Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Medtronic PLC common stock.
Rates of Return
Medtronic PLC (MDT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceMDT,t1 | DividendMDT,t1 | RMDT,t2 | PriceS&P 500,t | RS&P 500,t3 |
May 31, 2019 | $92.58 | 2,752.06 | ||||
1. | Jun 30, 2019 | $97.39 | 5.20% | 2,941.76 | 6.89% | |
2. | Jul 31, 2019 | $101.94 | $0.54 | 5.23% | 2,980.38 | 1.31% |
3. | Aug 31, 2019 | $107.89 | 5.84% | 2,926.46 | -1.81% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
69. | Feb 28, 2025 | $92.02 | 1.32% | 5,954.50 | -1.42% | |
70. | Mar 31, 2025 | $89.86 | $0.70 | -1.59% | 5,611.85 | -5.75% |
Average (R): | 0.40% | 1.15% | ||||
Standard deviation: | 6.45% | 5.00% |
Medtronic PLC (MDT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceMDT,t1 | DividendMDT,t1 | RMDT,t2 | PriceS&P 500,t | RS&P 500,t3 |
May 31, 2019 | $92.58 | 2,752.06 | ||||
1. | Jun 30, 2019 | $97.39 | 5.20% | 2,941.76 | 6.89% | |
2. | Jul 31, 2019 | $101.94 | $0.54 | 5.23% | 2,980.38 | 1.31% |
3. | Aug 31, 2019 | $107.89 | 5.84% | 2,926.46 | -1.81% | |
4. | Sep 30, 2019 | $108.62 | $0.54 | 1.18% | 2,976.74 | 1.72% |
5. | Oct 31, 2019 | $108.90 | 0.26% | 3,037.56 | 2.04% | |
6. | Nov 30, 2019 | $111.39 | 2.29% | 3,140.98 | 3.40% | |
7. | Dec 31, 2019 | $113.45 | $0.54 | 2.33% | 3,230.78 | 2.86% |
8. | Jan 31, 2020 | $115.44 | 1.75% | 3,225.52 | -0.16% | |
9. | Feb 29, 2020 | $100.67 | -12.79% | 2,954.22 | -8.41% | |
10. | Mar 31, 2020 | $90.18 | $0.54 | -9.88% | 2,584.59 | -12.51% |
11. | Apr 30, 2020 | $97.63 | 8.26% | 2,912.43 | 12.68% | |
12. | May 31, 2020 | $98.58 | 0.97% | 3,044.31 | 4.53% | |
13. | Jun 30, 2020 | $91.70 | $0.58 | -6.39% | 3,100.29 | 1.84% |
14. | Jul 31, 2020 | $96.48 | 5.21% | 3,271.12 | 5.51% | |
15. | Aug 31, 2020 | $107.47 | 11.39% | 3,500.31 | 7.01% | |
16. | Sep 30, 2020 | $103.92 | $0.58 | -2.76% | 3,363.00 | -3.92% |
17. | Oct 31, 2020 | $100.57 | -3.22% | 3,269.96 | -2.77% | |
18. | Nov 30, 2020 | $113.70 | 13.06% | 3,621.63 | 10.75% | |
19. | Dec 31, 2020 | $117.14 | $0.58 | 3.54% | 3,756.07 | 3.71% |
20. | Jan 31, 2021 | $111.33 | -4.96% | 3,714.24 | -1.11% | |
21. | Feb 28, 2021 | $116.97 | 5.07% | 3,811.15 | 2.61% | |
22. | Mar 31, 2021 | $118.13 | $0.58 | 1.49% | 3,972.89 | 4.24% |
23. | Apr 30, 2021 | $130.92 | 10.83% | 4,181.17 | 5.24% | |
24. | May 31, 2021 | $126.59 | -3.31% | 4,204.11 | 0.55% | |
25. | Jun 30, 2021 | $124.13 | $0.63 | -1.45% | 4,297.50 | 2.22% |
26. | Jul 31, 2021 | $131.31 | 5.78% | 4,395.26 | 2.27% | |
27. | Aug 31, 2021 | $133.48 | 1.65% | 4,522.68 | 2.90% | |
28. | Sep 30, 2021 | $125.35 | $0.63 | -5.62% | 4,307.54 | -4.76% |
29. | Oct 31, 2021 | $119.86 | -4.38% | 4,605.38 | 6.91% | |
30. | Nov 30, 2021 | $106.70 | -10.98% | 4,567.00 | -0.83% | |
31. | Dec 31, 2021 | $103.45 | $0.63 | -2.46% | 4,766.18 | 4.36% |
32. | Jan 31, 2022 | $103.49 | 0.04% | 4,515.55 | -5.26% | |
33. | Feb 28, 2022 | $104.99 | 1.45% | 4,373.94 | -3.14% | |
34. | Mar 31, 2022 | $110.95 | $0.63 | 6.28% | 4,530.41 | 3.58% |
35. | Apr 30, 2022 | $104.36 | -5.94% | 4,131.93 | -8.80% | |
36. | May 31, 2022 | $100.15 | -4.03% | 4,132.15 | 0.01% | |
37. | Jun 30, 2022 | $89.75 | $0.68 | -9.71% | 3,785.38 | -8.39% |
38. | Jul 31, 2022 | $92.52 | 3.09% | 4,130.29 | 9.11% | |
39. | Aug 31, 2022 | $87.92 | -4.97% | 3,955.00 | -4.24% | |
40. | Sep 30, 2022 | $80.75 | $0.68 | -7.38% | 3,585.62 | -9.34% |
41. | Oct 31, 2022 | $87.34 | 8.16% | 3,871.98 | 7.99% | |
42. | Nov 30, 2022 | $79.04 | -9.50% | 4,080.11 | 5.38% | |
43. | Dec 31, 2022 | $77.72 | $0.68 | -0.81% | 3,839.50 | -5.90% |
44. | Jan 31, 2023 | $83.69 | 7.68% | 4,076.60 | 6.18% | |
45. | Feb 28, 2023 | $82.80 | -1.06% | 3,970.15 | -2.61% | |
46. | Mar 31, 2023 | $80.62 | $0.68 | -1.81% | 4,109.31 | 3.51% |
47. | Apr 30, 2023 | $90.95 | 12.81% | 4,169.48 | 1.46% | |
48. | May 31, 2023 | $82.76 | -9.00% | 4,179.83 | 0.25% | |
49. | Jun 30, 2023 | $88.10 | $0.69 | 7.29% | 4,376.86 | 4.71% |
50. | Jul 31, 2023 | $87.76 | -0.39% | 4,588.96 | 4.85% | |
51. | Aug 31, 2023 | $81.50 | -7.13% | 4,507.66 | -1.77% | |
52. | Sep 30, 2023 | $78.36 | $0.69 | -3.01% | 4,288.05 | -4.87% |
53. | Oct 31, 2023 | $70.56 | -9.95% | 4,193.80 | -2.20% | |
54. | Nov 30, 2023 | $79.27 | 12.34% | 4,567.80 | 8.92% | |
55. | Dec 31, 2023 | $82.38 | $0.69 | 4.79% | 4,769.83 | 4.42% |
56. | Jan 31, 2024 | $87.54 | 6.26% | 4,845.65 | 1.59% | |
57. | Feb 29, 2024 | $83.36 | -4.77% | 5,096.27 | 5.17% | |
58. | Mar 31, 2024 | $87.15 | $0.69 | 5.37% | 5,254.35 | 3.10% |
59. | Apr 30, 2024 | $80.24 | -7.93% | 5,035.69 | -4.16% | |
60. | May 31, 2024 | $81.37 | 1.41% | 5,277.51 | 4.80% | |
61. | Jun 30, 2024 | $78.71 | $0.70 | -2.41% | 5,460.48 | 3.47% |
62. | Jul 31, 2024 | $80.32 | 2.05% | 5,522.30 | 1.13% | |
63. | Aug 31, 2024 | $88.58 | 10.28% | 5,648.40 | 2.28% | |
64. | Sep 30, 2024 | $90.03 | $0.70 | 2.43% | 5,762.48 | 2.02% |
65. | Oct 31, 2024 | $89.25 | -0.87% | 5,705.45 | -0.99% | |
66. | Nov 30, 2024 | $86.54 | -3.04% | 6,032.38 | 5.73% | |
67. | Dec 31, 2024 | $79.88 | $0.70 | -6.89% | 5,881.63 | -2.50% |
68. | Jan 31, 2025 | $90.82 | 13.70% | 6,040.53 | 2.70% | |
69. | Feb 28, 2025 | $92.02 | 1.32% | 5,954.50 | -1.42% | |
70. | Mar 31, 2025 | $89.86 | $0.70 | -1.59% | 5,611.85 | -5.75% |
Average (R): | 0.40% | 1.15% | ||||
Standard deviation: | 6.45% | 5.00% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of MDT during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RMDT,t | RS&P 500,t | (RMDT,t–RMDT)2 | (RS&P 500,t–RS&P 500)2 | (RMDT,t–RMDT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Jun 30, 2019 | 5.20% | 6.89% | 23.04 | 33.02 | 27.58 |
2. | Jul 31, 2019 | 5.23% | 1.31% | 23.34 | 0.03 | 0.80 |
3. | Aug 31, 2019 | 5.84% | -1.81% | 29.61 | 8.74 | -16.09 |
. | . | . | . | . | . | . |
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69. | Feb 28, 2025 | 1.32% | -1.42% | 0.86 | 6.61 | -2.38 |
70. | Mar 31, 2025 | -1.59% | -5.75% | 3.93 | 47.63 | 13.68 |
Total (Σ): | 2,874.69 | 1,727.94 | 1,387.95 |
t | Date | RMDT,t | RS&P 500,t | (RMDT,t–RMDT)2 | (RS&P 500,t–RS&P 500)2 | (RMDT,t–RMDT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Jun 30, 2019 | 5.20% | 6.89% | 23.04 | 33.02 | 27.58 |
2. | Jul 31, 2019 | 5.23% | 1.31% | 23.34 | 0.03 | 0.80 |
3. | Aug 31, 2019 | 5.84% | -1.81% | 29.61 | 8.74 | -16.09 |
4. | Sep 30, 2019 | 1.18% | 1.72% | 0.61 | 0.33 | 0.45 |
5. | Oct 31, 2019 | 0.26% | 2.04% | 0.02 | 0.80 | -0.12 |
6. | Nov 30, 2019 | 2.29% | 3.40% | 3.58 | 5.10 | 4.27 |
7. | Dec 31, 2019 | 2.33% | 2.86% | 3.76 | 2.93 | 3.32 |
8. | Jan 31, 2020 | 1.75% | -0.16% | 1.85 | 1.72 | -1.78 |
9. | Feb 29, 2020 | -12.79% | -8.41% | 173.97 | 91.36 | 126.07 |
10. | Mar 31, 2020 | -9.88% | -12.51% | 105.66 | 186.57 | 140.40 |
11. | Apr 30, 2020 | 8.26% | 12.68% | 61.87 | 133.11 | 90.75 |
12. | May 31, 2020 | 0.97% | 4.53% | 0.33 | 11.43 | 1.95 |
13. | Jun 30, 2020 | -6.39% | 1.84% | 46.05 | 0.48 | -4.69 |
14. | Jul 31, 2020 | 5.21% | 5.51% | 23.21 | 19.04 | 21.02 |
15. | Aug 31, 2020 | 11.39% | 7.01% | 120.91 | 34.33 | 64.43 |
16. | Sep 30, 2020 | -2.76% | -3.92% | 9.98 | 25.70 | 16.01 |
17. | Oct 31, 2020 | -3.22% | -2.77% | 13.10 | 15.32 | 14.16 |
18. | Nov 30, 2020 | 13.06% | 10.75% | 160.28 | 92.30 | 121.63 |
19. | Dec 31, 2020 | 3.54% | 3.71% | 9.86 | 6.58 | 8.06 |
20. | Jan 31, 2021 | -4.96% | -1.11% | 28.68 | 5.11 | 12.11 |
21. | Feb 28, 2021 | 5.07% | 2.61% | 21.82 | 2.14 | 6.83 |
22. | Mar 31, 2021 | 1.49% | 4.24% | 1.19 | 9.59 | 3.38 |
23. | Apr 30, 2021 | 10.83% | 5.24% | 108.82 | 16.77 | 42.72 |
24. | May 31, 2021 | -3.31% | 0.55% | 13.71 | 0.36 | 2.22 |
25. | Jun 30, 2021 | -1.45% | 2.22% | 3.39 | 1.15 | -1.98 |
26. | Jul 31, 2021 | 5.78% | 2.27% | 29.04 | 1.27 | 6.08 |
27. | Aug 31, 2021 | 1.65% | 2.90% | 1.58 | 3.07 | 2.20 |
28. | Sep 30, 2021 | -5.62% | -4.76% | 36.17 | 34.86 | 35.51 |
29. | Oct 31, 2021 | -4.38% | 6.91% | 22.80 | 33.26 | -27.54 |
30. | Nov 30, 2021 | -10.98% | -0.83% | 129.38 | 3.92 | 22.53 |
31. | Dec 31, 2021 | -2.46% | 4.36% | 8.13 | 10.33 | -9.16 |
32. | Jan 31, 2022 | 0.04% | -5.26% | 0.13 | 41.03 | 2.28 |
33. | Feb 28, 2022 | 1.45% | -3.14% | 1.11 | 18.35 | -4.52 |
34. | Mar 31, 2022 | 6.28% | 3.58% | 34.59 | 5.91 | 14.29 |
35. | Apr 30, 2022 | -5.94% | -8.80% | 40.13 | 98.86 | 62.99 |
36. | May 31, 2022 | -4.03% | 0.01% | 19.62 | 1.30 | 5.06 |
37. | Jun 30, 2022 | -9.71% | -8.39% | 102.02 | 90.99 | 96.35 |
38. | Jul 31, 2022 | 3.09% | 9.11% | 7.24 | 63.43 | 21.43 |
39. | Aug 31, 2022 | -4.97% | -4.24% | 28.81 | 29.06 | 28.93 |
40. | Sep 30, 2022 | -7.38% | -9.34% | 60.48 | 109.97 | 81.55 |
41. | Oct 31, 2022 | 8.16% | 7.99% | 60.31 | 46.78 | 53.11 |
42. | Nov 30, 2022 | -9.50% | 5.38% | 97.98 | 17.88 | -41.85 |
43. | Dec 31, 2022 | -0.81% | -5.90% | 1.45 | 49.62 | 8.49 |
44. | Jan 31, 2023 | 7.68% | 6.18% | 53.09 | 25.28 | 36.64 |
45. | Feb 28, 2023 | -1.06% | -2.61% | 2.13 | 14.13 | 5.48 |
46. | Mar 31, 2023 | -1.81% | 3.51% | 4.87 | 5.56 | -5.20 |
47. | Apr 30, 2023 | 12.81% | 1.46% | 154.20 | 0.10 | 3.94 |
48. | May 31, 2023 | -9.00% | 0.25% | 88.36 | 0.81 | 8.45 |
49. | Jun 30, 2023 | 7.29% | 4.71% | 47.48 | 12.72 | 24.58 |
50. | Jul 31, 2023 | -0.39% | 4.85% | 0.61 | 13.68 | -2.89 |
51. | Aug 31, 2023 | -7.13% | -1.77% | 56.68 | 8.52 | 21.97 |
52. | Sep 30, 2023 | -3.01% | -4.87% | 11.57 | 36.23 | 20.47 |
53. | Oct 31, 2023 | -9.95% | -2.20% | 107.11 | 11.19 | 34.62 |
54. | Nov 30, 2023 | 12.34% | 8.92% | 142.77 | 60.39 | 92.85 |
55. | Dec 31, 2023 | 4.79% | 4.42% | 19.35 | 10.73 | 14.41 |
56. | Jan 31, 2024 | 6.26% | 1.59% | 34.44 | 0.20 | 2.60 |
57. | Feb 29, 2024 | -4.77% | 5.17% | 26.73 | 16.20 | -20.81 |
58. | Mar 31, 2024 | 5.37% | 3.10% | 24.79 | 3.82 | 9.73 |
59. | Apr 30, 2024 | -7.93% | -4.16% | 69.29 | 28.18 | 44.19 |
60. | May 31, 2024 | 1.41% | 4.80% | 1.03 | 13.36 | 3.70 |
61. | Jun 30, 2024 | -2.41% | 3.47% | 7.86 | 5.38 | -6.50 |
62. | Jul 31, 2024 | 2.05% | 1.13% | 2.72 | 0.00 | -0.02 |
63. | Aug 31, 2024 | 10.28% | 2.28% | 97.78 | 1.29 | 11.24 |
64. | Sep 30, 2024 | 2.43% | 2.02% | 4.13 | 0.76 | 1.77 |
65. | Oct 31, 2024 | -0.87% | -0.99% | 1.59 | 4.57 | 2.70 |
66. | Nov 30, 2024 | -3.04% | 5.73% | 11.78 | 21.00 | -15.73 |
67. | Dec 31, 2024 | -6.89% | -2.50% | 53.03 | 13.29 | 26.55 |
68. | Jan 31, 2025 | 13.70% | 2.70% | 176.90 | 2.42 | 20.68 |
69. | Feb 28, 2025 | 1.32% | -1.42% | 0.86 | 6.61 | -2.38 |
70. | Mar 31, 2025 | -1.59% | -5.75% | 3.93 | 47.63 | 13.68 |
Total (Σ): | 2,874.69 | 1,727.94 | 1,387.95 |
Show all
VarianceMDT = Σ(RMDT,t–RMDT)2 ÷ (70 – 1)
= 2,874.69 ÷ (70 – 1)
= 41.66
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (70 – 1)
= 1,727.94 ÷ (70 – 1)
= 25.04
CovarianceMDT, S&P 500 = Σ(RMDT,t–RMDT)×(RS&P 500,t–RS&P 500) ÷ (70 – 1)
= 1,387.95 ÷ (70 – 1)
= 20.12
Systematic Risk (β) Estimation
VarianceMDT | 41.66 |
VarianceS&P 500 | 25.04 |
CovarianceMDT, S&P 500 | 20.12 |
Correlation coefficientMDT, S&P 5001 | 0.62 |
βMDT2 | 0.80 |
αMDT3 | -0.53% |
Calculations
1 Correlation coefficientMDT, S&P 500
= CovarianceMDT, S&P 500 ÷ (Standard deviationMDT × Standard deviationS&P 500)
= 20.12 ÷ (6.45% × 5.00%)
= 0.62
2 βMDT
= CovarianceMDT, S&P 500 ÷ VarianceS&P 500
= 20.12 ÷ 25.04
= 0.80
3 αMDT
= AverageMDT – βMDT × AverageS&P 500
= 0.40% – 0.80 × 1.15%
= -0.53%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.85% |
Expected rate of return on market portfolio2 | E(RM) | 14.71% |
Systematic risk (β) of Medtronic PLC common stock | βMDT | 0.80 |
Expected rate of return on Medtronic PLC common stock3 | E(RMDT) | 12.77% |
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(RMDT) = RF + βMDT [E(RM) – RF]
= 4.85% + 0.80 [14.71% – 4.85%]
= 12.77%