Question

In: Finance

An investor is considering purchasing a Treasury bond with a 20 year maturity, an 8% coupon...

An investor is considering purchasing a Treasury bond with a 20 year maturity, an 8% coupon and a 9% required rate of return. The bond pays interest semiannually.

a)What is the bond's modified duration?

b)If promised yields rise 25 basis points immediately after the purchase what is the predicted price change in dollars based on the bond's duration?

(please solve with formula not the macauly duration chart)

Solutions

Expert Solution

a)

Duration of Bond

where,

y = ytm

c = coupon rate

t = maturity time

In above case,

Semi annual Coupon rate (c) = 0.08/2 = 0.04

Semi annual YTM(y) i.e required rate = 0.09/2 = 0.045

Time to maturity (t) semi-annual = 20*2 =40

putting the values :

Bond's Modified Duration:

b)

We can calculate the approx change in Price of bond if interest rate changed with the help of modified duration.

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.

jeff jeffy answered 4 hours ago
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