Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Comcast Corp. common stock.
Rates of Return
Comcast Corp. (CMCSA) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceCMCSA,t1 | DividendCMCSA,t1 | RCMCSA,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2019 | $36.57 | 2,704.10 | ||||
1. | Feb 28, 2019 | $38.67 | 5.74% | 2,784.49 | 2.97% | |
2. | Mar 31, 2019 | $39.98 | 3.39% | 2,834.40 | 1.79% | |
3. | Apr 30, 2019 | $43.53 | $0.21 | 9.40% | 2,945.83 | 3.93% |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
58. | Nov 30, 2023 | $41.89 | 1.45% | 4,567.80 | 8.92% | |
59. | Dec 31, 2023 | $43.85 | 4.68% | 4,769.83 | 4.42% | |
Average (R): | 0.76% | 1.11% | ||||
Standard deviation: | 7.38% | 5.31% |
Comcast Corp. (CMCSA) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceCMCSA,t1 | DividendCMCSA,t1 | RCMCSA,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2019 | $36.57 | 2,704.10 | ||||
1. | Feb 28, 2019 | $38.67 | 5.74% | 2,784.49 | 2.97% | |
2. | Mar 31, 2019 | $39.98 | 3.39% | 2,834.40 | 1.79% | |
3. | Apr 30, 2019 | $43.53 | $0.21 | 9.40% | 2,945.83 | 3.93% |
4. | May 31, 2019 | $41.00 | -5.81% | 2,752.06 | -6.58% | |
5. | Jun 30, 2019 | $42.28 | 3.12% | 2,941.76 | 6.89% | |
6. | Jul 31, 2019 | $43.17 | $0.21 | 2.60% | 2,980.38 | 1.31% |
7. | Aug 31, 2019 | $44.26 | 2.52% | 2,926.46 | -1.81% | |
8. | Sep 30, 2019 | $45.08 | 1.85% | 2,976.74 | 1.72% | |
9. | Oct 31, 2019 | $44.82 | $0.21 | -0.11% | 3,037.56 | 2.04% |
10. | Nov 30, 2019 | $44.15 | -1.49% | 3,140.98 | 3.40% | |
11. | Dec 31, 2019 | $44.97 | 1.86% | 3,230.78 | 2.86% | |
12. | Jan 31, 2020 | $43.19 | $0.21 | -3.49% | 3,225.52 | -0.16% |
13. | Feb 29, 2020 | $40.43 | -6.39% | 2,954.22 | -8.41% | |
14. | Mar 31, 2020 | $34.38 | $0.23 | -14.40% | 2,584.59 | -12.51% |
15. | Apr 30, 2020 | $37.63 | 9.45% | 2,912.43 | 12.68% | |
16. | May 31, 2020 | $39.60 | 5.24% | 3,044.31 | 4.53% | |
17. | Jun 30, 2020 | $38.98 | $0.23 | -0.98% | 3,100.29 | 1.84% |
18. | Jul 31, 2020 | $42.80 | 9.80% | 3,271.12 | 5.51% | |
19. | Aug 31, 2020 | $44.81 | 4.70% | 3,500.31 | 7.01% | |
20. | Sep 30, 2020 | $46.26 | 3.24% | 3,363.00 | -3.92% | |
21. | Oct 31, 2020 | $42.24 | $0.23 | -8.19% | 3,269.96 | -2.77% |
22. | Nov 30, 2020 | $50.24 | 18.94% | 3,621.63 | 10.75% | |
23. | Dec 31, 2020 | $52.40 | 4.30% | 3,756.07 | 3.71% | |
24. | Jan 31, 2021 | $49.57 | $0.23 | -4.96% | 3,714.24 | -1.11% |
25. | Feb 28, 2021 | $52.72 | 6.35% | 3,811.15 | 2.61% | |
26. | Mar 31, 2021 | $54.11 | 2.64% | 3,972.89 | 4.24% | |
27. | Apr 30, 2021 | $56.15 | $0.25 | 4.23% | 4,181.17 | 5.24% |
28. | May 31, 2021 | $57.34 | 2.12% | 4,204.11 | 0.55% | |
29. | Jun 30, 2021 | $57.02 | -0.56% | 4,297.50 | 2.22% | |
30. | Jul 31, 2021 | $58.83 | $0.25 | 3.61% | 4,395.26 | 2.27% |
31. | Aug 31, 2021 | $60.68 | 3.14% | 4,522.68 | 2.90% | |
32. | Sep 30, 2021 | $55.93 | -7.83% | 4,307.54 | -4.76% | |
33. | Oct 31, 2021 | $51.43 | $0.25 | -7.60% | 4,605.38 | 6.91% |
34. | Nov 30, 2021 | $49.98 | -2.82% | 4,567.00 | -0.83% | |
35. | Dec 31, 2021 | $50.33 | 0.70% | 4,766.18 | 4.36% | |
36. | Jan 31, 2022 | $49.99 | $0.25 | -0.18% | 4,515.55 | -5.26% |
37. | Feb 28, 2022 | $46.76 | -6.46% | 4,373.94 | -3.14% | |
38. | Mar 31, 2022 | $46.82 | 0.13% | 4,530.41 | 3.58% | |
39. | Apr 30, 2022 | $39.76 | $0.27 | -14.50% | 4,131.93 | -8.80% |
40. | May 31, 2022 | $44.28 | 11.37% | 4,132.15 | 0.01% | |
41. | Jun 30, 2022 | $39.24 | -11.38% | 3,785.38 | -8.39% | |
42. | Jul 31, 2022 | $37.52 | $0.27 | -3.70% | 4,130.29 | 9.11% |
43. | Aug 31, 2022 | $36.19 | -3.54% | 3,955.00 | -4.24% | |
44. | Sep 30, 2022 | $29.33 | -18.96% | 3,585.62 | -9.34% | |
45. | Oct 31, 2022 | $31.74 | $0.27 | 9.14% | 3,871.98 | 7.99% |
46. | Nov 30, 2022 | $36.64 | 15.44% | 4,080.11 | 5.38% | |
47. | Dec 31, 2022 | $34.97 | -4.56% | 3,839.50 | -5.90% | |
48. | Jan 31, 2023 | $39.35 | $0.27 | 13.30% | 4,076.60 | 6.18% |
49. | Feb 28, 2023 | $37.17 | -5.54% | 3,970.15 | -2.61% | |
50. | Mar 31, 2023 | $37.91 | 1.99% | 4,109.31 | 3.51% | |
51. | Apr 30, 2023 | $41.37 | $0.29 | 9.89% | 4,169.48 | 1.46% |
52. | May 31, 2023 | $39.35 | -4.88% | 4,179.83 | 0.25% | |
53. | Jun 30, 2023 | $41.55 | 5.59% | 4,376.86 | 4.71% | |
54. | Jul 31, 2023 | $45.26 | $0.29 | 9.63% | 4,588.96 | 4.85% |
55. | Aug 31, 2023 | $46.76 | 3.31% | 4,507.66 | -1.77% | |
56. | Sep 30, 2023 | $44.34 | -5.18% | 4,288.05 | -4.87% | |
57. | Oct 31, 2023 | $41.29 | $0.29 | -6.22% | 4,193.80 | -2.20% |
58. | Nov 30, 2023 | $41.89 | 1.45% | 4,567.80 | 8.92% | |
59. | Dec 31, 2023 | $43.85 | 4.68% | 4,769.83 | 4.42% | |
Average (R): | 0.76% | 1.11% | ||||
Standard deviation: | 7.38% | 5.31% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of CMCSA during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RCMCSA,t | RS&P 500,t | (RCMCSA,t–RCMCSA)2 | (RS&P 500,t–RS&P 500)2 | (RCMCSA,t–RCMCSA)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 28, 2019 | 5.74% | 2.97% | 24.78 | 3.49 | 9.29 |
2. | Mar 31, 2019 | 3.39% | 1.79% | 6.88 | 0.47 | 1.80 |
3. | Apr 30, 2019 | 9.40% | 3.93% | 74.65 | 7.98 | 24.41 |
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. | . | . | . | . | . | . |
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58. | Nov 30, 2023 | 1.45% | 8.92% | 0.47 | 61.03 | 5.38 |
59. | Dec 31, 2023 | 4.68% | 4.42% | 15.32 | 11.00 | 12.98 |
Total (Σ): | 3,156.75 | 1,634.30 | 1,670.14 |
t | Date | RCMCSA,t | RS&P 500,t | (RCMCSA,t–RCMCSA)2 | (RS&P 500,t–RS&P 500)2 | (RCMCSA,t–RCMCSA)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 28, 2019 | 5.74% | 2.97% | 24.78 | 3.49 | 9.29 |
2. | Mar 31, 2019 | 3.39% | 1.79% | 6.88 | 0.47 | 1.80 |
3. | Apr 30, 2019 | 9.40% | 3.93% | 74.65 | 7.98 | 24.41 |
4. | May 31, 2019 | -5.81% | -6.58% | 43.26 | 59.04 | 50.54 |
5. | Jun 30, 2019 | 3.12% | 6.89% | 5.56 | 33.49 | 13.64 |
6. | Jul 31, 2019 | 2.60% | 1.31% | 3.37 | 0.04 | 0.38 |
7. | Aug 31, 2019 | 2.52% | -1.81% | 3.10 | 8.50 | -5.13 |
8. | Sep 30, 2019 | 1.85% | 1.72% | 1.18 | 0.37 | 0.67 |
9. | Oct 31, 2019 | -0.11% | 2.04% | 0.77 | 0.88 | -0.82 |
10. | Nov 30, 2019 | -1.49% | 3.40% | 5.11 | 5.28 | -5.19 |
11. | Dec 31, 2019 | 1.86% | 2.86% | 1.19 | 3.07 | 1.92 |
12. | Jan 31, 2020 | -3.49% | -0.16% | 18.11 | 1.61 | 5.40 |
13. | Feb 29, 2020 | -6.39% | -8.41% | 51.20 | 90.57 | 68.10 |
14. | Mar 31, 2020 | -14.40% | -12.51% | 229.83 | 185.44 | 206.45 |
15. | Apr 30, 2020 | 9.45% | 12.68% | 75.49 | 134.06 | 100.60 |
16. | May 31, 2020 | 5.24% | 4.53% | 19.98 | 11.71 | 15.30 |
17. | Jun 30, 2020 | -0.98% | 1.84% | 3.06 | 0.54 | -1.28 |
18. | Jul 31, 2020 | 9.80% | 5.51% | 81.63 | 19.40 | 39.79 |
19. | Aug 31, 2020 | 4.70% | 7.01% | 15.46 | 34.82 | 23.20 |
20. | Sep 30, 2020 | 3.24% | -3.92% | 6.11 | 25.29 | -12.43 |
21. | Oct 31, 2020 | -8.19% | -2.77% | 80.24 | 15.00 | 34.69 |
22. | Nov 30, 2020 | 18.94% | 10.75% | 330.31 | 93.10 | 175.36 |
23. | Dec 31, 2020 | 4.30% | 3.71% | 12.49 | 6.79 | 9.21 |
24. | Jan 31, 2021 | -4.96% | -1.11% | 32.80 | 4.93 | 12.71 |
25. | Feb 28, 2021 | 6.35% | 2.61% | 31.25 | 2.26 | 8.40 |
26. | Mar 31, 2021 | 2.64% | 4.24% | 3.50 | 9.85 | 5.87 |
27. | Apr 30, 2021 | 4.23% | 5.24% | 12.02 | 17.11 | 14.34 |
28. | May 31, 2021 | 2.12% | 0.55% | 1.83 | 0.31 | -0.75 |
29. | Jun 30, 2021 | -0.56% | 2.22% | 1.75 | 1.24 | -1.48 |
30. | Jul 31, 2021 | 3.61% | 2.27% | 8.11 | 1.37 | 3.33 |
31. | Aug 31, 2021 | 3.14% | 2.90% | 5.66 | 3.22 | 4.27 |
32. | Sep 30, 2021 | -7.83% | -4.76% | 73.84 | 34.37 | 50.38 |
33. | Oct 31, 2021 | -7.60% | 6.91% | 69.95 | 33.74 | -48.58 |
34. | Nov 30, 2021 | -2.82% | -0.83% | 12.85 | 3.76 | 6.95 |
35. | Dec 31, 2021 | 0.70% | 4.36% | 0.00 | 10.60 | -0.21 |
36. | Jan 31, 2022 | -0.18% | -5.26% | 0.89 | 40.51 | 6.01 |
37. | Feb 28, 2022 | -6.46% | -3.14% | 52.22 | 17.99 | 30.65 |
38. | Mar 31, 2022 | 0.13% | 3.58% | 0.41 | 6.11 | -1.57 |
39. | Apr 30, 2022 | -14.50% | -8.80% | 233.09 | 98.04 | 151.17 |
40. | May 31, 2022 | 11.37% | 0.01% | 112.43 | 1.21 | -11.67 |
41. | Jun 30, 2022 | -11.38% | -8.39% | 147.55 | 90.21 | 115.37 |
42. | Jul 31, 2022 | -3.70% | 9.11% | 19.89 | 64.09 | -35.71 |
43. | Aug 31, 2022 | -3.54% | -4.24% | 18.57 | 28.62 | 23.06 |
44. | Sep 30, 2022 | -18.96% | -9.34% | 388.89 | 109.11 | 205.99 |
45. | Oct 31, 2022 | 9.14% | 7.99% | 70.10 | 47.34 | 57.61 |
46. | Nov 30, 2022 | 15.44% | 5.38% | 215.30 | 18.23 | 62.65 |
47. | Dec 31, 2022 | -4.56% | -5.90% | 28.33 | 49.04 | 37.28 |
48. | Jan 31, 2023 | 13.30% | 6.18% | 157.06 | 25.70 | 63.53 |
49. | Feb 28, 2023 | -5.54% | -2.61% | 39.75 | 13.82 | 23.44 |
50. | Mar 31, 2023 | 1.99% | 3.51% | 1.50 | 5.76 | 2.94 |
51. | Apr 30, 2023 | 9.89% | 1.46% | 83.30 | 0.13 | 3.27 |
52. | May 31, 2023 | -4.88% | 0.25% | 31.90 | 0.74 | 4.84 |
53. | Jun 30, 2023 | 5.59% | 4.71% | 23.29 | 13.02 | 17.41 |
54. | Jul 31, 2023 | 9.63% | 4.85% | 78.54 | 13.99 | 33.14 |
55. | Aug 31, 2023 | 3.31% | -1.77% | 6.50 | 8.28 | -7.34 |
56. | Sep 30, 2023 | -5.18% | -4.87% | 35.29 | 35.73 | 35.51 |
57. | Oct 31, 2023 | -6.22% | -2.20% | 48.85 | 10.92 | 23.09 |
58. | Nov 30, 2023 | 1.45% | 8.92% | 0.47 | 61.03 | 5.38 |
59. | Dec 31, 2023 | 4.68% | 4.42% | 15.32 | 11.00 | 12.98 |
Total (Σ): | 3,156.75 | 1,634.30 | 1,670.14 |
Show all
VarianceCMCSA = Σ(RCMCSA,t–RCMCSA)2 ÷ (59 – 1)
= 3,156.75 ÷ (59 – 1)
= 54.43
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceCMCSA, S&P 500 = Σ(RCMCSA,t–RCMCSA)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,670.14 ÷ (59 – 1)
= 28.80
Systematic Risk (β) Estimation
VarianceCMCSA | 54.43 |
VarianceS&P 500 | 28.18 |
CovarianceCMCSA, S&P 500 | 28.80 |
Correlation coefficientCMCSA, S&P 5001 | 0.74 |
βCMCSA2 | 1.02 |
αCMCSA3 | -0.37% |
Calculations
1 Correlation coefficientCMCSA, S&P 500
= CovarianceCMCSA, S&P 500 ÷ (Standard deviationCMCSA × Standard deviationS&P 500)
= 28.80 ÷ (7.38% × 5.31%)
= 0.74
2 βCMCSA
= CovarianceCMCSA, S&P 500 ÷ VarianceS&P 500
= 28.80 ÷ 28.18
= 1.02
3 αCMCSA
= AverageCMCSA – βCMCSA × AverageS&P 500
= 0.76% – 1.02 × 1.11%
= -0.37%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.68% |
Expected rate of return on market portfolio2 | E(RM) | 13.78% |
Systematic risk (β) of Comcast Corp. common stock | βCMCSA | 1.02 |
Expected rate of return on Comcast Corp. common stock3 | E(RCMCSA) | 13.98% |
1 Unweighted average of bid yields on all outstanding fixed-coupon U.S. Treasury bonds neither due or callable in less than 10 years (risk-free rate of return proxy).
3 E(RCMCSA) = RF + βCMCSA [E(RM) – RF]
= 4.68% + 1.02 [13.78% – 4.68%]
= 13.98%