Investors remember 1987 as the year stocks lost 20% of their value in a single day. For 1987 as a whole, the mean return of all common stocks on the New York Stock Exchange was μ = -4%. (That is, these stocks lost an average of -4%. of their value in 1987.) The standard deviation of returns was about σ = 29%.
(a) What are the mean and the standard deviation of the distribution of 6-stock portfolios in 1987.
μ = %
σ = %
(b) Assuming that the population distribution of returns on individual common stocks is normal, what is the probability that a randomly chosen stock showed a return of at least 3% in 1987?
(c) Assuming that the population distribution of returns on individual common stocks is normal, what is the probability that a randomly chosen portfolio of 4 stocks showed a return of at least 3% in 1987?
(d) What percentage of 4-stock portfolios lost money in 1987?