1) Stock Returns: Consider monthly stock in the pharmaceutical manufacturer in decades after WW2. Average monthly return was 1.4%, with the standard deviation of 6.0%.
Without additional information about returns, what suppositions 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 prepare some reservations about suppositions ?
Making the suppositions of a., what fraction of months did stock drop 10% or more? Express your result in the intuitive form such as “one in 10 months”.
What fraction of months did same stock increase by at least 10%? How does this frequency compare with the frequency of dropping by at least 10%? Is this due to the mean or due to the sd of the returns?
What is the chance that the stock will fall by more than 15% next month? What additional suppositions are you making when answering this problem?
2) ABC Company wishes to study the number of credit applications received per day for the last 300 days. The information is reported on the next page.
Number of Credit Applications Frequency (Number of Days)
0 50
1 77
2 81
3 48
4 31
5 or more 13
To interpret, there were 50 days on which no credit applications were received, 77 days on which only one application was received, and so on. Will it be reasonable to conclude that population distribution is Poisson with the mean of 2.0? Use.05 significance level. Hint: To determine the expected frequencies use Poisson distribution with the mean of 2.0. Determine the probability of exactly one success given Poisson distribution with a mean of 2.0. Multiply this probability by 300 to determine the expected frequency for the number of days in which there was exactly one application. Find out the expected frequency for the other days in a similar manner.