Question
In: Finance
Week Date Apple Inc. (AAPL) McDonald's Corporation (MCD) Southwest Airlines Co. (LUV) S&P 500 Index (GSPC)...
| Week | Date | Apple Inc. (AAPL) | McDonald's Corporation (MCD) | Southwest Airlines Co. (LUV) | S&P 500 Index (GSPC) |
| 1 | 30-Oct-17 | ||||
| 2 | 6-Nov-17 | 1.2549% | -1.8187% | -1.1872% | -0.2141% |
| 3 | 13-Nov-17 | -2.2355% | 0.6847% | 2.2714% | -0.1336% |
| 4 | 20-Nov-17 | 2.8316% | 1.4330% | 0.7893% | 0.9140% |
| 5 | 27-Nov-17 | -2.2409% | 2.2269% | 8.6687% | 1.5293% |
| 6 | 4-Dec-17 | -0.9841% | 0.7554% | 5.6980% | 0.3512% |
| 7 | 11-Dec-17 | 2.7198% | 0.5289% | 2.3625% | 0.9168% |
| 8 | 18-Dec-17 | 0.5968% | -1.5205% | 1.9672% | 0.2814% |
| 9 | 25-Dec-17 | -3.3001% | 0.4109% | -0.7899% | -0.3626% |
| 10 | 1-Jan-18 | 3.4068% | 1.1225% | -1.7302% | 2.6010% |
| 11 | 8-Jan-18 | 1.1923% | -0.2775% | 1.6204% | 1.5708% |
| 12 | 15-Jan-18 | 0.7741% | 1.4668% | -0.4753% | 0.8635% |
| 13 | 22-Jan-18 | -3.8916% | 1.2742% | -6.5013% | 2.2265% |
| 14 | 29-Jan-18 | -6.4234% | -5.0327% | -3.4767% | -3.8547% |
| 15 | 5-Feb-18 | -2.5435% | -5.0677% | -5.4626% | -5.1620% |
| 16 | 12-Feb-18 | 10.6908% | -1.8712% | 5.0018% | 4.3011% |
| 17 | 19-Feb-18 | 1.7815% | 3.3355% | -0.4815% | 0.5519% |
| 18 | 26-Feb-18 | 0.4004% | -9.0662% | -0.3110% | -2.0402% |
| 19 | 5-Mar-18 | 2.1421% | 6.7192% | 3.2588% | 3.5418% |
| 20 | 12-Mar-18 | -1.0876% | 3.2562% | 2.2327% | -1.2402% |
| 21 | 19-Mar-18 | -7.3475% | -4.5455% | -6.8637% | -5.9502% |
| 22 | 26-Mar-18 | 1.7224% | 0.9033% | 0.9873% | 2.0326% |
| 23 | 2-Apr-18 | 0.3530% | 3.1142% | -3.4742% | -1.3783% |
| 24 | 9-Apr-18 | 3.7739% | 0.2977% | -0.3979% | 1.9900% |
| 25 | 16-Apr-18 | -5.1591% | -1.8302% | -0.5448% | 0.5210% |
| 26 | 23-Apr-18 | -2.0475% | -0.2960% | -2.2640% | -0.0086% |
| 27 | 30-Apr-18 | 13.2468% | 4.2514% | -1.4011% | -0.2431% |
| 28 | 7-May-18 | 2.5939% | 0.2181% | -0.6063% | 2.4142% |
(i) Generate a covariance and correlation matrix of these stocks. Interprete your results.
(ii) Compute the weekly rate of return and the variance of an equally weighted portfolio formed from the three stocks
(iii) Examine and compare the pattern of the returns of your portfolio with those of the individual stocks, and the stock index. Compare the corresponding variances. Comment on your observations
Solutions
Expert Solution
Ans 1) Covariance Matrix
Covariance matrix
| Apple Inc. (AAPL) | McDonald's Corporation(MCD) | Southwest Airlines Co. (LUV) | S&P 500 Index (GSPC) | |
| Apple Inc. (AAPL) | 1 | 0.000521292 | 0.000508845 | 0.0005781 |
| McDonald'sCorporation(MCD) | 0.00052129 | 1 | 0.000376826 | 0.00043445 |
| Southwest Airlines Co. (LUV) | 0.00050884 | 0.000376826 | 1 | 0.000461747 |
| S&P 500 Index (GSPC) | 0.0005781 | 0.00043445 | 0.000461747 | 1 |
Correlation matrix
| Apple Inc. (AAPL) | McDonald's Corporation(MCD) | Southwest Airlines Co. (LUV) | S&P 500 Index (GSPC) | |
| Apple Inc. (AAPL) | 1 | 0.358725793 | 0.323015812 | 0.542678636 |
| McDonald's Corporation(MCD) | 0.35872579 | 1 | 0.327911528 | 0.559057845 |
| Southwest Airlines Co. (LUV) | 0.32301581 | 0.327911528 | 1 | 0.548121937 |
| S&P 500 Index (GSPC) | 0.54267864 | 0.559057845 | 0.548121937 | 1 |
While looking at correlation matrix one can say that there is moderate positive correlation between stock and index and there is positive but less correlation between each stocks.
Ans 2) I find weekly rate of return using geometric mean which is given as follows:
| Weekly average return of the portfolio | 1+r | geometric mean return | Variance |
| -0.58% | 99.42% | 0.107% | 0.14% |
| 0.24% | 100.24% | ||
| 1.68% | 101.68% | ||
| 2.88% | 102.88% | ||
| 1.82% | 101.82% | ||
| 1.87% | 101.87% | ||
| 0.35% | 100.35% | ||
| -1.23% | 98.77% | ||
| 0.93% | 100.93% | ||
| 0.85% | 100.85% | ||
| 0.59% | 100.59% | ||
| -3.04% | 96.96% | ||
| -4.98% | 95.02% | ||
| -4.36% | 95.64% | ||
| 4.61% | 104.61% | ||
| 1.55% | 101.55% | ||
| -2.99% | 97.01% | ||
| 4.04% | 104.04% | ||
| 1.47% | 101.47% | ||
| -6.25% | 93.75% | ||
| 1.20% | 101.20% | ||
| 0.00% | 100.00% | ||
| 1.22% | 101.22% | ||
| -2.51% | 97.49% | ||
| -1.54% | 98.46% | ||
| 5.37% | 105.37% | ||
| 0.74% | 100.74% |
weekly rate of return of the portfolio is .107% and variance is .14%.
Ans 3)
| Week | Apple Inc. (AAPL) | McDonald's Corporation(MCD) | Southwest Airlines Co. (LUV) | S&P 500 Index (GSPC) |
| 1 | ||||
| 2 | 101.25% | 98.18% | 98.81% | 99.79% |
| 3 | 97.76% | 100.68% | 102.27% | 99.87% |
| 4 | 102.83% | 101.43% | 100.79% | 100.91% |
| 5 | 97.76% | 102.23% | 108.67% | 101.53% |
| 6 | 99.02% | 100.76% | 105.70% | 100.35% |
| 7 | 102.72% | 100.53% | 102.36% | 100.92% |
| 8 | 100.60% | 98.48% | 101.97% | 100.28% |
| 9 | 96.70% | 100.41% | 99.21% | 99.64% |
| 10 | 103.41% | 101.12% | 98.27% | 102.60% |
| 11 | 101.19% | 99.72% | 101.62% | 101.57% |
| 12 | 100.77% | 101.47% | 99.52% | 100.86% |
| 13 | 96.11% | 101.27% | 93.50% | 102.23% |
| 14 | 93.58% | 94.97% | 96.52% | 96.15% |
| 15 | 97.46% | 94.93% | 94.54% | 94.84% |
| 16 | 110.69% | 98.13% | 105.00% | 104.30% |
| 17 | 101.78% | 103.34% | 99.52% | 100.55% |
| 18 | 100.40% | 90.93% | 99.69% | 97.96% |
| 19 | 102.14% | 106.72% | 103.26% | 103.54% |
| 20 | 98.91% | 103.26% | 102.23% | 98.76% |
| 21 | 92.65% | 95.45% | 93.14% | 94.05% |
| 22 | 101.72% | 100.90% | 100.99% | 102.03% |
| 23 | 100.35% | 103.11% | 96.53% | 98.62% |
| 24 | 103.77% | 100.30% | 99.60% | 101.99% |
| 25 | 94.84% | 98.17% | 99.46% | 100.52% |
| 26 | 97.95% | 99.70% | 97.74% | 99.99% |
| 27 | 113.25% | 104.25% | 98.60% | 99.76% |
| 28 | 102.59% | 100.22% | 99.39% | 102.41% |
| geometric mean | 0.36% | -0.03% | -0.10% | 0.20% |
| Variance | 0.19% | 0.10% | 0.12% | 0.05% |
variance of portfolio is .14% which is greater than two stocks and index but less than Apple.
Similarly at the same time return is greater than two stocks but less than Apple and S&P 500 index. S&P 500 has best risk adjusted return and it is better than even our portfolio. So our portfolio is underperformed in comparision to S&P 500 index.
jeff jeffy answered 2 years agoRelated Solutions
Appendix 1.1: Table 1.1 - Weekly discrete rate of returns Week Date Apple Inc. (AAPL) McDonald's...
Appendix 1.1:
Table 1.1 - Weekly discrete rate of returns
Week
Date
Apple Inc. (AAPL)
McDonald's Corporation (MCD)
Southwest Airlines Co. (LUV)
S&P 500 Index (GSPC)
1
30-Oct-17
2
6-Nov-17
1.2549%
-1.8187%
-1.1872%
-0.2141%
3
13-Nov-17
-2.2355%
0.6847%
2.2714%
-0.1336%
4
20-Nov-17
2.8316%
1.4330%
0.7893%
0.9140%
5
27-Nov-17
-2.2409%
2.2269%
8.6687%
1.5293%
6
4-Dec-17
-0.9841%
0.7554%
5.6980%
0.3512%
7
11-Dec-17
2.7198%
0.5289%
2.3625%
0.9168%
8
18-Dec-17
0.5968%
-1.5205%
1.9672%
0.2814%
9
25-Dec-17
-3.3001%
0.4109%
-0.7899%
-0.3626%
10
1-Jan-18
3.4068%
1.1225%...
Appendix 1.1: Table 1.1 - Weekly discrete rate of returns Week Date Apple Inc. (AAPL) McDonald's...
Appendix 1.1:
Table 1.1 - Weekly discrete rate of returns
Week
Date
Apple Inc. (AAPL)
McDonald's Corporation (MCD)
Southwest Airlines Co. (LUV)
S&P 500 Index (GSPC)
1
30-Oct-17
2
6-Nov-17
1.2549%
-1.8187%
-1.1872%
-0.2141%
3
13-Nov-17
-2.2355%
0.6847%
2.2714%
-0.1336%
4
20-Nov-17
2.8316%
1.4330%
0.7893%
0.9140%
5
27-Nov-17
-2.2409%
2.2269%
8.6687%
1.5293%
6
4-Dec-17
-0.9841%
0.7554%
5.6980%
0.3512%
7
11-Dec-17
2.7198%
0.5289%
2.3625%
0.9168%
8
18-Dec-17
0.5968%
-1.5205%
1.9672%
0.2814%
9
25-Dec-17
-3.3001%
0.4109%
-0.7899%
-0.3626%
10
1-Jan-18
3.4068%
1.1225%...
Appendix 1.1: Table 1.1 - Weekly discrete rate of returns Week Date Apple Inc. (AAPL) McDonald's...
Appendix 1.1:
Table 1.1 - Weekly discrete rate of returns
Week
Date
Apple Inc. (AAPL)
McDonald's Corporation (MCD)
Southwest Airlines Co. (LUV)
S&P 500 Index (GSPC)
1
30-Oct-17
2
6-Nov-17
1.2549%
-1.8187%
-1.1872%
-0.2141%
3
13-Nov-17
-2.2355%
0.6847%
2.2714%
-0.1336%
4
20-Nov-17
2.8316%
1.4330%
0.7893%
0.9140%
5
27-Nov-17
-2.2409%
2.2269%
8.6687%
1.5293%
6
4-Dec-17
-0.9841%
0.7554%
5.6980%
0.3512%
7
11-Dec-17
2.7198%
0.5289%
2.3625%
0.9168%
8
18-Dec-17
0.5968%
-1.5205%
1.9672%
0.2814%
9
25-Dec-17
-3.3001%
0.4109%
-0.7899%
-0.3626%
10
1-Jan-18
3.4068%
1.1225%...
Appendix 1.1: Table 1.1 - Weekly discrete rate of returns Week Date Apple Inc. (AAPL) McDonald's...
Appendix 1.1:
Table 1.1 - Weekly discrete rate of returns
Week
Date
Apple Inc. (AAPL)
McDonald's Corporation (MCD)
Southwest Airlines Co. (LUV)
S&P 500 Index (GSPC)
1
30-Oct-17
2
6-Nov-17
1.2549%
-1.8187%
-1.1872%
-0.2141%
3
13-Nov-17
-2.2355%
0.6847%
2.2714%
-0.1336%
4
20-Nov-17
2.8316%
1.4330%
0.7893%
0.9140%
5
27-Nov-17
-2.2409%
2.2269%
8.6687%
1.5293%
6
4-Dec-17
-0.9841%
0.7554%
5.6980%
0.3512%
7
11-Dec-17
2.7198%
0.5289%
2.3625%
0.9168%
8
18-Dec-17
0.5968%
-1.5205%
1.9672%
0.2814%
9
25-Dec-17
-3.3001%
0.4109%
-0.7899%
-0.3626%
10
1-Jan-18
3.4068%
1.1225%...
The following historic data are available for the S&P 500 and AAPL:
The following historic data are available for the
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