# Default Premium

Default premium is the component of interest rate that is attributed to the risk of the borrower failing to pay back the principal. It can be estimated based on the difference between the required (nominal) yield on a company’s debt and the nominal yield on a risk-free debt such as US Treasury bond of comparable maturity.

The difference between required return on a company’s bond and the *real* risk-free rate is attributable to the combined effect of inflation risk, default risk, liquidity risk and maturity risk of the bond relative to a risk-free investment such as an investment in US Treasury securities. We can isolate the chunk of interest rate that is attributable to default risk by comparing investments which are identical except for the difference in default risk.

Let’s say we compare a 10-year corporate bond with a 10-year Treasury bond, we have neutralized the inflation risk and maturity risk and the difference will be attributable to default risk and liquidity risk. If corporate bond has a liquid market, the liquidity risk will be zero and the whole difference will be attributable to default risk. If a certain liquidity premium exists it can be subtracted from the difference to arrive at a default risk premium.

## Formula

$$ Default\ risk\ premium\ =\ {\rm Yield}_{CB}\ -\ {\rm Yield}_{TB}-\ LRP $$

Where **Yield _{CB}** is the yield on corporate bond and

**Yield**is the yield on treasury bond of comparable maturity and

_{TB}**LRP**is the liquidity risk premium, if any.

## Example

Yield on 10-year US Treasury bond is 4.2% and yield on a AA-rated corporate bond with 10 years to maturity is 6%. Liquidity risk is estimated at 0.5%.

$$ Default\ risk\ premium\ =\ 6\%\ -\ 4.2\%-\ 0.5\%=1.3\% $$