The following table (Table 1) represents CLOSING prices for America Online (AOL), Anheuser Busch (BUD), Coca-Cola (KO), and TransWorld Airlines (TWA). Assume the return on a Treasury Bill is 4% per year (.33% per month). Clearly indicate your answers by underlining or putting them in a box.

The data in Tables 1 and 2 can be downloaded in spreadsheet form from the class Blackboard site.

AUTONUM \* Arabic (a) Calculate the MONTHLY returns for each asset (AOL, BUD, KO, TWA).

(b) Calculate the variance and standard deviation of RETURNS for each asset (AOL, BUD, KO, TWA) over the 36-month period from 7/96-6/99.

(c) Comment on the difference between expected return and realized return.

(d) Find the total return over the 36-month period for each stock. Which stock had the highest and lowest returns? Was this expected? Are these results consistent with the general risk-return relationship?

(e) Are these the actual closing prices or prices adjusted for changes in capitalization, i.e. stock splits, etc.? How do you know?

AUTONUM \* Arabic (a) Calculate the COVARIANCE and CORRELATION matrix for all pairs. Display your answers in a 4×4 table.

(b) Verify that covariance between the asset and itself is equal to its variance (there may be some rounding error).

(c) Verify that the correlation between all pairs of assets falls in the range [-1,1]. Verify that the correlation with an asset and itself is 1.

(d) Do all assets move together? Interpret your results.

AUTONUM \* Arabic Graph the Capital Allocation Line for BUD and the risk-free asset. Extend the line past the 100% investment in BUD, i.e. short the risk-free asset. How do you interpret a weight in the risk-free < 0%?

AUTONUM \* Arabic (a) Graph the Efficient Frontier for only 2 assets, AOL and TWA. Use the formula

VAR(w_{1}X + w_{2}Y) = w_{1}^{2}VAR(X) + w_{2}^{2}VAR(Y) +2w_{1}w_{2}COV(X,Y).

(b) What is the Minimum Variance portfolio? Identify by weight in each asset to the nearest 0.1%

AUTONUM \* Arabic Verify that the portfolio weights (in Table 2) sum to 1 for EACH of the 50 portfolios.

AUTONUM \* Arabic Calculate the Expected Return for each of the 50 portfolios.

AUTONUM \* Arabic Calculate the Variance and Standard Deviation for each portfolio. Since the assets are not independent, i.e. COV¹0, you must use following formula:

VAR (w_{1}X + w_{2}Y + w_{3}Z + w_{4}W) =

w_{1}^{2}VAR(X) + w_{2}^{2}VAR(Y) + w_{3}^{2}VAR(Z) + w_{4}^{2}VAR(W) +2 w_{1} w_{2}COV(X,Y) + 2 w_{1} w_{3}COV(X,Z) + 2 w_{1} w_{4}COV(X,W) + 2 w_{2} w_{3}COV(Y,Z) + 2 w_{2}w_{4}COV(Y,W) +2 w_{3}w_{4}COV(Z,W),

where w_{1}, w_{2, }w_{3}, and w_{4} are arbitrary constants. Note: w_{1} + w_{2 }+ w_{3} + w_{4} = 1.

AUTONUM \* Arabic Plot all the portfolios and identify the Efficient Frontier. List ALL portfolios that lie on the Efficient Frontier.

AUTONUM \* Arabic Identify the following portfolios by number:

Equally-weighted portfolio

The single-security portfolios (#1- #4)

The minimum variance portfolio

The “market” portfolio for the 4 securities (ignore the single security portfolios #1-#4). Hint: To identify the market portfolio, use the slope, i.e. Sharpe Ratio

AUTONUM \* Arabic Plot the CAL using the Treasury Bill. For this question, assume the annual T-bill rate is 12% to make the graph easier to read.

**Presentation**

Answers the questions briefly and to the point. Summarize your answers briefly in word file and email your actual spreadsheet,. Remember to circle or underline your final answers.

**Table 1**

Monthly closing prices for the AOL, BUD, KO, and TWA from July 1996 through June 1999.

DATE | AOL | BUD | KO | TWA |

6/1/99 | 115.375 | 71.125 | 61.563 | 4.938 |

5/3/99 | 119.250 | 73.063 | 68.500 | 5.188 |

4/1/99 | 142.750 | 73.125 | 68.063 | 5.438 |

3/1/99 | 147.000 | 76.125 | 61.375 | 5.188 |

2/1/99 | 88.938 | 76.688 | 63.875 | 5.938 |

1/4/99 | 87.875 | 70.688 | 65.313 | 4.750 |

12/1/98 | 77.563 | 65.625 | 67.000 | 4.875 |

11/2/98 | 43.781 | 60.625 | 70.063 | 5.125 |

10/1/98 | 31.844 | 59.500 | 67.563 | 5.000 |

9/1/98 | 27.906 | 54.000 | 57.625 | 5.688 |

8/3/98 | 20.484 | 46.750 | 65.125 | 6.625 |

7/1/98 | 29.281 | 51.813 | 80.500 | 8.313 |

6/1/98 | 26.281 | 47.188 | 85.500 | 10.375 |

5/1/98 | 20.828 | 45.938 | 78.375 | 10.375 |

4/1/98 | 19.984 | 45.813 | 75.875 | 9.688 |

3/2/98 | 17.078 | 46.250 | 77.438 | 12.313 |

2/2/98 | 15.172 | 46.875 | 68.625 | 13.063 |

1/2/98 | 11.953 | 44.938 | 64.750 | 11.625 |

12/1/97 | 11.313 | 44.000 | 66.688 | 10.063 |

11/3/97 | 9.375 | 43.188 | 62.500 | 7.563 |

10/1/97 | 9.625 | 39.938 | 56.625 | 7.438 |

9/2/97 | 9.430 | 45.125 | 61.000 | 7.875 |

8/1/97 | 8.063 | 42.625 | 57.313 | 7.313 |

7/1/97 | 8.438 | 42.938 | 69.125 | 6.938 |

6/2/97 | 6.953 | 41.938 | 68.000 | 8.563 |

5/1/97 | 6.891 | 42.875 | 68.500 | 8.688 |

4/1/97 | 5.641 | 42.875 | 63.625 | 7.250 |

3/3/97 | 5.313 | 41.250 | 55.750 | 6.938 |

2/3/97 | 4.688 | 44.500 | 61.000 | 5.875 |

1/2/97 | 4.625 | 42.500 | 57.875 | 6.438 |

12/2/96 | 4.156 | 40.000 | 52.625 | 6.563 |

11/1/96 | 4.406 | 42.375 | 51.125 | 7.750 |

10/1/96 | 3.391 | 38.500 | 50.500 | 8.000 |

9/3/96 | 4.438 | 37.750 | 50.875 | 9.625 |

8/1/96 | 3.781 | 37.875 | 50.000 | 13.250 |

7/1/96 | 3.813 | 37.375 | 46.875 | 10.750 |

**Table 2**

Portfolio weights for 50 random portfolios | ||||

Portfolio Number | AOL | BUD | KO | TWA |

1 | 1.00 | 0.00 | 0.00 | 0.00 |

2 | 0.00 | 1.00 | 0.00 | 0.00 |

3 | 0.00 | 0.00 | 1.00 | 0.00 |

4 | 0.00 | 0.00 | 0.00 | 1.00 |

5 | 0.25 | 0.25 | 0.25 | 0.25 |

6 | 0.50 | 0.50 | 0.00 | 0.00 |

7 | 0.50 | 0.00 | 0.50 | 0.00 |

8 | 0.50 | 0.00 | 0.00 | 0.50 |

9 | 0.00 | 0.50 | 0.50 | 0.00 |

10 | 0.00 | 0.50 | 0.00 | 0.50 |

11 | 0.00 | 0.00 | 0.50 | 0.50 |

12 | 0.16 | 0.27 | 0.49 | 0.08 |

13 | 0.12 | 0.47 | 0.33 | 0.08 |

14 | 0.21 | 0.30 | 0.18 | 0.31 |

15 | 0.46 | 0.35 | 0.45 | -0.26 |

16 | 0.39 | 0.24 | 0.02 | 0.35 |

17 | 0.36 | 0.20 | 0.18 | 0.26 |

18 | 0.27 | 0.44 | 0.24 | 0.05 |

19 | 0.20 | 0.33 | 0.49 | -0.02 |

20 | 0.28 | 0.50 | 0.00 | 0.22 |

21 | 0.06 | 0.19 | 0.35 | 0.40 |

22 | 0.36 | 0.32 | 0.12 | 0.20 |

23 | 0.23 | 0.46 | 0.24 | 0.07 |

24 | 0.48 | 0.19 | 0.37 | -0.04 |

25 | 0.00 | 0.34 | 0.25 | 0.40 |

26 | 0.38 | 0.25 | 0.03 | 0.34 |

27 | 0.21 | 0.34 | 0.42 | 0.02 |

28 | -0.55 | 0.80 | 0.36 | 0.39 |

29 | 0.37 | -0.02 | 0.41 | 0.24 |

30 | 0.22 | 0.25 | 0.21 | 0.33 |

31 | 0.47 | -0.10 | 0.28 | 0.36 |

32 | -0.14 | 0.49 | 0.17 | 0.48 |

33 | 0.45 | 0.01 | 0.29 | 0.25 |

34 | 0.04 | 0.21 | 0.44 | 0.31 |

35 | 0.18 | 0.23 | 0.41 | 0.19 |

36 | 0.35 | 0.10 | 0.49 | 0.06 |

37 | 0.02 | 0.16 | 0.42 | 0.40 |

38 | 0.33 | 0.33 | 0.12 | 0.22 |

39 | 0.35 | 0.37 | 0.34 | -0.06 |

40 | 0.26 | 0.14 | 0.35 | 0.26 |

41 | 0.18 | 0.13 | 0.27 | 0.42 |

42 | 0.48 | 0.07 | 0.16 | 0.28 |

43 | 0.45 | 0.17 | 0.24 | 0.14 |

44 | 0.41 | -0.23 | 0.50 | 0.32 |

45 | 0.43 | 0.04 | 0.03 | 0.50 |

46 | -0.01 | 0.44 | 0.36 | 0.21 |

47 | 0.07 | 0.65 | 0.21 | 0.07 |

48 | 0.22 | 0.02 | 0.31 | 0.46 |

49 | 0.38 | 0.41 | -0.15 | 0.36 |

50 | 0.08 | 0.40 | 0.32 | 0.20 |

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