Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Nike Inc. common stock.
Rates of Return
Nike Inc. (NKE) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceNKE,t1 | DividendNKE,t1 | RNKE,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jun 30, 2017 | $59.00 | 2,423.41 | ||||
1. | Jul 31, 2017 | $59.05 | 0.08% | 2,470.30 | 1.93% | |
2. | Aug 31, 2017 | $52.81 | $0.18 | -10.26% | 2,471.65 | 0.05% |
3. | Sep 30, 2017 | $51.85 | -1.82% | 2,519.36 | 1.93% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Apr 30, 2023 | $126.72 | 3.33% | 4,169.48 | 1.46% | |
71. | May 31, 2023 | $105.26 | -16.93% | 4,179.83 | 0.25% | |
Average (R): | 1.25% | 0.90% | ||||
Standard deviation: | 8.33% | 5.03% |
Nike Inc. (NKE) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceNKE,t1 | DividendNKE,t1 | RNKE,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jun 30, 2017 | $59.00 | 2,423.41 | ||||
1. | Jul 31, 2017 | $59.05 | 0.08% | 2,470.30 | 1.93% | |
2. | Aug 31, 2017 | $52.81 | $0.18 | -10.26% | 2,471.65 | 0.05% |
3. | Sep 30, 2017 | $51.85 | -1.82% | 2,519.36 | 1.93% | |
4. | Oct 31, 2017 | $54.99 | 6.06% | 2,575.26 | 2.22% | |
5. | Nov 30, 2017 | $60.42 | 9.87% | 2,647.58 | 2.81% | |
6. | Dec 31, 2017 | $62.55 | $0.20 | 3.86% | 2,673.61 | 0.98% |
7. | Jan 31, 2018 | $68.22 | 9.06% | 2,823.81 | 5.62% | |
8. | Feb 28, 2018 | $67.03 | -1.74% | 2,713.83 | -3.89% | |
9. | Mar 31, 2018 | $66.44 | $0.20 | -0.58% | 2,640.87 | -2.69% |
10. | Apr 30, 2018 | $68.39 | 2.93% | 2,648.05 | 0.27% | |
11. | May 31, 2018 | $71.80 | 4.99% | 2,705.27 | 2.16% | |
12. | Jun 30, 2018 | $79.68 | $0.20 | 11.25% | 2,718.37 | 0.48% |
13. | Jul 31, 2018 | $76.91 | -3.48% | 2,816.29 | 3.60% | |
14. | Aug 31, 2018 | $82.20 | $0.20 | 7.14% | 2,901.52 | 3.03% |
15. | Sep 30, 2018 | $84.72 | 3.07% | 2,913.98 | 0.43% | |
16. | Oct 31, 2018 | $75.04 | -11.43% | 2,711.74 | -6.94% | |
17. | Nov 30, 2018 | $75.12 | $0.22 | 0.40% | 2,760.17 | 1.79% |
18. | Dec 31, 2018 | $74.14 | -1.30% | 2,506.85 | -9.18% | |
19. | Jan 31, 2019 | $81.88 | 10.44% | 2,704.10 | 7.87% | |
20. | Feb 28, 2019 | $85.73 | 4.70% | 2,784.49 | 2.97% | |
21. | Mar 31, 2019 | $84.21 | $0.22 | -1.52% | 2,834.40 | 1.79% |
22. | Apr 30, 2019 | $87.83 | 4.30% | 2,945.83 | 3.93% | |
23. | May 31, 2019 | $77.14 | $0.22 | -11.92% | 2,752.06 | -6.58% |
24. | Jun 30, 2019 | $83.95 | 8.83% | 2,941.76 | 6.89% | |
25. | Jul 31, 2019 | $86.03 | 2.48% | 2,980.38 | 1.31% | |
26. | Aug 31, 2019 | $84.50 | $0.22 | -1.52% | 2,926.46 | -1.81% |
27. | Sep 30, 2019 | $93.92 | 11.15% | 2,976.74 | 1.72% | |
28. | Oct 31, 2019 | $89.55 | -4.65% | 3,037.56 | 2.04% | |
29. | Nov 30, 2019 | $93.49 | $0.245 | 4.67% | 3,140.98 | 3.40% |
30. | Dec 31, 2019 | $101.31 | 8.36% | 3,230.78 | 2.86% | |
31. | Jan 31, 2020 | $96.30 | -4.95% | 3,225.52 | -0.16% | |
32. | Feb 29, 2020 | $89.38 | $0.245 | -6.93% | 2,954.22 | -8.41% |
33. | Mar 31, 2020 | $82.74 | -7.43% | 2,584.59 | -12.51% | |
34. | Apr 30, 2020 | $87.18 | 5.37% | 2,912.43 | 12.68% | |
35. | May 31, 2020 | $98.58 | $0.245 | 13.36% | 3,044.31 | 4.53% |
36. | Jun 30, 2020 | $98.05 | -0.54% | 3,100.29 | 1.84% | |
37. | Jul 31, 2020 | $97.61 | -0.45% | 3,271.12 | 5.51% | |
38. | Aug 31, 2020 | $111.89 | $0.245 | 14.88% | 3,500.31 | 7.01% |
39. | Sep 30, 2020 | $125.54 | 12.20% | 3,363.00 | -3.92% | |
40. | Oct 31, 2020 | $120.08 | -4.35% | 3,269.96 | -2.77% | |
41. | Nov 30, 2020 | $134.70 | 12.18% | 3,621.63 | 10.75% | |
42. | Dec 31, 2020 | $141.47 | $0.275 | 5.23% | 3,756.07 | 3.71% |
43. | Jan 31, 2021 | $133.59 | -5.57% | 3,714.24 | -1.11% | |
44. | Feb 28, 2021 | $134.78 | $0.275 | 1.10% | 3,811.15 | 2.61% |
45. | Mar 31, 2021 | $132.89 | -1.40% | 3,972.89 | 4.24% | |
46. | Apr 30, 2021 | $132.62 | -0.20% | 4,181.17 | 5.24% | |
47. | May 31, 2021 | $136.46 | $0.275 | 3.10% | 4,204.11 | 0.55% |
48. | Jun 30, 2021 | $154.49 | 13.21% | 4,297.50 | 2.22% | |
49. | Jul 31, 2021 | $167.51 | 8.43% | 4,395.26 | 2.27% | |
50. | Aug 31, 2021 | $164.74 | $0.275 | -1.49% | 4,522.68 | 2.90% |
51. | Sep 30, 2021 | $145.23 | -11.84% | 4,307.54 | -4.76% | |
52. | Oct 31, 2021 | $167.29 | 15.19% | 4,605.38 | 6.91% | |
53. | Nov 30, 2021 | $169.24 | 1.17% | 4,567.00 | -0.83% | |
54. | Dec 31, 2021 | $166.67 | $0.305 | -1.34% | 4,766.18 | 4.36% |
55. | Jan 31, 2022 | $148.07 | -11.16% | 4,515.55 | -5.26% | |
56. | Feb 28, 2022 | $136.55 | -7.78% | 4,373.94 | -3.14% | |
57. | Mar 31, 2022 | $134.56 | $0.305 | -1.23% | 4,530.41 | 3.58% |
58. | Apr 30, 2022 | $124.70 | -7.33% | 4,131.93 | -8.80% | |
59. | May 31, 2022 | $118.85 | -4.69% | 4,132.15 | 0.01% | |
60. | Jun 30, 2022 | $102.20 | $0.305 | -13.75% | 3,785.38 | -8.39% |
61. | Jul 31, 2022 | $114.92 | 12.45% | 4,130.29 | 9.11% | |
62. | Aug 31, 2022 | $106.45 | -7.37% | 3,955.00 | -4.24% | |
63. | Sep 30, 2022 | $83.12 | $0.305 | -21.63% | 3,585.62 | -9.34% |
64. | Oct 31, 2022 | $92.68 | 11.50% | 3,871.98 | 7.99% | |
65. | Nov 30, 2022 | $109.69 | 18.35% | 4,080.11 | 5.38% | |
66. | Dec 31, 2022 | $117.01 | $0.34 | 6.98% | 3,839.50 | -5.90% |
67. | Jan 31, 2023 | $127.33 | 8.82% | 4,076.60 | 6.18% | |
68. | Feb 28, 2023 | $118.79 | -6.71% | 3,970.15 | -2.61% | |
69. | Mar 31, 2023 | $122.64 | $0.34 | 3.53% | 4,109.31 | 3.51% |
70. | Apr 30, 2023 | $126.72 | 3.33% | 4,169.48 | 1.46% | |
71. | May 31, 2023 | $105.26 | -16.93% | 4,179.83 | 0.25% | |
Average (R): | 1.25% | 0.90% | ||||
Standard deviation: | 8.33% | 5.03% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of NKE during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RNKE,t | RS&P 500,t | (RNKE,t–RNKE)2 | (RS&P 500,t–RS&P 500)2 | (RNKE,t–RNKE)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Jul 31, 2017 | 0.08% | 1.93% | 1.36 | 1.08 | -1.21 |
2. | Aug 31, 2017 | -10.26% | 0.05% | 132.52 | 0.71 | 9.69 |
3. | Sep 30, 2017 | -1.82% | 1.93% | 9.41 | 1.07 | -3.17 |
. | . | . | . | . | . | . |
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70. | Apr 30, 2023 | 3.33% | 1.46% | 4.32 | 0.32 | 1.18 |
71. | May 31, 2023 | -16.93% | 0.25% | 330.67 | 0.42 | 11.79 |
Total (Σ): | 4,860.93 | 1,772.87 | 1,983.24 |
t | Date | RNKE,t | RS&P 500,t | (RNKE,t–RNKE)2 | (RS&P 500,t–RS&P 500)2 | (RNKE,t–RNKE)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Jul 31, 2017 | 0.08% | 1.93% | 1.36 | 1.08 | -1.21 |
2. | Aug 31, 2017 | -10.26% | 0.05% | 132.52 | 0.71 | 9.69 |
3. | Sep 30, 2017 | -1.82% | 1.93% | 9.41 | 1.07 | -3.17 |
4. | Oct 31, 2017 | 6.06% | 2.22% | 23.10 | 1.75 | 6.36 |
5. | Nov 30, 2017 | 9.87% | 2.81% | 74.39 | 3.65 | 16.49 |
6. | Dec 31, 2017 | 3.86% | 0.98% | 6.80 | 0.01 | 0.23 |
7. | Jan 31, 2018 | 9.06% | 5.62% | 61.08 | 22.29 | 36.90 |
8. | Feb 28, 2018 | -1.74% | -3.89% | 8.96 | 22.96 | 14.34 |
9. | Mar 31, 2018 | -0.58% | -2.69% | 3.35 | 12.85 | 6.57 |
10. | Apr 30, 2018 | 2.93% | 0.27% | 2.84 | 0.39 | -1.05 |
11. | May 31, 2018 | 4.99% | 2.16% | 13.96 | 1.60 | 4.72 |
12. | Jun 30, 2018 | 11.25% | 0.48% | 100.08 | 0.17 | -4.13 |
13. | Jul 31, 2018 | -3.48% | 3.60% | 22.33 | 7.32 | -12.79 |
14. | Aug 31, 2018 | 7.14% | 3.03% | 34.68 | 4.54 | 12.54 |
15. | Sep 30, 2018 | 3.07% | 0.43% | 3.30 | 0.22 | -0.85 |
16. | Oct 31, 2018 | -11.43% | -6.94% | 160.66 | 61.42 | 99.34 |
17. | Nov 30, 2018 | 0.40% | 1.79% | 0.72 | 0.79 | -0.76 |
18. | Dec 31, 2018 | -1.30% | -9.18% | 6.52 | 101.49 | 25.73 |
19. | Jan 31, 2019 | 10.44% | 7.87% | 84.46 | 48.61 | 64.07 |
20. | Feb 28, 2019 | 4.70% | 2.97% | 11.92 | 4.31 | 7.17 |
21. | Mar 31, 2019 | -1.52% | 1.79% | 7.65 | 0.80 | -2.48 |
22. | Apr 30, 2019 | 4.30% | 3.93% | 9.30 | 9.21 | 9.25 |
23. | May 31, 2019 | -11.92% | -6.58% | 173.45 | 55.87 | 98.44 |
24. | Jun 30, 2019 | 8.83% | 6.89% | 57.44 | 35.96 | 45.44 |
25. | Jul 31, 2019 | 2.48% | 1.31% | 1.51 | 0.17 | 0.51 |
26. | Aug 31, 2019 | -1.52% | -1.81% | 7.68 | 7.32 | 7.50 |
27. | Sep 30, 2019 | 11.15% | 1.72% | 97.98 | 0.67 | 8.13 |
28. | Oct 31, 2019 | -4.65% | 2.04% | 34.84 | 1.31 | -6.77 |
29. | Nov 30, 2019 | 4.67% | 3.40% | 11.72 | 6.29 | 8.59 |
30. | Dec 31, 2019 | 8.36% | 2.86% | 50.62 | 3.85 | 13.96 |
31. | Jan 31, 2020 | -4.95% | -0.16% | 38.37 | 1.12 | 6.56 |
32. | Feb 29, 2020 | -6.93% | -8.41% | 66.93 | 86.63 | 76.15 |
33. | Mar 31, 2020 | -7.43% | -12.51% | 75.31 | 179.79 | 116.36 |
34. | Apr 30, 2020 | 5.37% | 12.68% | 16.95 | 138.95 | 48.53 |
35. | May 31, 2020 | 13.36% | 4.53% | 146.60 | 13.19 | 43.97 |
36. | Jun 30, 2020 | -0.54% | 1.84% | 3.19 | 0.89 | -1.68 |
37. | Jul 31, 2020 | -0.45% | 5.51% | 2.88 | 21.28 | -7.83 |
38. | Aug 31, 2020 | 14.88% | 7.01% | 185.81 | 37.33 | 83.28 |
39. | Sep 30, 2020 | 12.20% | -3.92% | 119.90 | 23.23 | -52.77 |
40. | Oct 31, 2020 | -4.35% | -2.77% | 31.34 | 13.42 | 20.51 |
41. | Nov 30, 2020 | 12.18% | 10.75% | 119.37 | 97.18 | 107.71 |
42. | Dec 31, 2020 | 5.23% | 3.71% | 15.85 | 7.93 | 11.21 |
43. | Jan 31, 2021 | -5.57% | -1.11% | 46.51 | 4.04 | 13.71 |
44. | Feb 28, 2021 | 1.10% | 2.61% | 0.02 | 2.93 | -0.26 |
45. | Mar 31, 2021 | -1.40% | 4.24% | 7.03 | 11.20 | -8.88 |
46. | Apr 30, 2021 | -0.20% | 5.24% | 2.11 | 18.89 | -6.31 |
47. | May 31, 2021 | 3.10% | 0.55% | 3.44 | 0.12 | -0.64 |
48. | Jun 30, 2021 | 13.21% | 2.22% | 143.12 | 1.75 | 15.85 |
49. | Jul 31, 2021 | 8.43% | 2.27% | 51.53 | 1.90 | 9.89 |
50. | Aug 31, 2021 | -1.49% | 2.90% | 7.50 | 4.01 | -5.48 |
51. | Sep 30, 2021 | -11.84% | -4.76% | 171.41 | 31.96 | 74.02 |
52. | Oct 31, 2021 | 15.19% | 6.91% | 194.33 | 36.21 | 83.89 |
53. | Nov 30, 2021 | 1.17% | -0.83% | 0.01 | 2.99 | 0.14 |
54. | Dec 31, 2021 | -1.34% | 4.36% | 6.70 | 12.00 | -8.97 |
55. | Jan 31, 2022 | -11.16% | -5.26% | 153.99 | 37.89 | 76.38 |
56. | Feb 28, 2022 | -7.78% | -3.14% | 81.53 | 16.26 | 36.41 |
57. | Mar 31, 2022 | -1.23% | 3.58% | 6.17 | 7.19 | -6.66 |
58. | Apr 30, 2022 | -7.33% | -8.80% | 73.56 | 93.94 | 83.13 |
59. | May 31, 2022 | -4.69% | 0.01% | 35.29 | 0.79 | 5.30 |
60. | Jun 30, 2022 | -13.75% | -8.39% | 225.06 | 86.28 | 139.35 |
61. | Jul 31, 2022 | 12.45% | 9.11% | 125.37 | 67.49 | 91.98 |
62. | Aug 31, 2022 | -7.37% | -4.24% | 74.30 | 26.43 | 44.31 |
63. | Sep 30, 2022 | -21.63% | -9.34% | 523.46 | 104.78 | 234.20 |
64. | Oct 31, 2022 | 11.50% | 7.99% | 105.10 | 50.26 | 72.68 |
65. | Nov 30, 2022 | 18.35% | 5.38% | 292.55 | 20.06 | 76.60 |
66. | Dec 31, 2022 | 6.98% | -5.90% | 32.88 | 46.16 | -38.95 |
67. | Jan 31, 2023 | 8.82% | 6.18% | 57.31 | 27.86 | 39.96 |
68. | Feb 28, 2023 | -6.71% | -2.61% | 63.30 | 12.31 | 27.91 |
69. | Mar 31, 2023 | 3.53% | 3.51% | 5.19 | 6.80 | 5.94 |
70. | Apr 30, 2023 | 3.33% | 1.46% | 4.32 | 0.32 | 1.18 |
71. | May 31, 2023 | -16.93% | 0.25% | 330.67 | 0.42 | 11.79 |
Total (Σ): | 4,860.93 | 1,772.87 | 1,983.24 |
Show all
VarianceNKE = Σ(RNKE,t–RNKE)2 ÷ (71 – 1)
= 4,860.93 ÷ (71 – 1)
= 69.44
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,772.87 ÷ (71 – 1)
= 25.33
CovarianceNKE, S&P 500 = Σ(RNKE,t–RNKE)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,983.24 ÷ (71 – 1)
= 28.33
Systematic Risk (β) Estimation
VarianceNKE | 69.44 |
VarianceS&P 500 | 25.33 |
CovarianceNKE, S&P 500 | 28.33 |
Correlation coefficientNKE, S&P 5001 | 0.68 |
βNKE2 | 1.12 |
αNKE3 | 0.25% |
Calculations
1 Correlation coefficientNKE, S&P 500
= CovarianceNKE, S&P 500 ÷ (Standard deviationNKE × Standard deviationS&P 500)
= 28.33 ÷ (8.33% × 5.03%)
= 0.68
2 βNKE
= CovarianceNKE, S&P 500 ÷ VarianceS&P 500
= 28.33 ÷ 25.33
= 1.12
3 αNKE
= AverageNKE – βNKE × AverageS&P 500
= 1.25% – 1.12 × 0.90%
= 0.25%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.43% |
Expected rate of return on market portfolio2 | E(RM) | 13.61% |
Systematic risk (β) of Nike Inc. common stock | βNKE | 1.12 |
Expected rate of return on Nike Inc. common stock3 | E(RNKE) | 14.70% |
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(RNKE) = RF + βNKE [E(RM) – RF]
= 4.43% + 1.12 [13.61% – 4.43%]
= 14.70%