MGMT 136 - Assignment 1 - Fall, 1996



MGMT 136 - Assignment 5 – Fall, 2002

1. Given the following information, which was generated using 1991 - 2000 returns, and the assumption of the Single Factor Model, what is the covariance between AT&T and Home Depot?

Beta coefficient of AT&T 0.56

Beta coefficient of Home Depot 1.16

Standard deviation of the Market (NASDAQ) .338

2. Assume the following:

Adolph Coors has a residual variance of .120, and AT&T has a residual variance of .064. The covariance between the residuals of Adolph Coors and AT&T is .042. Assume that a portfolio of Adolph Coors and AT&T is constructed with a 30 percent weight for Adolph Coors, and a 70 percent weight for AT&T.

a) What is the residual variance of the portfolio if the Single Factor Model is assumed?

b) What is the residual variance of the portfolio without the Single Factor Model assumption?

3. The following data were generated using 1991 - 2000 annual returns:

Stock Beta Total Variance Residual Variance

General Mills 0.244 .0372 .0358

IBM 1.140 .1459 .1155

Suppose that a portfolio of General Mills and IBM is formed, with a weight of .35 for General Mills, and a weight of .65 for IBM.

a) What is the beta coefficient of the portfolio?

b) Compute the residual variance of the portfolio, assuming the Single Factor Model.

c) Compute the total variance of the portfolio assuming the Single Factor Model.

4. Using 1991 - 2000 annual returns the following variances and correlation coefficients were generated for the two stocks, McGraw Hill and Safeway. In addition, the variance of the market index (S&P 500) was .023.

Correlation Coefficient Between

Stock Total Variance the Stock and the Market (S&P 500)

McGraw Hill .0419 .77

Safeway .1870 .07

a) What is the beta coefficient of each stock?

b) Calculate the systematic risk of each stock.

c) Calculate the unsystematic risk of each stock.

d) Compare and contrast the stock correlation coefficients with the stocks’ levels of systematic risk.

5. The following data were generated using historical returns during the period, 1991 - 2000:

Standard deviation of Sears Roebuck .342

Standard deviation of Microsoft .560

Standard deviation of the market index (S&P 500) .153

Correlation coefficient between Sears Roebuck .18

and the market index

Correlation coefficient between Microsoft .72

and the market index

Correlation coefficient between Sears Roebuck and -.145

Microsoft

a) What are the beta values for Sears Roebuck and Microsoft?

b) What is the covariance between Sears Roebuck and Microsoft assuming the Single Factor Model?

c) What is the true covariance between Sears Roebuck and Microsoft?

d) Suppose a portfolio is constructed with weights of 1.25 for Sears Roebuck, and -.25 for Microsoft. What is the beta coefficient of this portfolio?

e) Compute the variance of the portfolio in part (d) above, assuming the Markowitz Model.

f) Compute the variance of the portfolio in part (d) above, assuming the Single Factor Model.

6. A two-factor model is being employed, one being an inflation index (I), and the other being an index of unexpected changes in the growth of industrial production (g). In addition, the following information is provided:

Stock Inflation Beta Growth Beta Residual Variance

1 .30 .15 .04

2 .90 .85 .02

Variance of the inflation index .08

Variance of the growth index .05

Covariance between the residuals of stocks 1 and 2 .03

Covariance between (I) and (g) 0

a) Compute the variance of stock 1.

b) Assume you constructed a portfolio of stocks 1 and 2 with weights of .35 for stock 1, and .65 for stock 2. Compute the residual variance of this portfolio two ways:

i. Making the simplifying assumption of the two-factor model about residual covariance.

ii. Without making the simplifying assumption about residual covariance.

c) Compute the inflation beta and the growth beta for the portfolio constructed in part (b) above.

d) For the portfolio of stocks 1 and 2 constructed in part (b) above, compute the variance of the portfolio in two ways:

i. Making the simplifying assumption of the two-factor model about residual covariance.

ii. Without making the simplifying assumption about residual covariance.

7. This problem involves the following data for the market index and the three stocks indicated:

| |Market Index |Home Depot | | |

|Year |(S&P 500) |161.6 |Merck & Co |Nike |

|1991 |30.48 |50.3 |88.9 |13.4 |

|1992 |7.62 |-22.0 |-20.3 |11.0 |

|1993 |10.06 |16.5 |-18.3 |14.2 |

|1994 |1.32 |3.8 |14.9 |2.3 |

|1995 |37.53 |5.0 |76.6 |34.4 |

|1996 |22.95 |76.2 |23.9 |9.0 |

|1997 |33.35 |108.0 |35.6 |64.4 |

|1998 |28.58 |69.0 |41.3 |41.0 |

|1999 |21.04 |-33.3 |-7.5 |22.4 |

|2000 |-9.10 | |41.8 |-3.6 |

a) Using annual returns from 1991 through 2000 for the three stocks above, construct the efficient set of 10 portfolios according to the Markowitz Mean-Variance Model. (Note: The market index is not used in this part of the analysis). Assume no constraint on short sales. For purposes of this problem, the first 10 portfolios generated by the program are sufficient (i.e., no recalculations are necessary).

b) Using annual returns from 1991 through 2000 for the three stocks and the market index above, construct the efficient set of 10 portfolios according to the Single Factor Model. Also, as in part (a) above, assume no constraint on short sales, and the first 10 portfolios generated are sufficient with no recalculations necessary.

c) On one graph, plot both of the efficient sets obtained in parts (a) and (b) above in mean return - standard deviation space. When plotting the Single Factor Model efficient set, plot return against the single index model’s estimate of standard deviation (indicated SI .S.D. in the program).

d) Briefly discuss the implications of the graph in part (c) above.

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

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

Google Online Preview   Download