Capital Asset Pricing Model (CAPM)
Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Walgreens Boots Alliance Inc. common stock.
Rates of Return
Walgreens Boots Alliance Inc., monthly rates of return
| Walgreens Boots Alliance Inc. (WBA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceWBA,t1 | DividendWBA,t1 | RWBA,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Sep 30, 2013 | $53.80 | 1,681.55 | ||||
| 1. | Oct 31, 2013 | $59.24 | 10.11% | 1,756.54 | 4.46% | |
| 2. | Nov 30, 2013 | $59.20 | $0.315 | 0.46% | 1,805.81 | 2.80% |
| 3. | Dec 31, 2013 | $57.44 | -2.97% | 1,848.36 | 2.36% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Jul 31, 2019 | $54.49 | -0.33% | 2,980.38 | 1.31% | |
| 71. | Aug 31, 2019 | $51.19 | $0.458 | -5.22% | 2,926.46 | -1.81% |
| Average (R): | 0.37% | 0.84% | ||||
| Standard deviation: | 7.21% | 3.32% | ||||
| Walgreens Boots Alliance Inc. (WBA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceWBA,t1 | DividendWBA,t1 | RWBA,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Sep 30, 2013 | $53.80 | 1,681.55 | ||||
| 1. | Oct 31, 2013 | $59.24 | 10.11% | 1,756.54 | 4.46% | |
| 2. | Nov 30, 2013 | $59.20 | $0.315 | 0.46% | 1,805.81 | 2.80% |
| 3. | Dec 31, 2013 | $57.44 | -2.97% | 1,848.36 | 2.36% | |
| 4. | Jan 31, 2014 | $57.35 | -0.16% | 1,782.59 | -3.56% | |
| 5. | Feb 28, 2014 | $67.95 | $0.315 | 19.03% | 1,859.45 | 4.31% |
| 6. | Mar 31, 2014 | $66.03 | -2.83% | 1,872.34 | 0.69% | |
| 7. | Apr 30, 2014 | $67.90 | 2.83% | 1,883.95 | 0.62% | |
| 8. | May 31, 2014 | $71.91 | $0.315 | 6.37% | 1,923.57 | 2.10% |
| 9. | Jun 30, 2014 | $74.13 | 3.09% | 1,960.23 | 1.91% | |
| 10. | Jul 31, 2014 | $68.77 | -7.23% | 1,930.67 | -1.51% | |
| 11. | Aug 31, 2014 | $60.52 | $0.3375 | -11.51% | 2,003.37 | 3.77% |
| 12. | Sep 30, 2014 | $59.27 | -2.07% | 1,972.29 | -1.55% | |
| 13. | Oct 31, 2014 | $64.22 | 8.35% | 2,018.05 | 2.32% | |
| 14. | Nov 30, 2014 | $68.61 | $0.3375 | 7.36% | 2,067.56 | 2.45% |
| 15. | Dec 31, 2014 | $76.20 | 11.06% | 2,058.90 | -0.42% | |
| 16. | Jan 31, 2015 | $73.75 | -3.22% | 1,994.99 | -3.10% | |
| 17. | Feb 28, 2015 | $83.08 | $0.3375 | 13.11% | 2,104.50 | 5.49% |
| 18. | Mar 31, 2015 | $84.68 | 1.93% | 2,067.89 | -1.74% | |
| 19. | Apr 30, 2015 | $82.93 | -2.07% | 2,085.51 | 0.85% | |
| 20. | May 31, 2015 | $85.84 | $0.3375 | 3.92% | 2,107.39 | 1.05% |
| 21. | Jun 30, 2015 | $84.44 | -1.63% | 2,063.11 | -2.10% | |
| 22. | Jul 31, 2015 | $96.63 | 14.44% | 2,103.84 | 1.97% | |
| 23. | Aug 31, 2015 | $86.55 | $0.36 | -10.06% | 1,972.18 | -6.26% |
| 24. | Sep 30, 2015 | $83.10 | -3.99% | 1,920.03 | -2.64% | |
| 25. | Oct 31, 2015 | $84.68 | 1.90% | 2,079.36 | 8.30% | |
| 26. | Nov 30, 2015 | $84.03 | $0.36 | -0.34% | 2,080.41 | 0.05% |
| 27. | Dec 31, 2015 | $85.16 | 1.34% | 2,043.94 | -1.75% | |
| 28. | Jan 31, 2016 | $79.72 | -6.39% | 1,940.24 | -5.07% | |
| 29. | Feb 29, 2016 | $78.94 | $0.36 | -0.53% | 1,932.23 | -0.41% |
| 30. | Mar 31, 2016 | $84.24 | 6.71% | 2,059.74 | 6.60% | |
| 31. | Apr 30, 2016 | $79.28 | -5.89% | 2,065.30 | 0.27% | |
| 32. | May 31, 2016 | $77.40 | $0.36 | -1.92% | 2,096.95 | 1.53% |
| 33. | Jun 30, 2016 | $83.27 | 7.58% | 2,098.86 | 0.09% | |
| 34. | Jul 31, 2016 | $79.25 | -4.83% | 2,173.60 | 3.56% | |
| 35. | Aug 31, 2016 | $80.71 | $0.375 | 2.32% | 2,170.95 | -0.12% |
| 36. | Sep 30, 2016 | $80.62 | -0.11% | 2,168.27 | -0.12% | |
| 37. | Oct 31, 2016 | $82.73 | 2.62% | 2,126.15 | -1.94% | |
| 38. | Nov 30, 2016 | $84.73 | $0.375 | 2.87% | 2,198.81 | 3.42% |
| 39. | Dec 31, 2016 | $82.76 | -2.33% | 2,238.83 | 1.82% | |
| 40. | Jan 31, 2017 | $81.94 | -0.99% | 2,278.87 | 1.79% | |
| 41. | Feb 28, 2017 | $86.38 | $0.375 | 5.88% | 2,363.64 | 3.72% |
| 42. | Mar 31, 2017 | $83.05 | -3.86% | 2,362.72 | -0.04% | |
| 43. | Apr 30, 2017 | $86.54 | 4.20% | 2,384.20 | 0.91% | |
| 44. | May 31, 2017 | $81.02 | $0.375 | -5.95% | 2,411.80 | 1.16% |
| 45. | Jun 30, 2017 | $78.31 | -3.34% | 2,423.41 | 0.48% | |
| 46. | Jul 31, 2017 | $80.67 | 3.01% | 2,470.30 | 1.93% | |
| 47. | Aug 31, 2017 | $81.50 | $0.40 | 1.52% | 2,471.65 | 0.05% |
| 48. | Sep 30, 2017 | $77.22 | -5.25% | 2,519.36 | 1.93% | |
| 49. | Oct 31, 2017 | $66.27 | -14.18% | 2,575.26 | 2.22% | |
| 50. | Nov 30, 2017 | $72.76 | $0.40 | 10.40% | 2,647.58 | 2.81% |
| 51. | Dec 31, 2017 | $72.62 | -0.19% | 2,673.61 | 0.98% | |
| 52. | Jan 31, 2018 | $75.26 | 3.64% | 2,823.81 | 5.62% | |
| 53. | Feb 28, 2018 | $68.89 | $0.40 | -7.93% | 2,713.83 | -3.89% |
| 54. | Mar 31, 2018 | $65.47 | -4.96% | 2,640.87 | -2.69% | |
| 55. | Apr 30, 2018 | $66.45 | 1.50% | 2,648.05 | 0.27% | |
| 56. | May 31, 2018 | $62.39 | $0.40 | -5.51% | 2,705.27 | 2.16% |
| 57. | Jun 30, 2018 | $60.02 | -3.80% | 2,718.37 | 0.48% | |
| 58. | Jul 31, 2018 | $67.62 | 12.66% | 2,816.29 | 3.60% | |
| 59. | Aug 31, 2018 | $68.56 | $0.44 | 2.04% | 2,901.52 | 3.03% |
| 60. | Sep 30, 2018 | $72.90 | 6.33% | 2,913.98 | 0.43% | |
| 61. | Oct 31, 2018 | $79.77 | 9.42% | 2,711.74 | -6.94% | |
| 62. | Nov 30, 2018 | $84.67 | $0.44 | 6.69% | 2,760.17 | 1.79% |
| 63. | Dec 31, 2018 | $68.33 | -19.30% | 2,506.85 | -9.18% | |
| 64. | Jan 31, 2019 | $72.26 | 5.75% | 2,704.10 | 7.87% | |
| 65. | Feb 28, 2019 | $71.19 | $0.44 | -0.87% | 2,784.49 | 2.97% |
| 66. | Mar 31, 2019 | $63.27 | -11.13% | 2,834.40 | 1.79% | |
| 67. | Apr 30, 2019 | $53.57 | -15.33% | 2,945.83 | 3.93% | |
| 68. | May 31, 2019 | $49.34 | $0.44 | -7.07% | 2,752.06 | -6.58% |
| 69. | Jun 30, 2019 | $54.67 | 10.80% | 2,941.76 | 6.89% | |
| 70. | Jul 31, 2019 | $54.49 | -0.33% | 2,980.38 | 1.31% | |
| 71. | Aug 31, 2019 | $51.19 | $0.458 | -5.22% | 2,926.46 | -1.81% |
| Average (R): | 0.37% | 0.84% | ||||
| Standard deviation: | 7.21% | 3.32% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of WBA during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Walgreens Boots Alliance Inc., calculation of variance and covariance of returns
| t | Date | RWBA,t | RS&P 500,t | (RWBA,t–RWBA)2 | (RS&P 500,t–RS&P 500)2 | (RWBA,t–RWBA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Oct 31, 2013 | 10.11% | 4.46% | 94.97 | 13.12 | 35.29 |
| 2. | Nov 30, 2013 | 0.46% | 2.80% | 0.01 | 3.87 | 0.19 |
| 3. | Dec 31, 2013 | -2.97% | 2.36% | 11.15 | 2.31 | -5.07 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Jul 31, 2019 | -0.33% | 1.31% | 0.48 | 0.23 | -0.33 |
| 71. | Aug 31, 2019 | -5.22% | -1.81% | 31.16 | 7.01 | 14.78 |
| Total (Σ): | 3,643.64 | 771.17 | 709.61 | |||
| t | Date | RWBA,t | RS&P 500,t | (RWBA,t–RWBA)2 | (RS&P 500,t–RS&P 500)2 | (RWBA,t–RWBA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Oct 31, 2013 | 10.11% | 4.46% | 94.97 | 13.12 | 35.29 |
| 2. | Nov 30, 2013 | 0.46% | 2.80% | 0.01 | 3.87 | 0.19 |
| 3. | Dec 31, 2013 | -2.97% | 2.36% | 11.15 | 2.31 | -5.07 |
| 4. | Jan 31, 2014 | -0.16% | -3.56% | 0.27 | 19.33 | 2.30 |
| 5. | Feb 28, 2014 | 19.03% | 4.31% | 348.42 | 12.07 | 64.84 |
| 6. | Mar 31, 2014 | -2.83% | 0.69% | 10.19 | 0.02 | 0.46 |
| 7. | Apr 30, 2014 | 2.83% | 0.62% | 6.08 | 0.05 | -0.54 |
| 8. | May 31, 2014 | 6.37% | 2.10% | 36.04 | 1.60 | 7.59 |
| 9. | Jun 30, 2014 | 3.09% | 1.91% | 7.40 | 1.14 | 2.91 |
| 10. | Jul 31, 2014 | -7.23% | -1.51% | 57.71 | 5.50 | 17.82 |
| 11. | Aug 31, 2014 | -11.51% | 3.77% | 140.95 | 8.57 | -34.76 |
| 12. | Sep 30, 2014 | -2.07% | -1.55% | 5.91 | 5.71 | 5.81 |
| 13. | Oct 31, 2014 | 8.35% | 2.32% | 63.77 | 2.20 | 11.84 |
| 14. | Nov 30, 2014 | 7.36% | 2.45% | 48.93 | 2.61 | 11.30 |
| 15. | Dec 31, 2014 | 11.06% | -0.42% | 114.41 | 1.58 | -13.44 |
| 16. | Jan 31, 2015 | -3.22% | -3.10% | 12.83 | 15.54 | 14.12 |
| 17. | Feb 28, 2015 | 13.11% | 5.49% | 162.36 | 21.63 | 59.27 |
| 18. | Mar 31, 2015 | 1.93% | -1.74% | 2.43 | 6.64 | -4.02 |
| 19. | Apr 30, 2015 | -2.07% | 0.85% | 5.92 | 0.00 | -0.03 |
| 20. | May 31, 2015 | 3.92% | 1.05% | 12.60 | 0.04 | 0.75 |
| 21. | Jun 30, 2015 | -1.63% | -2.10% | 3.99 | 8.64 | 5.87 |
| 22. | Jul 31, 2015 | 14.44% | 1.97% | 197.96 | 1.29 | 15.99 |
| 23. | Aug 31, 2015 | -10.06% | -6.26% | 108.69 | 50.35 | 73.98 |
| 24. | Sep 30, 2015 | -3.99% | -2.64% | 18.94 | 12.13 | 15.16 |
| 25. | Oct 31, 2015 | 1.90% | 8.30% | 2.36 | 55.66 | 11.45 |
| 26. | Nov 30, 2015 | -0.34% | 0.05% | 0.50 | 0.62 | 0.56 |
| 27. | Dec 31, 2015 | 1.34% | -1.75% | 0.96 | 6.71 | -2.54 |
| 28. | Jan 31, 2016 | -6.39% | -5.07% | 45.62 | 34.95 | 39.93 |
| 29. | Feb 29, 2016 | -0.53% | -0.41% | 0.80 | 1.56 | 1.12 |
| 30. | Mar 31, 2016 | 6.71% | 6.60% | 40.29 | 33.19 | 36.57 |
| 31. | Apr 30, 2016 | -5.89% | 0.27% | 39.12 | 0.32 | 3.55 |
| 32. | May 31, 2016 | -1.92% | 1.53% | 5.21 | 0.48 | -1.59 |
| 33. | Jun 30, 2016 | 7.58% | 0.09% | 52.10 | 0.56 | -5.39 |
| 34. | Jul 31, 2016 | -4.83% | 3.56% | 26.98 | 7.41 | -14.14 |
| 35. | Aug 31, 2016 | 2.32% | -0.12% | 3.80 | 0.92 | -1.87 |
| 36. | Sep 30, 2016 | -0.11% | -0.12% | 0.23 | 0.92 | 0.46 |
| 37. | Oct 31, 2016 | 2.62% | -1.94% | 5.07 | 7.73 | -6.26 |
| 38. | Nov 30, 2016 | 2.87% | 3.42% | 6.27 | 6.65 | 6.46 |
| 39. | Dec 31, 2016 | -2.33% | 1.82% | 7.24 | 0.96 | -2.64 |
| 40. | Jan 31, 2017 | -0.99% | 1.79% | 1.84 | 0.90 | -1.29 |
| 41. | Feb 28, 2017 | 5.88% | 3.72% | 30.36 | 8.31 | 15.88 |
| 42. | Mar 31, 2017 | -3.86% | -0.04% | 17.82 | 0.77 | 3.70 |
| 43. | Apr 30, 2017 | 4.20% | 0.91% | 14.71 | 0.01 | 0.27 |
| 44. | May 31, 2017 | -5.95% | 1.16% | 39.84 | 0.10 | -2.02 |
| 45. | Jun 30, 2017 | -3.34% | 0.48% | 13.77 | 0.13 | 1.32 |
| 46. | Jul 31, 2017 | 3.01% | 1.93% | 7.01 | 1.20 | 2.90 |
| 47. | Aug 31, 2017 | 1.52% | 0.05% | 1.34 | 0.61 | -0.91 |
| 48. | Sep 30, 2017 | -5.25% | 1.93% | 31.56 | 1.19 | -6.14 |
| 49. | Oct 31, 2017 | -14.18% | 2.22% | 211.60 | 1.91 | -20.09 |
| 50. | Nov 30, 2017 | 10.40% | 2.81% | 100.61 | 3.88 | 19.76 |
| 51. | Dec 31, 2017 | -0.19% | 0.98% | 0.31 | 0.02 | -0.08 |
| 52. | Jan 31, 2018 | 3.64% | 5.62% | 10.69 | 22.85 | 15.63 |
| 53. | Feb 28, 2018 | -7.93% | -3.89% | 68.87 | 22.40 | 39.28 |
| 54. | Mar 31, 2018 | -4.96% | -2.69% | 28.42 | 12.44 | 18.80 |
| 55. | Apr 30, 2018 | 1.50% | 0.27% | 1.28 | 0.32 | -0.64 |
| 56. | May 31, 2018 | -5.51% | 2.16% | 34.51 | 1.75 | -7.77 |
| 57. | Jun 30, 2018 | -3.80% | 0.48% | 17.35 | 0.13 | 1.47 |
| 58. | Jul 31, 2018 | 12.66% | 3.60% | 151.20 | 7.64 | 33.99 |
| 59. | Aug 31, 2018 | 2.04% | 3.03% | 2.80 | 4.79 | 3.66 |
| 60. | Sep 30, 2018 | 6.33% | 0.43% | 35.57 | 0.17 | -2.44 |
| 61. | Oct 31, 2018 | 9.42% | -6.94% | 82.04 | 60.50 | -70.45 |
| 62. | Nov 30, 2018 | 6.69% | 1.79% | 40.04 | 0.90 | 6.00 |
| 63. | Dec 31, 2018 | -19.30% | -9.18% | 386.70 | 100.31 | 196.96 |
| 64. | Jan 31, 2019 | 5.75% | 7.87% | 29.00 | 49.43 | 37.86 |
| 65. | Feb 28, 2019 | -0.87% | 2.97% | 1.53 | 4.56 | -2.64 |
| 66. | Mar 31, 2019 | -11.13% | 1.79% | 132.05 | 0.91 | -10.97 |
| 67. | Apr 30, 2019 | -15.33% | 3.93% | 246.41 | 9.57 | -48.56 |
| 68. | May 31, 2019 | -7.07% | -6.58% | 55.37 | 54.99 | 55.18 |
| 69. | Jun 30, 2019 | 10.80% | 6.89% | 108.92 | 36.66 | 63.19 |
| 70. | Jul 31, 2019 | -0.33% | 1.31% | 0.48 | 0.23 | -0.33 |
| 71. | Aug 31, 2019 | -5.22% | -1.81% | 31.16 | 7.01 | 14.78 |
| Total (Σ): | 3,643.64 | 771.17 | 709.61 | |||
Show all
VarianceWBA = Σ(RWBA,t–RWBA)2 ÷ (71 – 1)
= 3,643.64 ÷ (71 – 1)
= 52.05
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 771.17 ÷ (71 – 1)
= 11.02
CovarianceWBA, S&P 500 = Σ(RWBA,t–RWBA)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 709.61 ÷ (71 – 1)
= 10.14
Systematic Risk (β) Estimation
| VarianceWBA | 52.05 |
| VarianceS&P 500 | 11.02 |
| CovarianceWBA, S&P 500 | 10.14 |
| Correlation coefficientWBA, S&P 5001 | 0.42 |
| βWBA2 | 0.92 |
| αWBA3 | -0.40% |
Calculations
1 Correlation coefficientWBA, S&P 500
= CovarianceWBA, S&P 500 ÷ (Standard deviationWBA × Standard deviationS&P 500)
= 10.14 ÷ (7.21% × 3.32%)
= 0.42
2 βWBA
= CovarianceWBA, S&P 500 ÷ VarianceS&P 500
= 10.14 ÷ 11.02
= 0.92
3 αWBA
= AverageWBA – βWBA × AverageS&P 500
= 0.37% – 0.92 × 0.84%
= -0.40%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.57% |
| Expected rate of return on market portfolio2 | E(RM) | 13.82% |
| Systematic risk (β) of Walgreens Boots Alliance Inc. common stock | βWBA | 0.92 |
| Expected rate of return on Walgreens Boots Alliance Inc. common stock3 | E(RWBA) | 13.08% |
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(RWBA) = RF + βWBA [E(RM) – RF]
= 4.57% + 0.92 [13.82% – 4.57%]
= 13.08%