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(Please show your detailed work)

2. Suppose that instead of buying XYZ shares (The initial margin is 60% and the maintenance margin is 40%), you short sold 1000 shares of XYZ at $250 per share on the margin. How far can the stock go up before you receive a margin call? 

3. Consider the following probability distribution for stocks A and B: 

State    Probability  Return on A  Return on B

1    0.25  7.5%  9%

2      0.40  10.5%  11%

3    0.35  13.5%  15.5%

1)  What are the expected rates of return of stocks A and B respectively?

2)  What are the variances and standard deviations of stocks A and B respectively?

3)  If you invest 35% of your money in A and 65% in B, what would be your portfolio’s expected rate of return and standard deviation? 

4. The universe of available securities includes two risky stock funds, A and B, and T-bills. The data are as follows:

Expected Return  Standard Deviation

 A  10%  18%

 B  15%  30%

 T-bills  3.25%  0

The correlation coefficient between A and B =0.45

1)  What is the covariance between funds A and B?

2)  Find the optimal risky portfolio, P, and its expected return and standard deviation.

3)  Find the slope of the CAL supported by T-bills and portfolio P.

4)  How much will an investor with A = 5 invest in funds A and B and in T-bills? 

   

5. Here are data for two companies. The T-bill rate is 2.25% and market risk premium is 7%. 

 Company      ABC      XYZ

Realized Return  13%  9%

Beta  1.3  0.95

1)  What would be the fair return for each company, according to the CAPM?

2)  Which company(s) is(are) underpriced and which company(s) is(are) overpriced? Why?

6. Please explain why and how diversification reduces portfolio risk. (Preferably use graph and mathematic expressions to elaborate).

2. Suppose that instead of buying XYZ shares (The initial margin is 60% and the maintenance margin is 40%), you short sold 1000 shares of XYZ at $250 per share on the margin. How far can the stock go up before you receive a margin call? (8’)

3. Consider the following probability distribution for stocks A and B: (12’)

State Probability Return on A Return on B

1 0.25 7.5% 9%

2 0.40 10.5% 11%

3 0.35 13.5% 15.5%

1) What are the expected rates of return of stocks A and B respectively?

2) What are the variances and standard deviations of stocks A and B respectively?

3) If you invest 35% of your money in A and 65% in B, what would be your portfolio’s expected rate of return and standard deviation? 

4. The universe of available securities includes two risky stock funds, A and B, and T-bills. The data are as follows: (16’)

Expected Return Standard Deviation

A 10% 18%

B 15% 30%

T-bills 3.25% 0

The correlation coefficient between A and B =0.45

1) What is the covariance between funds A and B?

2) Find the optimal risky portfolio, P, and its expected return and standard deviation.

3) Find the slope of the CAL supported by T-bills and portfolio P.

4) How much will an investor with A = 5 invest in funds A and B and in T-bills?

5. Here are data for two companies. The T-bill rate is 2.25% and market risk premium is 7%. (8’) Company ABC XYZ

Realized Return 13% 9%

Beta 1.3 0.95

1) What would be the fair return for each company, according to the CAPM?

2) Which company(s) is(are) underpriced and which company(s) is(are) overpriced? Why?

6. Please explain why and how diversification reduces portfolio risk. (Preferably use graph and mathematic expressions to elaborate). (10’)