Portfolio Management

Portfolio Management

Fall 2014

Use the data below to solve problems 1-8

				Security
		A		B	C		D

Expected Return		14%		16%	12%		13%
Variance		0.766		0.735	0.563		0.353
Beta		1.05		1.2	0.9		0.95
			Security
	A		B			C	D
A	0.766
B	0%		0.735
C	0.236		0.27			0.563
D	0.249		0.285			0.214	0.95

1- Calculate the proportions of Security A and Security B that represent the minimum variance portfolio.

2- What is the Beta of equally weighted portfolio of the 4 securities?

3- Assume that the market portfolio variance is 0.25 and the unsystematic risk is equal to zero, what is the variance for the portfolio you constructed in problem 2

4- What is the expected return and variance of a theoretical portfolio made up of the following long and short position in stocks A ,B, and C.

30% short A

50 % long B

80% long C

5- Assume that securities C and D are well-diversified portfolios, suppose market variance changes to 0.32. What is the covariance between C and D.

6- A security has a variance of return of 25% what is the standard deviation of its returns.

7- Calculate the correlation between securities B and C.

8- Given Beta 1 is 1.10, beta 2 is 1.25, and the covariance between 1 and 2 is 1.55, find the variance of the market.

9- If there are 1700 stock in an index, how many covariance would have to be computed to use the Markowitz full co-variances Model.

		Security
	A	B

Expected Return	12%	13%
standard deviation	0.021	0.029
Beta	1.1	1.2

10- Suppose the risk free rate is 8% . what is the expected return and variance of a portfolio contains 50% of the risk free rate and 50% security B ( use the above table) ?would you hold the portfolio?

11- A portfolio with beta of 1 has an expected return of 14%, the risk free interest rate is 7%. Show that the expected return of a portfolio with a Beta of 2 is not 28%.

12- A portfolio has a variance of 0.26. Xyz stock has a variance of 0.20; the correlation between xyz and the portfolio is 0.79. Will the inclusion of xyz in the portfolio will reduce its risk.

13- Consider the following information

Stock prices $46.69

Current dividends 1.98

Future dividends growth 5.5%

Beta 1.1

30 days T Bill rate 2.55%

Equity risk premium 8.2%

For this stock you want to set a buy limit at 90%of the intrinsic value of the stock as determined using the DDM model. What should the price be.

10 years ago

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