CAB Technology has issued bonds that pay 9.00% annual rate(paid semiannually) coupons at par value with...

CAB Technology has issued bonds that pay 9.00% annual rate(paid semiannually) coupons at par value with a yield to maturity of 9.00%, fifteen years until maturity and currently have a duration of 8.51 years. If the maturity of the bond was less than fifteen years, te modified duration would be ------ compared to the original modified duration.

A. smaller

B. larger

C. Not enough information

D. unchanged

please give me detailed explaination

Expert Solution

Correct Answer: A. smaller

Duration measures how long it takes, in years, for an investor to be repaid the bond’s price by the bond’s total cash flows. At the same time, duration is a measure of sensitivity of a bond's or fixed income portfolio's price to changes in interest rates

Duration of Bond and Bond's maturity is directly related which means if other factors remain same Bond with longer maturity has higher duration value and vice versa.

In given case, if maturity of bond was less than 15 years then Duration of Bond would be smaller than original duration of bond.

Now, Modified duration is function of Duration and directly related to Duration, equation for modified duration given below:

With above equation, we can say if yield rate remain same, Modified duration decreases as Duration decreases and vice versa.

Thus, in given case, if maturity was less than 15 years, the modified duration would be smaller compared to the original modified duration.

jeff jeffy answered 1 year ago

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