why inverse, shoud be positive, question error

问题如下：

When it comes to the Macaulay duration of a bond, which of the following is not true?

选项：

A.

It is inversely related with the bond's yield-to-maturity.

B.

It is usually inversely related with the bond's time-to-maturity.

C.

For a zero-coupon bond, its macaulay duration equals to its maturity.

解释：

B is correct.

A bond's Macaulay duration is usually positively related with its time-to-maturity. The longer the time-to-maturity, the higher the Macaulay duration. Zero-coupon bond only has one payment at the time of maturity, thus its Macaulay duration is equal to its time-to-maturity.

考点：Properties of Duration

解析：A选项：麦考利久期的权重是每一笔现金流的现值所占的权重。YTM越大，折现回来的现值就越小，这样一来加权平均就越小，duration越小，呈反向关系，故选项A正确。

B选项：麦考利久期与债券期限呈正向关系。债券期限越长，麦考利久期越长。故选项B说法不正确，当选。

C选项：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正确。