Asked by Petergay Senior on Jun 27, 2024
Verified
You have a 15-year maturity, 4% coupon, 6% yield bond with duration of 10.5 years and a convexity of 128.75. The bond is currently priced at $805.76. If the interest rate were to increase 200 basis points, your predicted new price for the bond (including convexity) is ________.
A) $638.85
B) $642.54
C) $666.88
D) $705.03
Convexity
A measure of the curvature or the degree of the curve in the relationship between bond prices and bond yields.
Basis Points
A unit of measure used in finance to describe the percentage change in the value or rate of a financial instrument; one basis point is equivalent to 0.01%.
Predicted New Price
An estimation of a security's future price based on various factors, including market trends, economic indicators, and company performance.
- Understand the principle of convexity and its effects on variations in bond prices.
Verified Answer
ZK
Zybrea KnightJul 01, 2024
Final Answer :
C
Explanation :
ΔP/P = −D*(Δy) + 0.5(Convexity)(Δy)2
D* = D/(1 + y) = 10.5/1.06 = 9.906
−D*(Δy) = −9.906 × −2% = −19.81%
0.5(Convexity)(Δy)2 = 0.5(128.75)(−2%)2 = 2.575%
ΔP/P = = −D*(Δy) + 0.5(Convexity)(Δy)2 = −19.81% + 2.575% = −17.235%
New price = $805.76 × (1 − 0.17236) = $666.88
D* = D/(1 + y) = 10.5/1.06 = 9.906
−D*(Δy) = −9.906 × −2% = −19.81%
0.5(Convexity)(Δy)2 = 0.5(128.75)(−2%)2 = 2.575%
ΔP/P = = −D*(Δy) + 0.5(Convexity)(Δy)2 = −19.81% + 2.575% = −17.235%
New price = $805.76 × (1 − 0.17236) = $666.88
Learning Objectives
- Understand the principle of convexity and its effects on variations in bond prices.