yield on a risk free investment. The risk free yields used by default are those from the U.S. Treasury yield curve. The calculation assumes that market participants use a logarithmic utility function for the return on a combination of the risky bond and the risk free bond. The use of a logarithmic utility function is a reasonable assumption, and in any event, the use of some other risk averse utility function should not result in any significant difference. By seeking to maximize the expectation of the logarithmic utility, you can come up with a formula for the default probability. The details of this can be found in our book Bet Smart: The Kelly System for Gambling and Investing

Some warnings about the limitations of this calculator should be mentioned. First note that the default probabilities calculated are the maximum values given the assumptions used. The two main assumptions are that the defaulted bonds have a zero recovery rate, and that the price of the bond does not change over a coupon period. These assumptions are not serious if your goal is to just look at the relative default probabilities of bonds. In any case, you should not look at the probabilities given by this calculator as hard and fast numbers. They are estimates based upon assumptions. It is possible to do a much more sophisticated analysis of default probabilities. If you are interested in a more sophisticated analysis, please contact us.

- Stefan Hollos and Richard Hollos