Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Broadcom Inc. common stock.
Rates of Return
Broadcom Inc. (AVGO) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceAVGO,t1 | DividendAVGO,t1 | RAVGO,t2 | PriceS&P 500,t | RS&P 500,t3 |
Nov 30, 2017 | $277.94 | 2,647.58 | ||||
1. | Dec 31, 2017 | $256.90 | $1.75 | -6.94% | 2,673.61 | 0.98% |
2. | Jan 31, 2018 | $248.03 | -3.45% | 2,823.81 | 5.62% | |
3. | Feb 28, 2018 | $246.46 | -0.63% | 2,713.83 | -3.89% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Sep 30, 2023 | $830.58 | $4.60 | -9.50% | 4,288.05 | -4.87% |
71. | Oct 31, 2023 | $841.37 | 1.30% | 4,193.80 | -2.20% | |
Average (R): | 2.22% | 0.78% | ||||
Standard deviation: | 8.67% | 5.13% |
Broadcom Inc. (AVGO) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceAVGO,t1 | DividendAVGO,t1 | RAVGO,t2 | PriceS&P 500,t | RS&P 500,t3 |
Nov 30, 2017 | $277.94 | 2,647.58 | ||||
1. | Dec 31, 2017 | $256.90 | $1.75 | -6.94% | 2,673.61 | 0.98% |
2. | Jan 31, 2018 | $248.03 | -3.45% | 2,823.81 | 5.62% | |
3. | Feb 28, 2018 | $246.46 | -0.63% | 2,713.83 | -3.89% | |
4. | Mar 31, 2018 | $235.65 | $1.75 | -3.68% | 2,640.87 | -2.69% |
5. | Apr 30, 2018 | $229.42 | -2.64% | 2,648.05 | 0.27% | |
6. | May 31, 2018 | $252.07 | 9.87% | 2,705.27 | 2.16% | |
7. | Jun 30, 2018 | $242.64 | $1.75 | -3.05% | 2,718.37 | 0.48% |
8. | Jul 31, 2018 | $221.77 | -8.60% | 2,816.29 | 3.60% | |
9. | Aug 31, 2018 | $219.03 | -1.24% | 2,901.52 | 3.03% | |
10. | Sep 30, 2018 | $246.73 | $1.75 | 13.45% | 2,913.98 | 0.43% |
11. | Oct 31, 2018 | $223.49 | -9.42% | 2,711.74 | -6.94% | |
12. | Nov 30, 2018 | $237.41 | 6.23% | 2,760.17 | 1.79% | |
13. | Dec 31, 2018 | $254.28 | $2.65 | 8.22% | 2,506.85 | -9.18% |
14. | Jan 31, 2019 | $268.25 | 5.49% | 2,704.10 | 7.87% | |
15. | Feb 28, 2019 | $275.36 | 2.65% | 2,784.49 | 2.97% | |
16. | Mar 31, 2019 | $300.71 | $2.65 | 10.17% | 2,834.40 | 1.79% |
17. | Apr 30, 2019 | $318.40 | 5.88% | 2,945.83 | 3.93% | |
18. | May 31, 2019 | $251.64 | -20.97% | 2,752.06 | -6.58% | |
19. | Jun 30, 2019 | $287.86 | $2.65 | 15.45% | 2,941.76 | 6.89% |
20. | Jul 31, 2019 | $289.99 | 0.74% | 2,980.38 | 1.31% | |
21. | Aug 31, 2019 | $282.64 | -2.53% | 2,926.46 | -1.81% | |
22. | Sep 30, 2019 | $276.07 | $2.65 | -1.39% | 2,976.74 | 1.72% |
23. | Oct 31, 2019 | $292.85 | 6.08% | 3,037.56 | 2.04% | |
24. | Nov 30, 2019 | $316.21 | 7.98% | 3,140.98 | 3.40% | |
25. | Dec 31, 2019 | $316.02 | $3.25 | 0.97% | 3,230.78 | 2.86% |
26. | Jan 31, 2020 | $305.16 | -3.44% | 3,225.52 | -0.16% | |
27. | Feb 29, 2020 | $272.62 | -10.66% | 2,954.22 | -8.41% | |
28. | Mar 31, 2020 | $237.10 | $3.25 | -11.84% | 2,584.59 | -12.51% |
29. | Apr 30, 2020 | $271.62 | 14.56% | 2,912.43 | 12.68% | |
30. | May 31, 2020 | $291.27 | 7.23% | 3,044.31 | 4.53% | |
31. | Jun 30, 2020 | $315.61 | $3.25 | 9.47% | 3,100.29 | 1.84% |
32. | Jul 31, 2020 | $316.75 | 0.36% | 3,271.12 | 5.51% | |
33. | Aug 31, 2020 | $347.15 | 9.60% | 3,500.31 | 7.01% | |
34. | Sep 30, 2020 | $364.32 | $3.25 | 5.88% | 3,363.00 | -3.92% |
35. | Oct 31, 2020 | $349.63 | -4.03% | 3,269.96 | -2.77% | |
36. | Nov 30, 2020 | $401.58 | 14.86% | 3,621.63 | 10.75% | |
37. | Dec 31, 2020 | $437.85 | $3.60 | 9.93% | 3,756.07 | 3.71% |
38. | Jan 31, 2021 | $450.50 | 2.89% | 3,714.24 | -1.11% | |
39. | Feb 28, 2021 | $469.87 | 4.30% | 3,811.15 | 2.61% | |
40. | Mar 31, 2021 | $463.66 | $3.60 | -0.56% | 3,972.89 | 4.24% |
41. | Apr 30, 2021 | $456.20 | -1.61% | 4,181.17 | 5.24% | |
42. | May 31, 2021 | $472.33 | 3.54% | 4,204.11 | 0.55% | |
43. | Jun 30, 2021 | $476.84 | $3.60 | 1.72% | 4,297.50 | 2.22% |
44. | Jul 31, 2021 | $485.40 | 1.80% | 4,395.26 | 2.27% | |
45. | Aug 31, 2021 | $497.21 | 2.43% | 4,522.68 | 2.90% | |
46. | Sep 30, 2021 | $484.93 | $3.60 | -1.75% | 4,307.54 | -4.76% |
47. | Oct 31, 2021 | $531.67 | 9.64% | 4,605.38 | 6.91% | |
48. | Nov 30, 2021 | $553.68 | 4.14% | 4,567.00 | -0.83% | |
49. | Dec 31, 2021 | $665.41 | $4.10 | 20.92% | 4,766.18 | 4.36% |
50. | Jan 31, 2022 | $585.88 | -11.95% | 4,515.55 | -5.26% | |
51. | Feb 28, 2022 | $587.44 | 0.27% | 4,373.94 | -3.14% | |
52. | Mar 31, 2022 | $629.68 | $4.10 | 7.89% | 4,530.41 | 3.58% |
53. | Apr 30, 2022 | $554.39 | -11.96% | 4,131.93 | -8.80% | |
54. | May 31, 2022 | $580.13 | 4.64% | 4,132.15 | 0.01% | |
55. | Jun 30, 2022 | $485.81 | $4.10 | -15.55% | 3,785.38 | -8.39% |
56. | Jul 31, 2022 | $535.48 | 10.22% | 4,130.29 | 9.11% | |
57. | Aug 31, 2022 | $499.11 | -6.79% | 3,955.00 | -4.24% | |
58. | Sep 30, 2022 | $444.01 | $4.10 | -10.22% | 3,585.62 | -9.34% |
59. | Oct 31, 2022 | $470.12 | 5.88% | 3,871.98 | 7.99% | |
60. | Nov 30, 2022 | $551.03 | 17.21% | 4,080.11 | 5.38% | |
61. | Dec 31, 2022 | $559.13 | $4.60 | 2.30% | 3,839.50 | -5.90% |
62. | Jan 31, 2023 | $585.01 | 4.63% | 4,076.60 | 6.18% | |
63. | Feb 28, 2023 | $594.29 | 1.59% | 3,970.15 | -2.61% | |
64. | Mar 31, 2023 | $641.54 | $4.60 | 8.72% | 4,109.31 | 3.51% |
65. | Apr 30, 2023 | $626.50 | -2.34% | 4,169.48 | 1.46% | |
66. | May 31, 2023 | $807.96 | 28.96% | 4,179.83 | 0.25% | |
67. | Jun 30, 2023 | $867.43 | $4.60 | 7.93% | 4,376.86 | 4.71% |
68. | Jul 31, 2023 | $898.65 | 3.60% | 4,588.96 | 4.85% | |
69. | Aug 31, 2023 | $922.89 | 2.70% | 4,507.66 | -1.77% | |
70. | Sep 30, 2023 | $830.58 | $4.60 | -9.50% | 4,288.05 | -4.87% |
71. | Oct 31, 2023 | $841.37 | 1.30% | 4,193.80 | -2.20% | |
Average (R): | 2.22% | 0.78% | ||||
Standard deviation: | 8.67% | 5.13% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of AVGO during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RAVGO,t | RS&P 500,t | (RAVGO,t–RAVGO)2 | (RS&P 500,t–RS&P 500)2 | (RAVGO,t–RAVGO)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Dec 31, 2017 | -6.94% | 0.98% | 83.89 | 0.04 | -1.85 |
2. | Jan 31, 2018 | -3.45% | 5.62% | 32.17 | 23.40 | -27.43 |
3. | Feb 28, 2018 | -0.63% | -3.89% | 8.13 | 21.86 | 13.33 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Sep 30, 2023 | -9.50% | -4.87% | 137.42 | 31.95 | 66.27 |
71. | Oct 31, 2023 | 1.30% | -2.20% | 0.85 | 8.87 | 2.74 |
Total (Σ): | 5,262.88 | 1,843.80 | 1,962.24 |
t | Date | RAVGO,t | RS&P 500,t | (RAVGO,t–RAVGO)2 | (RS&P 500,t–RS&P 500)2 | (RAVGO,t–RAVGO)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Dec 31, 2017 | -6.94% | 0.98% | 83.89 | 0.04 | -1.85 |
2. | Jan 31, 2018 | -3.45% | 5.62% | 32.17 | 23.40 | -27.43 |
3. | Feb 28, 2018 | -0.63% | -3.89% | 8.13 | 21.86 | 13.33 |
4. | Mar 31, 2018 | -3.68% | -2.69% | 34.75 | 12.04 | 20.45 |
5. | Apr 30, 2018 | -2.64% | 0.27% | 23.65 | 0.26 | 2.47 |
6. | May 31, 2018 | 9.87% | 2.16% | 58.58 | 1.90 | 10.56 |
7. | Jun 30, 2018 | -3.05% | 0.48% | 27.73 | 0.09 | 1.56 |
8. | Jul 31, 2018 | -8.60% | 3.60% | 117.08 | 7.96 | -30.53 |
9. | Aug 31, 2018 | -1.24% | 3.03% | 11.93 | 5.04 | -7.76 |
10. | Sep 30, 2018 | 13.45% | 0.43% | 126.04 | 0.12 | -3.94 |
11. | Oct 31, 2018 | -9.42% | -6.94% | 135.45 | 59.62 | 89.86 |
12. | Nov 30, 2018 | 6.23% | 1.79% | 16.08 | 1.01 | 4.03 |
13. | Dec 31, 2018 | 8.22% | -9.18% | 36.04 | 99.17 | -59.78 |
14. | Jan 31, 2019 | 5.49% | 7.87% | 10.73 | 50.24 | 23.21 |
15. | Feb 28, 2019 | 2.65% | 2.97% | 0.19 | 4.81 | 0.95 |
16. | Mar 31, 2019 | 10.17% | 1.79% | 63.20 | 1.02 | 8.04 |
17. | Apr 30, 2019 | 5.88% | 3.93% | 13.42 | 9.93 | 11.54 |
18. | May 31, 2019 | -20.97% | -6.58% | 537.60 | 54.15 | 170.62 |
19. | Jun 30, 2019 | 15.45% | 6.89% | 174.97 | 37.36 | 80.85 |
20. | Jul 31, 2019 | 0.74% | 1.31% | 2.19 | 0.28 | -0.79 |
21. | Aug 31, 2019 | -2.53% | -1.81% | 22.60 | 6.71 | 12.31 |
22. | Sep 30, 2019 | -1.39% | 1.72% | 13.00 | 0.88 | -3.38 |
23. | Oct 31, 2019 | 6.08% | 2.04% | 14.89 | 1.59 | 4.87 |
24. | Nov 30, 2019 | 7.98% | 3.40% | 33.15 | 6.89 | 15.11 |
25. | Dec 31, 2019 | 0.97% | 2.86% | 1.57 | 4.32 | -2.60 |
26. | Jan 31, 2020 | -3.44% | -0.16% | 31.98 | 0.89 | 5.34 |
27. | Feb 29, 2020 | -10.66% | -8.41% | 165.95 | 84.49 | 118.41 |
28. | Mar 31, 2020 | -11.84% | -12.51% | 197.57 | 176.70 | 186.84 |
29. | Apr 30, 2020 | 14.56% | 12.68% | 152.28 | 141.70 | 146.89 |
30. | May 31, 2020 | 7.23% | 4.53% | 25.15 | 14.04 | 18.79 |
31. | Jun 30, 2020 | 9.47% | 1.84% | 52.61 | 1.12 | 7.67 |
32. | Jul 31, 2020 | 0.36% | 5.51% | 3.45 | 22.37 | -8.79 |
33. | Aug 31, 2020 | 9.60% | 7.01% | 54.44 | 38.76 | 45.94 |
34. | Sep 30, 2020 | 5.88% | -3.92% | 13.42 | 22.12 | -17.23 |
35. | Oct 31, 2020 | -4.03% | -2.77% | 39.08 | 12.58 | 22.17 |
36. | Nov 30, 2020 | 14.86% | 10.75% | 159.76 | 99.48 | 126.07 |
37. | Dec 31, 2020 | 9.93% | 3.71% | 59.43 | 8.59 | 22.60 |
38. | Jan 31, 2021 | 2.89% | -1.11% | 0.45 | 3.59 | -1.27 |
39. | Feb 28, 2021 | 4.30% | 2.61% | 4.33 | 3.34 | 3.80 |
40. | Mar 31, 2021 | -0.56% | 4.24% | 7.70 | 11.99 | -9.61 |
41. | Apr 30, 2021 | -1.61% | 5.24% | 14.65 | 19.91 | -17.08 |
42. | May 31, 2021 | 3.54% | 0.55% | 1.73 | 0.05 | -0.31 |
43. | Jun 30, 2021 | 1.72% | 2.22% | 0.25 | 2.08 | -0.72 |
44. | Jul 31, 2021 | 1.80% | 2.27% | 0.18 | 2.23 | -0.63 |
45. | Aug 31, 2021 | 2.43% | 2.90% | 0.05 | 4.49 | 0.45 |
46. | Sep 30, 2021 | -1.75% | -4.76% | 15.72 | 30.67 | 21.96 |
47. | Oct 31, 2021 | 9.64% | 6.91% | 55.05 | 37.62 | 45.51 |
48. | Nov 30, 2021 | 4.14% | -0.83% | 3.69 | 2.61 | -3.10 |
49. | Dec 31, 2021 | 20.92% | 4.36% | 349.73 | 12.82 | 66.96 |
50. | Jan 31, 2022 | -11.95% | -5.26% | 200.82 | 36.47 | 85.58 |
51. | Feb 28, 2022 | 0.27% | -3.14% | 3.81 | 15.34 | 7.65 |
52. | Mar 31, 2022 | 7.89% | 3.58% | 32.14 | 7.82 | 15.86 |
53. | Apr 30, 2022 | -11.96% | -8.80% | 200.95 | 91.71 | 135.75 |
54. | May 31, 2022 | 4.64% | 0.01% | 5.88 | 0.60 | -1.88 |
55. | Jun 30, 2022 | -15.55% | -8.39% | 315.80 | 84.14 | 163.01 |
56. | Jul 31, 2022 | 10.22% | 9.11% | 64.08 | 69.40 | 66.69 |
57. | Aug 31, 2022 | -6.79% | -4.24% | 81.20 | 25.25 | 45.28 |
58. | Sep 30, 2022 | -10.22% | -9.34% | 154.68 | 102.42 | 125.87 |
59. | Oct 31, 2022 | 5.88% | 7.99% | 13.41 | 51.92 | 26.38 |
60. | Nov 30, 2022 | 17.21% | 5.38% | 224.75 | 21.11 | 68.88 |
61. | Dec 31, 2022 | 2.30% | -5.90% | 0.01 | 44.59 | -0.57 |
62. | Jan 31, 2023 | 4.63% | 6.18% | 5.81 | 29.10 | 13.00 |
63. | Feb 28, 2023 | 1.59% | -2.61% | 0.40 | 11.51 | 2.15 |
64. | Mar 31, 2023 | 8.72% | 3.51% | 42.32 | 7.42 | 17.72 |
65. | Apr 30, 2023 | -2.34% | 1.46% | 20.82 | 0.47 | -3.12 |
66. | May 31, 2023 | 28.96% | 0.25% | 715.30 | 0.28 | -14.24 |
67. | Jun 30, 2023 | 7.93% | 4.71% | 32.61 | 15.47 | 22.46 |
68. | Jul 31, 2023 | 3.60% | 4.85% | 1.90 | 16.53 | 5.61 |
69. | Aug 31, 2023 | 2.70% | -1.77% | 0.23 | 6.51 | -1.22 |
70. | Sep 30, 2023 | -9.50% | -4.87% | 137.42 | 31.95 | 66.27 |
71. | Oct 31, 2023 | 1.30% | -2.20% | 0.85 | 8.87 | 2.74 |
Total (Σ): | 5,262.88 | 1,843.80 | 1,962.24 |
Show all
VarianceAVGO = Σ(RAVGO,t–RAVGO)2 ÷ (71 – 1)
= 5,262.88 ÷ (71 – 1)
= 75.18
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,843.80 ÷ (71 – 1)
= 26.34
CovarianceAVGO, S&P 500 = Σ(RAVGO,t–RAVGO)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,962.24 ÷ (71 – 1)
= 28.03
Systematic Risk (β) Estimation
VarianceAVGO | 75.18 |
VarianceS&P 500 | 26.34 |
CovarianceAVGO, S&P 500 | 28.03 |
Correlation coefficientAVGO, S&P 5001 | 0.63 |
βAVGO2 | 1.06 |
αAVGO3 | 1.39% |
Calculations
1 Correlation coefficientAVGO, S&P 500
= CovarianceAVGO, S&P 500 ÷ (Standard deviationAVGO × Standard deviationS&P 500)
= 28.03 ÷ (8.67% × 5.13%)
= 0.63
2 βAVGO
= CovarianceAVGO, S&P 500 ÷ VarianceS&P 500
= 28.03 ÷ 26.34
= 1.06
3 αAVGO
= AverageAVGO – βAVGO × AverageS&P 500
= 2.22% – 1.06 × 0.78%
= 1.39%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.43% |
Expected rate of return on market portfolio2 | E(RM) | 13.60% |
Systematic risk (β) of Broadcom Inc. common stock | βAVGO | 1.06 |
Expected rate of return on Broadcom Inc. common stock3 | E(RAVGO) | 14.19% |
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(RAVGO) = RF + βAVGO [E(RM) – RF]
= 4.43% + 1.06 [13.60% – 4.43%]
= 14.19%