# Estimate new price of corporate bond

May I ask if change of the corporate bond’s yield in the following example actually mean change of the corporate bond’s G-spread? Because the expected change in corporate bond yield is taking into account both (1) increase in benchmark yield and (2) decrease in “corporate bond yield”. Please advise, thank you!

==========

A manager gathers the following information on three bonds. He plans to buy 1 million par of the corporate bond.

Price Yield (YTM) Maturity Effective D 7-year corporate bond 101.50 3.77% 6.7 6.1 5-year government bond 99.96 1.90% 4.9 4.7 7-year government bond 99.56 2.20% 7.0 6.5

The manager is aware that there is some controversy in the industry regarding whether it is best to compute G-spread by matching maturity or duration. Maturity has often been used and is regarded as simpler. Some theoretical arguments favor an interpolation based on duration as more accurate. The analyst has determined the difference in the two methods is not generally large and favors the more traditional “use maturity” approach. 1. Calculate the initial benchmark (G-spread) of the corporate bond based on interpolated maturity matching. 2. Calculate the hedge position to eliminate interest rate risk for the 1 million par of the corporate bond and calculate the expected return on the hedged position. After buying the corporate bond, the yield of the 5- and 7-year government bonds increase 10 and 15 bp respectively, while the corporate bond’s yield declines 3 bp. 3. Estimate the new price of the corporate bond.

Answers: 1. Determine the weight of the two government bonds; the weight in the 5-year government bond is denoted as w: 6.7 = w(4.9) + (1 – w)(7.0) 6.7 = 4.9w – 7.0w + 7.0 0.3 = 2.1w w = 14.3% in 5-year government bond and 85.7% in 7-year government bond That makes the benchmark yield: 0.143(1.90%) + 0.857(2.20%) = 2.16% and spread: 3.77 – 2.16 = 1.61% 2. Cost of the purchase is 1 million × 101.50 / 100 = 1,015,000. Short the 5-year and 7-year government bonds (market value amount) equal to 14.3% and 85.7% of 1,015,000 respectively. Expected return: yield purchased – yield shorted = 3.77 – 2.16 = 1.61% 3. Expected change in benchmark yield = 0.143(10) + 0.857(15) = +14.3 bp Expected change in corporate bond yield = 14.3 – 3bp = +11.3bp Estimated price change of corporate = –6.1(0.00113) = –0.0069 = –0.69% Estimated new price: (1 – 0.0069)(101.50) = 100.80