Question

A newly issued bond has a maturity of 10 years and pays a 7% coupon rate (with coupon payments coming once annually). The bond sells at par value of $100.

(a) What are the duration, modified duration and dollar duration of the bond? What is its convexity?

(b) Find the actual price of the bond assuming that its yield to maturity immediately increases from 7% to 8%?

(c) What price would be predicted by using duration? What is the prediction error?

(d) What price would be predicted by using duration-with-convexity? What is the prediction error?

Answer 1

SOLUTION:-

A)

Duration of bond:-

  The time duration of a bond is subject change due to interest rate sensitivity.Higher the duration of bond , it is greater that the volating on intrest rate. Macaulay duration method is used in measuring bond's duration as given below

Macaulay Duration =   

Modified duration of a bond:-

The modified duration is an adjusted version of the Macaulay duration. The modified duration determines the changes in a bond's duration and price for each percentage change in the yeild to maturity.

Modified Duration:-   

Dollar Modified:-

The changes in the U.S dollar valu of a bond for every 1% change in it's yield. It is calculated as the product of a bond's duration and the market value of thet bond.

Convexity:-

The non-linear relationship between the bond pricing and change of interest rate.

P = Price of bond

YTM = Yeild To Maturity can be + or -

Delta P and YTM are described in % in above formula

B)

Price of a bond summation of present value of all future cash flow of bond.

Price of Bond =   

Bond Price = $93.29 if intrest rate changes to 8%.

Duration of Bond = 692/ 93.29 = 7.42 years

C)

Bond Price Change = Yield Change   Modified duration Bond Price

Bond Price change = 0.01 7.42 93.29 = $6.92

D)

Bond Price Chenges = Duration Yield Change + Convexity Adjustment

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