question archive Bond B 20 years; 7% annual coupon , YTM=10% (a) If the interest rate rises, will the actual price of Bond B be higher or lower than the estimated price based on duration approximation?
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Bond B 20 years; 7% annual coupon , YTM=10%
(a) If the interest rate rises, will the actual price of Bond B be higher or lower than the estimated price based on duration approximation?
Answer - If the interest rate rises, the actual price of Bond B will be lower than the estimated price based on duration approximation.
Reason- There is an inverse relationship between the interest rates and price of the bond. When the interest rate rises, the bond price falls and vice-versa.
Solution -
Given -
Years - 20
YTM = 10%
Annual Coupon Rate = 7%
Assume Face value of Bond B = 1000
Calcualtion of Bond Pricing at Interest Rate = 10%
10 % = {(1000*7%) + [(1000-Bond Price)/20] / (1000+Bond Price)/2}
On solving this, we get
Bond Price = 750 (approx.)
Now let us assume that the interest rate increases by 2%, then
Years - 20
YTM = 12%
Annual Coupon Rate = 7%
Assume Face value of Bond B = 1000
Calcualtion of Bond Pricing at Interest Rate = 12%
12 % = {(1000*7%) + [(1000-Bond Price)/20] / (1000+Bond Price)/2}
On solving this, we get
Bond Price = 626 (approx.)
Conclusion - So, we see that when YTM increases from 10 to 12 %, the Bond Pricing falls.