4. Solve the following problems:

i. The market and Stock J have the following probability distributions:

Probability	rM	rJ
0.3	15%	20%
0.4	9%	5%
0.3	18%	12%

Calculate the expected rates of return for the market and Stock J.

ii. Suppose rRF = 5%, rM = 10%, and rA = 12%

a. Calculate Stock As beta.

b. If Stock As beta were 2.0, then what would be As new required rate of return?

iii. Your retirement fund consists of a $5,000 investment in each of 15 different common stocks. The portfolios beta is 1.20. Suppose you sell one of the stocks with a beta of 0.8 for $5,000 and use the proceeds to buy another stock whose beta is 1.6. Calculate your portfolios new beta.

iiii. Suppose you manage a $4 million fund that consists of four stocks with the following investments:

Stock	Investment	Beta
A	$400,000	1.50
B	$600,000	0.50
C	$1,000,000	1.25
D	$2,000,000	0.75

If the markets required rate of return is 14% and the risk-free rate is 6%, what is the funds required rate of return?