continuously compounded return是默认m趋于无穷大的，即一年一直不断在复利吗？

NO.PZ2017092702000093

问题如下：

The weekly closing prices of Mordice Corporation shares are as follows:

The continuously compounded return of Mordice Corporation shares for the period August 1 to August 15 is closest to:

选项：

6.90%

7.14%

8.95%

解释：

A is correct.

The continuously compounded return of an asset over a period is equal to the natural log of period’s change. In this case: ln(120/112) = 6.90%

资产在一段时间内的连续复合回报等于期间变化的自然对数。在本题中：ln(120/112) = 6.90%

为什么不能直接用（1+r/m）^m=FV/PV 这样来算呢，这样算出来是答案B。

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1 个答案

星星_品职助教 · 2021年11月09日

同学你好，

（1+r/m）^m=FV/PV是离散情况下的公式，

而连续复利（continuously compounded）相当于每时每刻都在复利。此时需要对（1+r/m）^m求极限，过程不需要掌握，结果为（1+r/m）^m在连续复利的背景下等于e的r次方。

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continuously compounded return是默认m趋于无穷大的，即一年一直不断在复利吗？

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