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 Intuit Inc. common stock.
Rates of Return
Intuit Inc., monthly rates of return
| Intuit Inc. (INTU) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceINTU,t1 | DividendINTU,t1 | RINTU,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Aug 31, 2018 | $219.47 | 2,901.52 | ||||
| 1. | Sep 30, 2018 | $227.40 | 3.61% | 2,913.98 | 0.43% | |
| 2. | Oct 31, 2018 | $211.00 | $0.47 | -7.01% | 2,711.74 | -6.94% |
| 3. | Nov 30, 2018 | $214.53 | 1.67% | 2,760.17 | 1.79% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Jun 30, 2024 | $657.21 | 14.01% | 5,460.48 | 3.47% | |
| 71. | Jul 31, 2024 | $647.35 | $0.90 | -1.36% | 5,522.30 | 1.13% |
| Average (R): | 1.91% | 1.05% | ||||
| Standard deviation: | 8.10% | 5.24% | ||||
| Intuit Inc. (INTU) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceINTU,t1 | DividendINTU,t1 | RINTU,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Aug 31, 2018 | $219.47 | 2,901.52 | ||||
| 1. | Sep 30, 2018 | $227.40 | 3.61% | 2,913.98 | 0.43% | |
| 2. | Oct 31, 2018 | $211.00 | $0.47 | -7.01% | 2,711.74 | -6.94% |
| 3. | Nov 30, 2018 | $214.53 | 1.67% | 2,760.17 | 1.79% | |
| 4. | Dec 31, 2018 | $196.85 | -8.24% | 2,506.85 | -9.18% | |
| 5. | Jan 31, 2019 | $215.82 | $0.47 | 9.88% | 2,704.10 | 7.87% |
| 6. | Feb 28, 2019 | $247.13 | 14.51% | 2,784.49 | 2.97% | |
| 7. | Mar 31, 2019 | $261.41 | 5.78% | 2,834.40 | 1.79% | |
| 8. | Apr 30, 2019 | $251.06 | $0.47 | -3.78% | 2,945.83 | 3.93% |
| 9. | May 31, 2019 | $244.85 | -2.47% | 2,752.06 | -6.58% | |
| 10. | Jun 30, 2019 | $261.33 | 6.73% | 2,941.76 | 6.89% | |
| 11. | Jul 31, 2019 | $277.31 | $0.47 | 6.29% | 2,980.38 | 1.31% |
| 12. | Aug 31, 2019 | $288.36 | 3.98% | 2,926.46 | -1.81% | |
| 13. | Sep 30, 2019 | $265.94 | -7.78% | 2,976.74 | 1.72% | |
| 14. | Oct 31, 2019 | $257.50 | $0.53 | -2.97% | 3,037.56 | 2.04% |
| 15. | Nov 30, 2019 | $258.89 | 0.54% | 3,140.98 | 3.40% | |
| 16. | Dec 31, 2019 | $261.93 | 1.17% | 3,230.78 | 2.86% | |
| 17. | Jan 31, 2020 | $280.38 | $0.53 | 7.25% | 3,225.52 | -0.16% |
| 18. | Feb 29, 2020 | $265.85 | -5.18% | 2,954.22 | -8.41% | |
| 19. | Mar 31, 2020 | $230.00 | -13.49% | 2,584.59 | -12.51% | |
| 20. | Apr 30, 2020 | $269.81 | $0.53 | 17.54% | 2,912.43 | 12.68% |
| 21. | May 31, 2020 | $290.32 | 7.60% | 3,044.31 | 4.53% | |
| 22. | Jun 30, 2020 | $296.19 | 2.02% | 3,100.29 | 1.84% | |
| 23. | Jul 31, 2020 | $306.37 | $0.53 | 3.62% | 3,271.12 | 5.51% |
| 24. | Aug 31, 2020 | $345.39 | 12.74% | 3,500.31 | 7.01% | |
| 25. | Sep 30, 2020 | $326.21 | -5.55% | 3,363.00 | -3.92% | |
| 26. | Oct 31, 2020 | $314.68 | $0.59 | -3.35% | 3,269.96 | -2.77% |
| 27. | Nov 30, 2020 | $352.02 | 11.87% | 3,621.63 | 10.75% | |
| 28. | Dec 31, 2020 | $379.85 | 7.91% | 3,756.07 | 3.71% | |
| 29. | Jan 31, 2021 | $361.23 | $0.59 | -4.75% | 3,714.24 | -1.11% |
| 30. | Feb 28, 2021 | $390.14 | 8.00% | 3,811.15 | 2.61% | |
| 31. | Mar 31, 2021 | $383.06 | -1.81% | 3,972.89 | 4.24% | |
| 32. | Apr 30, 2021 | $412.16 | $0.59 | 7.75% | 4,181.17 | 5.24% |
| 33. | May 31, 2021 | $439.09 | 6.53% | 4,204.11 | 0.55% | |
| 34. | Jun 30, 2021 | $490.17 | 11.63% | 4,297.50 | 2.22% | |
| 35. | Jul 31, 2021 | $529.97 | $0.59 | 8.24% | 4,395.26 | 2.27% |
| 36. | Aug 31, 2021 | $566.11 | 6.82% | 4,522.68 | 2.90% | |
| 37. | Sep 30, 2021 | $539.51 | -4.70% | 4,307.54 | -4.76% | |
| 38. | Oct 31, 2021 | $625.99 | $0.68 | 16.16% | 4,605.38 | 6.91% |
| 39. | Nov 30, 2021 | $652.30 | 4.20% | 4,567.00 | -0.83% | |
| 40. | Dec 31, 2021 | $643.22 | -1.39% | 4,766.18 | 4.36% | |
| 41. | Jan 31, 2022 | $555.23 | $0.68 | -13.57% | 4,515.55 | -5.26% |
| 42. | Feb 28, 2022 | $474.37 | -14.56% | 4,373.94 | -3.14% | |
| 43. | Mar 31, 2022 | $480.84 | 1.36% | 4,530.41 | 3.58% | |
| 44. | Apr 30, 2022 | $418.75 | $0.68 | -12.77% | 4,131.93 | -8.80% |
| 45. | May 31, 2022 | $414.46 | -1.02% | 4,132.15 | 0.01% | |
| 46. | Jun 30, 2022 | $385.44 | -7.00% | 3,785.38 | -8.39% | |
| 47. | Jul 31, 2022 | $456.17 | $0.68 | 18.53% | 4,130.29 | 9.11% |
| 48. | Aug 31, 2022 | $431.78 | -5.35% | 3,955.00 | -4.24% | |
| 49. | Sep 30, 2022 | $387.32 | -10.30% | 3,585.62 | -9.34% | |
| 50. | Oct 31, 2022 | $427.50 | $0.78 | 10.58% | 3,871.98 | 7.99% |
| 51. | Nov 30, 2022 | $407.59 | -4.66% | 4,080.11 | 5.38% | |
| 52. | Dec 31, 2022 | $389.22 | -4.51% | 3,839.50 | -5.90% | |
| 53. | Jan 31, 2023 | $422.67 | $0.78 | 8.79% | 4,076.60 | 6.18% |
| 54. | Feb 28, 2023 | $407.18 | -3.66% | 3,970.15 | -2.61% | |
| 55. | Mar 31, 2023 | $445.83 | 9.49% | 4,109.31 | 3.51% | |
| 56. | Apr 30, 2023 | $443.95 | $0.78 | -0.25% | 4,169.48 | 1.46% |
| 57. | May 31, 2023 | $419.12 | -5.59% | 4,179.83 | 0.25% | |
| 58. | Jun 30, 2023 | $458.19 | 9.32% | 4,376.86 | 4.71% | |
| 59. | Jul 31, 2023 | $511.70 | $0.78 | 11.85% | 4,588.96 | 4.85% |
| 60. | Aug 31, 2023 | $541.81 | 5.88% | 4,507.66 | -1.77% | |
| 61. | Sep 30, 2023 | $510.94 | -5.70% | 4,288.05 | -4.87% | |
| 62. | Oct 31, 2023 | $494.95 | $0.90 | -2.95% | 4,193.80 | -2.20% |
| 63. | Nov 30, 2023 | $571.46 | 15.46% | 4,567.80 | 8.92% | |
| 64. | Dec 31, 2023 | $625.03 | 9.37% | 4,769.83 | 4.42% | |
| 65. | Jan 31, 2024 | $631.33 | $0.90 | 1.15% | 4,845.65 | 1.59% |
| 66. | Feb 29, 2024 | $662.89 | 5.00% | 5,096.27 | 5.17% | |
| 67. | Mar 31, 2024 | $650.00 | -1.94% | 5,254.35 | 3.10% | |
| 68. | Apr 30, 2024 | $625.62 | $0.90 | -3.61% | 5,035.69 | -4.16% |
| 69. | May 31, 2024 | $576.44 | -7.86% | 5,277.51 | 4.80% | |
| 70. | Jun 30, 2024 | $657.21 | 14.01% | 5,460.48 | 3.47% | |
| 71. | Jul 31, 2024 | $647.35 | $0.90 | -1.36% | 5,522.30 | 1.13% |
| Average (R): | 1.91% | 1.05% | ||||
| Standard deviation: | 8.10% | 5.24% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of INTU during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Intuit Inc., calculation of variance and covariance of returns
| t | Date | RINTU,t | RS&P 500,t | (RINTU,t–RINTU)2 | (RS&P 500,t–RS&P 500)2 | (RINTU,t–RINTU)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Sep 30, 2018 | 3.61% | 0.43% | 2.90 | 0.38 | -1.05 |
| 2. | Oct 31, 2018 | -7.01% | -6.94% | 79.50 | 63.79 | 71.22 |
| 3. | Nov 30, 2018 | 1.67% | 1.79% | 0.06 | 0.55 | -0.18 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Jun 30, 2024 | 14.01% | 3.47% | 146.43 | 5.86 | 29.29 |
| 71. | Jul 31, 2024 | -1.36% | 1.13% | 10.72 | 0.01 | -0.28 |
| Total (Σ): | 4,591.87 | 1,918.93 | 2,285.60 | |||
| t | Date | RINTU,t | RS&P 500,t | (RINTU,t–RINTU)2 | (RS&P 500,t–RS&P 500)2 | (RINTU,t–RINTU)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Sep 30, 2018 | 3.61% | 0.43% | 2.90 | 0.38 | -1.05 |
| 2. | Oct 31, 2018 | -7.01% | -6.94% | 79.50 | 63.79 | 71.22 |
| 3. | Nov 30, 2018 | 1.67% | 1.79% | 0.06 | 0.55 | -0.18 |
| 4. | Dec 31, 2018 | -8.24% | -9.18% | 103.07 | 104.54 | 103.80 |
| 5. | Jan 31, 2019 | 9.88% | 7.87% | 63.43 | 46.54 | 54.33 |
| 6. | Feb 28, 2019 | 14.51% | 2.97% | 158.67 | 3.71 | 24.26 |
| 7. | Mar 31, 2019 | 5.78% | 1.79% | 14.96 | 0.56 | 2.88 |
| 8. | Apr 30, 2019 | -3.78% | 3.93% | 32.38 | 8.32 | -16.42 |
| 9. | May 31, 2019 | -2.47% | -6.58% | 19.23 | 58.13 | 33.43 |
| 10. | Jun 30, 2019 | 6.73% | 6.89% | 23.23 | 34.18 | 28.18 |
| 11. | Jul 31, 2019 | 6.29% | 1.31% | 19.22 | 0.07 | 1.17 |
| 12. | Aug 31, 2019 | 3.98% | -1.81% | 4.30 | 8.16 | -5.92 |
| 13. | Sep 30, 2019 | -7.78% | 1.72% | 93.82 | 0.45 | -6.50 |
| 14. | Oct 31, 2019 | -2.97% | 2.04% | 23.87 | 0.99 | -4.87 |
| 15. | Nov 30, 2019 | 0.54% | 3.40% | 1.88 | 5.56 | -3.23 |
| 16. | Dec 31, 2019 | 1.17% | 2.86% | 0.54 | 3.28 | -1.34 |
| 17. | Jan 31, 2020 | 7.25% | -0.16% | 28.46 | 1.46 | -6.45 |
| 18. | Feb 29, 2020 | -5.18% | -8.41% | 50.32 | 89.45 | 67.09 |
| 19. | Mar 31, 2020 | -13.49% | -12.51% | 237.04 | 183.84 | 208.75 |
| 20. | Apr 30, 2020 | 17.54% | 12.68% | 244.23 | 135.44 | 181.87 |
| 21. | May 31, 2020 | 7.60% | 4.53% | 32.38 | 12.12 | 19.81 |
| 22. | Jun 30, 2020 | 2.02% | 1.84% | 0.01 | 0.63 | 0.09 |
| 23. | Jul 31, 2020 | 3.62% | 5.51% | 2.91 | 19.92 | 7.61 |
| 24. | Aug 31, 2020 | 12.74% | 7.01% | 117.18 | 35.52 | 64.52 |
| 25. | Sep 30, 2020 | -5.55% | -3.92% | 55.72 | 24.70 | 37.09 |
| 26. | Oct 31, 2020 | -3.35% | -2.77% | 27.72 | 14.54 | 20.08 |
| 27. | Nov 30, 2020 | 11.87% | 10.75% | 99.10 | 94.24 | 96.64 |
| 28. | Dec 31, 2020 | 7.91% | 3.71% | 35.94 | 7.10 | 15.98 |
| 29. | Jan 31, 2021 | -4.75% | -1.11% | 44.33 | 4.67 | 14.38 |
| 30. | Feb 28, 2021 | 8.00% | 2.61% | 37.11 | 2.44 | 9.52 |
| 31. | Mar 31, 2021 | -1.81% | 4.24% | 13.88 | 10.22 | -11.91 |
| 32. | Apr 30, 2021 | 7.75% | 5.24% | 34.10 | 17.61 | 24.50 |
| 33. | May 31, 2021 | 6.53% | 0.55% | 21.37 | 0.25 | -2.30 |
| 34. | Jun 30, 2021 | 11.63% | 2.22% | 94.52 | 1.38 | 11.42 |
| 35. | Jul 31, 2021 | 8.24% | 2.27% | 40.05 | 1.51 | 7.77 |
| 36. | Aug 31, 2021 | 6.82% | 2.90% | 24.09 | 3.43 | 9.09 |
| 37. | Sep 30, 2021 | -4.70% | -4.76% | 43.69 | 33.68 | 38.36 |
| 38. | Oct 31, 2021 | 16.16% | 6.91% | 202.90 | 34.43 | 83.58 |
| 39. | Nov 30, 2021 | 4.20% | -0.83% | 5.25 | 3.53 | -4.31 |
| 40. | Dec 31, 2021 | -1.39% | 4.36% | 10.91 | 10.99 | -10.95 |
| 41. | Jan 31, 2022 | -13.57% | -5.26% | 239.79 | 39.76 | 97.64 |
| 42. | Feb 28, 2022 | -14.56% | -3.14% | 271.41 | 17.50 | 68.91 |
| 43. | Mar 31, 2022 | 1.36% | 3.58% | 0.30 | 6.40 | -1.38 |
| 44. | Apr 30, 2022 | -12.77% | -8.80% | 215.58 | 96.87 | 144.51 |
| 45. | May 31, 2022 | -1.02% | 0.01% | 8.62 | 1.08 | 3.06 |
| 46. | Jun 30, 2022 | -7.00% | -8.39% | 79.44 | 89.09 | 84.13 |
| 47. | Jul 31, 2022 | 18.53% | 9.11% | 276.08 | 65.04 | 134.01 |
| 48. | Aug 31, 2022 | -5.35% | -4.24% | 52.68 | 27.99 | 38.40 |
| 49. | Sep 30, 2022 | -10.30% | -9.34% | 149.04 | 107.87 | 126.80 |
| 50. | Oct 31, 2022 | 10.58% | 7.99% | 75.07 | 48.16 | 60.13 |
| 51. | Nov 30, 2022 | -4.66% | 5.38% | 43.14 | 18.74 | -28.43 |
| 52. | Dec 31, 2022 | -4.51% | -5.90% | 41.19 | 48.22 | 44.57 |
| 53. | Jan 31, 2023 | 8.79% | 6.18% | 47.38 | 26.30 | 35.30 |
| 54. | Feb 28, 2023 | -3.66% | -2.61% | 31.09 | 13.38 | 20.40 |
| 55. | Mar 31, 2023 | 9.49% | 3.51% | 57.47 | 6.04 | 18.64 |
| 56. | Apr 30, 2023 | -0.25% | 1.46% | 4.66 | 0.17 | -0.90 |
| 57. | May 31, 2023 | -5.59% | 0.25% | 56.31 | 0.64 | 5.99 |
| 58. | Jun 30, 2023 | 9.32% | 4.71% | 54.92 | 13.45 | 27.18 |
| 59. | Jul 31, 2023 | 11.85% | 4.85% | 98.76 | 14.43 | 37.76 |
| 60. | Aug 31, 2023 | 5.88% | -1.77% | 15.79 | 7.94 | -11.20 |
| 61. | Sep 30, 2023 | -5.70% | -4.87% | 57.89 | 35.03 | 45.03 |
| 62. | Oct 31, 2023 | -2.95% | -2.20% | 23.66 | 10.53 | 15.78 |
| 63. | Nov 30, 2023 | 15.46% | 8.92% | 183.52 | 61.96 | 106.63 |
| 64. | Dec 31, 2023 | 9.37% | 4.42% | 55.70 | 11.40 | 25.20 |
| 65. | Jan 31, 2024 | 1.15% | 1.59% | 0.58 | 0.29 | -0.41 |
| 66. | Feb 29, 2024 | 5.00% | 5.17% | 9.53 | 17.02 | 12.74 |
| 67. | Mar 31, 2024 | -1.94% | 3.10% | 14.87 | 4.22 | -7.92 |
| 68. | Apr 30, 2024 | -3.61% | -4.16% | 30.51 | 27.13 | 28.77 |
| 69. | May 31, 2024 | -7.86% | 4.80% | 95.49 | 14.10 | -36.70 |
| 70. | Jun 30, 2024 | 14.01% | 3.47% | 146.43 | 5.86 | 29.29 |
| 71. | Jul 31, 2024 | -1.36% | 1.13% | 10.72 | 0.01 | -0.28 |
| Total (Σ): | 4,591.87 | 1,918.93 | 2,285.60 | |||
Show all
VarianceINTU = Σ(RINTU,t–RINTU)2 ÷ (71 – 1)
= 4,591.87 ÷ (71 – 1)
= 65.60
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,918.93 ÷ (71 – 1)
= 27.41
CovarianceINTU, S&P 500 = Σ(RINTU,t–RINTU)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,285.60 ÷ (71 – 1)
= 32.65
Systematic Risk (β) Estimation
| VarianceINTU | 65.60 |
| VarianceS&P 500 | 27.41 |
| CovarianceINTU, S&P 500 | 32.65 |
| Correlation coefficientINTU, S&P 5001 | 0.77 |
| βINTU2 | 1.19 |
| αINTU3 | 0.66% |
Calculations
1 Correlation coefficientINTU, S&P 500
= CovarianceINTU, S&P 500 ÷ (Standard deviationINTU × Standard deviationS&P 500)
= 32.65 ÷ (8.10% × 5.24%)
= 0.77
2 βINTU
= CovarianceINTU, S&P 500 ÷ VarianceS&P 500
= 32.65 ÷ 27.41
= 1.19
3 αINTU
= AverageINTU – βINTU × AverageS&P 500
= 1.91% – 1.19 × 1.05%
= 0.66%
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 Intuit Inc. common stock | βINTU | 1.19 |
| Expected rate of return on Intuit Inc. common stock3 | E(RINTU) | 15.53% |
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(RINTU) = RF + βINTU [E(RM) – RF]
= 4.65% + 1.19 [13.79% – 4.65%]
= 15.53%