Question

A fixed-income trader observes a three-year, 6.50% annual-pay corporate bond trading at 105.500 per 100 of par value. The research team at the hedge fund determines that the risk-neutral annual probability of default used to calculate the conditional POD for each date for the bond, given a recovery rate of 30%, is 1.5%. The government bond yield curve is flat at 3.00%.

A) Based on these assumptions, does the trader deem the corporate bond to be overvalued or undervalued? By how much?
(To do this question you will need to calculate the risk-free value of the bond, and then the CVA as shown below.)
B) How does the yield spread of the bond compare to its theoretical spread?

Answer 1

To determine if a three-year corporate bond is over or undervalued, calculate the bond's risk-free present value and adjust for Credit Valuation Adjustment. Compare the adjusted price to the market price. For the yield spread, compare the bond's theoretical spread, which accounts for default risk and liquidity premium, to its actual market yield spread.

Step-by-step explanation:

To determine whether the three-year, 6.50% annual-pay corporate bond is overvalued or undervalued, we need to calculate the risk-free value of the bond and adjust for Credit Valuation Adjustment (CVA).

First, calculate the present value of the bond's cash flows discounted at the government bond yield (risk-free rate of 3.00%). The bond's cash flows consist of three annual interest payments of 6.50% of the par value and the repayment of par at maturity. The calculation is as follows:

• Year 1: $6.50 / (1 + 0.03) = $6.31
• Year 2: $6.50 / (1 + 0.03)^2 = $6.13
• Year 3: ($6.50 + $100) / (1 + 0.03)^3 = $97.55

The total risk-free value is the sum: $6.31 + $6.13 + $97.55 = $109.99

Next, apply CVA to account for the bond's risk of default. Given a 1.5% annual probability of default and a 30% recovery rate, the expected loss from default is (1 - recovery rate) * probability of default * risk-free value of the bond, for each year.

The adjusted price for the bond, after CVA, would be lower than $109.99, which needs to be compared with the observed market price of $105.50. If the adjusted price is higher than $105.50, the bond is undervalued; if it's lower, the bond is overvalued.

Regarding the bond's yield spread, it would be the difference between the bond's yield to maturity and the risk-free government bond yield. The theoretical spread would account for the bond's default risk and liquidity premium over the risk-free rate. To compare the actual yield spread with the theoretical spread, we need to calculate the bond's yield to maturity and adjust for risk considerations as highlighted above, and then compare the result with the bond's market yield spread.