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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% -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%

(a) Extract for each week, the yield of the 26-week Treasury bill (or equivalently the 90 day or 180-day bank accepted bill from the financial media (i.e. Federal Reserve Bank: http://www.federalreserve.gov/default.htm) over your sample period. (Remember sometimes reported yields are usually annualised figures. Convert the yields to weekly numbers. Use these as a proxy for the risk free rate).

(b) Estimate the Security Characteristic Line (SCL) for each of your stocks and the equal weighted portfolio, based on the ‘Market Model’, using excess returns (discrete returns less the risk free rate), using Excel regression analysis functions. Show your results graphically. From your results, compute the Beta and the Jensen’s Alpha of each stock and the portfolio.

(c) Calculate the total risk (the return variance) of each stock and the portfolio. Partition the total risk to their respective systematic and unsystematic risk components.

(d) Based on your observations and results in parts (b) and (c) above, comment on each of your stock's and portfolio's performance, and on their risk characteristics, comparing and contrasting the magnitude and the proportions of their systematic and unsystematic risk components. What further insights can you gain on the characteristics and behaviour of your stocks and portfolio compared to the analysis and observations you made in Part 1 (c) and Part 2 (b)?

Solutions

Expert Solution

Answer a)

Weekly discrete rate of returns Treasury bill
Week Date Apple Inc. (AAPL) McDonald's Corporation (MCD) Southwest Airlines Co. (LUV) S&P 500 Index (GSPC) Date Annual 180-Day Bank Accepted Bill Rate Weekly 180-Day Bank Accepted Bill Rate
1 30-Oct-17 30-Oct-17
2 6-Nov-17 1.2549% -1.8187% -1.1872% -0.2141% 6-Nov-17 1.28% 0.00024615
3 13-Nov-17 -2.2355% 0.6847% 2.2714% -0.1336% 13-Nov-17 1.35% 0.00025962
4 20-Nov-17 2.8316% 1.4330% 0.7893% 0.9140% 20-Nov-17 1.43% 0.00027500
5 27-Nov-17 -2.2409% 2.2269% 8.6687% 1.5293% 27-Nov-17 1.39% 0.00026731
6 4-Dec-17 -0.9841% 0.7554% 5.6980% 0.3512% 4-Dec-17 1.42% 0.00027308
7 11-Dec-17 2.7198% 0.5289% 2.3625% 0.9168% 11-Dec-17 1.44% 0.00027692
8 18-Dec-17 0.5968% -1.5205% 1.9672% 0.2814% 18-Dec-17 1.48% 0.00028462
9 25-Dec-17 -3.3001% 0.4109% -0.7899% -0.3626% *25-Dec-17 1.49% 0.00028654
10 1-Jan-18 3.4068% 1.1225% -1.7302% 2.6010% *1-Jan-18 1.58% 0.00030385
11 8-Jan-18 1.1923% -0.2775% 1.6204% 1.5708% 8-Jan-18 1.57% 0.00030192
12 15-Jan-18 0.7741% 1.4668% -0.4753% 0.8635% *15-Jan-18 1.60% 0.00030769
13 22-Jan-18 -3.8916% 1.2742% -6.5013% 2.2265% 22-Jan-18 1.62% 0.00031154
14 29-Jan-18 -6.4234% -5.0327% -3.4767% -3.8547% 29-Jan-18 1.63% 0.00031346
15 5-Feb-18 -2.5435% -5.0677% -5.4626% -5.1620% 5-Feb-18 1.64% 0.00031538
16 12-Feb-18 10.6908% -1.8712% 5.0018% 4.3011% 12-Feb-18 1.78% 0.00034231
17 19-Feb-18 1.7815% 3.3355% -0.4815% 0.5519% *19-Feb-18 1.83% 0.00035192
18 26-Feb-18 0.4004% -9.0662% -0.3110% -2.0402% 26-Feb-18 1.83% 0.00035192
19 5-Mar-18 2.1421% 6.7192% 3.2588% 3.5418% 5-Mar-18 1.82% 0.00035000
20 12-Mar-18 -1.0876% 3.2562% 2.2327% -1.2402% 12-Mar-18 1.85% 0.00035577
21 19-Mar-18 -7.3475% -4.5455% -6.8637% -5.9502% 19-Mar-18 1.94% 0.00037308
22 26-Mar-18 1.7224% 0.9033% 0.9873% 2.0326% 26-Mar-18 1.90% 0.00036538
23 2-Apr-18 0.3530% 3.1142% -3.4742% -1.3783% 2-Apr-18 1.88% 0.00036154
24 9-Apr-18 3.7739% 0.2977% -0.3979% 1.9900% 9-Apr-18 1.89% 0.00036346
25 16-Apr-18 -5.1591% -1.8302% -0.5448% 0.5210% 16-Apr-18 1.94% 0.00037308
26 23-Apr-18 -2.0475% -0.2960% -2.2640% -0.0086% 23-Apr-18 1.99% 0.00038269
27 30-Apr-18 13.2468% 4.2514% -1.4011% -0.2431% 30-Apr-18 1.99% 0.00038269
28 7-May-18 2.5939% 0.2181% -0.6063% 2.4142% 7-May-18 2.00% 0.00038462

Equation for SCL , intercept = Alpha , Beta = systematic risk

Expeceted return of portfolio = W1R1 + W2R2 + W3R3

Similarly Variance of portfolio = W12S12 +  W22S22 + W32 S32 + 2.W1s1*W2S2* r12 + 2.W1s1*W3S3* r13+2.W2S2*W3S3r23

Where , w1,2,3 = weight of share in stock = 1/3 =0.33.

Answer B,C)

EXCESSIVE RETURN Table From ( Stcok return - Annual 180-Day Bank Accepted Bill Rate
eek Date Apple Inc. (AAPL) McDonald's Corporation (MCD) Southwest Airlines Co. (LUV) S&P 500 Index (GSPC) Porfolio return
1 30-Oct-17
2 6-Nov-17 -0.03% -3.10% -2.47% -1.49% -1.86%
3 13-Nov-17 -3.59% -0.67% 0.92% -1.48% -1.11%
4 20-Nov-17 1.40% 0.00% -0.64% -0.52% 0.24%
5 27-Nov-17 -3.63% 0.84% 7.28% 0.14% 1.47%
6 4-Dec-17 -2.40% -0.66% 4.28% -1.07% 0.38%
7 11-Dec-17 1.28% -0.91% 0.92% -0.52% 0.41%
8 18-Dec-17 -0.88% -3.00% 0.49% -1.20% -1.14%
9 25-Dec-17 -4.79% -1.08% -2.28% -1.85% -2.70%
10 1-Jan-18 1.83% -0.46% -3.31% 1.02% -0.66%
11 8-Jan-18 -0.38% -1.85% 0.05% 0.00% -0.73%
12 15-Jan-18 -0.83% -0.13% -2.08% -0.74% -1.02%
13 22-Jan-18 -5.51% -0.35% -8.12% 0.61% -4.63%
14 29-Jan-18 -8.05% -6.66% -5.11% -5.48% -6.56%
15 5-Feb-18 -4.18% -6.71% -7.10% -6.80% -5.95%
16 12-Feb-18 8.91% -3.65% 3.22% 2.52% 2.78%
17 19-Feb-18 -0.05% 1.51% -2.31% -1.28% -0.30%
18 26-Feb-18 -1.43% -10.90% -2.14% -3.87% -4.79%
19 5-Mar-18 0.32% 4.90% 1.44% 1.72% 2.18%
20 12-Mar-18 -2.94% 1.41% 0.38% -3.09% -0.40%
21 19-Mar-18 -9.29% -6.49% -8.80% -7.89% -8.13%
22 26-Mar-18 -0.18% -1.00% -0.91% 0.13% -0.71%
23 2-Apr-18 -1.53% 1.23% -5.35% -3.26% -1.88%
24 9-Apr-18 1.88% -1.59% -2.29% 0.10% -0.68%
25 16-Apr-18 -7.10% -3.77% -2.48% -1.42% -4.43%
26 23-Apr-18 -4.04% -2.29% -4.25% -2.00% -3.51%
27 30-Apr-18 11.26% 2.26% -3.39% -2.23% 3.32%
28 7-May-18 0.59% -1.78% -2.61% 0.41% -1.27%
By use of SCL regression
Alpha(intercept) 0.002030202 -0.00551 -0.00475 -0.00289
Beta(systematic risk) 0.982335468 0.758977 0.855848 0.857059
Standev 0.044332766 0.03258 0.03612 0.028025
Variance 0.001965394 0.001061 0.001305 0.000785
Unsystematic risk -0.9380027 -0.7264 -0.81973 -0.82903

Answer d)

It is very clear that portfolio return is higher than two stock MCD and LUV , but less than APPL and Index.

Similarly , Variance (risk) is less than all three individual stocks .

So, the portfolio is with moderate return and moderate risk category , but not able to cross the INDEX.


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