1) Expected Return and Standard deviation This problem will give you some practice calculating measures of prospective portfolio performance There are two assets and three states of the economy:

State of Probability of Rate of Return if State Occurs

Economy State of Economy Stock A Stock B

Recession. 20 -.15 .20

Normal. 50 .20 .30

Boom. 30 .60 .40

What are the expected returns and standard deviation for these two stocks?

2

Portfolio risk and and return

Using the information in the previous problem, suppose you have the $20,000 total. If you put $15,000 into Stock A and the remainder in Stock B, what will be the expected return, and standard deviation of your portfolio?

3

Risk and return suppose you observe the following situation:

Security Beta Expected Return

Cooley, Inc 1.8% 22%

Moyer Co. 1.6% 20.44

If the risk-free rate is 7 percent , are the securities correctly priced? What would the risk-free rate have to be if they are correctly priced?

I am having trouble with the questions 2 and 3 but this is what I have for question 1

Total Investments = $20,000

Investment in Stock A = $15,000

Investment in Stock B = $5,000

Calculation of Weights of Portfolio

Weight of Stock A in portfolio = $15,000 / $20,000 = 0.75

Weight of Stock B in portfolio = $5,000 / $20,000 = 0.25

Calculation of Covariance of Stock A & Stock B

RA & RB = Return of Stock A & Stock B respectively in different economic scenario

ER(A) & ER(B) = Expected Return of Stock A & Stock B respectively

COV(A,B) = 0.20 * (-0.15 - 0.25)(0.20 - 0.31) + 0.50 * (0.20 - 0.25)(0.30 - 0.31) + 0.30 * (0.60 - 0.25)(0.40 - 0.31)

COV(A,B) = 0.0088 + 0.00025 + 0.00945

COV(A,B) = 0.0185

a) Calculation of Expected Return of portfolio

where, ER(A) & ER(B) = Expected Return of Stock A & Stock B respectively

WA & WB = Weight of Stock A & Stock B respectively

ERp = 0.25*0.75 +0.31*0.25

ERp = 0.265 or 26.5%

b) Calculation of Standard Deviation of portfolio

where, = Standard Deviation of Stock A & Stock B

WA & WB = Weight of Stock A & Stock B

COV(A,B) = Covariance of Stock A & Stock B

0.2159138 or 21.59%