Problems based on Normal Distribution
Stock Returns: Consider the monthly stock in a pharmaceutical manufacturer in decades after WW2. The average monthly return was 1.4%, with a standard deviation of 6.0%.
1. Without further information about the returns, what assumptions do you want to make to be able to play "what if" games, such as those in the b., c. and d. below? Can you formulate some reservations about the assumptions?
2. Making the assumptions of a., what fraction of months did the stock drop 10% or more? Re-express your result in an intuitive form such as "one in 10 months".
3. What fraction of months did the same stock increase by at least 10%? How does this frequency compare with the frequency of dropping by at least 10%? Is this because of the mean or due to the sd of the returns?
4. What is the chance that the stock will fall by more than 15% next month? What additional assumption are you making while answering this problem?