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, 2017 | $84.28 | 2,411.80 | ||||
1. | Jun 30, 2017 | $88.75 | 5.30% | 2,423.41 | 0.48% | |
2. | Jul 31, 2017 | $83.97 | $0.46 | -4.87% | 2,470.30 | 1.93% |
3. | Aug 31, 2017 | $80.62 | -3.99% | 2,471.65 | 0.05% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Mar 31, 2023 | $80.62 | $0.68 | -1.81% | 4,109.31 | 3.51% |
71. | Apr 30, 2023 | $90.95 | 12.81% | 4,169.48 | 1.46% | |
Average (R): | 0.48% | 0.90% | ||||
Standard deviation: | 5.90% | 5.03% |
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, 2017 | $84.28 | 2,411.80 | ||||
1. | Jun 30, 2017 | $88.75 | 5.30% | 2,423.41 | 0.48% | |
2. | Jul 31, 2017 | $83.97 | $0.46 | -4.87% | 2,470.30 | 1.93% |
3. | Aug 31, 2017 | $80.62 | -3.99% | 2,471.65 | 0.05% | |
4. | Sep 30, 2017 | $77.77 | $0.46 | -2.96% | 2,519.36 | 1.93% |
5. | Oct 31, 2017 | $80.52 | 3.54% | 2,575.26 | 2.22% | |
6. | Nov 30, 2017 | $82.13 | 2.00% | 2,647.58 | 2.81% | |
7. | Dec 31, 2017 | $80.75 | $0.46 | -1.12% | 2,673.61 | 0.98% |
8. | Jan 31, 2018 | $85.89 | 6.37% | 2,823.81 | 5.62% | |
9. | Feb 28, 2018 | $79.89 | -6.99% | 2,713.83 | -3.89% | |
10. | Mar 31, 2018 | $80.22 | $0.46 | 0.99% | 2,640.87 | -2.69% |
11. | Apr 30, 2018 | $80.13 | -0.11% | 2,648.05 | 0.27% | |
12. | May 31, 2018 | $86.32 | 7.72% | 2,705.27 | 2.16% | |
13. | Jun 30, 2018 | $85.61 | -0.82% | 2,718.37 | 0.48% | |
14. | Jul 31, 2018 | $90.23 | $0.50 | 5.98% | 2,816.29 | 3.60% |
15. | Aug 31, 2018 | $96.41 | 6.85% | 2,901.52 | 3.03% | |
16. | Sep 30, 2018 | $98.37 | $0.50 | 2.55% | 2,913.98 | 0.43% |
17. | Oct 31, 2018 | $89.82 | -8.69% | 2,711.74 | -6.94% | |
18. | Nov 30, 2018 | $97.53 | 8.58% | 2,760.17 | 1.79% | |
19. | Dec 31, 2018 | $90.96 | $0.50 | -6.22% | 2,506.85 | -9.18% |
20. | Jan 31, 2019 | $88.39 | -2.83% | 2,704.10 | 7.87% | |
21. | Feb 28, 2019 | $90.50 | 2.39% | 2,784.49 | 2.97% | |
22. | Mar 31, 2019 | $91.08 | $0.50 | 1.19% | 2,834.40 | 1.79% |
23. | Apr 30, 2019 | $88.81 | -2.49% | 2,945.83 | 3.93% | |
24. | May 31, 2019 | $92.58 | 4.25% | 2,752.06 | -6.58% | |
25. | Jun 30, 2019 | $97.39 | 5.20% | 2,941.76 | 6.89% | |
26. | Jul 31, 2019 | $101.94 | $0.54 | 5.23% | 2,980.38 | 1.31% |
27. | Aug 31, 2019 | $107.89 | 5.84% | 2,926.46 | -1.81% | |
28. | Sep 30, 2019 | $108.62 | $0.54 | 1.18% | 2,976.74 | 1.72% |
29. | Oct 31, 2019 | $108.90 | 0.26% | 3,037.56 | 2.04% | |
30. | Nov 30, 2019 | $111.39 | 2.29% | 3,140.98 | 3.40% | |
31. | Dec 31, 2019 | $113.45 | $0.54 | 2.33% | 3,230.78 | 2.86% |
32. | Jan 31, 2020 | $115.44 | 1.75% | 3,225.52 | -0.16% | |
33. | Feb 29, 2020 | $100.67 | -12.79% | 2,954.22 | -8.41% | |
34. | Mar 31, 2020 | $90.18 | $0.54 | -9.88% | 2,584.59 | -12.51% |
35. | Apr 30, 2020 | $97.63 | 8.26% | 2,912.43 | 12.68% | |
36. | May 31, 2020 | $98.58 | 0.97% | 3,044.31 | 4.53% | |
37. | Jun 30, 2020 | $91.70 | $0.58 | -6.39% | 3,100.29 | 1.84% |
38. | Jul 31, 2020 | $96.48 | 5.21% | 3,271.12 | 5.51% | |
39. | Aug 31, 2020 | $107.47 | 11.39% | 3,500.31 | 7.01% | |
40. | Sep 30, 2020 | $103.92 | $0.58 | -2.76% | 3,363.00 | -3.92% |
41. | Oct 31, 2020 | $100.57 | -3.22% | 3,269.96 | -2.77% | |
42. | Nov 30, 2020 | $113.70 | 13.06% | 3,621.63 | 10.75% | |
43. | Dec 31, 2020 | $117.14 | $0.58 | 3.54% | 3,756.07 | 3.71% |
44. | Jan 31, 2021 | $111.33 | -4.96% | 3,714.24 | -1.11% | |
45. | Feb 28, 2021 | $116.97 | 5.07% | 3,811.15 | 2.61% | |
46. | Mar 31, 2021 | $118.13 | $0.58 | 1.49% | 3,972.89 | 4.24% |
47. | Apr 30, 2021 | $130.92 | 10.83% | 4,181.17 | 5.24% | |
48. | May 31, 2021 | $126.59 | -3.31% | 4,204.11 | 0.55% | |
49. | Jun 30, 2021 | $124.13 | $0.63 | -1.45% | 4,297.50 | 2.22% |
50. | Jul 31, 2021 | $131.31 | 5.78% | 4,395.26 | 2.27% | |
51. | Aug 31, 2021 | $133.48 | 1.65% | 4,522.68 | 2.90% | |
52. | Sep 30, 2021 | $125.35 | $0.63 | -5.62% | 4,307.54 | -4.76% |
53. | Oct 31, 2021 | $119.86 | -4.38% | 4,605.38 | 6.91% | |
54. | Nov 30, 2021 | $106.70 | -10.98% | 4,567.00 | -0.83% | |
55. | Dec 31, 2021 | $103.45 | $0.63 | -2.46% | 4,766.18 | 4.36% |
56. | Jan 31, 2022 | $103.49 | 0.04% | 4,515.55 | -5.26% | |
57. | Feb 28, 2022 | $104.99 | 1.45% | 4,373.94 | -3.14% | |
58. | Mar 31, 2022 | $110.95 | $0.63 | 6.28% | 4,530.41 | 3.58% |
59. | Apr 30, 2022 | $104.36 | -5.94% | 4,131.93 | -8.80% | |
60. | May 31, 2022 | $100.15 | -4.03% | 4,132.15 | 0.01% | |
61. | Jun 30, 2022 | $89.75 | $0.68 | -9.71% | 3,785.38 | -8.39% |
62. | Jul 31, 2022 | $92.52 | 3.09% | 4,130.29 | 9.11% | |
63. | Aug 31, 2022 | $87.92 | -4.97% | 3,955.00 | -4.24% | |
64. | Sep 30, 2022 | $80.75 | $0.68 | -7.38% | 3,585.62 | -9.34% |
65. | Oct 31, 2022 | $87.34 | 8.16% | 3,871.98 | 7.99% | |
66. | Nov 30, 2022 | $79.04 | -9.50% | 4,080.11 | 5.38% | |
67. | Dec 31, 2022 | $77.72 | $0.68 | -0.81% | 3,839.50 | -5.90% |
68. | Jan 31, 2023 | $83.69 | 7.68% | 4,076.60 | 6.18% | |
69. | Feb 28, 2023 | $82.80 | -1.06% | 3,970.15 | -2.61% | |
70. | Mar 31, 2023 | $80.62 | $0.68 | -1.81% | 4,109.31 | 3.51% |
71. | Apr 30, 2023 | $90.95 | 12.81% | 4,169.48 | 1.46% | |
Average (R): | 0.48% | 0.90% | ||||
Standard deviation: | 5.90% | 5.03% |
Show all
1 Data in US$ 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, 2017 | 5.30% | 0.48% | 23.28 | 0.18 | -2.02 |
2. | Jul 31, 2017 | -4.87% | 1.93% | 28.59 | 1.07 | -5.53 |
3. | Aug 31, 2017 | -3.99% | 0.05% | 19.97 | 0.71 | 3.78 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Mar 31, 2023 | -1.81% | 3.51% | 5.25 | 6.79 | -5.97 |
71. | Apr 30, 2023 | 12.81% | 1.46% | 152.13 | 0.32 | 6.96 |
Total (Σ): | 2,435.45 | 1,772.62 | 1,270.98 |
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, 2017 | 5.30% | 0.48% | 23.28 | 0.18 | -2.02 |
2. | Jul 31, 2017 | -4.87% | 1.93% | 28.59 | 1.07 | -5.53 |
3. | Aug 31, 2017 | -3.99% | 0.05% | 19.97 | 0.71 | 3.78 |
4. | Sep 30, 2017 | -2.96% | 1.93% | 11.86 | 1.06 | -3.55 |
5. | Oct 31, 2017 | 3.54% | 2.22% | 9.35 | 1.74 | 4.03 |
6. | Nov 30, 2017 | 2.00% | 2.81% | 2.31 | 3.64 | 2.90 |
7. | Dec 31, 2017 | -1.12% | 0.98% | 2.56 | 0.01 | -0.13 |
8. | Jan 31, 2018 | 6.37% | 5.62% | 34.65 | 22.26 | 27.77 |
9. | Feb 28, 2018 | -6.99% | -3.89% | 55.72 | 22.99 | 35.79 |
10. | Mar 31, 2018 | 0.99% | -2.69% | 0.26 | 12.88 | -1.83 |
11. | Apr 30, 2018 | -0.11% | 0.27% | 0.35 | 0.39 | 0.37 |
12. | May 31, 2018 | 7.72% | 2.16% | 52.50 | 1.59 | 9.14 |
13. | Jun 30, 2018 | -0.82% | 0.48% | 1.69 | 0.17 | 0.54 |
14. | Jul 31, 2018 | 5.98% | 3.60% | 30.27 | 7.30 | 14.87 |
15. | Aug 31, 2018 | 6.85% | 3.03% | 40.58 | 4.52 | 13.55 |
16. | Sep 30, 2018 | 2.55% | 0.43% | 4.30 | 0.22 | -0.98 |
17. | Oct 31, 2018 | -8.69% | -6.94% | 84.10 | 61.47 | 71.90 |
18. | Nov 30, 2018 | 8.58% | 1.79% | 65.69 | 0.79 | 7.18 |
19. | Dec 31, 2018 | -6.22% | -9.18% | 44.93 | 101.56 | 67.55 |
20. | Jan 31, 2019 | -2.83% | 7.87% | 10.92 | 48.56 | -23.03 |
21. | Feb 28, 2019 | 2.39% | 2.97% | 3.64 | 4.30 | 3.96 |
22. | Mar 31, 2019 | 1.19% | 1.79% | 0.51 | 0.80 | 0.64 |
23. | Apr 30, 2019 | -2.49% | 3.93% | 8.83 | 9.19 | -9.01 |
24. | May 31, 2019 | 4.25% | -6.58% | 14.18 | 55.92 | -28.16 |
25. | Jun 30, 2019 | 5.20% | 6.89% | 22.24 | 35.92 | 28.27 |
26. | Jul 31, 2019 | 5.23% | 1.31% | 22.54 | 0.17 | 1.96 |
27. | Aug 31, 2019 | 5.84% | -1.81% | 28.71 | 7.34 | -14.51 |
28. | Sep 30, 2019 | 1.18% | 1.72% | 0.49 | 0.67 | 0.57 |
29. | Oct 31, 2019 | 0.26% | 2.04% | 0.05 | 1.31 | -0.25 |
30. | Nov 30, 2019 | 2.29% | 3.40% | 3.27 | 6.27 | 4.53 |
31. | Dec 31, 2019 | 2.33% | 2.86% | 3.44 | 3.84 | 3.63 |
32. | Jan 31, 2020 | 1.75% | -0.16% | 1.63 | 1.13 | -1.36 |
33. | Feb 29, 2020 | -12.79% | -8.41% | 176.19 | 86.69 | 123.59 |
34. | Mar 31, 2020 | -9.88% | -12.51% | 107.39 | 179.88 | 138.98 |
35. | Apr 30, 2020 | 8.26% | 12.68% | 60.56 | 138.87 | 91.71 |
36. | May 31, 2020 | 0.97% | 4.53% | 0.24 | 13.16 | 1.79 |
37. | Jun 30, 2020 | -6.39% | 1.84% | 47.19 | 0.88 | -6.45 |
38. | Jul 31, 2020 | 5.21% | 5.51% | 22.41 | 21.25 | 21.82 |
39. | Aug 31, 2020 | 11.39% | 7.01% | 119.07 | 37.29 | 66.63 |
40. | Sep 30, 2020 | -2.76% | -3.92% | 10.51 | 23.26 | 15.64 |
41. | Oct 31, 2020 | -3.22% | -2.77% | 13.71 | 13.44 | 13.58 |
42. | Nov 30, 2020 | 13.06% | 10.75% | 158.17 | 97.11 | 123.94 |
43. | Dec 31, 2020 | 3.54% | 3.71% | 9.34 | 7.91 | 8.60 |
44. | Jan 31, 2021 | -4.96% | -1.11% | 29.58 | 4.05 | 10.95 |
45. | Feb 28, 2021 | 5.07% | 2.61% | 21.04 | 2.92 | 7.84 |
46. | Mar 31, 2021 | 1.49% | 4.24% | 1.02 | 11.18 | 3.37 |
47. | Apr 30, 2021 | 10.83% | 5.24% | 107.08 | 18.86 | 44.94 |
48. | May 31, 2021 | -3.31% | 0.55% | 14.34 | 0.12 | 1.33 |
49. | Jun 30, 2021 | -1.45% | 2.22% | 3.70 | 1.75 | -2.54 |
50. | Jul 31, 2021 | 5.78% | 2.27% | 28.15 | 1.89 | 7.29 |
51. | Aug 31, 2021 | 1.65% | 2.90% | 1.38 | 4.00 | 2.35 |
52. | Sep 30, 2021 | -5.62% | -4.76% | 37.18 | 32.00 | 34.49 |
53. | Oct 31, 2021 | -4.38% | 6.91% | 23.61 | 36.17 | -29.22 |
54. | Nov 30, 2021 | -10.98% | -0.83% | 131.30 | 3.00 | 19.86 |
55. | Dec 31, 2021 | -2.46% | 4.36% | 8.61 | 11.98 | -10.16 |
56. | Jan 31, 2022 | 0.04% | -5.26% | 0.19 | 37.93 | 2.71 |
57. | Feb 28, 2022 | 1.45% | -3.14% | 0.94 | 16.29 | -3.92 |
58. | Mar 31, 2022 | 6.28% | 3.58% | 33.61 | 7.17 | 15.52 |
59. | Apr 30, 2022 | -5.94% | -8.80% | 41.20 | 94.00 | 62.23 |
60. | May 31, 2022 | -4.03% | 0.01% | 20.37 | 0.80 | 4.04 |
61. | Jun 30, 2022 | -9.71% | -8.39% | 103.72 | 86.34 | 94.63 |
62. | Jul 31, 2022 | 3.09% | 9.11% | 6.80 | 67.43 | 21.41 |
63. | Aug 31, 2022 | -4.97% | -4.24% | 29.71 | 26.46 | 28.04 |
64. | Sep 30, 2022 | -7.38% | -9.34% | 61.79 | 104.85 | 80.49 |
65. | Oct 31, 2022 | 8.16% | 7.99% | 59.01 | 50.22 | 54.44 |
66. | Nov 30, 2022 | -9.50% | 5.38% | 99.64 | 20.03 | -44.67 |
67. | Dec 31, 2022 | -0.81% | -5.90% | 1.66 | 46.20 | 8.76 |
68. | Jan 31, 2023 | 7.68% | 6.18% | 51.87 | 27.83 | 38.00 |
69. | Feb 28, 2023 | -1.06% | -2.61% | 2.38 | 12.33 | 5.42 |
70. | Mar 31, 2023 | -1.81% | 3.51% | 5.25 | 6.79 | -5.97 |
71. | Apr 30, 2023 | 12.81% | 1.46% | 152.13 | 0.32 | 6.96 |
Total (Σ): | 2,435.45 | 1,772.62 | 1,270.98 |
Show all
VarianceMDT = Σ(RMDT,t–RMDT)2 ÷ (71 – 1)
= 2,435.45 ÷ (71 – 1)
= 34.79
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,772.62 ÷ (71 – 1)
= 25.32
CovarianceMDT, S&P 500 = Σ(RMDT,t–RMDT)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,270.98 ÷ (71 – 1)
= 18.16
Systematic Risk (β) Estimation
VarianceMDT | 34.79 |
VarianceS&P 500 | 25.32 |
CovarianceMDT, S&P 500 | 18.16 |
Correlation coefficientMDT, S&P 5001 | 0.61 |
βMDT2 | 0.72 |
αMDT3 | -0.17% |
Calculations
1 Correlation coefficientMDT, S&P 500
= CovarianceMDT, S&P 500 ÷ (Standard deviationMDT × Standard deviationS&P 500)
= 18.16 ÷ (5.90% × 5.03%)
= 0.61
2 βMDT
= CovarianceMDT, S&P 500 ÷ VarianceS&P 500
= 18.16 ÷ 25.32
= 0.72
3 αMDT
= AverageMDT – βMDT × AverageS&P 500
= 0.48% – 0.72 × 0.90%
= -0.17%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.86% |
Expected rate of return on market portfolio2 | E(RM) | 13.52% |
Systematic risk (β) of Medtronic PLC common stock | βMDT | 0.72 |
Expected rate of return on Medtronic PLC common stock3 | E(RMDT) | 11.07% |
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]
= 4.86% + 0.72 [13.52% – 4.86%]
= 11.07%