You are allocating money equally among 400 stocks. You believe:

i.                    All stocks have the same levels of standard deviation at 40%;

ii.                  All stocks have the same pair-wise correlation

a.       What is the standard deviation of a portfolio of 400 equally weighted stocks if the correlation is 0.0? (1 point)

b.       What is the standard deviation of a portfolio of 400 equally weighted stocks if the correlation is 0.8? (1 point)

c.       If you observe from the option market that the implied volatility of 35% for individual stock, but 21% for the 400 equally weight portfolio, what is the implied pair-wise correlation between stocks? (2 points)