Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Autodesk Inc. common stock.
Rates of Return
Autodesk Inc. (ADSK) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceADSK,t1 | DividendADSK,t1 | RADSK,t2 | PriceS&P 500,t | RS&P 500,t3 |
Feb 28, 2015 | $64.24 | 2,104.50 | ||||
1. | Mar 31, 2015 | $58.64 | -8.72% | 2,067.89 | -1.74% | |
2. | Apr 30, 2015 | $56.83 | -3.09% | 2,085.51 | 0.85% | |
3. | May 31, 2015 | $54.15 | -4.72% | 2,107.39 | 1.05% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Dec 31, 2020 | $305.34 | 8.96% | 3,756.07 | 3.71% | |
71. | Jan 31, 2021 | $277.43 | -9.14% | 3,714.24 | -1.11% | |
Average (R): | 2.58% | 0.89% | ||||
Standard deviation: | 10.14% | 4.30% |
Autodesk Inc. (ADSK) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceADSK,t1 | DividendADSK,t1 | RADSK,t2 | PriceS&P 500,t | RS&P 500,t3 |
Feb 28, 2015 | $64.24 | 2,104.50 | ||||
1. | Mar 31, 2015 | $58.64 | -8.72% | 2,067.89 | -1.74% | |
2. | Apr 30, 2015 | $56.83 | -3.09% | 2,085.51 | 0.85% | |
3. | May 31, 2015 | $54.15 | -4.72% | 2,107.39 | 1.05% | |
4. | Jun 30, 2015 | $50.08 | -7.52% | 2,063.11 | -2.10% | |
5. | Jul 31, 2015 | $50.58 | 1.00% | 2,103.84 | 1.97% | |
6. | Aug 31, 2015 | $46.75 | -7.57% | 1,972.18 | -6.26% | |
7. | Sep 30, 2015 | $44.14 | -5.58% | 1,920.03 | -2.64% | |
8. | Oct 31, 2015 | $55.19 | 25.03% | 2,079.36 | 8.30% | |
9. | Nov 30, 2015 | $63.47 | 15.00% | 2,080.41 | 0.05% | |
10. | Dec 31, 2015 | $60.93 | -4.00% | 2,043.94 | -1.75% | |
11. | Jan 31, 2016 | $46.82 | -23.16% | 1,940.24 | -5.07% | |
12. | Feb 29, 2016 | $51.74 | 10.51% | 1,932.23 | -0.41% | |
13. | Mar 31, 2016 | $58.31 | 12.70% | 2,059.74 | 6.60% | |
14. | Apr 30, 2016 | $59.82 | 2.59% | 2,065.30 | 0.27% | |
15. | May 31, 2016 | $58.27 | -2.59% | 2,096.95 | 1.53% | |
16. | Jun 30, 2016 | $54.14 | -7.09% | 2,098.86 | 0.09% | |
17. | Jul 31, 2016 | $59.45 | 9.81% | 2,173.60 | 3.56% | |
18. | Aug 31, 2016 | $67.40 | 13.37% | 2,170.95 | -0.12% | |
19. | Sep 30, 2016 | $72.33 | 7.31% | 2,168.27 | -0.12% | |
20. | Oct 31, 2016 | $72.28 | -0.07% | 2,126.15 | -1.94% | |
21. | Nov 30, 2016 | $72.61 | 0.46% | 2,198.81 | 3.42% | |
22. | Dec 31, 2016 | $74.01 | 1.93% | 2,238.83 | 1.82% | |
23. | Jan 31, 2017 | $81.34 | 9.90% | 2,278.87 | 1.79% | |
24. | Feb 28, 2017 | $86.30 | 6.10% | 2,363.64 | 3.72% | |
25. | Mar 31, 2017 | $86.47 | 0.20% | 2,362.72 | -0.04% | |
26. | Apr 30, 2017 | $90.07 | 4.16% | 2,384.20 | 0.91% | |
27. | May 31, 2017 | $111.77 | 24.09% | 2,411.80 | 1.16% | |
28. | Jun 30, 2017 | $100.82 | -9.80% | 2,423.41 | 0.48% | |
29. | Jul 31, 2017 | $110.79 | 9.89% | 2,470.30 | 1.93% | |
30. | Aug 31, 2017 | $114.46 | 3.31% | 2,471.65 | 0.05% | |
31. | Sep 30, 2017 | $112.26 | -1.92% | 2,519.36 | 1.93% | |
32. | Oct 31, 2017 | $124.96 | 11.31% | 2,575.26 | 2.22% | |
33. | Nov 30, 2017 | $109.70 | -12.21% | 2,647.58 | 2.81% | |
34. | Dec 31, 2017 | $104.83 | -4.44% | 2,673.61 | 0.98% | |
35. | Jan 31, 2018 | $115.62 | 10.29% | 2,823.81 | 5.62% | |
36. | Feb 28, 2018 | $117.47 | 1.60% | 2,713.83 | -3.89% | |
37. | Mar 31, 2018 | $125.58 | 6.90% | 2,640.87 | -2.69% | |
38. | Apr 30, 2018 | $125.90 | 0.25% | 2,648.05 | 0.27% | |
39. | May 31, 2018 | $129.10 | 2.54% | 2,705.27 | 2.16% | |
40. | Jun 30, 2018 | $131.09 | 1.54% | 2,718.37 | 0.48% | |
41. | Jul 31, 2018 | $128.44 | -2.02% | 2,816.29 | 3.60% | |
42. | Aug 31, 2018 | $154.35 | 20.17% | 2,901.52 | 3.03% | |
43. | Sep 30, 2018 | $156.11 | 1.14% | 2,913.98 | 0.43% | |
44. | Oct 31, 2018 | $129.25 | -17.21% | 2,711.74 | -6.94% | |
45. | Nov 30, 2018 | $144.50 | 11.80% | 2,760.17 | 1.79% | |
46. | Dec 31, 2018 | $128.61 | -11.00% | 2,506.85 | -9.18% | |
47. | Jan 31, 2019 | $147.20 | 14.45% | 2,704.10 | 7.87% | |
48. | Feb 28, 2019 | $163.01 | 10.74% | 2,784.49 | 2.97% | |
49. | Mar 31, 2019 | $155.82 | -4.41% | 2,834.40 | 1.79% | |
50. | Apr 30, 2019 | $178.21 | 14.37% | 2,945.83 | 3.93% | |
51. | May 31, 2019 | $160.91 | -9.71% | 2,752.06 | -6.58% | |
52. | Jun 30, 2019 | $162.90 | 1.24% | 2,941.76 | 6.89% | |
53. | Jul 31, 2019 | $156.17 | -4.13% | 2,980.38 | 1.31% | |
54. | Aug 31, 2019 | $142.82 | -8.55% | 2,926.46 | -1.81% | |
55. | Sep 30, 2019 | $147.70 | 3.42% | 2,976.74 | 1.72% | |
56. | Oct 31, 2019 | $147.36 | -0.23% | 3,037.56 | 2.04% | |
57. | Nov 30, 2019 | $180.90 | 22.76% | 3,140.98 | 3.40% | |
58. | Dec 31, 2019 | $183.46 | 1.42% | 3,230.78 | 2.86% | |
59. | Jan 31, 2020 | $196.85 | 7.30% | 3,225.52 | -0.16% | |
60. | Feb 29, 2020 | $190.88 | -3.03% | 2,954.22 | -8.41% | |
61. | Mar 31, 2020 | $156.10 | -18.22% | 2,584.59 | -12.51% | |
62. | Apr 30, 2020 | $187.13 | 19.88% | 2,912.43 | 12.68% | |
63. | May 31, 2020 | $210.38 | 12.42% | 3,044.31 | 4.53% | |
64. | Jun 30, 2020 | $239.19 | 13.69% | 3,100.29 | 1.84% | |
65. | Jul 31, 2020 | $236.43 | -1.15% | 3,271.12 | 5.51% | |
66. | Aug 31, 2020 | $245.70 | 3.92% | 3,500.31 | 7.01% | |
67. | Sep 30, 2020 | $231.01 | -5.98% | 3,363.00 | -3.92% | |
68. | Oct 31, 2020 | $235.54 | 1.96% | 3,269.96 | -2.77% | |
69. | Nov 30, 2020 | $280.23 | 18.97% | 3,621.63 | 10.75% | |
70. | Dec 31, 2020 | $305.34 | 8.96% | 3,756.07 | 3.71% | |
71. | Jan 31, 2021 | $277.43 | -9.14% | 3,714.24 | -1.11% | |
Average (R): | 2.58% | 0.89% | ||||
Standard deviation: | 10.14% | 4.30% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of ADSK during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RADSK,t | RS&P 500,t | (RADSK,t–RADSK)2 | (RS&P 500,t–RS&P 500)2 | (RADSK,t–RADSK)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Mar 31, 2015 | -8.72% | -1.74% | 127.63 | 6.94 | 29.76 |
2. | Apr 30, 2015 | -3.09% | 0.85% | 32.11 | 0.00 | 0.24 |
3. | May 31, 2015 | -4.72% | 1.05% | 53.23 | 0.02 | -1.13 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Dec 31, 2020 | 8.96% | 3.71% | 40.71 | 7.94 | 17.98 |
71. | Jan 31, 2021 | -9.14% | -1.11% | 137.37 | 4.03 | 23.54 |
Total (Σ): | 7,204.46 | 1,292.68 | 2,010.27 |
t | Date | RADSK,t | RS&P 500,t | (RADSK,t–RADSK)2 | (RS&P 500,t–RS&P 500)2 | (RADSK,t–RADSK)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Mar 31, 2015 | -8.72% | -1.74% | 127.63 | 6.94 | 29.76 |
2. | Apr 30, 2015 | -3.09% | 0.85% | 32.11 | 0.00 | 0.24 |
3. | May 31, 2015 | -4.72% | 1.05% | 53.23 | 0.02 | -1.13 |
4. | Jun 30, 2015 | -7.52% | -2.10% | 101.93 | 8.98 | 30.25 |
5. | Jul 31, 2015 | 1.00% | 1.97% | 2.50 | 1.17 | -1.71 |
6. | Aug 31, 2015 | -7.57% | -6.26% | 103.07 | 51.16 | 72.62 |
7. | Sep 30, 2015 | -5.58% | -2.64% | 66.63 | 12.52 | 28.89 |
8. | Oct 31, 2015 | 25.03% | 8.30% | 504.18 | 54.81 | 166.24 |
9. | Nov 30, 2015 | 15.00% | 0.05% | 154.32 | 0.71 | -10.49 |
10. | Dec 31, 2015 | -4.00% | -1.75% | 43.32 | 7.01 | 17.43 |
11. | Jan 31, 2016 | -23.16% | -5.07% | 662.43 | 35.62 | 153.61 |
12. | Feb 29, 2016 | 10.51% | -0.41% | 62.86 | 1.71 | -10.37 |
13. | Mar 31, 2016 | 12.70% | 6.60% | 102.38 | 32.54 | 57.72 |
14. | Apr 30, 2016 | 2.59% | 0.27% | 0.00 | 0.39 | -0.01 |
15. | May 31, 2016 | -2.59% | 1.53% | 26.74 | 0.41 | -3.30 |
16. | Jun 30, 2016 | -7.09% | 0.09% | 93.47 | 0.65 | 7.77 |
17. | Jul 31, 2016 | 9.81% | 3.56% | 52.24 | 7.11 | 19.27 |
18. | Aug 31, 2016 | 13.37% | -0.12% | 116.48 | 1.03 | -10.97 |
19. | Sep 30, 2016 | 7.31% | -0.12% | 22.42 | 1.04 | -4.82 |
20. | Oct 31, 2016 | -0.07% | -1.94% | 7.02 | 8.05 | 7.52 |
21. | Nov 30, 2016 | 0.46% | 3.42% | 4.51 | 6.36 | -5.36 |
22. | Dec 31, 2016 | 1.93% | 1.82% | 0.43 | 0.86 | -0.60 |
23. | Jan 31, 2017 | 9.90% | 1.79% | 53.64 | 0.80 | 6.55 |
24. | Feb 28, 2017 | 6.10% | 3.72% | 12.37 | 7.98 | 9.94 |
25. | Mar 31, 2017 | 0.20% | -0.04% | 5.68 | 0.87 | 2.22 |
26. | Apr 30, 2017 | 4.16% | 0.91% | 2.51 | 0.00 | 0.02 |
27. | May 31, 2017 | 24.09% | 1.16% | 462.78 | 0.07 | 5.66 |
28. | Jun 30, 2017 | -9.80% | 0.48% | 153.19 | 0.17 | 5.12 |
29. | Jul 31, 2017 | 9.89% | 1.93% | 53.42 | 1.08 | 7.60 |
30. | Aug 31, 2017 | 3.31% | 0.05% | 0.54 | 0.71 | -0.62 |
31. | Sep 30, 2017 | -1.92% | 1.93% | 20.27 | 1.07 | -4.66 |
32. | Oct 31, 2017 | 11.31% | 2.22% | 76.26 | 1.75 | 11.56 |
33. | Nov 30, 2017 | -12.21% | 2.81% | 218.80 | 3.66 | -28.31 |
34. | Dec 31, 2017 | -4.44% | 0.98% | 49.27 | 0.01 | -0.62 |
35. | Jan 31, 2018 | 10.29% | 5.62% | 59.49 | 22.31 | 36.43 |
36. | Feb 28, 2018 | 1.60% | -3.89% | 0.96 | 22.94 | 4.69 |
37. | Mar 31, 2018 | 6.90% | -2.69% | 18.70 | 12.84 | -15.49 |
38. | Apr 30, 2018 | 0.25% | 0.27% | 5.41 | 0.39 | 1.45 |
39. | May 31, 2018 | 2.54% | 2.16% | 0.00 | 1.60 | -0.05 |
40. | Jun 30, 2018 | 1.54% | 0.48% | 1.08 | 0.17 | 0.43 |
41. | Jul 31, 2018 | -2.02% | 3.60% | 21.17 | 7.33 | -12.46 |
42. | Aug 31, 2018 | 20.17% | 3.03% | 309.51 | 4.54 | 37.50 |
43. | Sep 30, 2018 | 1.14% | 0.43% | 2.07 | 0.22 | 0.67 |
44. | Oct 31, 2018 | -17.21% | -6.94% | 391.48 | 61.39 | 155.02 |
45. | Nov 30, 2018 | 11.80% | 1.79% | 84.99 | 0.79 | 8.22 |
46. | Dec 31, 2018 | -11.00% | -9.18% | 184.32 | 101.45 | 136.75 |
47. | Jan 31, 2019 | 14.45% | 7.87% | 141.00 | 48.63 | 82.81 |
48. | Feb 28, 2019 | 10.74% | 2.97% | 66.59 | 4.32 | 16.96 |
49. | Mar 31, 2019 | -4.41% | 1.79% | 48.87 | 0.81 | -6.28 |
50. | Apr 30, 2019 | 14.37% | 3.93% | 138.98 | 9.22 | 35.80 |
51. | May 31, 2019 | -9.71% | -6.58% | 150.99 | 55.84 | 91.82 |
52. | Jun 30, 2019 | 1.24% | 6.89% | 1.80 | 35.98 | -8.06 |
53. | Jul 31, 2019 | -4.13% | 1.31% | 45.04 | 0.17 | -2.81 |
54. | Aug 31, 2019 | -8.55% | -1.81% | 123.84 | 7.31 | 30.09 |
55. | Sep 30, 2019 | 3.42% | 1.72% | 0.70 | 0.68 | 0.69 |
56. | Oct 31, 2019 | -0.23% | 2.04% | 7.90 | 1.32 | -3.23 |
57. | Nov 30, 2019 | 22.76% | 3.40% | 407.25 | 6.30 | 50.65 |
58. | Dec 31, 2019 | 1.42% | 2.86% | 1.36 | 3.86 | -2.29 |
59. | Jan 31, 2020 | 7.30% | -0.16% | 22.26 | 1.12 | -4.99 |
60. | Feb 29, 2020 | -3.03% | -8.41% | 31.50 | 86.60 | 52.23 |
61. | Mar 31, 2020 | -18.22% | -12.51% | 432.68 | 179.74 | 278.87 |
62. | Apr 30, 2020 | 19.88% | 12.68% | 299.23 | 139.00 | 203.94 |
63. | May 31, 2020 | 12.42% | 4.53% | 96.91 | 13.20 | 35.77 |
64. | Jun 30, 2020 | 13.69% | 1.84% | 123.53 | 0.89 | 10.49 |
65. | Jul 31, 2020 | -1.15% | 5.51% | 13.94 | 21.30 | -17.23 |
66. | Aug 31, 2020 | 3.92% | 7.01% | 1.80 | 37.35 | 8.19 |
67. | Sep 30, 2020 | -5.98% | -3.92% | 73.25 | 23.21 | 41.23 |
68. | Oct 31, 2020 | 1.96% | -2.77% | 0.38 | 13.41 | 2.27 |
69. | Nov 30, 2020 | 18.97% | 10.75% | 268.74 | 97.22 | 161.64 |
70. | Dec 31, 2020 | 8.96% | 3.71% | 40.71 | 7.94 | 17.98 |
71. | Jan 31, 2021 | -9.14% | -1.11% | 137.37 | 4.03 | 23.54 |
Total (Σ): | 7,204.46 | 1,292.68 | 2,010.27 |
Show all
VarianceADSK = Σ(RADSK,t–RADSK)2 ÷ (71 – 1)
= 7,204.46 ÷ (71 – 1)
= 102.92
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,292.68 ÷ (71 – 1)
= 18.47
CovarianceADSK, S&P 500 = Σ(RADSK,t–RADSK)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,010.27 ÷ (71 – 1)
= 28.72
Systematic Risk (β) Estimation
VarianceADSK | 102.92 |
VarianceS&P 500 | 18.47 |
CovarianceADSK, S&P 500 | 28.72 |
Correlation coefficientADSK, S&P 5001 | 0.66 |
βADSK2 | 1.56 |
αADSK3 | 1.19% |
Calculations
1 Correlation coefficientADSK, S&P 500
= CovarianceADSK, S&P 500 ÷ (Standard deviationADSK × Standard deviationS&P 500)
= 28.72 ÷ (10.14% × 4.30%)
= 0.66
2 βADSK
= CovarianceADSK, S&P 500 ÷ VarianceS&P 500
= 28.72 ÷ 18.47
= 1.56
3 αADSK
= AverageADSK – βADSK × AverageS&P 500
= 2.58% – 1.56 × 0.89%
= 1.19%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.42% |
Expected rate of return on market portfolio2 | E(RM) | 13.61% |
Systematic risk (β) of Autodesk Inc. common stock | βADSK | 1.56 |
Expected rate of return on Autodesk Inc. common stock3 | E(RADSK) | 18.70% |
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(RADSK) = RF + βADSK [E(RM) – RF]
= 4.42% + 1.56 [13.61% – 4.42%]
= 18.70%