A newly issued bond has the following characteristics: Par value = $1000 Coupon

Question

A newly issued bond has the following characteristics: Par value = $1000 Coupon rate = 8% Yield to Maturity = 8% Time to maturity = 15 years Duration = 10 years 1. Calculate modified duration using the information above. 2. If the yield to maturity increases to 8.5%, what will be the change (in dollar amount) in bond price? 3. Identify the direction of change in modified duration if: i. the coupon of the bond is 4%, not 8%. ii. the maturity of the bond is 7 years, not 15 years. 4. How can you construct a portfolio with a duration of 8 years using this bond and a 5 year zero coupon bond?

Explanation / Answer

Since coupon rate and yield to maturity is equall so Current price of bond is equal to par value that is $ 1000 Interest amount 80 Time to maturity 15 years Yield to maturity 8.50% Present value of interest = Interest *Cumulative discount factor = 80 x 8.304 = 664 Present value of par value = Par value x Discount factor = 1000 x .294 = 294 Total of present value = 958 Existing price = $ 1,000.00 Revised price = $     958.00 Change in price = $        42.00 Cumulative discount factor = (1-(1+i)^-n)/i = (1-(1.085)^-15)/.085 = 8.304

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