Sara Bauer is a fixed income portfolio manager. Knowing that the current shape o

Question

Sara Bauer is a fixed income portfolio manager. Knowing that the current shape of the yield curve is flat, she considers the purchase of a newly issued, option-free corporate bond priced at par with semiannual coupon payment; the bond is described below.

7% option-free bond, maturity in 10 years

Up 10 basis pts.

Change in yields

Down 10 basis pts.

Price

99.29

100.71

Convexity

35.00

Bauer is also considering the purchase of a second newly issued, option-free corporate bond, which is listed below. She wants to evaluate this second bond’s price sensitivity to an instantaneous, downward parallel shift in the yield curve of 200 basis points. Estimate the total % change of the bond if the yield curve experiences an instantaneous, downward parallel shift of 200 basis points.

7.25% option-free bond, maturity in 12 years

Original issue price

Par value, YTM 7.25%

Modified duration (at original price)

7.90

Convexity measure

41.55

Convexity adjustment (yield change of 200 basis points)

1.66

Up 10 basis pts.

Change in yields

Down 10 basis pts.

Price

99.29

100.71

Convexity

35.00

Explanation / Answer

Solution:

Percentage price change using duration = -7.90 x -0.02 = 15.80%

Percentage price using convexity adjustment = (0.02)^2 x 41.55 = 0.0166%

Total estimated price change = 17.46%

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