NO.PZ2016031001000119
问题如下：
Which of the following statements about duration is correct?
选项：
A.A bond’s coupon rate and duration are positively related.
B.A bond’s duration is inversely related to its yield-to-maturity.
C.The Macaulay duration of a zero-coupon bond is less than its time-to-maturity.
解释：
B is correct.
A bond’s yield-to-maturity is inversely related to its duration: The higher the yield-to-maturity, the lower its duration and the lower the interest rate risk.
A bond’s coupon rate is inversely related to its duration. Zero-coupon bonds do not pay periodic coupon payments; therefore, the Macaulay duration of a zero-coupon bond is its time-to-maturity.
考点：Properties of Duration
解析：coupon rate越大，代表期间现金流越多，也就是前期的现金流较多，还款更快，duration越小，呈反向关系，故A选项不正确。
YTM和duration的变化情况，可以从斜率或一阶导出发去考虑。折现率越大，斜率的绝对值越小（duration代表斜率的绝对值），所以利率越大，duration越小。两者是反向关系。故选项B正确。
Macaulay duration衡量的是现金流的平均还款期（现金流到账时间），而零息债券只有一笔现金流，所以其macaulay duration就等于它的time-to-maturity，故选项C不正确。
YTM和duration的变化情况，可以从斜率或一阶导出发去考虑。折现率越大，斜率的绝对值越小（duration代表斜率的绝对值），所以利率越大，duration越小。两者是反向关系。
YTM和duration的关系能不能用其他的理解角度再解释一下，不是很能理解这个斜率一阶导的角度
