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 TJX Cos. Inc. common stock.
Rates of Return
TJX Cos. Inc., monthly rates of return
| TJX Cos. Inc. (TJX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceTJX,t1 | DividendTJX,t1 | RTJX,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Feb 28, 2018 | $41.34 | 2,713.83 | ||||
| 1. | Mar 31, 2018 | $40.78 | -1.35% | 2,640.87 | -2.69% | |
| 2. | Apr 30, 2018 | $42.42 | 4.02% | 2,648.05 | 0.27% | |
| 3. | May 31, 2018 | $45.16 | $0.195 | 6.92% | 2,705.27 | 2.16% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Dec 31, 2023 | $93.81 | 6.47% | 4,769.83 | 4.42% | |
| 71. | Jan 31, 2024 | $94.91 | 1.17% | 4,845.65 | 1.59% | |
| Average (R): | 1.53% | 0.95% | ||||
| Standard deviation: | 6.96% | 5.18% | ||||
| TJX Cos. Inc. (TJX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceTJX,t1 | DividendTJX,t1 | RTJX,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Feb 28, 2018 | $41.34 | 2,713.83 | ||||
| 1. | Mar 31, 2018 | $40.78 | -1.35% | 2,640.87 | -2.69% | |
| 2. | Apr 30, 2018 | $42.42 | 4.02% | 2,648.05 | 0.27% | |
| 3. | May 31, 2018 | $45.16 | $0.195 | 6.92% | 2,705.27 | 2.16% |
| 4. | Jun 30, 2018 | $47.59 | 5.38% | 2,718.37 | 0.48% | |
| 5. | Jul 31, 2018 | $48.63 | 2.19% | 2,816.29 | 3.60% | |
| 6. | Aug 31, 2018 | $54.99 | $0.195 | 13.48% | 2,901.52 | 3.03% |
| 7. | Sep 30, 2018 | $56.01 | 1.85% | 2,913.98 | 0.43% | |
| 8. | Oct 31, 2018 | $54.94 | -1.91% | 2,711.74 | -6.94% | |
| 9. | Nov 30, 2018 | $48.85 | $0.195 | -10.73% | 2,760.17 | 1.79% |
| 10. | Dec 31, 2018 | $44.74 | -8.41% | 2,506.85 | -9.18% | |
| 11. | Jan 31, 2019 | $49.73 | 11.15% | 2,704.10 | 7.87% | |
| 12. | Feb 28, 2019 | $51.29 | $0.195 | 3.53% | 2,784.49 | 2.97% |
| 13. | Mar 31, 2019 | $53.21 | 3.74% | 2,834.40 | 1.79% | |
| 14. | Apr 30, 2019 | $54.88 | 3.14% | 2,945.83 | 3.93% | |
| 15. | May 31, 2019 | $50.29 | $0.23 | -7.94% | 2,752.06 | -6.58% |
| 16. | Jun 30, 2019 | $52.88 | 5.15% | 2,941.76 | 6.89% | |
| 17. | Jul 31, 2019 | $54.56 | 3.18% | 2,980.38 | 1.31% | |
| 18. | Aug 31, 2019 | $54.97 | $0.23 | 1.17% | 2,926.46 | -1.81% |
| 19. | Sep 30, 2019 | $55.74 | 1.40% | 2,976.74 | 1.72% | |
| 20. | Oct 31, 2019 | $57.65 | 3.43% | 3,037.56 | 2.04% | |
| 21. | Nov 30, 2019 | $61.13 | $0.23 | 6.44% | 3,140.98 | 3.40% |
| 22. | Dec 31, 2019 | $61.06 | -0.11% | 3,230.78 | 2.86% | |
| 23. | Jan 31, 2020 | $59.04 | -3.31% | 3,225.52 | -0.16% | |
| 24. | Feb 29, 2020 | $59.80 | $0.23 | 1.68% | 2,954.22 | -8.41% |
| 25. | Mar 31, 2020 | $47.81 | -20.05% | 2,584.59 | -12.51% | |
| 26. | Apr 30, 2020 | $49.05 | 2.59% | 2,912.43 | 12.68% | |
| 27. | May 31, 2020 | $52.76 | 7.56% | 3,044.31 | 4.53% | |
| 28. | Jun 30, 2020 | $50.56 | -4.17% | 3,100.29 | 1.84% | |
| 29. | Jul 31, 2020 | $51.99 | 2.83% | 3,271.12 | 5.51% | |
| 30. | Aug 31, 2020 | $54.79 | 5.39% | 3,500.31 | 7.01% | |
| 31. | Sep 30, 2020 | $55.65 | 1.57% | 3,363.00 | -3.92% | |
| 32. | Oct 31, 2020 | $50.80 | -8.72% | 3,269.96 | -2.77% | |
| 33. | Nov 30, 2020 | $63.51 | 25.02% | 3,621.63 | 10.75% | |
| 34. | Dec 31, 2020 | $68.29 | 7.53% | 3,756.07 | 3.71% | |
| 35. | Jan 31, 2021 | $64.04 | -6.22% | 3,714.24 | -1.11% | |
| 36. | Feb 28, 2021 | $65.99 | $0.26 | 3.45% | 3,811.15 | 2.61% |
| 37. | Mar 31, 2021 | $66.15 | 0.24% | 3,972.89 | 4.24% | |
| 38. | Apr 30, 2021 | $71.00 | 7.33% | 4,181.17 | 5.24% | |
| 39. | May 31, 2021 | $67.54 | $0.26 | -4.51% | 4,204.11 | 0.55% |
| 40. | Jun 30, 2021 | $67.42 | -0.18% | 4,297.50 | 2.22% | |
| 41. | Jul 31, 2021 | $68.81 | 2.06% | 4,395.26 | 2.27% | |
| 42. | Aug 31, 2021 | $72.72 | $0.26 | 6.06% | 4,522.68 | 2.90% |
| 43. | Sep 30, 2021 | $65.98 | -9.27% | 4,307.54 | -4.76% | |
| 44. | Oct 31, 2021 | $65.49 | -0.74% | 4,605.38 | 6.91% | |
| 45. | Nov 30, 2021 | $69.40 | $0.26 | 6.37% | 4,567.00 | -0.83% |
| 46. | Dec 31, 2021 | $75.92 | 9.39% | 4,766.18 | 4.36% | |
| 47. | Jan 31, 2022 | $71.97 | -5.20% | 4,515.55 | -5.26% | |
| 48. | Feb 28, 2022 | $66.10 | $0.26 | -7.79% | 4,373.94 | -3.14% |
| 49. | Mar 31, 2022 | $60.58 | -8.35% | 4,530.41 | 3.58% | |
| 50. | Apr 30, 2022 | $61.28 | 1.16% | 4,131.93 | -8.80% | |
| 51. | May 31, 2022 | $63.57 | $0.295 | 4.22% | 4,132.15 | 0.01% |
| 52. | Jun 30, 2022 | $55.85 | -12.14% | 3,785.38 | -8.39% | |
| 53. | Jul 31, 2022 | $61.16 | 9.51% | 4,130.29 | 9.11% | |
| 54. | Aug 31, 2022 | $62.35 | $0.295 | 2.43% | 3,955.00 | -4.24% |
| 55. | Sep 30, 2022 | $62.12 | -0.37% | 3,585.62 | -9.34% | |
| 56. | Oct 31, 2022 | $72.10 | 16.07% | 3,871.98 | 7.99% | |
| 57. | Nov 30, 2022 | $80.05 | $0.295 | 11.44% | 4,080.11 | 5.38% |
| 58. | Dec 31, 2022 | $79.60 | -0.56% | 3,839.50 | -5.90% | |
| 59. | Jan 31, 2023 | $81.86 | 2.84% | 4,076.60 | 6.18% | |
| 60. | Feb 28, 2023 | $76.60 | $0.295 | -6.07% | 3,970.15 | -2.61% |
| 61. | Mar 31, 2023 | $78.36 | 2.30% | 4,109.31 | 3.51% | |
| 62. | Apr 30, 2023 | $78.82 | 0.59% | 4,169.48 | 1.46% | |
| 63. | May 31, 2023 | $76.79 | $0.3325 | -2.15% | 4,179.83 | 0.25% |
| 64. | Jun 30, 2023 | $84.79 | 10.42% | 4,376.86 | 4.71% | |
| 65. | Jul 31, 2023 | $86.53 | 2.05% | 4,588.96 | 4.85% | |
| 66. | Aug 31, 2023 | $92.48 | $0.3325 | 7.26% | 4,507.66 | -1.77% |
| 67. | Sep 30, 2023 | $88.88 | -3.89% | 4,288.05 | -4.87% | |
| 68. | Oct 31, 2023 | $88.07 | -0.91% | 4,193.80 | -2.20% | |
| 69. | Nov 30, 2023 | $88.11 | $0.3325 | 0.42% | 4,567.80 | 8.92% |
| 70. | Dec 31, 2023 | $93.81 | 6.47% | 4,769.83 | 4.42% | |
| 71. | Jan 31, 2024 | $94.91 | 1.17% | 4,845.65 | 1.59% | |
| Average (R): | 1.53% | 0.95% | ||||
| Standard deviation: | 6.96% | 5.18% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of TJX during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
TJX Cos. Inc., calculation of variance and covariance of returns
| t | Date | RTJX,t | RS&P 500,t | (RTJX,t–RTJX)2 | (RS&P 500,t–RS&P 500)2 | (RTJX,t–RTJX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Mar 31, 2018 | -1.35% | -2.69% | 8.31 | 13.26 | 10.50 |
| 2. | Apr 30, 2018 | 4.02% | 0.27% | 6.22 | 0.46 | -1.70 |
| 3. | May 31, 2018 | 6.92% | 2.16% | 29.06 | 1.46 | 6.51 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Dec 31, 2023 | 6.47% | 4.42% | 24.41 | 12.04 | 17.15 |
| 71. | Jan 31, 2024 | 1.17% | 1.59% | 0.13 | 0.41 | -0.23 |
| Total (Σ): | 3,391.41 | 1,876.53 | 1,621.98 | |||
| t | Date | RTJX,t | RS&P 500,t | (RTJX,t–RTJX)2 | (RS&P 500,t–RS&P 500)2 | (RTJX,t–RTJX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Mar 31, 2018 | -1.35% | -2.69% | 8.31 | 13.26 | 10.50 |
| 2. | Apr 30, 2018 | 4.02% | 0.27% | 6.22 | 0.46 | -1.70 |
| 3. | May 31, 2018 | 6.92% | 2.16% | 29.06 | 1.46 | 6.51 |
| 4. | Jun 30, 2018 | 5.38% | 0.48% | 14.84 | 0.22 | -1.81 |
| 5. | Jul 31, 2018 | 2.19% | 3.60% | 0.43 | 7.02 | 1.74 |
| 6. | Aug 31, 2018 | 13.48% | 3.03% | 142.83 | 4.30 | 24.78 |
| 7. | Sep 30, 2018 | 1.85% | 0.43% | 0.11 | 0.27 | -0.17 |
| 8. | Oct 31, 2018 | -1.91% | -6.94% | 11.82 | 62.30 | 27.14 |
| 9. | Nov 30, 2018 | -10.73% | 1.79% | 150.26 | 0.69 | -10.21 |
| 10. | Dec 31, 2018 | -8.41% | -9.18% | 98.84 | 102.63 | 100.71 |
| 11. | Jan 31, 2019 | 11.15% | 7.87% | 92.65 | 47.82 | 66.56 |
| 12. | Feb 28, 2019 | 3.53% | 2.97% | 4.00 | 4.08 | 4.04 |
| 13. | Mar 31, 2019 | 3.74% | 1.79% | 4.91 | 0.70 | 1.86 |
| 14. | Apr 30, 2019 | 3.14% | 3.93% | 2.59 | 8.87 | 4.80 |
| 15. | May 31, 2019 | -7.94% | -6.58% | 89.73 | 56.71 | 71.34 |
| 16. | Jun 30, 2019 | 5.15% | 6.89% | 13.12 | 35.28 | 21.52 |
| 17. | Jul 31, 2019 | 3.18% | 1.31% | 2.72 | 0.13 | 0.59 |
| 18. | Aug 31, 2019 | 1.17% | -1.81% | 0.13 | 7.63 | 0.98 |
| 19. | Sep 30, 2019 | 1.40% | 1.72% | 0.02 | 0.59 | -0.10 |
| 20. | Oct 31, 2019 | 3.43% | 2.04% | 3.60 | 1.19 | 2.07 |
| 21. | Nov 30, 2019 | 6.44% | 3.40% | 24.08 | 6.01 | 12.03 |
| 22. | Dec 31, 2019 | -0.11% | 2.86% | 2.70 | 3.63 | -3.13 |
| 23. | Jan 31, 2020 | -3.31% | -0.16% | 23.39 | 1.24 | 5.40 |
| 24. | Feb 29, 2020 | 1.68% | -8.41% | 0.02 | 87.68 | -1.39 |
| 25. | Mar 31, 2020 | -20.05% | -12.51% | 465.62 | 181.30 | 290.55 |
| 26. | Apr 30, 2020 | 2.59% | 12.68% | 1.14 | 137.63 | 12.50 |
| 27. | May 31, 2020 | 7.56% | 4.53% | 36.43 | 12.78 | 21.58 |
| 28. | Jun 30, 2020 | -4.17% | 1.84% | 32.47 | 0.78 | -5.05 |
| 29. | Jul 31, 2020 | 2.83% | 5.51% | 1.69 | 20.77 | 5.93 |
| 30. | Aug 31, 2020 | 5.39% | 7.01% | 14.88 | 36.65 | 23.35 |
| 31. | Sep 30, 2020 | 1.57% | -3.92% | 0.00 | 23.77 | -0.20 |
| 32. | Oct 31, 2020 | -8.72% | -2.77% | 104.92 | 13.83 | 38.10 |
| 33. | Nov 30, 2020 | 25.02% | 10.75% | 551.86 | 96.07 | 230.26 |
| 34. | Dec 31, 2020 | 7.53% | 3.71% | 35.98 | 7.61 | 16.55 |
| 35. | Jan 31, 2021 | -6.22% | -1.11% | 60.09 | 4.27 | 16.02 |
| 36. | Feb 28, 2021 | 3.45% | 2.61% | 3.70 | 2.74 | 3.18 |
| 37. | Mar 31, 2021 | 0.24% | 4.24% | 1.65 | 10.83 | -4.23 |
| 38. | Apr 30, 2021 | 7.33% | 5.24% | 33.68 | 18.40 | 24.90 |
| 39. | May 31, 2021 | -4.51% | 0.55% | 36.42 | 0.16 | 2.44 |
| 40. | Jun 30, 2021 | -0.18% | 2.22% | 2.91 | 1.61 | -2.16 |
| 41. | Jul 31, 2021 | 2.06% | 2.27% | 0.28 | 1.75 | 0.71 |
| 42. | Aug 31, 2021 | 6.06% | 2.90% | 20.54 | 3.79 | 8.82 |
| 43. | Sep 30, 2021 | -9.27% | -4.76% | 116.56 | 32.60 | 61.65 |
| 44. | Oct 31, 2021 | -0.74% | 6.91% | 5.16 | 35.54 | -13.54 |
| 45. | Nov 30, 2021 | 6.37% | -0.83% | 23.42 | 3.19 | -8.64 |
| 46. | Dec 31, 2021 | 9.39% | 4.36% | 61.89 | 11.62 | 26.81 |
| 47. | Jan 31, 2022 | -5.20% | -5.26% | 45.31 | 38.58 | 41.81 |
| 48. | Feb 28, 2022 | -7.79% | -3.14% | 86.92 | 16.72 | 38.12 |
| 49. | Mar 31, 2022 | -8.35% | 3.58% | 97.60 | 6.89 | -25.93 |
| 50. | Apr 30, 2022 | 1.16% | -8.80% | 0.14 | 95.04 | 3.63 |
| 51. | May 31, 2022 | 4.22% | 0.01% | 7.24 | 0.90 | -2.55 |
| 52. | Jun 30, 2022 | -12.14% | -8.39% | 186.93 | 87.33 | 127.77 |
| 53. | Jul 31, 2022 | 9.51% | 9.11% | 63.67 | 66.56 | 65.10 |
| 54. | Aug 31, 2022 | 2.43% | -4.24% | 0.81 | 27.01 | -4.68 |
| 55. | Sep 30, 2022 | -0.37% | -9.34% | 3.60 | 105.94 | 19.52 |
| 56. | Oct 31, 2022 | 16.07% | 7.99% | 211.34 | 49.47 | 102.25 |
| 57. | Nov 30, 2022 | 11.44% | 5.38% | 98.16 | 19.56 | 43.81 |
| 58. | Dec 31, 2022 | -0.56% | -5.90% | 4.37 | 46.92 | 14.32 |
| 59. | Jan 31, 2023 | 2.84% | 6.18% | 1.72 | 27.27 | 6.85 |
| 60. | Feb 28, 2023 | -6.07% | -2.61% | 57.66 | 12.70 | 27.06 |
| 61. | Mar 31, 2023 | 2.30% | 3.51% | 0.59 | 6.51 | 1.96 |
| 62. | Apr 30, 2023 | 0.59% | 1.46% | 0.89 | 0.26 | -0.48 |
| 63. | May 31, 2023 | -2.15% | 0.25% | 13.56 | 0.50 | 2.59 |
| 64. | Jun 30, 2023 | 10.42% | 4.71% | 79.03 | 14.14 | 33.43 |
| 65. | Jul 31, 2023 | 2.05% | 4.85% | 0.27 | 15.16 | 2.04 |
| 66. | Aug 31, 2023 | 7.26% | -1.77% | 32.86 | 7.42 | -15.62 |
| 67. | Sep 30, 2023 | -3.89% | -4.87% | 29.39 | 33.93 | 31.58 |
| 68. | Oct 31, 2023 | -0.91% | -2.20% | 5.95 | 9.93 | 7.69 |
| 69. | Nov 30, 2023 | 0.42% | 8.92% | 1.22 | 63.44 | -8.80 |
| 70. | Dec 31, 2023 | 6.47% | 4.42% | 24.41 | 12.04 | 17.15 |
| 71. | Jan 31, 2024 | 1.17% | 1.59% | 0.13 | 0.41 | -0.23 |
| Total (Σ): | 3,391.41 | 1,876.53 | 1,621.98 | |||
Show all
VarianceTJX = Σ(RTJX,t–RTJX)2 ÷ (71 – 1)
= 3,391.41 ÷ (71 – 1)
= 48.45
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,876.53 ÷ (71 – 1)
= 26.81
CovarianceTJX, S&P 500 = Σ(RTJX,t–RTJX)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,621.98 ÷ (71 – 1)
= 23.17
Systematic Risk (β) Estimation
| VarianceTJX | 48.45 |
| VarianceS&P 500 | 26.81 |
| CovarianceTJX, S&P 500 | 23.17 |
| Correlation coefficientTJX, S&P 5001 | 0.64 |
| βTJX2 | 0.86 |
| αTJX3 | 0.70% |
Calculations
1 Correlation coefficientTJX, S&P 500
= CovarianceTJX, S&P 500 ÷ (Standard deviationTJX × Standard deviationS&P 500)
= 23.17 ÷ (6.96% × 5.18%)
= 0.64
2 βTJX
= CovarianceTJX, S&P 500 ÷ VarianceS&P 500
= 23.17 ÷ 26.81
= 0.86
3 αTJX
= AverageTJX – βTJX × AverageS&P 500
= 1.53% – 0.86 × 0.95%
= 0.70%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.65% |
| Expected rate of return on market portfolio2 | E(RM) | 13.79% |
| Systematic risk (β) of TJX Cos. Inc. common stock | βTJX | 0.86 |
| Expected rate of return on TJX Cos. Inc. common stock3 | E(RTJX) | 12.55% |
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(RTJX) = RF + βTJX [E(RM) – RF]
= 4.65% + 0.86 [13.79% – 4.65%]
= 12.55%