久期 Duration 种测量债券有效期限的方法 A measure of the effective maturity of a bond 每次利息或本金的支付时间的加权平均,权重应与 每次支付的现值相联系 The weighted average of the times until each payment is received, with the weights proportional to the present value of the payment ■除了零息债券,久期短于债券的到期日 Duration is shorter than maturity for all bonds except zero coupon bonds 久期等于零息债券的到期日 Duration is equal to maturity for zero coupon bonds 16-6
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久期:计算 Duration Calculation WI=CF, /(1+y)'/Pr rice D=∑t×1 t=1 CFt= Cash Flow for period t Y=债券的到期收益Wt=权重 D=久期 CFt=t时的现金流 t=时间 16-7
16-7 t t t w CF (1 y ) Price D t w t T t 1 CF t Cash Flow for period t Y=债券的到期收益 W t = 权重 D=久期 CF t = t 时的现金流 t=时间
久期:计算 Duration Calculation 2 (3) 5 名称 至支付的 支付/美元半年5%折现权重 (1)×(4) 时间/年 支付美元 债券A 8%债券 0.5 40 38.095 0.0395 0.0198 1.0 36.281 0.0376 0.0376 34.553 0.0358 0.0537 2.0 1040 855.611 0.8871 1.7742 总计 964.540 1.0000 1.8853 债券B 零息票债券0.5-1.5 0 2.0 1000 822.70 2 总计 822.70 1.0
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久期:计算 Duration Calculation B C D G Time until PV of CF Column(c) Payment (Discount rate times Period(Years) Cash Flow 5% per period) Weight Column(F) 4 A.8% coupon bond 0.5 40 38095 0.0395 0.0197 10 40 36.281 0.0376 0.0376 34.554 0.0358 0.0537 1040 855611 08871 1.7741 964.540 0000 1852 10 BZero-coupon 0.5 000 00000 0.0000 0.000 0.0000 0.0000 315 0.000 0.0000 0.0000 4201002202 1.0000 2.0000 822.702 1.0000 2.0000 16 Semiannual int rate: 0.05 T 18 Weight =Present value of each payment column E) divided by the bond price
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久期/价格关系 Duration/Price Relationship 价格变化与久期成比例而与到期日无关 Price change is proportional to duration and not to maturity △PP=-DX[△(1+y)/(1+y) D’=修正久期 modified duration D=D/(1+y) △PP=-Dx△y 16-10
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