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. (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, 2017 | $141.45 | 2,471.65 | ||||
1. | Sep 30, 2017 | $142.14 | 0.49% | 2,519.36 | 1.93% | |
2. | Oct 31, 2017 | $151.02 | $0.39 | 6.52% | 2,575.26 | 2.22% |
3. | Nov 30, 2017 | $157.22 | 4.11% | 2,647.58 | 2.81% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Jun 30, 2023 | $458.19 | 9.32% | 4,376.86 | 4.71% | |
71. | Jul 31, 2023 | $511.70 | $0.78 | 11.85% | 4,588.96 | 4.85% |
Average (R): | 2.18% | 1.00% | ||||
Standard deviation: | 7.67% | 5.07% |
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, 2017 | $141.45 | 2,471.65 | ||||
1. | Sep 30, 2017 | $142.14 | 0.49% | 2,519.36 | 1.93% | |
2. | Oct 31, 2017 | $151.02 | $0.39 | 6.52% | 2,575.26 | 2.22% |
3. | Nov 30, 2017 | $157.22 | 4.11% | 2,647.58 | 2.81% | |
4. | Dec 31, 2017 | $157.78 | 0.36% | 2,673.61 | 0.98% | |
5. | Jan 31, 2018 | $167.90 | $0.39 | 6.66% | 2,823.81 | 5.62% |
6. | Feb 28, 2018 | $166.86 | -0.62% | 2,713.83 | -3.89% | |
7. | Mar 31, 2018 | $173.35 | 3.89% | 2,640.87 | -2.69% | |
8. | Apr 30, 2018 | $184.79 | $0.39 | 6.82% | 2,648.05 | 0.27% |
9. | May 31, 2018 | $201.60 | 9.10% | 2,705.27 | 2.16% | |
10. | Jun 30, 2018 | $204.31 | 1.34% | 2,718.37 | 0.48% | |
11. | Jul 31, 2018 | $204.24 | $0.39 | 0.16% | 2,816.29 | 3.60% |
12. | Aug 31, 2018 | $219.47 | 7.46% | 2,901.52 | 3.03% | |
13. | Sep 30, 2018 | $227.40 | 3.61% | 2,913.98 | 0.43% | |
14. | Oct 31, 2018 | $211.00 | $0.47 | -7.01% | 2,711.74 | -6.94% |
15. | Nov 30, 2018 | $214.53 | 1.67% | 2,760.17 | 1.79% | |
16. | Dec 31, 2018 | $196.85 | -8.24% | 2,506.85 | -9.18% | |
17. | Jan 31, 2019 | $215.82 | $0.47 | 9.88% | 2,704.10 | 7.87% |
18. | Feb 28, 2019 | $247.13 | 14.51% | 2,784.49 | 2.97% | |
19. | Mar 31, 2019 | $261.41 | 5.78% | 2,834.40 | 1.79% | |
20. | Apr 30, 2019 | $251.06 | $0.47 | -3.78% | 2,945.83 | 3.93% |
21. | May 31, 2019 | $244.85 | -2.47% | 2,752.06 | -6.58% | |
22. | Jun 30, 2019 | $261.33 | 6.73% | 2,941.76 | 6.89% | |
23. | Jul 31, 2019 | $277.31 | $0.47 | 6.29% | 2,980.38 | 1.31% |
24. | Aug 31, 2019 | $288.36 | 3.98% | 2,926.46 | -1.81% | |
25. | Sep 30, 2019 | $265.94 | -7.78% | 2,976.74 | 1.72% | |
26. | Oct 31, 2019 | $257.50 | $0.53 | -2.97% | 3,037.56 | 2.04% |
27. | Nov 30, 2019 | $258.89 | 0.54% | 3,140.98 | 3.40% | |
28. | Dec 31, 2019 | $261.93 | 1.17% | 3,230.78 | 2.86% | |
29. | Jan 31, 2020 | $280.38 | $0.53 | 7.25% | 3,225.52 | -0.16% |
30. | Feb 29, 2020 | $265.85 | -5.18% | 2,954.22 | -8.41% | |
31. | Mar 31, 2020 | $230.00 | -13.49% | 2,584.59 | -12.51% | |
32. | Apr 30, 2020 | $269.81 | $0.53 | 17.54% | 2,912.43 | 12.68% |
33. | May 31, 2020 | $290.32 | 7.60% | 3,044.31 | 4.53% | |
34. | Jun 30, 2020 | $296.19 | 2.02% | 3,100.29 | 1.84% | |
35. | Jul 31, 2020 | $306.37 | $0.53 | 3.62% | 3,271.12 | 5.51% |
36. | Aug 31, 2020 | $345.39 | 12.74% | 3,500.31 | 7.01% | |
37. | Sep 30, 2020 | $326.21 | -5.55% | 3,363.00 | -3.92% | |
38. | Oct 31, 2020 | $314.68 | $0.59 | -3.35% | 3,269.96 | -2.77% |
39. | Nov 30, 2020 | $352.02 | 11.87% | 3,621.63 | 10.75% | |
40. | Dec 31, 2020 | $379.85 | 7.91% | 3,756.07 | 3.71% | |
41. | Jan 31, 2021 | $361.23 | $0.59 | -4.75% | 3,714.24 | -1.11% |
42. | Feb 28, 2021 | $390.14 | 8.00% | 3,811.15 | 2.61% | |
43. | Mar 31, 2021 | $383.06 | -1.81% | 3,972.89 | 4.24% | |
44. | Apr 30, 2021 | $412.16 | $0.59 | 7.75% | 4,181.17 | 5.24% |
45. | May 31, 2021 | $439.09 | 6.53% | 4,204.11 | 0.55% | |
46. | Jun 30, 2021 | $490.17 | 11.63% | 4,297.50 | 2.22% | |
47. | Jul 31, 2021 | $529.97 | $0.59 | 8.24% | 4,395.26 | 2.27% |
48. | Aug 31, 2021 | $566.11 | 6.82% | 4,522.68 | 2.90% | |
49. | Sep 30, 2021 | $539.51 | -4.70% | 4,307.54 | -4.76% | |
50. | Oct 31, 2021 | $625.99 | $0.68 | 16.16% | 4,605.38 | 6.91% |
51. | Nov 30, 2021 | $652.30 | 4.20% | 4,567.00 | -0.83% | |
52. | Dec 31, 2021 | $643.22 | -1.39% | 4,766.18 | 4.36% | |
53. | Jan 31, 2022 | $555.23 | $0.68 | -13.57% | 4,515.55 | -5.26% |
54. | Feb 28, 2022 | $474.37 | -14.56% | 4,373.94 | -3.14% | |
55. | Mar 31, 2022 | $480.84 | 1.36% | 4,530.41 | 3.58% | |
56. | Apr 30, 2022 | $418.75 | $0.68 | -12.77% | 4,131.93 | -8.80% |
57. | May 31, 2022 | $414.46 | -1.02% | 4,132.15 | 0.01% | |
58. | Jun 30, 2022 | $385.44 | -7.00% | 3,785.38 | -8.39% | |
59. | Jul 31, 2022 | $456.17 | $0.68 | 18.53% | 4,130.29 | 9.11% |
60. | Aug 31, 2022 | $431.78 | -5.35% | 3,955.00 | -4.24% | |
61. | Sep 30, 2022 | $387.32 | -10.30% | 3,585.62 | -9.34% | |
62. | Oct 31, 2022 | $427.50 | $0.78 | 10.58% | 3,871.98 | 7.99% |
63. | Nov 30, 2022 | $407.59 | -4.66% | 4,080.11 | 5.38% | |
64. | Dec 31, 2022 | $389.22 | -4.51% | 3,839.50 | -5.90% | |
65. | Jan 31, 2023 | $422.67 | $0.78 | 8.79% | 4,076.60 | 6.18% |
66. | Feb 28, 2023 | $407.18 | -3.66% | 3,970.15 | -2.61% | |
67. | Mar 31, 2023 | $445.83 | 9.49% | 4,109.31 | 3.51% | |
68. | Apr 30, 2023 | $443.95 | $0.78 | -0.25% | 4,169.48 | 1.46% |
69. | May 31, 2023 | $419.12 | -5.59% | 4,179.83 | 0.25% | |
70. | Jun 30, 2023 | $458.19 | 9.32% | 4,376.86 | 4.71% | |
71. | Jul 31, 2023 | $511.70 | $0.78 | 11.85% | 4,588.96 | 4.85% |
Average (R): | 2.18% | 1.00% | ||||
Standard deviation: | 7.67% | 5.07% |
Show all
1 Data in US$ 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
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, 2017 | 0.49% | 1.93% | 2.85 | 0.86 | -1.57 |
2. | Oct 31, 2017 | 6.52% | 2.22% | 18.88 | 1.48 | 5.28 |
3. | Nov 30, 2017 | 4.11% | 2.81% | 3.72 | 3.26 | 3.48 |
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. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Jun 30, 2023 | 9.32% | 4.71% | 51.06 | 13.77 | 26.51 |
71. | Jul 31, 2023 | 11.85% | 4.85% | 93.55 | 14.77 | 37.17 |
Total (Σ): | 4,115.51 | 1,800.45 | 2,125.44 |
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, 2017 | 0.49% | 1.93% | 2.85 | 0.86 | -1.57 |
2. | Oct 31, 2017 | 6.52% | 2.22% | 18.88 | 1.48 | 5.28 |
3. | Nov 30, 2017 | 4.11% | 2.81% | 3.72 | 3.26 | 3.48 |
4. | Dec 31, 2017 | 0.36% | 0.98% | 3.31 | 0.00 | 0.04 |
5. | Jan 31, 2018 | 6.66% | 5.62% | 20.11 | 21.29 | 20.70 |
6. | Feb 28, 2018 | -0.62% | -3.89% | 7.82 | 23.99 | 13.69 |
7. | Mar 31, 2018 | 3.89% | -2.69% | 2.93 | 13.63 | -6.32 |
8. | Apr 30, 2018 | 6.82% | 0.27% | 21.60 | 0.53 | -3.40 |
9. | May 31, 2018 | 9.10% | 2.16% | 47.89 | 1.34 | 8.01 |
10. | Jun 30, 2018 | 1.34% | 0.48% | 0.69 | 0.27 | 0.43 |
11. | Jul 31, 2018 | 0.16% | 3.60% | 4.08 | 6.75 | -5.25 |
12. | Aug 31, 2018 | 7.46% | 3.03% | 27.88 | 4.09 | 10.68 |
13. | Sep 30, 2018 | 3.61% | 0.43% | 2.06 | 0.33 | -0.82 |
14. | Oct 31, 2018 | -7.01% | -6.94% | 84.30 | 63.10 | 72.94 |
15. | Nov 30, 2018 | 1.67% | 1.79% | 0.25 | 0.61 | -0.39 |
16. | Dec 31, 2018 | -8.24% | -9.18% | 108.53 | 103.65 | 106.06 |
17. | Jan 31, 2019 | 9.88% | 7.87% | 59.28 | 47.13 | 52.86 |
18. | Feb 28, 2019 | 14.51% | 2.97% | 152.05 | 3.88 | 24.29 |
19. | Mar 31, 2019 | 5.78% | 1.79% | 12.97 | 0.62 | 2.84 |
20. | Apr 30, 2019 | -3.78% | 3.93% | 35.47 | 8.57 | -17.44 |
21. | May 31, 2019 | -2.47% | -6.58% | 21.62 | 57.47 | 35.25 |
22. | Jun 30, 2019 | 6.73% | 6.89% | 20.74 | 34.69 | 26.82 |
23. | Jul 31, 2019 | 6.29% | 1.31% | 16.96 | 0.10 | 1.27 |
24. | Aug 31, 2019 | 3.98% | -1.81% | 3.27 | 7.91 | -5.09 |
25. | Sep 30, 2019 | -7.78% | 1.72% | 99.03 | 0.51 | -7.11 |
26. | Oct 31, 2019 | -2.97% | 2.04% | 26.53 | 1.08 | -5.36 |
27. | Nov 30, 2019 | 0.54% | 3.40% | 2.68 | 5.77 | -3.93 |
28. | Dec 31, 2019 | 1.17% | 2.86% | 1.00 | 3.44 | -1.86 |
29. | Jan 31, 2020 | 7.25% | -0.16% | 25.70 | 1.36 | -5.91 |
30. | Feb 29, 2020 | -5.18% | -8.41% | 54.15 | 88.63 | 69.28 |
31. | Mar 31, 2020 | -13.49% | -12.51% | 245.28 | 182.66 | 211.67 |
32. | Apr 30, 2020 | 17.54% | 12.68% | 236.01 | 136.45 | 179.45 |
33. | May 31, 2020 | 7.60% | 4.53% | 29.43 | 12.42 | 19.12 |
34. | Jun 30, 2020 | 2.02% | 1.84% | 0.02 | 0.70 | -0.13 |
35. | Jul 31, 2020 | 3.62% | 5.51% | 2.07 | 20.31 | 6.49 |
36. | Aug 31, 2020 | 12.74% | 7.01% | 111.51 | 36.04 | 63.39 |
37. | Sep 30, 2020 | -5.55% | -3.92% | 59.75 | 24.27 | 38.08 |
38. | Oct 31, 2020 | -3.35% | -2.77% | 30.58 | 14.21 | 20.85 |
39. | Nov 30, 2020 | 11.87% | 10.75% | 93.89 | 95.09 | 94.49 |
40. | Dec 31, 2020 | 7.91% | 3.71% | 32.83 | 7.34 | 15.52 |
41. | Jan 31, 2021 | -4.75% | -1.11% | 47.93 | 4.48 | 14.66 |
42. | Feb 28, 2021 | 8.00% | 2.61% | 33.95 | 2.58 | 9.36 |
43. | Mar 31, 2021 | -1.81% | 4.24% | 15.93 | 10.50 | -12.93 |
44. | Apr 30, 2021 | 7.75% | 5.24% | 31.07 | 17.97 | 23.63 |
45. | May 31, 2021 | 6.53% | 0.55% | 18.99 | 0.21 | -1.98 |
46. | Jun 30, 2021 | 11.63% | 2.22% | 89.43 | 1.48 | 11.52 |
47. | Jul 31, 2021 | 8.24% | 2.27% | 36.77 | 1.62 | 7.71 |
48. | Aug 31, 2021 | 6.82% | 2.90% | 21.56 | 3.59 | 8.80 |
49. | Sep 30, 2021 | -4.70% | -4.76% | 47.27 | 33.18 | 39.60 |
50. | Oct 31, 2021 | 16.16% | 6.91% | 195.41 | 34.94 | 82.63 |
51. | Nov 30, 2021 | 4.20% | -0.83% | 4.11 | 3.37 | -3.72 |
52. | Dec 31, 2021 | -1.39% | 4.36% | 12.73 | 11.28 | -11.98 |
53. | Jan 31, 2022 | -13.57% | -5.26% | 248.07 | 39.21 | 98.62 |
54. | Feb 28, 2022 | -14.56% | -3.14% | 280.22 | 17.13 | 69.29 |
55. | Mar 31, 2022 | 1.36% | 3.58% | 0.66 | 6.63 | -2.09 |
56. | Apr 30, 2022 | -12.77% | -8.80% | 223.44 | 96.02 | 146.47 |
57. | May 31, 2022 | -1.02% | 0.01% | 10.25 | 1.00 | 3.19 |
58. | Jun 30, 2022 | -7.00% | -8.39% | 84.24 | 88.27 | 86.23 |
59. | Jul 31, 2022 | 18.53% | 9.11% | 267.34 | 65.75 | 132.58 |
60. | Aug 31, 2022 | -5.35% | -4.24% | 56.60 | 27.53 | 39.48 |
61. | Sep 30, 2022 | -10.30% | -9.34% | 155.58 | 106.97 | 129.01 |
62. | Oct 31, 2022 | 10.58% | 7.99% | 70.54 | 48.76 | 58.65 |
63. | Nov 30, 2022 | -4.66% | 5.38% | 46.70 | 19.11 | -29.88 |
64. | Dec 31, 2022 | -4.51% | -5.90% | 44.67 | 47.62 | 46.12 |
65. | Jan 31, 2023 | 8.79% | 6.18% | 43.80 | 26.75 | 34.23 |
66. | Feb 28, 2023 | -3.66% | -2.61% | 34.12 | 13.06 | 21.11 |
67. | Mar 31, 2023 | 9.49% | 3.51% | 53.52 | 6.26 | 18.30 |
68. | Apr 30, 2023 | -0.25% | 1.46% | 5.87 | 0.21 | -1.12 |
69. | May 31, 2023 | -5.59% | 0.25% | 60.36 | 0.57 | 5.87 |
70. | Jun 30, 2023 | 9.32% | 4.71% | 51.06 | 13.77 | 26.51 |
71. | Jul 31, 2023 | 11.85% | 4.85% | 93.55 | 14.77 | 37.17 |
Total (Σ): | 4,115.51 | 1,800.45 | 2,125.44 |
Show all
VarianceINTU = Σ(RINTU,t–RINTU)2 ÷ (71 – 1)
= 4,115.51 ÷ (71 – 1)
= 58.79
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,800.45 ÷ (71 – 1)
= 25.72
CovarianceINTU, S&P 500 = Σ(RINTU,t–RINTU)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,125.44 ÷ (71 – 1)
= 30.36
Systematic Risk (β) Estimation
VarianceINTU | 58.79 |
VarianceS&P 500 | 25.72 |
CovarianceINTU, S&P 500 | 30.36 |
Correlation coefficientINTU, S&P 5001 | 0.78 |
βINTU2 | 1.18 |
αINTU3 | 0.99% |
Calculations
1 Correlation coefficientINTU, S&P 500
= CovarianceINTU, S&P 500 ÷ (Standard deviationINTU × Standard deviationS&P 500)
= 30.36 ÷ (7.67% × 5.07%)
= 0.78
2 βINTU
= CovarianceINTU, S&P 500 ÷ VarianceS&P 500
= 30.36 ÷ 25.72
= 1.18
3 αINTU
= AverageINTU – βINTU × AverageS&P 500
= 2.18% – 1.18 × 1.00%
= 0.99%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.53% |
Expected rate of return on market portfolio2 | E(RM) | 13.63% |
Systematic risk (β) of Intuit Inc. common stock | βINTU | 1.18 |
Expected rate of return on Intuit Inc. common stock3 | E(RINTU) | 15.27% |
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]
= 4.53% + 1.18 [13.63% – 4.53%]
= 15.27%