fundamentals of finance - asset expected return exercise...
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Asset expected return – Exercise 1
Exercise 1
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A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1. In cell J1, calculate the sum of the asset weights.
J1: = SUM(D1:H1)
1.000
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1. In cell J1, calculate the sum of the asset weights.
J1: = SUM(D1:H1)
1.000
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1. In cell J1, calculate the sum of the asset weights.
J1: = SUM(D1:H1)
1.000
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
2. Set the values of the asset weights in cells B4:B8 equal to the values in cells D1:H1.
B4: = D1
0.200
B5: = E1
0.200
B6: = F1
0.200
B7: = G1
0.200
B8: = H1
0.200
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
3. Calculate the return contribution wiE(Ri ) of each of the assets in cells D10:H10.
D10: = D1*D2
0.016
Copy D10 to E10:H10.
0.021 0.024 0.015 0.017
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
3. Calculate the return contribution wiE(Ri ) of each of the assets in cells D10:H10.
D10: = D1*D2
0.016
Copy D10 to E10:H10.
0.021 0.024 0.015 0.017
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
3. Calculate the return contribution wiE(Ri ) of each of the assets in cells D10:H10.
D10: = D1*D2
0.016
Copy D10 to E10:H10.
0.021 0.024 0.015 0.017
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
3. Calculate the return contribution wiE(Ri ) of each of the assets in cells D10:H10.
D10: = D1*D2
0.016
Copy D10 to E10:H10.
0.021 0.024 0.015 0.017
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
3. Calculate the return contribution wiE(Ri ) of each of the assets in cells D10:H10.
D10: = D1*D2
0.016
Copy D10 to E10:H10.
0.021 0.024 0.015 0.017
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017
4. In cell J10, calculate the expected return of the portfolio as the sum of the return contributions.
J10: = SUM(D10:H10)
0.094
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017
4. In cell J10, calculate the expected return of the portfolio as the sum of the return contributions.
J10: = SUM(D10:H10)
0.094
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017
4. In cell J10, calculate the expected return of the portfolio as the sum of the return contributions.
J10: = SUM(D10:H10)
0.094
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
5. Calculate the risk contribution5∑
i=1
wiwjσij = wj
5∑i=1
wiσij of each of the assets in cells D11:H11.
D11: = D1*($B4*D4+$B5*D5+$B6*D6+$B7*D7+$B8*D8)
0.007
Copy D11 to E11:H11.
0.008 0.010 0.006 0.005
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
5. Calculate the risk contribution5∑
i=1
wiwjσij = wj
5∑i=1
wiσij of each of the assets in cells D11:H11.
D11: = D1*($B4*D4+$B5*D5+$B6*D6+$B7*D7+$B8*D8)
0.007
Copy D11 to E11:H11.
0.008 0.010 0.006 0.005
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
5. Calculate the risk contribution5∑
i=1
wiwjσij = wj
5∑i=1
wiσij of each of the assets in cells D11:H11.
D11: = D1*($B4*D4+$B5*D5+$B6*D6+$B7*D7+$B8*D8)
0.007
Copy D11 to E11:H11.
0.008 0.010 0.006 0.005
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
5. Calculate the risk contribution5∑
i=1
wiwjσij = wj
5∑i=1
wiσij of each of the assets in cells D11:H11.
D11: = D1*($B4*D4+$B5*D5+$B6*D6+$B7*D7+$B8*D8)
0.007
Copy D11 to E11:H11.
0.008 0.010 0.006 0.005
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
5. Calculate the risk contribution5∑
i=1
wiwjσij = wj
5∑i=1
wiσij of each of the assets in cells D11:H11.
D11: = D1*($B4*D4+$B5*D5+$B6*D6+$B7*D7+$B8*D8)
0.007
Copy D11 to E11:H11.
0.008 0.010 0.006 0.005
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005
6. In cell J11, calculate the return variance of the portfolio as the sum of the risk contributions.
J11: = SUM(D11:H11)
0.036
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005
6. In cell J11, calculate the return variance of the portfolio as the sum of the risk contributions.
J11: = SUM(D11:H11)
0.036
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005
6. In cell J11, calculate the return variance of the portfolio as the sum of the risk contributions.
J11: = SUM(D11:H11)
0.036
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
7. In cell J12, calculate the volatility of the portfolio as the square root of the return variance.
J12: = SQRT(J11)
0.191
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
7. In cell J12, calculate the volatility of the portfolio as the square root of the return variance.
J12: = SQRT(J11)
0.191
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
7. In cell J12, calculate the volatility of the portfolio as the square root of the return variance.
J12: = SQRT(J11)
0.191
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
8. In cell B14, calculate the Sharpe’s ratio of the portfolio.
B14: = (J10-B13)/J12
0.336
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
8. In cell B14, calculate the Sharpe’s ratio of the portfolio.
B14: = (J10-B13)/J12
0.336
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
8. In cell B14, calculate the Sharpe’s ratio of the portfolio.
B14: = (J10-B13)/J12
0.336
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
0.336
9. Apply Data/Analysis/Solver to identify the minimum variance portfolio with the non-negativity constraint.
Set Objective: $J$11 Objective: Min
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
0.336
9. Apply Data/Analysis/Solver to identify the minimum variance portfolio with the non-negativity constraint.
Set Objective: $J$11
Objective: Min
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
0.336
9. Apply Data/Analysis/Solver to identify the minimum variance portfolio with the non-negativity constraint.
Set Objective: $J$11 Objective: Min
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
0.336
9. Apply Data/Analysis/Solver to identify the minimum variance portfolio with the non-negativity constraint.
Set Objective: $J$11 Objective: Min
By Changing Variable Cells: $D$1:$H$1
Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
0.336
9. Apply Data/Analysis/Solver to identify the minimum variance portfolio with the non-negativity constraint.
Set Objective: $J$11 Objective: Min
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
0.336
9. Apply Data/Analysis/Solver to identify the minimum variance portfolio with the non-negativity constraint.
Set Objective: $J$11 Objective: Min
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative
Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.200 0.200 0.200 0.200 0.200
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.200
0.200
0.200
0.200
0.200
0.016 0.021 0.024 0.015 0.017 0.094
0.007 0.008 0.010 0.006 0.005 0.036
0.191
0.336
9. Apply Data/Analysis/Solver to identify the minimum variance portfolio with the non-negativity constraint.
Set Objective: $J$11 Objective: Min
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.231 0.096 0.115 0.197 0.361
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.231
0.096
0.115
0.197
0.361
0.019 0.010 0.014 0.015 0.031 0.089
0.008 0.003 0.004 0.006 0.012 0.033
0.181
0.324
9. Apply Data/Analysis/Solver to identify the minimum variance portfolio with the non-negativity constraint.
Set Objective: $J$11 Objective: Min
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.231 0.096 0.115 0.197 0.361
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.231
0.096
0.115
0.197
0.361
0.019 0.010 0.014 0.015 0.031 0.089
0.008 0.003 0.004 0.006 0.012 0.033
0.181
0.324
10. Apply Data/Analysis/Solver to identify the tangent portfolio with the non-negativity constraint.
Set Objective: $B$14 Objective: Max
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.231 0.096 0.115 0.197 0.361
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.231
0.096
0.115
0.197
0.361
0.019 0.010 0.014 0.015 0.031 0.089
0.008 0.003 0.004 0.006 0.012 0.033
0.181
0.324
10. Apply Data/Analysis/Solver to identify the tangent portfolio with the non-negativity constraint.
Set Objective: $B$14
Objective: Max
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.231 0.096 0.115 0.197 0.361
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.231
0.096
0.115
0.197
0.361
0.019 0.010 0.014 0.015 0.031 0.089
0.008 0.003 0.004 0.006 0.012 0.033
0.181
0.324
10. Apply Data/Analysis/Solver to identify the tangent portfolio with the non-negativity constraint.
Set Objective: $B$14 Objective: Max
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.231 0.096 0.115 0.197 0.361
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.231
0.096
0.115
0.197
0.361
0.019 0.010 0.014 0.015 0.031 0.089
0.008 0.003 0.004 0.006 0.012 0.033
0.181
0.324
10. Apply Data/Analysis/Solver to identify the tangent portfolio with the non-negativity constraint.
Set Objective: $B$14 Objective: Max
By Changing Variable Cells: $D$1:$H$1
Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.231 0.096 0.115 0.197 0.361
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.231
0.096
0.115
0.197
0.361
0.019 0.010 0.014 0.015 0.031 0.089
0.008 0.003 0.004 0.006 0.012 0.033
0.181
0.324
10. Apply Data/Analysis/Solver to identify the tangent portfolio with the non-negativity constraint.
Set Objective: $B$14 Objective: Max
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.231 0.096 0.115 0.197 0.361
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.231
0.096
0.115
0.197
0.361
0.019 0.010 0.014 0.015 0.031 0.089
0.008 0.003 0.004 0.006 0.012 0.033
0.181
0.324
10. Apply Data/Analysis/Solver to identify the tangent portfolio with the non-negativity constraint.
Set Objective: $B$14 Objective: Max
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative
Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.231 0.096 0.115 0.197 0.361
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.231
0.096
0.115
0.197
0.361
0.019 0.010 0.014 0.015 0.031 0.089
0.008 0.003 0.004 0.006 0.012 0.033
0.181
0.324
10. Apply Data/Analysis/Solver to identify the tangent portfolio with the non-negativity constraint.
Set Objective: $B$14 Objective: Max
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance
Asset expected return – Exercise 1
Exercise 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
A B C D E F G H I J
Asset weight
Asset expected return
Covariance matrix
Portfolio expected return
Portfolio return variance
Portfolio volatility
Risk-free rate
Sharpe’s ratio
0.136 0.232 0.206 0.115 0.313
0.082 0.105 0.122 0.076 0.085
0.08370 0.03358 0.02030 0.01982 0.01132
0.03358 0.09189 0.03226 0.02484 0.02132
0.02030 0.03226 0.18625 0.00252 0.00866
0.01982 0.02484 0.00252 0.09669 0.01826
0.01132 0.02132 0.00866 0.01826 0.06541
0.030
1.000
0.136
0.232
0.206
0.115
0.313
0.011 0.024 0.025 0.009 0.027 0.096
0.004 0.010 0.011 0.003 0.010 0.037
0.192
0.343
10. Apply Data/Analysis/Solver to identify the tangent portfolio with the non-negativity constraint.
Set Objective: $B$14 Objective: Max
By Changing Variable Cells: $D$1:$H$1 Subject to the Constraints: $J$1 = 1
Make Unconstrained Variables Non-Negative Solve
Jukka Perttunen Fundamentals of finance