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 Williams-Sonoma Inc. common stock.
Rates of Return
Williams-Sonoma Inc., monthly rates of return
| Williams-Sonoma Inc. (WSM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceWSM,t1 | DividendWSM,t1 | RWSM,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Feb 28, 2018 | $51.76 | 2,713.83 | ||||
| 1. | Mar 31, 2018 | $52.76 | 1.93% | 2,640.87 | -2.69% | |
| 2. | Apr 30, 2018 | $47.80 | $0.43 | -8.59% | 2,648.05 | 0.27% |
| 3. | May 31, 2018 | $55.37 | 15.84% | 2,705.27 | 2.16% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Dec 31, 2023 | $201.78 | 7.59% | 4,769.83 | 4.42% | |
| 71. | Jan 31, 2024 | $193.39 | $0.90 | -3.71% | 4,845.65 | 1.59% |
| Average (R): | 2.88% | 0.95% | ||||
| Standard deviation: | 13.17% | 5.18% | ||||
| Williams-Sonoma Inc. (WSM) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceWSM,t1 | DividendWSM,t1 | RWSM,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Feb 28, 2018 | $51.76 | 2,713.83 | ||||
| 1. | Mar 31, 2018 | $52.76 | 1.93% | 2,640.87 | -2.69% | |
| 2. | Apr 30, 2018 | $47.80 | $0.43 | -8.59% | 2,648.05 | 0.27% |
| 3. | May 31, 2018 | $55.37 | 15.84% | 2,705.27 | 2.16% | |
| 4. | Jun 30, 2018 | $61.38 | 10.85% | 2,718.37 | 0.48% | |
| 5. | Jul 31, 2018 | $58.49 | $0.43 | -4.01% | 2,816.29 | 3.60% |
| 6. | Aug 31, 2018 | $70.23 | 20.07% | 2,901.52 | 3.03% | |
| 7. | Sep 30, 2018 | $65.72 | -6.42% | 2,913.98 | 0.43% | |
| 8. | Oct 31, 2018 | $59.38 | $0.43 | -8.99% | 2,711.74 | -6.94% |
| 9. | Nov 30, 2018 | $56.63 | -4.63% | 2,760.17 | 1.79% | |
| 10. | Dec 31, 2018 | $50.45 | -10.91% | 2,506.85 | -9.18% | |
| 11. | Jan 31, 2019 | $54.43 | $0.43 | 8.74% | 2,704.10 | 7.87% |
| 12. | Feb 28, 2019 | $58.16 | 6.85% | 2,784.49 | 2.97% | |
| 13. | Mar 31, 2019 | $56.27 | -3.25% | 2,834.40 | 1.79% | |
| 14. | Apr 30, 2019 | $57.17 | $0.48 | 2.45% | 2,945.83 | 3.93% |
| 15. | May 31, 2019 | $58.50 | 2.33% | 2,752.06 | -6.58% | |
| 16. | Jun 30, 2019 | $65.00 | 11.11% | 2,941.76 | 6.89% | |
| 17. | Jul 31, 2019 | $66.68 | $0.48 | 3.32% | 2,980.38 | 1.31% |
| 18. | Aug 31, 2019 | $65.80 | -1.32% | 2,926.46 | -1.81% | |
| 19. | Sep 30, 2019 | $67.98 | 3.31% | 2,976.74 | 1.72% | |
| 20. | Oct 31, 2019 | $66.79 | $0.48 | -1.04% | 3,037.56 | 2.04% |
| 21. | Nov 30, 2019 | $69.40 | 3.91% | 3,140.98 | 3.40% | |
| 22. | Dec 31, 2019 | $73.44 | 5.82% | 3,230.78 | 2.86% | |
| 23. | Jan 31, 2020 | $70.08 | $0.48 | -3.92% | 3,225.52 | -0.16% |
| 24. | Feb 29, 2020 | $62.39 | -10.97% | 2,954.22 | -8.41% | |
| 25. | Mar 31, 2020 | $42.52 | -31.85% | 2,584.59 | -12.51% | |
| 26. | Apr 30, 2020 | $61.84 | $0.48 | 46.57% | 2,912.43 | 12.68% |
| 27. | May 31, 2020 | $83.21 | 34.56% | 3,044.31 | 4.53% | |
| 28. | Jun 30, 2020 | $82.01 | -1.44% | 3,100.29 | 1.84% | |
| 29. | Jul 31, 2020 | $87.12 | $0.48 | 6.82% | 3,271.12 | 5.51% |
| 30. | Aug 31, 2020 | $87.76 | 0.73% | 3,500.31 | 7.01% | |
| 31. | Sep 30, 2020 | $90.44 | 3.05% | 3,363.00 | -3.92% | |
| 32. | Oct 31, 2020 | $91.21 | $0.53 | 1.44% | 3,269.96 | -2.77% |
| 33. | Nov 30, 2020 | $109.47 | 20.02% | 3,621.63 | 10.75% | |
| 34. | Dec 31, 2020 | $101.84 | -6.97% | 3,756.07 | 3.71% | |
| 35. | Jan 31, 2021 | $128.92 | $0.53 | 27.11% | 3,714.24 | -1.11% |
| 36. | Feb 28, 2021 | $131.29 | 1.84% | 3,811.15 | 2.61% | |
| 37. | Mar 31, 2021 | $179.20 | 36.49% | 3,972.89 | 4.24% | |
| 38. | Apr 30, 2021 | $170.75 | $0.59 | -4.39% | 4,181.17 | 5.24% |
| 39. | May 31, 2021 | $169.54 | -0.71% | 4,204.11 | 0.55% | |
| 40. | Jun 30, 2021 | $159.65 | -5.83% | 4,297.50 | 2.22% | |
| 41. | Jul 31, 2021 | $151.70 | $0.59 | -4.61% | 4,395.26 | 2.27% |
| 42. | Aug 31, 2021 | $186.70 | 23.07% | 4,522.68 | 2.90% | |
| 43. | Sep 30, 2021 | $177.33 | -5.02% | 4,307.54 | -4.76% | |
| 44. | Oct 31, 2021 | $185.73 | $0.71 | 5.14% | 4,605.38 | 6.91% |
| 45. | Nov 30, 2021 | $194.84 | 4.90% | 4,567.00 | -0.83% | |
| 46. | Dec 31, 2021 | $169.13 | -13.20% | 4,766.18 | 4.36% | |
| 47. | Jan 31, 2022 | $160.54 | $0.71 | -4.66% | 4,515.55 | -5.26% |
| 48. | Feb 28, 2022 | $144.86 | -9.77% | 4,373.94 | -3.14% | |
| 49. | Mar 31, 2022 | $145.00 | 0.10% | 4,530.41 | 3.58% | |
| 50. | Apr 30, 2022 | $130.48 | $0.78 | -9.48% | 4,131.93 | -8.80% |
| 51. | May 31, 2022 | $127.92 | -1.96% | 4,132.15 | 0.01% | |
| 52. | Jun 30, 2022 | $110.95 | -13.27% | 3,785.38 | -8.39% | |
| 53. | Jul 31, 2022 | $144.42 | $0.78 | 30.87% | 4,130.29 | 9.11% |
| 54. | Aug 31, 2022 | $148.75 | 3.00% | 3,955.00 | -4.24% | |
| 55. | Sep 30, 2022 | $117.85 | -20.77% | 3,585.62 | -9.34% | |
| 56. | Oct 31, 2022 | $123.83 | $0.78 | 5.74% | 3,871.98 | 7.99% |
| 57. | Nov 30, 2022 | $116.90 | -5.60% | 4,080.11 | 5.38% | |
| 58. | Dec 31, 2022 | $114.92 | -1.69% | 3,839.50 | -5.90% | |
| 59. | Jan 31, 2023 | $134.94 | $0.78 | 18.10% | 4,076.60 | 6.18% |
| 60. | Feb 28, 2023 | $124.92 | -7.43% | 3,970.15 | -2.61% | |
| 61. | Mar 31, 2023 | $121.66 | -2.61% | 4,109.31 | 3.51% | |
| 62. | Apr 30, 2023 | $121.04 | $0.90 | 0.23% | 4,169.48 | 1.46% |
| 63. | May 31, 2023 | $113.51 | -6.22% | 4,179.83 | 0.25% | |
| 64. | Jun 30, 2023 | $125.14 | 10.25% | 4,376.86 | 4.71% | |
| 65. | Jul 31, 2023 | $138.64 | $0.90 | 11.51% | 4,588.96 | 4.85% |
| 66. | Aug 31, 2023 | $141.20 | 1.85% | 4,507.66 | -1.77% | |
| 67. | Sep 30, 2023 | $155.40 | 10.06% | 4,288.05 | -4.87% | |
| 68. | Oct 31, 2023 | $150.24 | $0.90 | -2.74% | 4,193.80 | -2.20% |
| 69. | Nov 30, 2023 | $187.54 | 24.83% | 4,567.80 | 8.92% | |
| 70. | Dec 31, 2023 | $201.78 | 7.59% | 4,769.83 | 4.42% | |
| 71. | Jan 31, 2024 | $193.39 | $0.90 | -3.71% | 4,845.65 | 1.59% |
| Average (R): | 2.88% | 0.95% | ||||
| Standard deviation: | 13.17% | 5.18% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of WSM during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Williams-Sonoma Inc., calculation of variance and covariance of returns
| t | Date | RWSM,t | RS&P 500,t | (RWSM,t–RWSM)2 | (RS&P 500,t–RS&P 500)2 | (RWSM,t–RWSM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Mar 31, 2018 | 1.93% | -2.69% | 0.90 | 13.26 | 3.45 |
| 2. | Apr 30, 2018 | -8.59% | 0.27% | 131.45 | 0.46 | 7.81 |
| 3. | May 31, 2018 | 15.84% | 2.16% | 167.90 | 1.46 | 15.65 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Dec 31, 2023 | 7.59% | 4.42% | 22.22 | 12.04 | 16.36 |
| 71. | Jan 31, 2024 | -3.71% | 1.59% | 43.44 | 0.41 | -4.20 |
| Total (Σ): | 12,144.47 | 1,876.53 | 2,995.02 | |||
| t | Date | RWSM,t | RS&P 500,t | (RWSM,t–RWSM)2 | (RS&P 500,t–RS&P 500)2 | (RWSM,t–RWSM)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Mar 31, 2018 | 1.93% | -2.69% | 0.90 | 13.26 | 3.45 |
| 2. | Apr 30, 2018 | -8.59% | 0.27% | 131.45 | 0.46 | 7.81 |
| 3. | May 31, 2018 | 15.84% | 2.16% | 167.90 | 1.46 | 15.65 |
| 4. | Jun 30, 2018 | 10.85% | 0.48% | 63.60 | 0.22 | -3.74 |
| 5. | Jul 31, 2018 | -4.01% | 3.60% | 47.43 | 7.02 | -18.25 |
| 6. | Aug 31, 2018 | 20.07% | 3.03% | 295.59 | 4.30 | 35.65 |
| 7. | Sep 30, 2018 | -6.42% | 0.43% | 86.51 | 0.27 | 4.87 |
| 8. | Oct 31, 2018 | -8.99% | -6.94% | 140.94 | 62.30 | 93.71 |
| 9. | Nov 30, 2018 | -4.63% | 1.79% | 56.40 | 0.69 | -6.26 |
| 10. | Dec 31, 2018 | -10.91% | -9.18% | 190.22 | 102.63 | 139.72 |
| 11. | Jan 31, 2019 | 8.74% | 7.87% | 34.37 | 47.82 | 40.54 |
| 12. | Feb 28, 2019 | 6.85% | 2.97% | 15.79 | 4.08 | 8.03 |
| 13. | Mar 31, 2019 | -3.25% | 1.79% | 37.56 | 0.70 | -5.15 |
| 14. | Apr 30, 2019 | 2.45% | 3.93% | 0.18 | 8.87 | -1.27 |
| 15. | May 31, 2019 | 2.33% | -6.58% | 0.31 | 56.71 | 4.16 |
| 16. | Jun 30, 2019 | 11.11% | 6.89% | 67.77 | 35.28 | 48.90 |
| 17. | Jul 31, 2019 | 3.32% | 1.31% | 0.20 | 0.13 | 0.16 |
| 18. | Aug 31, 2019 | -1.32% | -1.81% | 17.63 | 7.63 | 11.60 |
| 19. | Sep 30, 2019 | 3.31% | 1.72% | 0.19 | 0.59 | 0.33 |
| 20. | Oct 31, 2019 | -1.04% | 2.04% | 15.39 | 1.19 | -4.28 |
| 21. | Nov 30, 2019 | 3.91% | 3.40% | 1.06 | 6.01 | 2.52 |
| 22. | Dec 31, 2019 | 5.82% | 2.86% | 8.66 | 3.63 | 5.61 |
| 23. | Jan 31, 2020 | -3.92% | -0.16% | 46.25 | 1.24 | 7.59 |
| 24. | Feb 29, 2020 | -10.97% | -8.41% | 191.88 | 87.68 | 129.71 |
| 25. | Mar 31, 2020 | -31.85% | -12.51% | 1,205.97 | 181.30 | 467.60 |
| 26. | Apr 30, 2020 | 46.57% | 12.68% | 1,908.58 | 137.63 | 512.52 |
| 27. | May 31, 2020 | 34.56% | 4.53% | 1,003.49 | 12.78 | 113.26 |
| 28. | Jun 30, 2020 | -1.44% | 1.84% | 18.67 | 0.78 | -3.83 |
| 29. | Jul 31, 2020 | 6.82% | 5.51% | 15.50 | 20.77 | 17.94 |
| 30. | Aug 31, 2020 | 0.73% | 7.01% | 4.60 | 36.65 | -12.98 |
| 31. | Sep 30, 2020 | 3.05% | -3.92% | 0.03 | 23.77 | -0.85 |
| 32. | Oct 31, 2020 | 1.44% | -2.77% | 2.08 | 13.83 | 5.36 |
| 33. | Nov 30, 2020 | 20.02% | 10.75% | 293.80 | 96.07 | 168.01 |
| 34. | Dec 31, 2020 | -6.97% | 3.71% | 97.00 | 7.61 | -27.18 |
| 35. | Jan 31, 2021 | 27.11% | -1.11% | 587.19 | 4.27 | -50.08 |
| 36. | Feb 28, 2021 | 1.84% | 2.61% | 1.08 | 2.74 | -1.72 |
| 37. | Mar 31, 2021 | 36.49% | 4.24% | 1,129.81 | 10.83 | 110.62 |
| 38. | Apr 30, 2021 | -4.39% | 5.24% | 52.78 | 18.40 | -31.17 |
| 39. | May 31, 2021 | -0.71% | 0.55% | 12.87 | 0.16 | 1.45 |
| 40. | Jun 30, 2021 | -5.83% | 2.22% | 75.91 | 1.61 | -11.05 |
| 41. | Jul 31, 2021 | -4.61% | 2.27% | 56.09 | 1.75 | -9.90 |
| 42. | Aug 31, 2021 | 23.07% | 2.90% | 407.75 | 3.79 | 39.30 |
| 43. | Sep 30, 2021 | -5.02% | -4.76% | 62.38 | 32.60 | 45.10 |
| 44. | Oct 31, 2021 | 5.14% | 6.91% | 5.10 | 35.54 | 13.46 |
| 45. | Nov 30, 2021 | 4.90% | -0.83% | 4.10 | 3.19 | -3.62 |
| 46. | Dec 31, 2021 | -13.20% | 4.36% | 258.39 | 11.62 | -54.79 |
| 47. | Jan 31, 2022 | -4.66% | -5.26% | 56.82 | 38.58 | 46.82 |
| 48. | Feb 28, 2022 | -9.77% | -3.14% | 159.92 | 16.72 | 51.71 |
| 49. | Mar 31, 2022 | 0.10% | 3.58% | 7.74 | 6.89 | -7.30 |
| 50. | Apr 30, 2022 | -9.48% | -8.80% | 152.64 | 95.04 | 120.44 |
| 51. | May 31, 2022 | -1.96% | 0.01% | 23.44 | 0.90 | 4.59 |
| 52. | Jun 30, 2022 | -13.27% | -8.39% | 260.67 | 87.33 | 150.88 |
| 53. | Jul 31, 2022 | 30.87% | 9.11% | 783.48 | 66.56 | 228.37 |
| 54. | Aug 31, 2022 | 3.00% | -4.24% | 0.01 | 27.01 | -0.62 |
| 55. | Sep 30, 2022 | -20.77% | -9.34% | 559.43 | 105.94 | 243.44 |
| 56. | Oct 31, 2022 | 5.74% | 7.99% | 8.16 | 49.47 | 20.09 |
| 57. | Nov 30, 2022 | -5.60% | 5.38% | 71.83 | 19.56 | -37.48 |
| 58. | Dec 31, 2022 | -1.69% | -5.90% | 20.91 | 46.92 | 31.32 |
| 59. | Jan 31, 2023 | 18.10% | 6.18% | 231.66 | 27.27 | 79.49 |
| 60. | Feb 28, 2023 | -7.43% | -2.61% | 106.18 | 12.70 | 36.73 |
| 61. | Mar 31, 2023 | -2.61% | 3.51% | 30.13 | 6.51 | -14.01 |
| 62. | Apr 30, 2023 | 0.23% | 1.46% | 7.02 | 0.26 | -1.35 |
| 63. | May 31, 2023 | -6.22% | 0.25% | 82.81 | 0.50 | 6.41 |
| 64. | Jun 30, 2023 | 10.25% | 4.71% | 54.27 | 14.14 | 27.71 |
| 65. | Jul 31, 2023 | 11.51% | 4.85% | 74.44 | 15.16 | 33.59 |
| 66. | Aug 31, 2023 | 1.85% | -1.77% | 1.07 | 7.42 | 2.81 |
| 67. | Sep 30, 2023 | 10.06% | -4.87% | 51.52 | 33.93 | -41.81 |
| 68. | Oct 31, 2023 | -2.74% | -2.20% | 31.59 | 9.93 | 17.71 |
| 69. | Nov 30, 2023 | 24.83% | 8.92% | 481.71 | 63.44 | 174.81 |
| 70. | Dec 31, 2023 | 7.59% | 4.42% | 22.22 | 12.04 | 16.36 |
| 71. | Jan 31, 2024 | -3.71% | 1.59% | 43.44 | 0.41 | -4.20 |
| Total (Σ): | 12,144.47 | 1,876.53 | 2,995.02 | |||
Show all
VarianceWSM = Σ(RWSM,t–RWSM)2 ÷ (71 – 1)
= 12,144.47 ÷ (71 – 1)
= 173.49
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,876.53 ÷ (71 – 1)
= 26.81
CovarianceWSM, S&P 500 = Σ(RWSM,t–RWSM)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,995.02 ÷ (71 – 1)
= 42.79
Systematic Risk (β) Estimation
| VarianceWSM | 173.49 |
| VarianceS&P 500 | 26.81 |
| CovarianceWSM, S&P 500 | 42.79 |
| Correlation coefficientWSM, S&P 5001 | 0.63 |
| βWSM2 | 1.60 |
| αWSM3 | 1.36% |
Calculations
1 Correlation coefficientWSM, S&P 500
= CovarianceWSM, S&P 500 ÷ (Standard deviationWSM × Standard deviationS&P 500)
= 42.79 ÷ (13.17% × 5.18%)
= 0.63
2 βWSM
= CovarianceWSM, S&P 500 ÷ VarianceS&P 500
= 42.79 ÷ 26.81
= 1.60
3 αWSM
= AverageWSM – βWSM × AverageS&P 500
= 2.88% – 1.60 × 0.95%
= 1.36%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 3.99% |
| Expected rate of return on market portfolio2 | E(RM) | 13.81% |
| Systematic risk (β) of Williams-Sonoma Inc. common stock | βWSM | 1.60 |
| Expected rate of return on Williams-Sonoma Inc. common stock3 | E(RWSM) | 19.66% |
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(RWSM) = RF + βWSM [E(RM) – RF]
= 3.99% + 1.60 [13.81% – 3.99%]
= 19.66%