Assume the annual mean return on ABC stock is around 15% and the annual standard deviation is around 25%. Assume the annual and daily returns on ABC stock are normally distributed.
a. What is the probability that ABC will lose money during a year?
b. There is a 5% chance that ABC will earn a return of at least what value during a year?
c. There is a 10% chance that ABC will earn a return of less than or equal to what value during a year?
d. What is the probability that ABC will earn at least 35% during a year?
e. Assume there are 252 trading days in a year. What is the probability that ABC will lose money on a given day? (Hint: Let Y be the annual return on ABC and Xi be the return on ABC on day i. Then [approximately] Y = X1 + X2 +...+ X252.)