For question 1, the suggested format is a table along the lines of the stock statistics-appendix in the lecture notes.

1. Population statistics: (All calculations in question 1 should be calculated using population statistics formulas):

The possible returns on stock X and the market portfolio, M, over the next year are:

Prob r r

	X	M
0.25	0.02	0.03
0.40	0.16	0.10
0.35	0.23	0.32

A. Calculate the expected returns on stock X and on M.

B. Calculate the covariance between stock X and M.

C. Calculate the correlation between stock X and M.

D. You have a portfolio with net worth $100,000 where of the wealth is invested in stock X and the remainder is in stock M; what is the expected return and standard deviation of this portfolio?

E. Vary the portfolio weight, W_x , invested in portfolio X between -1 (i.e., short selling $100,000 of X, and investing $200,000 in M) and 2 (i.e., investing

$200,000 in X, and short selling $100,000 in M). Plot a graph with the standard deviation of returns on the x-axis and expected returns on the y-axis, for the

portfolio, as a function of the portfolio weights: 1 W_x 2.

F. Are there any portfolio weights (in E.) that no investor would ever choose?

G. Is there a portfolio weight (in E.) that every investor should choose?