Question

Assume a bond with a $1,000 par value and an 8 percent coupon rate, two years remaining to maturity, and a 10 percent yield to maturity. The modified duration of this bond is_________.

Answer 1

We know that,

Price of the bond = Present value of annual coupons and face value discounted at ytm.

Face Value = 1000

Coupon Amount = 8% * 1000 = 80

Years Remaining = 2

ytm = 10%

Price = 80/(1+0.10)^1 + (80 + 1000)/(1+0.10)^2 =

= 72.73 + 892.56 = 965.29

Weightage for year 1 = 72.73/965.29 = 0.075345

Weightage for year 2 = 892.56/965.29 = 0.92465

Duration = Weightage for year 1 * 1 + Weightage for year 2 * 2

= 0.075345*1 + 0.92465 * 2 = 1.924645

Modified Duration = Duration / (1 + ytm) = 1.924645/(1 + 0.1) = 1.75 Answer

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