问一道题：NO.PZ2018120301000053 [ CFA III ]

Regression里面确实是用Benchmark interest rate回归的。

下面句子截自原版书：

Empirical duration is a measure of interest rate sensitivity that is determined from market data. A common way to calculate a bond's empirical duration is to run a regression of its price returns on changes in a benchmark interest rate.

因为衡量的是对Benchmark interest rate变动的敏感度，所以回归出来的Empirical duration是一个Curve duration数据，他只能和Effective duration相比，因为Effective duration也衡量的是对Benchmark interest rate变动的敏感度，也是Curve duration数据。

严格说是不能和Modified duration比，因为Modified duration是对YTM的敏感度，是一个Yield duration。

所以我们才有以下和Effective duration比大小的结论：

empirical duration is smaller than the theoretically based effective duration.

因为是Empirical duration和Effective duration相比，而实际的债券价格变动幅度又是小于计算Effective duration时的变动幅度的，所以Empirical duration自然比Effective duration要小。