Q. Stock A and B have the probability of returns for next year 

Economic condition   probability  return A%  return B%

BOOM                             0.1           20                  14

RECESSION                     0.4           -16                -20

NORMAL                         0.2            14                 18

RECOVERY                       0.1             9                  12

SLOW GROWTH              0.2              8                  10

Required 

a. calculate covariance and correlation of return of stock A and B.

b. risk of portfolio for a portfolio of 50% in each stock A and B.

Consider the following scenario analysis involving asset A and asset B:

a).Compute the expected returns and the standard deviation of returns for both assets. Then compute the correlation coefficient between the returns on the two assets.

b) Find the expected return and the standard deviation of the minimum variance portfolio of A and B, when short-selling is allowed.

This is a table about possible rates of return on Stock A and B:

The following data have been calculated:

SD(A) = 9.34%, SD(B) = 13.68%, Covariance between Stock A & B = 124.38%, Correlation between Stock A & B = 0.9735

(a) Would it be advisable to form a portfolio of both Stock A and B to diversify risk? Explain reasons in words.

(b) Short-selling either stock is allowed (ie. weights need not be all positive), find the minimun variance one can get by forming a portfolio of Stock A and B.