(Please show your detailed work)
- 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?
- 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?
- 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?
- 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?
- Please explain why and how diversification reduces portfolio risk. (Preferably use graph and mathematic expressions to elaborate).