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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),...

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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
Answers the questions
iefly and to the point. Summarize your answers
iefly 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
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
143 Votes
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...
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