Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Pfizer Inc. common stock.
Rates of Return
Pfizer Inc. (PFE) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PricePFE,t1 | DividendPFE,t1 | RPFE,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2020 | $37.24 | 3,225.52 | ||||
1. | Feb 29, 2020 | $33.42 | -10.26% | 2,954.22 | -8.41% | |
2. | Mar 31, 2020 | $32.64 | -2.33% | 2,584.59 | -12.51% | |
3. | Apr 30, 2020 | $38.36 | 17.52% | 2,912.43 | 12.68% | |
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58. | Nov 30, 2024 | $26.21 | $0.42 | -5.90% | 6,032.38 | 5.73% |
59. | Dec 31, 2024 | $26.53 | 1.22% | 5,881.63 | -2.50% | |
Average (R): | 0.16% | 1.16% | ||||
Standard deviation: | 8.12% | 5.28% |
Pfizer Inc. (PFE) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PricePFE,t1 | DividendPFE,t1 | RPFE,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2020 | $37.24 | 3,225.52 | ||||
1. | Feb 29, 2020 | $33.42 | -10.26% | 2,954.22 | -8.41% | |
2. | Mar 31, 2020 | $32.64 | -2.33% | 2,584.59 | -12.51% | |
3. | Apr 30, 2020 | $38.36 | 17.52% | 2,912.43 | 12.68% | |
4. | May 31, 2020 | $38.19 | $0.38 | 0.55% | 3,044.31 | 4.53% |
5. | Jun 30, 2020 | $32.70 | -14.38% | 3,100.29 | 1.84% | |
6. | Jul 31, 2020 | $38.48 | $0.38 | 18.84% | 3,271.12 | 5.51% |
7. | Aug 31, 2020 | $37.79 | -1.79% | 3,500.31 | 7.01% | |
8. | Sep 30, 2020 | $36.70 | -2.88% | 3,363.00 | -3.92% | |
9. | Oct 31, 2020 | $35.48 | -3.32% | 3,269.96 | -2.77% | |
10. | Nov 30, 2020 | $38.31 | $2.30819 | 14.48% | 3,621.63 | 10.75% |
11. | Dec 31, 2020 | $36.81 | -3.92% | 3,756.07 | 3.71% | |
12. | Jan 31, 2021 | $35.90 | $0.39 | -1.41% | 3,714.24 | -1.11% |
13. | Feb 28, 2021 | $33.49 | -6.71% | 3,811.15 | 2.61% | |
14. | Mar 31, 2021 | $36.23 | 8.18% | 3,972.89 | 4.24% | |
15. | Apr 30, 2021 | $38.65 | 6.68% | 4,181.17 | 5.24% | |
16. | May 31, 2021 | $38.73 | $0.39 | 1.22% | 4,204.11 | 0.55% |
17. | Jun 30, 2021 | $39.16 | 1.11% | 4,297.50 | 2.22% | |
18. | Jul 31, 2021 | $42.81 | $0.39 | 10.32% | 4,395.26 | 2.27% |
19. | Aug 31, 2021 | $46.07 | 7.62% | 4,522.68 | 2.90% | |
20. | Sep 30, 2021 | $43.01 | -6.64% | 4,307.54 | -4.76% | |
21. | Oct 31, 2021 | $43.74 | 1.70% | 4,605.38 | 6.91% | |
22. | Nov 30, 2021 | $53.73 | $0.39 | 23.73% | 4,567.00 | -0.83% |
23. | Dec 31, 2021 | $59.05 | 9.90% | 4,766.18 | 4.36% | |
24. | Jan 31, 2022 | $52.69 | $0.40 | -10.09% | 4,515.55 | -5.26% |
25. | Feb 28, 2022 | $46.94 | -10.91% | 4,373.94 | -3.14% | |
26. | Mar 31, 2022 | $51.77 | 10.29% | 4,530.41 | 3.58% | |
27. | Apr 30, 2022 | $49.07 | -5.22% | 4,131.93 | -8.80% | |
28. | May 31, 2022 | $53.04 | $0.40 | 8.91% | 4,132.15 | 0.01% |
29. | Jun 30, 2022 | $52.43 | -1.15% | 3,785.38 | -8.39% | |
30. | Jul 31, 2022 | $50.51 | $0.40 | -2.90% | 4,130.29 | 9.11% |
31. | Aug 31, 2022 | $45.23 | -10.45% | 3,955.00 | -4.24% | |
32. | Sep 30, 2022 | $43.76 | -3.25% | 3,585.62 | -9.34% | |
33. | Oct 31, 2022 | $46.55 | 6.38% | 3,871.98 | 7.99% | |
34. | Nov 30, 2022 | $50.13 | $0.40 | 8.55% | 4,080.11 | 5.38% |
35. | Dec 31, 2022 | $51.24 | 2.21% | 3,839.50 | -5.90% | |
36. | Jan 31, 2023 | $44.16 | $0.41 | -13.02% | 4,076.60 | 6.18% |
37. | Feb 28, 2023 | $40.57 | -8.13% | 3,970.15 | -2.61% | |
38. | Mar 31, 2023 | $40.80 | 0.57% | 4,109.31 | 3.51% | |
39. | Apr 30, 2023 | $38.89 | -4.68% | 4,169.48 | 1.46% | |
40. | May 31, 2023 | $38.02 | $0.41 | -1.18% | 4,179.83 | 0.25% |
41. | Jun 30, 2023 | $36.68 | -3.52% | 4,376.86 | 4.71% | |
42. | Jul 31, 2023 | $36.06 | $0.41 | -0.57% | 4,588.96 | 4.85% |
43. | Aug 31, 2023 | $35.38 | -1.89% | 4,507.66 | -1.77% | |
44. | Sep 30, 2023 | $33.17 | -6.25% | 4,288.05 | -4.87% | |
45. | Oct 31, 2023 | $30.56 | -7.87% | 4,193.80 | -2.20% | |
46. | Nov 30, 2023 | $30.47 | $0.41 | 1.05% | 4,567.80 | 8.92% |
47. | Dec 31, 2023 | $28.79 | -5.51% | 4,769.83 | 4.42% | |
48. | Jan 31, 2024 | $27.08 | $0.42 | -4.48% | 4,845.65 | 1.59% |
49. | Feb 29, 2024 | $26.56 | -1.92% | 5,096.27 | 5.17% | |
50. | Mar 31, 2024 | $27.75 | 4.48% | 5,254.35 | 3.10% | |
51. | Apr 30, 2024 | $25.62 | -7.68% | 5,035.69 | -4.16% | |
52. | May 31, 2024 | $28.66 | $0.42 | 13.51% | 5,277.51 | 4.80% |
53. | Jun 30, 2024 | $27.98 | -2.37% | 5,460.48 | 3.47% | |
54. | Jul 31, 2024 | $30.54 | $0.42 | 10.65% | 5,522.30 | 1.13% |
55. | Aug 31, 2024 | $29.01 | -5.01% | 5,648.40 | 2.28% | |
56. | Sep 30, 2024 | $28.94 | -0.24% | 5,762.48 | 2.02% | |
57. | Oct 31, 2024 | $28.30 | -2.21% | 5,705.45 | -0.99% | |
58. | Nov 30, 2024 | $26.21 | $0.42 | -5.90% | 6,032.38 | 5.73% |
59. | Dec 31, 2024 | $26.53 | 1.22% | 5,881.63 | -2.50% | |
Average (R): | 0.16% | 1.16% | ||||
Standard deviation: | 8.12% | 5.28% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of PFE during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RPFE,t | RS&P 500,t | (RPFE,t–RPFE)2 | (RS&P 500,t–RS&P 500)2 | (RPFE,t–RPFE)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 29, 2020 | -10.26% | -8.41% | 108.58 | 91.63 | 99.75 |
2. | Mar 31, 2020 | -2.33% | -12.51% | 6.23 | 186.96 | 34.13 |
3. | Apr 30, 2020 | 17.52% | 12.68% | 301.44 | 132.78 | 200.07 |
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58. | Nov 30, 2024 | -5.90% | 5.73% | 36.77 | 20.87 | -27.70 |
59. | Dec 31, 2024 | 1.22% | -2.50% | 1.12 | 13.40 | -3.87 |
Total (Σ): | 3,819.67 | 1,618.62 | 1,039.84 |
t | Date | RPFE,t | RS&P 500,t | (RPFE,t–RPFE)2 | (RS&P 500,t–RS&P 500)2 | (RPFE,t–RPFE)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Feb 29, 2020 | -10.26% | -8.41% | 108.58 | 91.63 | 99.75 |
2. | Mar 31, 2020 | -2.33% | -12.51% | 6.23 | 186.96 | 34.13 |
3. | Apr 30, 2020 | 17.52% | 12.68% | 301.44 | 132.78 | 200.07 |
4. | May 31, 2020 | 0.55% | 4.53% | 0.15 | 11.34 | 1.30 |
5. | Jun 30, 2020 | -14.38% | 1.84% | 211.35 | 0.46 | -9.85 |
6. | Jul 31, 2020 | 18.84% | 5.51% | 348.77 | 18.91 | 81.22 |
7. | Aug 31, 2020 | -1.79% | 7.01% | 3.82 | 34.17 | -11.43 |
8. | Sep 30, 2020 | -2.88% | -3.92% | 9.28 | 25.85 | 15.49 |
9. | Oct 31, 2020 | -3.32% | -2.77% | 12.16 | 15.43 | 13.70 |
10. | Nov 30, 2020 | 14.48% | 10.75% | 205.05 | 92.03 | 137.37 |
11. | Dec 31, 2020 | -3.92% | 3.71% | 16.63 | 6.51 | -10.40 |
12. | Jan 31, 2021 | -1.41% | -1.11% | 2.48 | 5.18 | 3.58 |
13. | Feb 28, 2021 | -6.71% | 2.61% | 47.27 | 2.10 | -9.95 |
14. | Mar 31, 2021 | 8.18% | 4.24% | 64.31 | 9.50 | 24.72 |
15. | Apr 30, 2021 | 6.68% | 5.24% | 42.47 | 16.66 | 26.60 |
16. | May 31, 2021 | 1.22% | 0.55% | 1.11 | 0.38 | -0.65 |
17. | Jun 30, 2021 | 1.11% | 2.22% | 0.90 | 1.12 | 1.00 |
18. | Jul 31, 2021 | 10.32% | 2.27% | 103.11 | 1.24 | 11.31 |
19. | Aug 31, 2021 | 7.62% | 2.90% | 55.54 | 3.02 | 12.95 |
20. | Sep 30, 2021 | -6.64% | -4.76% | 46.30 | 35.02 | 40.27 |
21. | Oct 31, 2021 | 1.70% | 6.91% | 2.36 | 33.10 | 8.83 |
22. | Nov 30, 2021 | 23.73% | -0.83% | 555.48 | 3.98 | -47.01 |
23. | Dec 31, 2021 | 9.90% | 4.36% | 94.85 | 10.24 | 31.16 |
24. | Jan 31, 2022 | -10.09% | -5.26% | 105.18 | 41.21 | 65.84 |
25. | Feb 28, 2022 | -10.91% | -3.14% | 122.66 | 18.47 | 47.59 |
26. | Mar 31, 2022 | 10.29% | 3.58% | 102.56 | 5.84 | 24.47 |
27. | Apr 30, 2022 | -5.22% | -8.80% | 28.92 | 99.14 | 53.55 |
28. | May 31, 2022 | 8.91% | 0.01% | 76.44 | 1.34 | -10.11 |
29. | Jun 30, 2022 | -1.15% | -8.39% | 1.72 | 91.26 | 12.54 |
30. | Jul 31, 2022 | -2.90% | 9.11% | 9.37 | 63.21 | -24.34 |
31. | Aug 31, 2022 | -10.45% | -4.24% | 112.70 | 29.22 | 57.38 |
32. | Sep 30, 2022 | -3.25% | -9.34% | 11.65 | 110.27 | 35.83 |
33. | Oct 31, 2022 | 6.38% | 7.99% | 38.60 | 46.58 | 42.41 |
34. | Nov 30, 2022 | 8.55% | 5.38% | 70.35 | 17.76 | 35.34 |
35. | Dec 31, 2022 | 2.21% | -5.90% | 4.21 | 49.82 | -14.48 |
36. | Jan 31, 2023 | -13.02% | 6.18% | 173.70 | 25.14 | -66.08 |
37. | Feb 28, 2023 | -8.13% | -2.61% | 68.76 | 14.23 | 31.28 |
38. | Mar 31, 2023 | 0.57% | 3.51% | 0.16 | 5.49 | 0.95 |
39. | Apr 30, 2023 | -4.68% | 1.46% | 23.46 | 0.09 | -1.47 |
40. | May 31, 2023 | -1.18% | 0.25% | 1.81 | 0.83 | 1.23 |
41. | Jun 30, 2023 | -3.52% | 4.71% | 13.59 | 12.62 | -13.10 |
42. | Jul 31, 2023 | -0.57% | 4.85% | 0.54 | 13.58 | -2.71 |
43. | Aug 31, 2023 | -1.89% | -1.77% | 4.20 | 8.60 | 6.01 |
44. | Sep 30, 2023 | -6.25% | -4.87% | 41.07 | 36.40 | 38.67 |
45. | Oct 31, 2023 | -7.87% | -2.20% | 64.50 | 11.28 | 26.98 |
46. | Nov 30, 2023 | 1.05% | 8.92% | 0.78 | 60.17 | 6.86 |
47. | Dec 31, 2023 | -5.51% | 4.42% | 32.22 | 10.64 | -18.51 |
48. | Jan 31, 2024 | -4.48% | 1.59% | 21.56 | 0.18 | -1.99 |
49. | Feb 29, 2024 | -1.92% | 5.17% | 4.34 | 16.09 | -8.35 |
50. | Mar 31, 2024 | 4.48% | 3.10% | 18.64 | 3.77 | 8.38 |
51. | Apr 30, 2024 | -7.68% | -4.16% | 61.44 | 28.33 | 41.72 |
52. | May 31, 2024 | 13.51% | 4.80% | 178.03 | 13.26 | 48.58 |
53. | Jun 30, 2024 | -2.37% | 3.47% | 6.43 | 5.32 | -5.85 |
54. | Jul 31, 2024 | 10.65% | 1.13% | 110.00 | 0.00 | -0.31 |
55. | Aug 31, 2024 | -5.01% | 2.28% | 26.75 | 1.26 | -5.80 |
56. | Sep 30, 2024 | -0.24% | 2.02% | 0.16 | 0.74 | -0.35 |
57. | Oct 31, 2024 | -2.21% | -0.99% | 5.64 | 4.63 | 5.11 |
58. | Nov 30, 2024 | -5.90% | 5.73% | 36.77 | 20.87 | -27.70 |
59. | Dec 31, 2024 | 1.22% | -2.50% | 1.12 | 13.40 | -3.87 |
Total (Σ): | 3,819.67 | 1,618.62 | 1,039.84 |
Show all
VariancePFE = Σ(RPFE,t–RPFE)2 ÷ (59 – 1)
= 3,819.67 ÷ (59 – 1)
= 65.86
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
CovariancePFE, S&P 500 = Σ(RPFE,t–RPFE)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,039.84 ÷ (59 – 1)
= 17.93
Systematic Risk (β) Estimation
VariancePFE | 65.86 |
VarianceS&P 500 | 27.91 |
CovariancePFE, S&P 500 | 17.93 |
Correlation coefficientPFE, S&P 5001 | 0.42 |
βPFE2 | 0.64 |
αPFE3 | -0.58% |
Calculations
1 Correlation coefficientPFE, S&P 500
= CovariancePFE, S&P 500 ÷ (Standard deviationPFE × Standard deviationS&P 500)
= 17.93 ÷ (8.12% × 5.28%)
= 0.42
2 βPFE
= CovariancePFE, S&P 500 ÷ VarianceS&P 500
= 17.93 ÷ 27.91
= 0.64
3 αPFE
= AveragePFE – βPFE × AverageS&P 500
= 0.16% – 0.64 × 1.16%
= -0.58%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.64% |
Expected rate of return on market portfolio2 | E(RM) | 14.89% |
Systematic risk (β) of Pfizer Inc. common stock | βPFE | 0.64 |
Expected rate of return on Pfizer Inc. common stock3 | E(RPFE) | 11.23% |
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(RPFE) = RF + βPFE [E(RM) – RF]
= 4.64% + 0.64 [14.89% – 4.64%]
= 11.23%