久期/价格关系 Duration/Price Relationship 为了确定久期和债券价格对利率变化的敏感性之间的关系,让 我们将表163中久期为18853年的2年期息票债券的价格敏 感性和久期与期限同为18853年的零息票债券的价格敏感性相 比较。如果久期真是测度利率风险暴露程度的有用尺度的话, 两者应当具有相同的价格敏感性 初验半和%的是要债养售价为9454差元如果债券 的价格将会跌至96419美 降了00359%。零息票债券 的期限为18853X2=3.7706个半年期(由于我们用的是5%的 半年利率,我们也需要以半年为单位来定义久期以保证单位的 致性)。半年利字最初为5%,它将以8319623美元(00 美元/05706)的价格出 利率上涨一个基点时,它的价 格将跌至8316636美元,资本同样损失了00359%。由此我们 可以得出结论,久期相等的资产对利率波动的敏感性实际是 样的 16-11
16-11
久期/价格关系 Duration/Price Relationship To confirm the relationship between duration and the sensitivity of bond price to interest rate changes, let's compare the price sensitivity of the two. ear coupon bond in Table 16. 3, which has a duration of 1.8852 years, to the sensitivity of a zero-coupon bond with maturity and duration of 1. 8852 years. Both should have equal price sensitivity if duration is a useful measure of interest rate exposure The coupon bond sells for $964 5405 at the initial semiannual interest rate of 5% if the bond's semiannual yield increases by 1 basis point(i. e. .01%) to 5.01%, its price will fall to $964. 1942, a percentage decline of. 0359% The zero-coupon bond has a matur rity of 1. 8852*2=3.7704 half-year periods. ( Because we use a half-year interest rate of 5%, we also need to define duration in terms of a number of half-year periods to maintain consistency of units. At the initial half-year interest rate of 5%, it sells at a rice of $831.9704 ($1, 000/1.053.7704. When the interest rate increases,its price falls to $831.6717($1,00011.05013.7704),for an identical. 0359% capital loss. We conclude, therefore, that equal-duration assets are in fact equally sensitive to interest rate movements 16-12
16-12
久期/价格关系 Duration/Price Relationship 不同债券价格对市场利率变动的敏感性 不一样。债券久期是衡量这种敏感性最重 要和最主要的标准。久期等于利率变动 个单位所引起的价格变动。如市场利率变 动1%,债券的价格变动3,则久期是3 16-13
16-13
久期法则 Rules for duration 久期法则1:零息票债券的久期等于它的到期时间 Rule 1 The duration of a zero-coupon bond equals its time to maturity 久期法则2:到期日不变时,债券的久期随着息票利 率的降低而延长。 Rule 2 Holding maturity constant, a bond's duration is higher when the coupon rate is lower
16-14