MGMT 136 - Assignment 1 - Fall, 1996



MGMT 136 - Assignment 4 – Fall, 2002

1. Suppose there were two portfolios known to be in the minimum variance set for a universe of three stocks (Avon Products, Black & Decker, and Eastman Kodak). There are no restrictions on short sales. The weights for each of the two portfolios are as follows:

Stock Weights

Avon Products Black & Decker Eastman Kodak

Portfolio #1 -.5 .6 .9

Portfolio #2 1.2 .4 -.6

a) What would the stock weights be for a portfolio constructed by investing $3,000 in Portfolio #1, and $7,000 in Portfolio #2?

b) Would the new portfolio in part (a) be on the minimum variance set?

c) Suppose you combined the portfolio in part (a) with portfolio #2 to form yet another portfolio. Would this new portfolio be on the minimum variance set?

2. Suppose the expected returns on three stocks (Avon Products, Campbell Soup, and Mobil Corp.) are as follows:

Expected Return

Avon Products .30

Campbell Soup .14

Mobil Corp. .08

Find the equation of the iso-expected return line, which corresponds to a portfolio expected return of .22 for these three stocks. The line is to be expressed in terms of the weights on Campbell Soup and Mobil Corp.

3. Stocks A, B,and C, have the following covariance matrix:

A B C

A .25 .15 .17

B .15 .21 .09

C .17 .09 .28

Given a zero weight for stock A, find the weights of stocks B and C for the two portfolios that have a variance of .24.

4. Using annual returns for the period, 1991 - 2000, the following data were generated:

Charles Schwab Intel Walt Disney

Arithmetic Mean Return (%) 76.9 44.7 15.4

Standard Deviation (%) 89.3 45.6 20.1

Matrix of correlation coefficients:

Charles Schwab Intel Walt Disney

Charles Schwab 1.0 -.02 -.11

Intel 1.0 .23

Walt Disney 1.0

a) Using the Markowitz Mean-Variance program in the computer software package, input the above data for the three companies. With no constraint on short sales, obtain hard copy of the 10 portfolios generated in the efficient set.

b) After completing part (a) above, press F6 to return to the previous screen display. Now, obtain hard copy of the efficient set of 10 portfolios with no short sales allowed

c) On one graph plot (1) the 10 portfolios printed out in part (a) above in mean return, standard deviation space, and (2) the 10 portfolios printed out in part (b).

d) Compare and contrast the efficient set with no constraint on short sales with the efficient set when no short sales are allowed.

5. Using annual returns for the period, 1991 - 2000, the following data were generated:

AT&T Boeing Exxon Mobil Sears Roebuck

Mean Return (%) 5.5 15.6 13.8 21.8

Standard Deviation (%) 33.4 32.4 11.7 34.2

Matrix of correlation coefficients:

AT&T Boeing Exxon Mobil Sears Roebuck

AT&T 1.0 -.57 .26 .18

Boeing 1.0 .30 .31

Exxon Mobil 1.0 .28

Sears Roebuck 1.0

a) Using the Markowitz Mean-Variance program in the computer software package, construct the efficient set using the three stocks (1) AT&T, (2) Boeing and (3) Exxon Mobil. After viewing on the screen the first 10 portfolios that are generated with no restrictions on short sales, press F5 (the recalculation key), select a return of 25%, and obtain hard copy of the next 10 portfolios generated.

b) Using the Markowitz Mean-Variance program, construct the efficient set using all four of the stocks above. After viewing on the screen the first 10 portfolios generated with no restrictions on short sales, press F5, select a return of 25%, and obtain hard copy of the next 10 portfolios generated.

c) On one graph, plot both the 10 portfolios printed out in part (a), and the 10 portfolios printed out in part (b), in mean return - standard deviation space.

d) Compare and contrast the efficient set when three stocks were included in the analysis, with the efficient set when four stocks were included in the analysis.

6. Using annual returns for the period, 1991 - 2000, the following data were generated:

Microsoft Safeway Walmart

Mean Return (%) 49.1 43.3 30.7

Standard Deviation (%) 56.0 43.2 50.7

Matrix of correlation coefficients:

Microsoft Safeway Walmart

Microsoft 1.0 .01 .76

Safeway 1.0 -.10

Walmart 1.0

a) Use the Markowitz Mean-Variance program to construct an efficient set consisting of Microsoft, Safeway and Walmart. After viewing on the screen the first 10 portfolios that are generated with no constraint on short sales, press F5 (the recalculation key), select a return of 50%, and obtain hard copy of the next 10 portfolios generated. Plot this latter efficient on a graph in mean return - standard deviation space.

b) Plot the 10 portfolios from part (a) in XM, XS, space on a graph similar to that shown below. XM and XS are the weights of Microsoft and Safeway. The weights shown on the computer output are in percentage form. Convert these percentages to decimals prior to graphing. Draw in the critical line.

[pic]

c) Plot the 10 portfolios from part (a) in XS, XW, space on a graph similar to that shown below. XS and XW are the weights of Safeway and Walmart. Again, convert the weights from percentages to decimals prior to graphing, and draw in the critical line.

[pic]

d) What is the relationship between the critical lines drawn in parts (b) and (c), and the efficient set graphed in part (a)?

7. In the years, 1991 - 2000, Campbell Soup, General Electric and Walt Disney, produced the following percent rates of return:

|Year |Campbell Soup |General Electric |Walt Disney |

|1991 |47.7 |33.3 |13.5 |

|1992 |1.6 |11.8 |51.1 |

|1993 |-0.8 |22.7 |-0.3 |

|1994 |10.5 |-2.7 |8.7 |

|1995 |38.9 |41.2 |29.0 |

|1996 |36.6 |37.3 |19.1 |

|1997 |47.8 |48.4 |42.9 |

|1998 |0.0 |39.0 |-8.5 |

|1999 |-28.2 |51.7 |-1.4 |

|2000 |-7.8 |-6.5 |-0.4 |

a) Using the Markowitz Mean-Variance program, input the data above, and:

1. Print the output showing the expected returns, standard deviations, and correlation coefficients of the securities.

2. After viewing on the screen the first 10 portfolios that are generated with no constraint on short sales, press F5 (the recalculation key), select a return of 30%, and obtain hard copy of the next 10 portfolios generated.

b) Using portfolio #5 as the market index, the market’s annual rates of return in each of the ten years (1991 – 2000) are:

|Year |Portfolio 5 |

|1991 |25.224543 |

|1992 |21.637084 |

|1993 |26.869010 |

|1994 |-5.289191 |

|1995 |39.987478 |

|1996 |34.571235 |

|1997 |47.706217 |

|1998 |44.399082 |

|1999 |69.963098 |

|2000 |-5.068516 |

c) Given your ten annual returns for the market index (portfolio #5), and for each of the three stocks, run the Single-Factor Model program, which will compute beta coefficients for you. Print the chart showing expected return, standard deviation, beta. and residual standard deviation, of the market index and three stocks.

Notes: (1) When entering historical returns in the Single Factor Model program, the first column is used to enter the Market’s returns. (2) There is a little glitch in the program. When the chart showing expected return, standard deviation, beta, and residual standard deviation is displayed, the Market’s beta is shown to be 0.0000, This is obviously incorrect since the Market’s beta is 1.0.

d) Plot the relationship between mean return and beta. Label each of the points representing the three stocks and the market index (portfolio 5). Draw in the line connecting all four of the data points. If you have done your calculations correctly, your graph should prove Property II.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download