Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like KLA Corp. common stock.
Rates of Return
KLA Corp. (KLAC) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceKLAC,t1 | DividendKLAC,t1 | RKLAC,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jul 31, 2017 | $92.63 | 2,470.30 | ||||
1. | Aug 31, 2017 | $93.69 | $0.59 | 1.78% | 2,471.65 | 0.05% |
2. | Sep 30, 2017 | $106.00 | 13.14% | 2,519.36 | 1.93% | |
3. | Oct 31, 2017 | $108.89 | 2.73% | 2,575.26 | 2.22% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | May 31, 2023 | $442.99 | $1.30 | 14.94% | 4,179.83 | 0.25% |
71. | Jun 30, 2023 | $485.02 | 9.49% | 4,376.86 | 4.71% | |
Average (R): | 2.96% | 0.94% | ||||
Standard deviation: | 9.62% | 5.05% |
KLA Corp. (KLAC) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceKLAC,t1 | DividendKLAC,t1 | RKLAC,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jul 31, 2017 | $92.63 | 2,470.30 | ||||
1. | Aug 31, 2017 | $93.69 | $0.59 | 1.78% | 2,471.65 | 0.05% |
2. | Sep 30, 2017 | $106.00 | 13.14% | 2,519.36 | 1.93% | |
3. | Oct 31, 2017 | $108.89 | 2.73% | 2,575.26 | 2.22% | |
4. | Nov 30, 2017 | $102.24 | $0.59 | -5.57% | 2,647.58 | 2.81% |
5. | Dec 31, 2017 | $105.07 | 2.77% | 2,673.61 | 0.98% | |
6. | Jan 31, 2018 | $109.80 | 4.50% | 2,823.81 | 5.62% | |
7. | Feb 28, 2018 | $113.31 | $0.59 | 3.73% | 2,713.83 | -3.89% |
8. | Mar 31, 2018 | $109.01 | -3.79% | 2,640.87 | -2.69% | |
9. | Apr 30, 2018 | $101.74 | -6.67% | 2,648.05 | 0.27% | |
10. | May 31, 2018 | $113.23 | $0.75 | 12.03% | 2,705.27 | 2.16% |
11. | Jun 30, 2018 | $102.53 | -9.45% | 2,718.37 | 0.48% | |
12. | Jul 31, 2018 | $117.42 | 14.52% | 2,816.29 | 3.60% | |
13. | Aug 31, 2018 | $116.21 | $0.75 | -0.39% | 2,901.52 | 3.03% |
14. | Sep 30, 2018 | $101.71 | -12.48% | 2,913.98 | 0.43% | |
15. | Oct 31, 2018 | $91.54 | -10.00% | 2,711.74 | -6.94% | |
16. | Nov 30, 2018 | $98.56 | $0.75 | 8.49% | 2,760.17 | 1.79% |
17. | Dec 31, 2018 | $89.49 | -9.20% | 2,506.85 | -9.18% | |
18. | Jan 31, 2019 | $106.57 | 19.09% | 2,704.10 | 7.87% | |
19. | Feb 28, 2019 | $115.49 | $0.75 | 9.07% | 2,784.49 | 2.97% |
20. | Mar 31, 2019 | $119.41 | 3.39% | 2,834.40 | 1.79% | |
21. | Apr 30, 2019 | $127.48 | 6.76% | 2,945.83 | 3.93% | |
22. | May 31, 2019 | $103.07 | $0.75 | -18.56% | 2,752.06 | -6.58% |
23. | Jun 30, 2019 | $118.20 | 14.68% | 2,941.76 | 6.89% | |
24. | Jul 31, 2019 | $136.32 | 15.33% | 2,980.38 | 1.31% | |
25. | Aug 31, 2019 | $147.90 | $0.75 | 9.04% | 2,926.46 | -1.81% |
26. | Sep 30, 2019 | $159.45 | 7.81% | 2,976.74 | 1.72% | |
27. | Oct 31, 2019 | $169.04 | 6.01% | 3,037.56 | 2.04% | |
28. | Nov 30, 2019 | $163.86 | $0.85 | -2.56% | 3,140.98 | 3.40% |
29. | Dec 31, 2019 | $178.17 | 8.73% | 3,230.78 | 2.86% | |
30. | Jan 31, 2020 | $165.74 | -6.98% | 3,225.52 | -0.16% | |
31. | Feb 29, 2020 | $153.71 | $0.85 | -6.75% | 2,954.22 | -8.41% |
32. | Mar 31, 2020 | $143.74 | -6.49% | 2,584.59 | -12.51% | |
33. | Apr 30, 2020 | $164.09 | 14.16% | 2,912.43 | 12.68% | |
34. | May 31, 2020 | $175.96 | $0.85 | 7.75% | 3,044.31 | 4.53% |
35. | Jun 30, 2020 | $194.48 | 10.53% | 3,100.29 | 1.84% | |
36. | Jul 31, 2020 | $199.83 | 2.75% | 3,271.12 | 5.51% | |
37. | Aug 31, 2020 | $205.14 | $0.90 | 3.11% | 3,500.31 | 7.01% |
38. | Sep 30, 2020 | $193.74 | -5.56% | 3,363.00 | -3.92% | |
39. | Oct 31, 2020 | $197.18 | 1.78% | 3,269.96 | -2.77% | |
40. | Nov 30, 2020 | $251.97 | $0.90 | 28.24% | 3,621.63 | 10.75% |
41. | Dec 31, 2020 | $258.91 | 2.75% | 3,756.07 | 3.71% | |
42. | Jan 31, 2021 | $280.07 | 8.17% | 3,714.24 | -1.11% | |
43. | Feb 28, 2021 | $311.23 | $0.90 | 11.45% | 3,811.15 | 2.61% |
44. | Mar 31, 2021 | $330.40 | 6.16% | 3,972.89 | 4.24% | |
45. | Apr 30, 2021 | $315.35 | -4.56% | 4,181.17 | 5.24% | |
46. | May 31, 2021 | $316.89 | $0.90 | 0.77% | 4,204.11 | 0.55% |
47. | Jun 30, 2021 | $324.21 | 2.31% | 4,297.50 | 2.22% | |
48. | Jul 31, 2021 | $348.16 | 7.39% | 4,395.26 | 2.27% | |
49. | Aug 31, 2021 | $339.96 | $1.05 | -2.05% | 4,522.68 | 2.90% |
50. | Sep 30, 2021 | $334.51 | -1.60% | 4,307.54 | -4.76% | |
51. | Oct 31, 2021 | $372.76 | 11.43% | 4,605.38 | 6.91% | |
52. | Nov 30, 2021 | $408.13 | $1.05 | 9.77% | 4,567.00 | -0.83% |
53. | Dec 31, 2021 | $430.11 | 5.39% | 4,766.18 | 4.36% | |
54. | Jan 31, 2022 | $389.27 | -9.50% | 4,515.55 | -5.26% | |
55. | Feb 28, 2022 | $348.50 | $1.05 | -10.20% | 4,373.94 | -3.14% |
56. | Mar 31, 2022 | $366.06 | 5.04% | 4,530.41 | 3.58% | |
57. | Apr 30, 2022 | $319.26 | -12.78% | 4,131.93 | -8.80% | |
58. | May 31, 2022 | $364.85 | $1.05 | 14.61% | 4,132.15 | 0.01% |
59. | Jun 30, 2022 | $319.08 | -12.54% | 3,785.38 | -8.39% | |
60. | Jul 31, 2022 | $383.54 | 20.20% | 4,130.29 | 9.11% | |
61. | Aug 31, 2022 | $344.13 | $1.30 | -9.94% | 3,955.00 | -4.24% |
62. | Sep 30, 2022 | $302.63 | -12.06% | 3,585.62 | -9.34% | |
63. | Oct 31, 2022 | $316.45 | 4.57% | 3,871.98 | 7.99% | |
64. | Nov 30, 2022 | $393.15 | $1.30 | 24.65% | 4,080.11 | 5.38% |
65. | Dec 31, 2022 | $377.03 | -4.10% | 3,839.50 | -5.90% | |
66. | Jan 31, 2023 | $392.48 | 4.10% | 4,076.60 | 6.18% | |
67. | Feb 28, 2023 | $379.38 | $1.30 | -3.01% | 3,970.15 | -2.61% |
68. | Mar 31, 2023 | $399.17 | 5.22% | 4,109.31 | 3.51% | |
69. | Apr 30, 2023 | $386.54 | -3.16% | 4,169.48 | 1.46% | |
70. | May 31, 2023 | $442.99 | $1.30 | 14.94% | 4,179.83 | 0.25% |
71. | Jun 30, 2023 | $485.02 | 9.49% | 4,376.86 | 4.71% | |
Average (R): | 2.96% | 0.94% | ||||
Standard deviation: | 9.62% | 5.05% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of KLAC during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RKLAC,t | RS&P 500,t | (RKLAC,t–RKLAC)2 | (RS&P 500,t–RS&P 500)2 | (RKLAC,t–RKLAC)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Aug 31, 2017 | 1.78% | 0.05% | 1.40 | 0.78 | 1.04 |
2. | Sep 30, 2017 | 13.14% | 1.93% | 103.55 | 0.99 | 10.12 |
3. | Oct 31, 2017 | 2.73% | 2.22% | 0.06 | 1.65 | -0.30 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | May 31, 2023 | 14.94% | 0.25% | 143.45 | 0.47 | -8.23 |
71. | Jun 30, 2023 | 9.49% | 4.71% | 42.57 | 14.27 | 24.65 |
Total (Σ): | 6,480.38 | 1,786.26 | 2,383.18 |
t | Date | RKLAC,t | RS&P 500,t | (RKLAC,t–RKLAC)2 | (RS&P 500,t–RS&P 500)2 | (RKLAC,t–RKLAC)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Aug 31, 2017 | 1.78% | 0.05% | 1.40 | 0.78 | 1.04 |
2. | Sep 30, 2017 | 13.14% | 1.93% | 103.55 | 0.99 | 10.12 |
3. | Oct 31, 2017 | 2.73% | 2.22% | 0.06 | 1.65 | -0.30 |
4. | Nov 30, 2017 | -5.57% | 2.81% | 72.73 | 3.51 | -15.97 |
5. | Dec 31, 2017 | 2.77% | 0.98% | 0.04 | 0.00 | -0.01 |
6. | Jan 31, 2018 | 4.50% | 5.62% | 2.37 | 21.92 | 7.20 |
7. | Feb 28, 2018 | 3.73% | -3.89% | 0.59 | 23.33 | -3.72 |
8. | Mar 31, 2018 | -3.79% | -2.69% | 45.67 | 13.14 | 24.49 |
9. | Apr 30, 2018 | -6.67% | 0.27% | 92.78 | 0.44 | 6.39 |
10. | May 31, 2018 | 12.03% | 2.16% | 82.22 | 1.50 | 11.11 |
11. | Jun 30, 2018 | -9.45% | 0.48% | 154.08 | 0.20 | 5.61 |
12. | Jul 31, 2018 | 14.52% | 3.60% | 133.62 | 7.11 | 30.82 |
13. | Aug 31, 2018 | -0.39% | 3.03% | 11.26 | 4.37 | -7.01 |
14. | Sep 30, 2018 | -12.48% | 0.43% | 238.41 | 0.26 | 7.82 |
15. | Oct 31, 2018 | -10.00% | -6.94% | 168.02 | 62.03 | 102.09 |
16. | Nov 30, 2018 | 8.49% | 1.79% | 30.52 | 0.72 | 4.70 |
17. | Dec 31, 2018 | -9.20% | -9.18% | 148.00 | 102.28 | 123.04 |
18. | Jan 31, 2019 | 19.09% | 7.87% | 259.94 | 48.06 | 111.77 |
19. | Feb 28, 2019 | 9.07% | 2.97% | 37.34 | 4.15 | 12.45 |
20. | Mar 31, 2019 | 3.39% | 1.79% | 0.19 | 0.73 | 0.37 |
21. | Apr 30, 2019 | 6.76% | 3.93% | 14.40 | 8.97 | 11.37 |
22. | May 31, 2019 | -18.56% | -6.58% | 463.24 | 56.45 | 161.71 |
23. | Jun 30, 2019 | 14.68% | 6.89% | 137.27 | 35.49 | 69.80 |
24. | Jul 31, 2019 | 15.33% | 1.31% | 152.94 | 0.14 | 4.66 |
25. | Aug 31, 2019 | 9.04% | -1.81% | 36.99 | 7.53 | -16.69 |
26. | Sep 30, 2019 | 7.81% | 1.72% | 23.49 | 0.61 | 3.79 |
27. | Oct 31, 2019 | 6.01% | 2.04% | 9.31 | 1.23 | 3.38 |
28. | Nov 30, 2019 | -2.56% | 3.40% | 30.52 | 6.10 | -13.64 |
29. | Dec 31, 2019 | 8.73% | 2.86% | 33.29 | 3.70 | 11.10 |
30. | Jan 31, 2020 | -6.98% | -0.16% | 98.80 | 1.21 | 10.92 |
31. | Feb 29, 2020 | -6.75% | -8.41% | 94.26 | 87.36 | 90.75 |
32. | Mar 31, 2020 | -6.49% | -12.51% | 89.29 | 180.84 | 127.07 |
33. | Apr 30, 2020 | 14.16% | 12.68% | 125.31 | 138.03 | 131.52 |
34. | May 31, 2020 | 7.75% | 4.53% | 22.93 | 12.91 | 17.20 |
35. | Jun 30, 2020 | 10.53% | 1.84% | 57.18 | 0.82 | 6.83 |
36. | Jul 31, 2020 | 2.75% | 5.51% | 0.05 | 20.92 | -0.97 |
37. | Aug 31, 2020 | 3.11% | 7.01% | 0.02 | 36.85 | 0.88 |
38. | Sep 30, 2020 | -5.56% | -3.92% | 72.60 | 23.61 | 41.40 |
39. | Oct 31, 2020 | 1.78% | -2.77% | 1.41 | 13.71 | 4.40 |
40. | Nov 30, 2020 | 28.24% | 10.75% | 639.08 | 96.41 | 248.22 |
41. | Dec 31, 2020 | 2.75% | 3.71% | 0.04 | 7.71 | -0.58 |
42. | Jan 31, 2021 | 8.17% | -1.11% | 27.14 | 4.20 | -10.68 |
43. | Feb 28, 2021 | 11.45% | 2.61% | 71.98 | 2.80 | 14.20 |
44. | Mar 31, 2021 | 6.16% | 4.24% | 10.22 | 10.94 | 10.57 |
45. | Apr 30, 2021 | -4.56% | 5.24% | 56.52 | 18.55 | -32.38 |
46. | May 31, 2021 | 0.77% | 0.55% | 4.79 | 0.15 | 0.85 |
47. | Jun 30, 2021 | 2.31% | 2.22% | 0.43 | 1.65 | -0.84 |
48. | Jul 31, 2021 | 7.39% | 2.27% | 19.57 | 1.79 | 5.92 |
49. | Aug 31, 2021 | -2.05% | 2.90% | 25.17 | 3.85 | -9.85 |
50. | Sep 30, 2021 | -1.60% | -4.76% | 20.85 | 32.41 | 25.99 |
51. | Oct 31, 2021 | 11.43% | 6.91% | 71.77 | 35.74 | 50.65 |
52. | Nov 30, 2021 | 9.77% | -0.83% | 46.34 | 3.13 | -12.04 |
53. | Dec 31, 2021 | 5.39% | 4.36% | 5.87 | 11.73 | 8.30 |
54. | Jan 31, 2022 | -9.50% | -5.26% | 155.21 | 38.37 | 77.17 |
55. | Feb 28, 2022 | -10.20% | -3.14% | 173.37 | 16.58 | 53.61 |
56. | Mar 31, 2022 | 5.04% | 3.58% | 4.31 | 6.98 | 5.48 |
57. | Apr 30, 2022 | -12.78% | -8.80% | 248.00 | 94.70 | 153.25 |
58. | May 31, 2022 | 14.61% | 0.01% | 135.62 | 0.87 | -10.84 |
59. | Jun 30, 2022 | -12.54% | -8.39% | 240.50 | 87.01 | 144.66 |
60. | Jul 31, 2022 | 20.20% | 9.11% | 297.17 | 66.84 | 140.94 |
61. | Aug 31, 2022 | -9.94% | -4.24% | 166.40 | 26.83 | 66.82 |
62. | Sep 30, 2022 | -12.06% | -9.34% | 225.68 | 105.58 | 154.36 |
63. | Oct 31, 2022 | 4.57% | 7.99% | 2.57 | 49.71 | 11.31 |
64. | Nov 30, 2022 | 24.65% | 5.38% | 470.25 | 19.71 | 96.27 |
65. | Dec 31, 2022 | -4.10% | -5.90% | 49.89 | 46.69 | 48.26 |
66. | Jan 31, 2023 | 4.10% | 6.18% | 1.29 | 27.45 | 5.94 |
67. | Feb 28, 2023 | -3.01% | -2.61% | 35.64 | 12.58 | 21.17 |
68. | Mar 31, 2023 | 5.22% | 3.51% | 5.08 | 6.60 | 5.79 |
69. | Apr 30, 2023 | -3.16% | 1.46% | 37.54 | 0.28 | -3.24 |
70. | May 31, 2023 | 14.94% | 0.25% | 143.45 | 0.47 | -8.23 |
71. | Jun 30, 2023 | 9.49% | 4.71% | 42.57 | 14.27 | 24.65 |
Total (Σ): | 6,480.38 | 1,786.26 | 2,383.18 |
Show all
VarianceKLAC = Σ(RKLAC,t–RKLAC)2 ÷ (71 – 1)
= 6,480.38 ÷ (71 – 1)
= 92.58
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,786.26 ÷ (71 – 1)
= 25.52
CovarianceKLAC, S&P 500 = Σ(RKLAC,t–RKLAC)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,383.18 ÷ (71 – 1)
= 34.05
Systematic Risk (β) Estimation
VarianceKLAC | 92.58 |
VarianceS&P 500 | 25.52 |
CovarianceKLAC, S&P 500 | 34.05 |
Correlation coefficientKLAC, S&P 5001 | 0.70 |
βKLAC2 | 1.33 |
αKLAC3 | 1.71% |
Calculations
1 Correlation coefficientKLAC, S&P 500
= CovarianceKLAC, S&P 500 ÷ (Standard deviationKLAC × Standard deviationS&P 500)
= 34.05 ÷ (9.62% × 5.05%)
= 0.70
2 βKLAC
= CovarianceKLAC, S&P 500 ÷ VarianceS&P 500
= 34.05 ÷ 25.52
= 1.33
3 αKLAC
= AverageKLAC – βKLAC × AverageS&P 500
= 2.96% – 1.33 × 0.94%
= 1.71%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.79% |
Expected rate of return on market portfolio2 | E(RM) | 13.48% |
Systematic risk (β) of KLA Corp. common stock | βKLAC | 1.33 |
Expected rate of return on KLA Corp. common stock3 | E(RKLAC) | 16.38% |
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(RKLAC) = RF + βKLAC [E(RM) – RF]
= 4.79% + 1.33 [13.48% – 4.79%]
= 16.38%