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# FIN 322 – Summer 1998 PAGE 2 FIN 205 - Efficient Frontier (Risk and Return) Professor A. Spieler The following table (Table 1) represents CLOSING prices for America Online (AOL), Anheuser Busch (BUD),...

FIN 322 – Summer 1998
PAGE
2
FIN 205 - Efficient Frontier (Risk and Return)
Professor A. Spiele
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 4x4 table.
(b) Verify that covariance between the asset and itself is equal to its variance (there may be some rounding e
or).
(c) Verify that the co
elation between all pairs of assets falls in the range [-1,1]. Verify that the co
elation 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(w1X + w2Y) = w12VAR(X) + w22VAR(Y) +2w1w2COV(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. COV(0, you must use following formula:
VAR (w1X + w2Y + w3Z + w4W) =
w12VAR(X) + w22VAR(Y) + w32VAR(Z) + w42VAR(W) +2 w1 w2COV(X,Y) + 2 w1 w3COV(X,Z) + 2 w1 w4COV(X,W) + 2 w2 w3COV(Y,Z) + 2 w2w4COV(Y,W) +2 w3w4COV(Z,W),
where w1, w2, w3, and w4 are a
itrary constants. Note: w1 + w2 + w3 + w4 = 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:
(a) Equally-weighted portfolio
(b) The single-security portfolios (#1- #4)
(c) The minimum variance portfolio
(d) 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
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
Numbe
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
Answered Same Day Jun 08, 2021

## Solution

Neenisha answered on Jun 10 2021
EFFICIENT FRONTIER ASSIGNMENT
Part 1(a)
Monthly Returns od stocks

DATE
AOL
BUD
KO
TWA
06/01/99
-3.25%
-2.65%
-10.13%
-4.82%
05/03/99
-16.46%
-0.08%
0.64%
-4.60%
04/01/99
-2.89%
-3.94%
10.90%
4.82%
03/01/99
65.28%
-0.73%
-3.91%
-12.63%
02/01/99
1.21%
8.49%
-2.20%
25.01%
01/04/99
13.29%
7.72%
-2.52%
-2.56%
12/01/98
77.16%
8.25%
-4.37%
-4.88%
11/02/98
37.49%
1.89%
3.70%
2.50%
10/01/98
14.11%
10.19%
17.25%
-12.10%
09/01/98
36.23%
15.51%
-11.52%
-14.14%
08/03/98
-30.04%
-9.77%
-19.10%
-20.31%
07/01/98
11.42%
9.80%
-5.85%
-19.87%
06/01/98
26.18%
2.72%
9.09%
0.00%
05/01/98
4.22%
0.27%
3.29%
7.09%
04/01/98
17.02%
-0.94%
-2.02%
-21.32%
03/02/98
12.56%
-1.33%
12.84%
-5.74%
02/02/98
26.93%
4.31%
5.98%
12.37%
01/02/98
5.66%
2.13%
-2.91%
15.52%
12/01/97
20.67%
1.88%
6.70%
33.06%
11/03/97
-2.60%
8.14%
10.38%
1.68%
10/01/97
2.07%
-11.49%
-7.17%
-5.55%
09/02/97
16.95%
5.87%
6.43%
7.68%
08/01/97
-4.44%
-0.73%
-17.09%
5.41%
07/01/97
21.36%
2.38%
1.65%
-18.98%
06/02/97
0.90%
-2.19%
-0.73%
-1.44%
05/01/97
22.16%
0.00%
7.66%
19.83%
04/01/97
6.17%
3.94%
14.13%
4.50%
03/03/97
13.33%
-7.30%
-8.61%
18.09%
02/03/97
1.36%
4.71%
5.40%
-8.74%
01/02/97
11.28%
6.25%
9.98%
-1.90%
12/02/96
-5.67%
-5.60%
2.93%
-15.32%
11/01/96
29.93%
10.06%
1.24%
-3.13%
10/01/96
-23.59%
1.99%
-0.74%
-16.88%
09/03/96
17.38%
-0.33%
1.75%
-27.36%
08/01/96
-0.84%
1.34%
6.67%
23.26%
07/01/96

Part 1(b)

AOL
BUD
KO
TWA
Variance
4.36%
0.33%
0.69%
2.04%
Standard Deviation
20.89%
5.78%
8.33%
14.28%
Part 1 (c)
Expected Return is the Return which is expected over the risk free return when adjusted for the Risk undertaken. These are the returns which are expected by the investor over the risk free return based on the risk undertaken. Realized Return are the actual returns realized for the asset. These are the returns which are calculated after the actual prices of the stock prices.
Risk Free Return =
0.33%

Realized Return
Expected Return...
SOLUTION.PDF