Suppose returns on a stock are lognormally distributed with expected (annualized)mean of of 0.10 and standard deviation of 0.20.What is the expected continuously compounded return on the stock for one month?
A)0.100%
B)0.333%
C)0.833%
D)1.667%

Question

Quizplus · Accepted Answer

The expected continuously compounded return can be calculated using the formula for the expected return in a lognormal distribution, which is $ \mu + \frac{\sigma^2}{2} $, where $ \mu $ is the mean and $ \sigma $ is the standard deviation. However, since these are annual figures and we need a monthly return, we divide the annual mean by 12 and adjust the variance accordingly. The calculation is $ \frac{0.10}{12} + \frac{(0.20)^2}{2} $, which simplifies to approximately 0.833% per month.

Suppose Returns on a Stock Are Lognormally Distributed with Expected