Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Walmart Inc. common stock.
Rates of Return
Walmart Inc. (WMT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceWMT,t1 | DividendWMT,t1 | RWMT,t2 | PriceS&P 500,t | RS&P 500,t3 |
Feb 28, 2017 | $70.93 | 2,363.64 | ||||
1. | Mar 31, 2017 | $72.08 | $0.51 | 2.34% | 2,362.72 | -0.04% |
2. | Apr 30, 2017 | $75.18 | 4.30% | 2,384.20 | 0.91% | |
3. | May 31, 2017 | $78.60 | $0.51 | 5.23% | 2,411.80 | 1.16% |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Dec 31, 2022 | $141.79 | $0.56 | -6.61% | 3,839.50 | -5.90% |
71. | Jan 31, 2023 | $143.87 | 1.47% | 4,076.60 | 6.18% | |
Average (R): | 1.33% | 0.90% | ||||
Standard deviation: | 5.69% | 5.01% |
Walmart Inc. (WMT) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceWMT,t1 | DividendWMT,t1 | RWMT,t2 | PriceS&P 500,t | RS&P 500,t3 |
Feb 28, 2017 | $70.93 | 2,363.64 | ||||
1. | Mar 31, 2017 | $72.08 | $0.51 | 2.34% | 2,362.72 | -0.04% |
2. | Apr 30, 2017 | $75.18 | 4.30% | 2,384.20 | 0.91% | |
3. | May 31, 2017 | $78.60 | $0.51 | 5.23% | 2,411.80 | 1.16% |
4. | Jun 30, 2017 | $75.68 | -3.72% | 2,423.41 | 0.48% | |
5. | Jul 31, 2017 | $79.99 | 5.70% | 2,470.30 | 1.93% | |
6. | Aug 31, 2017 | $78.07 | $0.51 | -1.76% | 2,471.65 | 0.05% |
7. | Sep 30, 2017 | $78.14 | 0.09% | 2,519.36 | 1.93% | |
8. | Oct 31, 2017 | $87.31 | 11.74% | 2,575.26 | 2.22% | |
9. | Nov 30, 2017 | $97.23 | 11.36% | 2,647.58 | 2.81% | |
10. | Dec 31, 2017 | $98.75 | $0.51 | 2.09% | 2,673.61 | 0.98% |
11. | Jan 31, 2018 | $106.60 | 7.95% | 2,823.81 | 5.62% | |
12. | Feb 28, 2018 | $90.01 | -15.56% | 2,713.83 | -3.89% | |
13. | Mar 31, 2018 | $88.97 | $0.52 | -0.58% | 2,640.87 | -2.69% |
14. | Apr 30, 2018 | $88.46 | -0.57% | 2,648.05 | 0.27% | |
15. | May 31, 2018 | $82.54 | $0.52 | -6.10% | 2,705.27 | 2.16% |
16. | Jun 30, 2018 | $85.65 | 3.77% | 2,718.37 | 0.48% | |
17. | Jul 31, 2018 | $89.23 | 4.18% | 2,816.29 | 3.60% | |
18. | Aug 31, 2018 | $95.86 | $0.52 | 8.01% | 2,901.52 | 3.03% |
19. | Sep 30, 2018 | $93.91 | -2.03% | 2,913.98 | 0.43% | |
20. | Oct 31, 2018 | $100.28 | 6.78% | 2,711.74 | -6.94% | |
21. | Nov 30, 2018 | $97.65 | -2.62% | 2,760.17 | 1.79% | |
22. | Dec 31, 2018 | $93.15 | $0.52 | -4.08% | 2,506.85 | -9.18% |
23. | Jan 31, 2019 | $95.83 | 2.88% | 2,704.10 | 7.87% | |
24. | Feb 28, 2019 | $98.99 | 3.30% | 2,784.49 | 2.97% | |
25. | Mar 31, 2019 | $97.53 | $0.53 | -0.94% | 2,834.40 | 1.79% |
26. | Apr 30, 2019 | $102.84 | 5.44% | 2,945.83 | 3.93% | |
27. | May 31, 2019 | $101.44 | $0.53 | -0.85% | 2,752.06 | -6.58% |
28. | Jun 30, 2019 | $110.49 | 8.92% | 2,941.76 | 6.89% | |
29. | Jul 31, 2019 | $110.38 | -0.10% | 2,980.38 | 1.31% | |
30. | Aug 31, 2019 | $114.26 | $0.53 | 4.00% | 2,926.46 | -1.81% |
31. | Sep 30, 2019 | $118.68 | 3.87% | 2,976.74 | 1.72% | |
32. | Oct 31, 2019 | $117.26 | -1.20% | 3,037.56 | 2.04% | |
33. | Nov 30, 2019 | $119.09 | 1.56% | 3,140.98 | 3.40% | |
34. | Dec 31, 2019 | $118.84 | $0.53 | 0.24% | 3,230.78 | 2.86% |
35. | Jan 31, 2020 | $114.49 | -3.66% | 3,225.52 | -0.16% | |
36. | Feb 29, 2020 | $107.68 | -5.95% | 2,954.22 | -8.41% | |
37. | Mar 31, 2020 | $113.62 | $0.54 | 6.02% | 2,584.59 | -12.51% |
38. | Apr 30, 2020 | $121.55 | 6.98% | 2,912.43 | 12.68% | |
39. | May 31, 2020 | $124.06 | $0.54 | 2.51% | 3,044.31 | 4.53% |
40. | Jun 30, 2020 | $119.78 | -3.45% | 3,100.29 | 1.84% | |
41. | Jul 31, 2020 | $129.40 | 8.03% | 3,271.12 | 5.51% | |
42. | Aug 31, 2020 | $138.85 | $0.54 | 7.72% | 3,500.31 | 7.01% |
43. | Sep 30, 2020 | $139.91 | 0.76% | 3,363.00 | -3.92% | |
44. | Oct 31, 2020 | $138.75 | -0.83% | 3,269.96 | -2.77% | |
45. | Nov 30, 2020 | $152.79 | 10.12% | 3,621.63 | 10.75% | |
46. | Dec 31, 2020 | $144.15 | $0.54 | -5.30% | 3,756.07 | 3.71% |
47. | Jan 31, 2021 | $140.49 | -2.54% | 3,714.24 | -1.11% | |
48. | Feb 28, 2021 | $129.92 | -7.52% | 3,811.15 | 2.61% | |
49. | Mar 31, 2021 | $135.83 | $0.55 | 4.97% | 3,972.89 | 4.24% |
50. | Apr 30, 2021 | $139.91 | 3.00% | 4,181.17 | 5.24% | |
51. | May 31, 2021 | $142.03 | $0.55 | 1.91% | 4,204.11 | 0.55% |
52. | Jun 30, 2021 | $141.02 | -0.71% | 4,297.50 | 2.22% | |
53. | Jul 31, 2021 | $142.55 | 1.08% | 4,395.26 | 2.27% | |
54. | Aug 31, 2021 | $148.10 | $0.55 | 4.28% | 4,522.68 | 2.90% |
55. | Sep 30, 2021 | $139.38 | -5.89% | 4,307.54 | -4.76% | |
56. | Oct 31, 2021 | $149.42 | 7.20% | 4,605.38 | 6.91% | |
57. | Nov 30, 2021 | $140.63 | -5.88% | 4,567.00 | -0.83% | |
58. | Dec 31, 2021 | $144.69 | $0.55 | 3.28% | 4,766.18 | 4.36% |
59. | Jan 31, 2022 | $139.81 | -3.37% | 4,515.55 | -5.26% | |
60. | Feb 28, 2022 | $135.16 | -3.33% | 4,373.94 | -3.14% | |
61. | Mar 31, 2022 | $148.92 | $0.56 | 10.59% | 4,530.41 | 3.58% |
62. | Apr 30, 2022 | $152.99 | 2.73% | 4,131.93 | -8.80% | |
63. | May 31, 2022 | $128.63 | $0.56 | -15.56% | 4,132.15 | 0.01% |
64. | Jun 30, 2022 | $121.58 | -5.48% | 3,785.38 | -8.39% | |
65. | Jul 31, 2022 | $132.05 | 8.61% | 4,130.29 | 9.11% | |
66. | Aug 31, 2022 | $132.55 | $0.56 | 0.80% | 3,955.00 | -4.24% |
67. | Sep 30, 2022 | $129.70 | -2.15% | 3,585.62 | -9.34% | |
68. | Oct 31, 2022 | $142.33 | 9.74% | 3,871.98 | 7.99% | |
69. | Nov 30, 2022 | $152.42 | 7.09% | 4,080.11 | 5.38% | |
70. | Dec 31, 2022 | $141.79 | $0.56 | -6.61% | 3,839.50 | -5.90% |
71. | Jan 31, 2023 | $143.87 | 1.47% | 4,076.60 | 6.18% | |
Average (R): | 1.33% | 0.90% | ||||
Standard deviation: | 5.69% | 5.01% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of WMT during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RWMT,t | RS&P 500,t | (RWMT,t–RWMT)2 | (RS&P 500,t–RS&P 500)2 | (RWMT,t–RWMT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Mar 31, 2017 | 2.34% | -0.04% | 1.02 | 0.87 | -0.95 |
2. | Apr 30, 2017 | 4.30% | 0.91% | 8.84 | 0.00 | 0.04 |
3. | May 31, 2017 | 5.23% | 1.16% | 15.20 | 0.07 | 1.02 |
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70. | Dec 31, 2022 | -6.61% | -5.90% | 62.96 | 46.14 | 53.90 |
71. | Jan 31, 2023 | 1.47% | 6.18% | 0.02 | 27.88 | 0.73 |
Total (Σ): | 2,268.88 | 1,754.14 | 970.23 |
t | Date | RWMT,t | RS&P 500,t | (RWMT,t–RWMT)2 | (RS&P 500,t–RS&P 500)2 | (RWMT,t–RWMT)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Mar 31, 2017 | 2.34% | -0.04% | 1.02 | 0.87 | -0.95 |
2. | Apr 30, 2017 | 4.30% | 0.91% | 8.84 | 0.00 | 0.04 |
3. | May 31, 2017 | 5.23% | 1.16% | 15.20 | 0.07 | 1.02 |
4. | Jun 30, 2017 | -3.72% | 0.48% | 25.43 | 0.17 | 2.09 |
5. | Jul 31, 2017 | 5.70% | 1.93% | 19.07 | 1.08 | 4.54 |
6. | Aug 31, 2017 | -1.76% | 0.05% | 9.55 | 0.71 | 2.60 |
7. | Sep 30, 2017 | 0.09% | 1.93% | 1.53 | 1.07 | -1.28 |
8. | Oct 31, 2017 | 11.74% | 2.22% | 108.31 | 1.75 | 13.77 |
9. | Nov 30, 2017 | 11.36% | 2.81% | 100.67 | 3.66 | 19.19 |
10. | Dec 31, 2017 | 2.09% | 0.98% | 0.58 | 0.01 | 0.07 |
11. | Jan 31, 2018 | 7.95% | 5.62% | 43.84 | 22.30 | 31.27 |
12. | Feb 28, 2018 | -15.56% | -3.89% | 285.31 | 22.94 | 80.91 |
13. | Mar 31, 2018 | -0.58% | -2.69% | 3.63 | 12.84 | 6.83 |
14. | Apr 30, 2018 | -0.57% | 0.27% | 3.62 | 0.39 | 1.19 |
15. | May 31, 2018 | -6.10% | 2.16% | 55.24 | 1.60 | -9.41 |
16. | Jun 30, 2018 | 3.77% | 0.48% | 5.95 | 0.17 | -1.00 |
17. | Jul 31, 2018 | 4.18% | 3.60% | 8.13 | 7.33 | 7.72 |
18. | Aug 31, 2018 | 8.01% | 3.03% | 44.69 | 4.54 | 14.25 |
19. | Sep 30, 2018 | -2.03% | 0.43% | 11.31 | 0.22 | 1.57 |
20. | Oct 31, 2018 | 6.78% | -6.94% | 29.76 | 61.40 | -42.74 |
21. | Nov 30, 2018 | -2.62% | 1.79% | 15.61 | 0.79 | -3.52 |
22. | Dec 31, 2018 | -4.08% | -9.18% | 29.20 | 101.46 | 54.43 |
23. | Jan 31, 2019 | 2.88% | 7.87% | 2.40 | 48.63 | 10.80 |
24. | Feb 28, 2019 | 3.30% | 2.97% | 3.88 | 4.32 | 4.09 |
25. | Mar 31, 2019 | -0.94% | 1.79% | 5.14 | 0.80 | -2.03 |
26. | Apr 30, 2019 | 5.44% | 3.93% | 16.94 | 9.22 | 12.50 |
27. | May 31, 2019 | -0.85% | -6.58% | 4.73 | 55.85 | 16.25 |
28. | Jun 30, 2019 | 8.92% | 6.89% | 57.66 | 35.97 | 45.54 |
29. | Jul 31, 2019 | -0.10% | 1.31% | 2.04 | 0.17 | -0.60 |
30. | Aug 31, 2019 | 4.00% | -1.81% | 7.11 | 7.31 | -7.21 |
31. | Sep 30, 2019 | 3.87% | 1.72% | 6.45 | 0.68 | 2.09 |
32. | Oct 31, 2019 | -1.20% | 2.04% | 6.37 | 1.32 | -2.90 |
33. | Nov 30, 2019 | 1.56% | 3.40% | 0.05 | 6.30 | 0.58 |
34. | Dec 31, 2019 | 0.24% | 2.86% | 1.19 | 3.86 | -2.15 |
35. | Jan 31, 2020 | -3.66% | -0.16% | 24.89 | 1.12 | 5.28 |
36. | Feb 29, 2020 | -5.95% | -8.41% | 52.94 | 86.61 | 67.72 |
37. | Mar 31, 2020 | 6.02% | -12.51% | 21.99 | 179.75 | -62.87 |
38. | Apr 30, 2020 | 6.98% | 12.68% | 31.94 | 138.98 | 66.62 |
39. | May 31, 2020 | 2.51% | 4.53% | 1.39 | 13.20 | 4.29 |
40. | Jun 30, 2020 | -3.45% | 1.84% | 22.83 | 0.89 | -4.51 |
41. | Jul 31, 2020 | 8.03% | 5.51% | 44.93 | 21.30 | 30.93 |
42. | Aug 31, 2020 | 7.72% | 7.01% | 40.86 | 37.35 | 39.06 |
43. | Sep 30, 2020 | 0.76% | -3.92% | 0.32 | 23.21 | 2.72 |
44. | Oct 31, 2020 | -0.83% | -2.77% | 4.65 | 13.41 | 7.90 |
45. | Nov 30, 2020 | 10.12% | 10.75% | 77.28 | 97.21 | 86.67 |
46. | Dec 31, 2020 | -5.30% | 3.71% | 43.95 | 7.93 | -18.67 |
47. | Jan 31, 2021 | -2.54% | -1.11% | 14.96 | 4.04 | 7.77 |
48. | Feb 28, 2021 | -7.52% | 2.61% | 78.36 | 2.94 | -15.17 |
49. | Mar 31, 2021 | 4.97% | 4.24% | 13.28 | 11.21 | 12.20 |
50. | Apr 30, 2021 | 3.00% | 5.24% | 2.81 | 18.90 | 7.28 |
51. | May 31, 2021 | 1.91% | 0.55% | 0.34 | 0.12 | -0.20 |
52. | Jun 30, 2021 | -0.71% | 2.22% | 4.16 | 1.76 | -2.70 |
53. | Jul 31, 2021 | 1.08% | 2.27% | 0.06 | 1.90 | -0.34 |
54. | Aug 31, 2021 | 4.28% | 2.90% | 8.71 | 4.02 | 5.91 |
55. | Sep 30, 2021 | -5.89% | -4.76% | 52.07 | 31.95 | 40.79 |
56. | Oct 31, 2021 | 7.20% | 6.91% | 34.52 | 36.23 | 35.36 |
57. | Nov 30, 2021 | -5.88% | -0.83% | 52.00 | 2.99 | 12.47 |
58. | Dec 31, 2021 | 3.28% | 4.36% | 3.80 | 12.01 | 6.76 |
59. | Jan 31, 2022 | -3.37% | -5.26% | 22.10 | 37.87 | 28.93 |
60. | Feb 28, 2022 | -3.33% | -3.14% | 21.66 | 16.25 | 18.76 |
61. | Mar 31, 2022 | 10.59% | 3.58% | 85.87 | 7.19 | 24.85 |
62. | Apr 30, 2022 | 2.73% | -8.80% | 1.97 | 93.91 | -13.61 |
63. | May 31, 2022 | -15.56% | 0.01% | 285.10 | 0.79 | 15.03 |
64. | Jun 30, 2022 | -5.48% | -8.39% | 46.36 | 86.25 | 63.24 |
65. | Jul 31, 2022 | 8.61% | 9.11% | 53.05 | 67.51 | 59.84 |
66. | Aug 31, 2022 | 0.80% | -4.24% | 0.28 | 26.41 | 2.70 |
67. | Sep 30, 2022 | -2.15% | -9.34% | 12.10 | 104.75 | 35.60 |
68. | Oct 31, 2022 | 9.74% | 7.99% | 70.72 | 50.28 | 59.63 |
69. | Nov 30, 2022 | 7.09% | 5.38% | 33.19 | 20.07 | 25.81 |
70. | Dec 31, 2022 | -6.61% | -5.90% | 62.96 | 46.14 | 53.90 |
71. | Jan 31, 2023 | 1.47% | 6.18% | 0.02 | 27.88 | 0.73 |
Total (Σ): | 2,268.88 | 1,754.14 | 970.23 |
Show all
VarianceWMT = Σ(RWMT,t–RWMT)2 ÷ (71 – 1)
= 2,268.88 ÷ (71 – 1)
= 32.41
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,754.14 ÷ (71 – 1)
= 25.06
CovarianceWMT, S&P 500 = Σ(RWMT,t–RWMT)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 970.23 ÷ (71 – 1)
= 13.86
Systematic Risk (β) Estimation
VarianceWMT | 32.41 |
VarianceS&P 500 | 25.06 |
CovarianceWMT, S&P 500 | 13.86 |
Correlation coefficientWMT, S&P 5001 | 0.49 |
βWMT2 | 0.55 |
αWMT3 | 0.83% |
Calculations
1 Correlation coefficientWMT, S&P 500
= CovarianceWMT, S&P 500 ÷ (Standard deviationWMT × Standard deviationS&P 500)
= 13.86 ÷ (5.69% × 5.01%)
= 0.49
2 βWMT
= CovarianceWMT, S&P 500 ÷ VarianceS&P 500
= 13.86 ÷ 25.06
= 0.55
3 αWMT
= AverageWMT – βWMT × AverageS&P 500
= 1.33% – 0.55 × 0.90%
= 0.83%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.46% |
Expected rate of return on market portfolio2 | E(RM) | 13.29% |
Systematic risk (β) of Walmart Inc. common stock | βWMT | 0.55 |
Expected rate of return on Walmart Inc. common stock3 | E(RWMT) | 9.34% |
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(RWMT) = RF + βWMT [E(RM) – RF]
= 4.46% + 0.55 [13.29% – 4.46%]
= 9.34%