Question

You find a bond with 3 years until maturity that has a coupon rate of 7.9 percent and a yield to maturity of 6.5 percent. What is the modified duration?

Answer 1

Assumin the par value to be 100

Annual cash flow = 7.9

Present value of year 1 cash flow = 7.9 / (1 + 0.065) = 7.4178

Present value of year 2 cash flow = 7.9 / (1 + 0.065)² = 6.9651

Present value of year 3 cash flow = 107.9 / (1 + 0.065)³ = 89.32

Total present value = 7.4178 + 6.9651 + 89.32 = 103.703

Weight of first cash flow = 7.4178 / 103.703= 0.07153

Weight of second cash flow = 6.9651 / 103.703 = 0.06716

Weight of third cash flow = 89.32 / 103.703 = 0.8613

Period1 * weight1 = 1 * 0.07153 = 0.07153

period2 * weight2 = 2 * 0.06716 = 0.13432

period3 * weight3 = 3 * 0.8613 = 2.5839

Macaulay duration = 0.07153 + 0.13432 + 2.5839 = 2.7896

Modified duration = Macaulay duration / 1 + r

Modified duration = 2.7896 / 1 + 0.065

Modified duration = 2.6193