Bond Price and Duration

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Bond Price and Duration

Postby anirban.dutta » Mon May 12, 2014 4:11 am

A 5-year bond with a yield of 11% (continuously compounded) pays an 8% coupon at the end of each year.
a) What is the bond's price?
b) What is the bond's duration?
c) Use the duration to calculate the effect on the bond's price of a 0.2% decrease in it's yield. Recalculate the bond's price on the basis of a 10.8% per annum yield and verify that the result is in agreement with your answer to "c".
d) What is the difference between this bond's Macaulay and modified duration?
e) At 11% yield, what is the first derivative of the bond's price change with respect to an (instantaneous) yield change?
f) At 11%, is the convexity positive or negative?

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Bond Price and Duration

Postby edupristine » Tue May 13, 2014 11:12 am

a. For continuous compounding Effective annual rate of return = e^(0.11) = 11.6278%. Now Bond's price is the NPV at effective rate of return. thus Bond's Price = $86.80.
b. Bonds duration is the Macaulay duration. Macaulay duration = percentage of return with respect to the return. Hence Bond's duration = 4.256.
c. The bond's price will increase, since the increase in decarease in YTM decreases the effective annual rate of return thus increasing the price. So price = NPV at e(0.108) = Price = $87.54

d. Macaulay duration & Modified duration is same for Continuous compounding, since Modified duration = (Macaulay Duration/(1+ YTM/n)) where n = number of compounding. In continuous compounding n tends to infinity, hence Modified duration = Macaulay duration.
f. Convexity = (V- +V+ 2V0)/((delta curve)square*V0). = 0.156.

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