Background: 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.
Question: 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. This is a unique characteristic of normally distributed variables. The sum/difference of two normally distributed variables follows a normal distribution as well.)