Measuring duration In general notation,Macaulay's duration (D): CF(t) D 含8州 CF PV of the Sec. 猫f的贺6号
Measuring duration Measuring duration In general notation, Macaulay’s duration (D): PV of the Sec. (1 +r) CF (t) (1 +r) CF (1 +r) CF (t) D = n t = 1 t t k t = 1 t t k t = 1 t t ∑ ∑ ∑ =
Measuring duration Example:1000 face value,10%coupon,3 year,12%YTM 100×1 +100×2 ,100×3,1000×3 (1.12)1 (1.122（1.123 (1.123 2597.6 3100 2.73 years 1000 951.96 (1.12)3 的资5+号
Measuring duration Measuring duration Example: 1000 face value, 10% coupon, 3 year, 12% YTM = 2.73 years 951.96 2597.6 (1.12) 1000 + (1.12) 100 (1.12) 1000 3 + (1.12) 100 3 + (1.12) 100 2 + (1.12) 100 1 D 3 t=1 t 3 1 2 3 3 = × × × × = ∑
Measuring duration ▣If YTM=5/O 1000 face value,10%coupon,3 year, 5%%YTM 100*1 +100*2+100*3+1000*3 (1.05) (1.05)2(1.05)3 (1.05)3 1136.16 3127.31 D 三 2.75 years 1136.16 行贺影小号
Measuring duration Measuring duration If YTM = 5% 1000 face value, 10% coupon, 3 year, 5% YTM 1136.16 (1.05) 1000 * 3 + (1.05) 100 * 3 + (1.05) 100 * 2 + (1.05) 100 * 1 D 1 2 3 3 = = 2.75 years 1136.16 3127.31 D =
Measuring duration ▣If YTM=20O 1000 face value,10%coupon,3 year,20%YTM 2131.95 D 三 2.68 years 789.35 猫f的贺6号
Measuring duration Measuring duration If YTM = 20% 1000 face value, 10% coupon, 3 yea r, 20% YTM = 2.68 years 789.35 2131.95 D =
Measuring duration If YTM 12%and Coupon =0 1000 face value,0%coupon,3 year,12%YTM 1000 1000×3 D 三 (1.12)3 3(by definition 1000 (1.12 猫1的對香+手
Measuring duration Measuring duration If YTM = 12% and Coupon = 0 1000 face value, 0% coupon, 3 yea r, 12% YTM 1000 |-------|-------|-------| 0 1 2 3 3 (by definition (1.12) 1000 (1.12) 1000 3 D 3 3 = × =