How to Calculate the Default Risk Premium
The default risk premium is a risky bond's yield minus the yield on a risk-free bond of the same maturity, quoted in percentage points.
The Default Risk Premium formula
Calculator
Enter the risky and risk-free yields to get the spread, the dollars it adds per bond and the default rate it covers.
Yield to maturity on the corporate or lower-rated bond.
A Treasury of the same maturity, so only credit risk separates the two.
Cents on the dollar investors expect back after a default.
The risky bond pays 3.2% more a year than the safe one, and that gap is the market's price for the chance of default.
- Premium as a share of the risky yield
- 43.2%
- Extra interest per $1,000 of face value
- $32
- Break-even annual default rate
- 5.33%
- Verdict
- Paid to carry default risk
43.2% of what this bond pays is compensation for credit risk rather than the going return on safe money.
Each $1,000 bond hands over $32 a year more than the Treasury, provided the issuer keeps paying.
With this recovery rate the spread covers expected losses up to a 5.33% default rate, and anything worse eats into the return.
A positive spread is the whole reason to hold the riskier bond, and it has to be weighed against the losses expected across many such bonds.
How to calculate Default Risk Premium, step by step
- 1Match the maturities. Pick a risk-free benchmark with the same time to maturity as the risky bond. Comparing a ten-year corporate bond with a three-month bill mixes credit risk in with the slope of the yield curve.
- 2Read both yields. Use yield to maturity for each bond rather than the coupon rate, so the price paid for the bond is accounted for.
- 3Subtract. Premium = risky yield − risk-free yield. The answer is in percentage points, and traders quote it in basis points, so a spread of 3.2 points is 320 basis points.
- 4Turn the spread into dollars. Multiply the premium by the face value to get the extra interest per year, since a spread means little until you see what it pays.
- 5Test it against expected losses. Divide the premium by the loss given default, which is 1 minus the recovery rate. The result is the annual default rate at which the extra yield exactly covers expected losses.
Worked example: Default Risk Premium
A corporate bond yields 7.4% while a Treasury of the same maturity yields 4.2%, so the default risk premium is 7.4 − 4.2 = 3.2%. That spread is 43.2% of the corporate yield and $32 of extra interest a year on every $1,000 of face value. If a default recovers 40 cents on the dollar, the loss given default is 60%, so the spread breaks even at a 5.33% annual default rate. Above that rate the extra yield stops covering expected losses.
Default Risk Premium questions
What is the difference between the default risk premium and the total spread over Treasuries?
The default risk premium is the slice that pays for credit risk alone. The full gap over a Treasury also carries a liquidity premium, since corporate bonds trade less often, and for longer bonds a maturity premium as well.
Why do junk bonds carry such wide default risk premiums?
Lower-rated issuers default more often and hand back less when they do, so investors demand more yield. Spreads widen across every issuer when the economy weakens, because expected default rates climb at the same time.
Does a wide spread mean a bond is a good deal?
Only if the spread beats expected losses. Multiply the default probability by the loss given default, and if that product is larger than the premium, the extra yield is not paying for the risk taken.
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