Assume the annual returns of Fund A are normally distributed with a mean and standard deviation of 30%. The annual returns of Fund B are also normally distributed, but with a mean and standard deviation of 40%. The returns of both funds are independent of each other. What is the mean and standard deviation of the difference of the returns of the two funds, Fund B minus Fund A? At the end of the year, Fund B has returned 80%, and Fund A has lost 12%. How likely is it that Fund B outperforms Fund A by this much or more?
Answer: Because the annual returns of both funds are normally distributed and independent, the difference in their returns is also normally distributed: ~( − , + ) The mean of this distribution is 10%, and the standard deviation is 50%. At the end of the year, the difference in the expected returns is 92%. This is 82% above the mean, or 1.64 standard deviations. Using Excel or consulting the table of confidence levels in the chapter, we see that this is a rare event. The probability of more than a 1.64 standard deviation event is only 5%.
Can someone explain how 50% s.d is calculated in the answer?
Answer: Because the annual returns of both funds are normally distributed and independent, the difference in their returns is also normally distributed: ~( − , + ) The mean of this distribution is 10%, and the standard deviation is 50%. At the end of the year, the difference in the expected returns is 92%. This is 82% above the mean, or 1.64 standard deviations. Using Excel or consulting the table of confidence levels in the chapter, we see that this is a rare event. The probability of more than a 1.64 standard deviation event is only 5%.
Can someone explain how 50% s.d is calculated in the answer?
