**Question 779** mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:

###r_\text{t monthly}=\ln \left( \dfrac{P_t}{P_{t-1}} \right)###He then took the arithmetic average and found it to be **0.8**% per month using this formula:

He also found the standard deviation of these monthly returns which was **15**% per month:

Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is **NOT** correct?