The following table lists possible rates of return on Company A and B.

State of the Economy Probability Company A Company B

Deep recession 0.05 -20% -30%

Mild recession 0.25 10 5

Average 0.35 15 20

Mild boom 0.20 20 25

Strong boom 0.15 25 30

(a) Based on the above data calculate by using the appropriate formulae

i. the standard deviations of returns for Company A and B          

ii. the covariance of returns between Company A and B

iii. the correlation between Company A and B

(b) If you wish to diversify risk would it be advisable to form a portfolio of both securities A and B? State your reasons. (No computations are required to answer this part of the question.)

(c) Find the minimum variance one can get by forming a portfolio of A and B. Short-selling either stock is allowed – i.e., weights need not be all positive.