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MGMT 136 - Assignment 3 –Fall, 2002
1.Assume the expected rates of return and standard deviations of return for the stocks, Adolph Coors and Pepsico, were as follows: (Note that the returns, standard deviations, and correlation coefficient were based on actual returns during the period, 1991 - 2000.)
Expected Rate of Return Standard Deviation of Returns
Adolph Coors 21.6% 35.9%
Pepsico 16.3% 22.3%
The correlation coefficient between the returns of Adolph Coors and Pepsico is .44.
Now, suppose you purchase $5,000 of Adolph Coors, purchase $2,000 of Pepsico, and borrow $2,000 at a certain rate of interest of 7.0%. If these transactions constitute your entire portfolio:
a)What are the “portfolio weights” for each component of the portfolio?
b)Compute the variance and expected rate of return of the portfolio.
2.Assume the following data have been generated by a security analyst: (Note: The following data were based on actual returns during the period, 1991 - 2000).
Expected ReturnStandard Deviation
Anheuser Busch.202.213
General Mills.107.193
Home Depot.435.613
Johnson & Johnson.235.244
Matrix of Correlation Coefficients:
Anheuser General Home Johnson &
Busch Mills Depot Johnson
Anheuser Busch1.0 .70 .47 .74
General Mills 1.0 .49 .63
Home Depot 1.0 .47
Johnson & Johnson 1.0
A portfolio is formed as follows: Sell short $300,000 of General Mills, buy $300,000 of Anheuser Busch, buy $600,000 of Home Depot, and buy $500,000 of Johnson & Johnson. The cash provided by the owner of the portfolio is $1,000,000, and any additional funds required to finance the portfolio are borrowed at an interest rate of 7 percent. There are no restrictions on the use of short sale proceeds.
a)Compute the portfolio weights for each component of the portfolio.
b)Compute the expected return of the portfolio.
c)Compute the standard deviation of the portfolio.
3.The following information has been provided: (Note: The following data were based on actual returns during the period, 1991 - 2000).
McGraw Hill Nike
Expected Return (%) 20.9 28.8
Standard Deviation (%) 20.5 47.0
The correlation coefficient between McGraw Hill and Nike is estimated to be - .35.
Compute the expected returns and standard deviations of each of the following portfolios of McGraw Hill and Nike. Also, plot the individual securities and the portfolios on a graph with expected return and standard deviation on the axes.
Weight of McGraw Hill Weight of Nike
Portfolio 1 -.50 1.50
Portfolio 2 .25 .75
Portfolio 3 .75 .25
Portfolio 4 1.50 -.50
4.The following information has been provided: (Note: The following data were based on actual returns during the period, 1991 - 2000).
Anheuser Busch Merck & Co.
Expected Return (%) 20.2 27.7
Standard Deviation (%) 21.3 37.2
The correlation coefficient between Anheuser Busch and Merck & Co. is estimated to be +.85. Compute the expected returns and standard deviations of each of the following portfolios of Anheuser Busch and Merck & Co. Also, plot the individual securities and the portfolios on a graph with expected return and standard deviation on the axes.
Weight of Anheuser BuschWeight of Merck & Co.
Portfolio 11.60 -.60
Portfolio 2 .70 .30
Portfolio 3-.50 1.50
5.Consider two stocks with the following characteristics:
Stock AStock B
Expected Return .12 .23
Standard Deviation .16 .35
Suppose you build a portfolio by buying $3,000 of Stock A, and $7,000 of Stock B. Compute the expected return and variance of returns of the portfolio under each of the following assumptions about the correlation coefficient between the returns on Stocks A and B:
a)Correlation coefficient = +1.00
b)Correlation coefficient = 0
c)Correlation coefficient = -1.00