Capital Asset Pricing Model (CAPM)

Difficulty: Intermediate


Rates of Return

Broadcom Inc., monthly 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, 2011 29.92 1,246.96
1. Dec 31, 2011 28.86 0.12 -3.14% 1,257.60 0.85%
2. Jan 31, 2012 33.94 17.60% 1,312.41 4.36%
3. Feb 29, 2012 37.61 10.81% 1,365.68 4.06%
. . . . . . .
. . . . . . .
. . . . . . .
70. Sep 30, 2017 242.54 1.02 -3.38% 2,519.36 1.93%
71. Oct 31, 2017 263.91 8.81% 2,575.26 2.22%
Average: 3.57% 1.06%
Standard Deviation: 8.14% 2.78%
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, 2011 29.92 1,246.96
1. Dec 31, 2011 28.86 0.12 -3.14% 1,257.60 0.85%
2. Jan 31, 2012 33.94 17.60% 1,312.41 4.36%
3. Feb 29, 2012 37.61 10.81% 1,365.68 4.06%
4. Mar 31, 2012 38.97 0.13 3.96% 1,408.47 3.13%
5. Apr 30, 2012 34.48 -11.52% 1,397.91 -0.75%
6. May 31, 2012 33.10 -4.00% 1,310.33 -6.27%
7. Jun 30, 2012 35.90 0.15 8.91% 1,362.16 3.96%
8. Jul 31, 2012 36.90 2.79% 1,379.32 1.26%
9. Aug 31, 2012 36.57 -0.89% 1,406.58 1.98%
10. Sep 30, 2012 34.87 0.16 -4.21% 1,440.67 2.42%
11. Oct 31, 2012 33.03 -5.28% 1,412.16 -1.98%
12. Nov 30, 2012 35.10 6.27% 1,416.18 0.28%
13. Dec 31, 2012 31.65 0.17 -9.34% 1,426.19 0.71%
14. Jan 31, 2013 35.77 13.02% 1,498.11 5.04%
15. Feb 28, 2013 34.22 -4.33% 1,514.68 1.11%
16. Mar 31, 2013 35.92 0.19 5.52% 1,569.19 3.60%
17. Apr 30, 2013 31.96 -11.02% 1,597.57 1.81%
18. May 31, 2013 37.73 18.05% 1,630.74 2.08%
19. Jun 30, 2013 37.38 0.21 -0.37% 1,606.28 -1.50%
20. Jul 31, 2013 36.68 -1.87% 1,685.73 4.95%
21. Aug 31, 2013 38.51 4.99% 1,632.97 -3.13%
22. Sep 30, 2013 43.08 0.23 12.46% 1,681.55 2.97%
23. Oct 31, 2013 45.43 5.45% 1,756.54 4.46%
24. Nov 30, 2013 44.73 -1.54% 1,805.81 2.80%
25. Dec 31, 2013 52.88 0.25 18.78% 1,848.36 2.36%
26. Jan 31, 2014 54.64 3.33% 1,782.59 -3.56%
27. Feb 28, 2014 61.70 12.92% 1,859.45 4.31%
28. Mar 31, 2014 64.41 0.27 4.83% 1,872.34 0.69%
29. Apr 30, 2014 63.50 -1.41% 1,883.95 0.62%
30. May 31, 2014 70.67 11.29% 1,923.57 2.10%
31. Jun 30, 2014 72.07 0.29 2.39% 1,960.23 1.91%
32. Jul 31, 2014 69.38 -3.73% 1,930.67 -1.51%
33. Aug 31, 2014 82.09 18.32% 2,003.37 3.77%
34. Sep 30, 2014 87.00 0.32 6.37% 1,972.29 -1.55%
35. Oct 31, 2014 86.25 -0.86% 2,018.05 2.32%
36. Nov 30, 2014 93.40 8.29% 2,067.56 2.45%
37. Dec 31, 2014 100.59 0.35 8.07% 2,058.90 -0.42%
38. Jan 31, 2015 102.88 2.28% 1,994.99 -3.10%
39. Feb 28, 2015 127.62 24.05% 2,104.50 5.49%
40. Mar 31, 2015 126.98 0.38 -0.20% 2,067.89 -1.74%
41. Apr 30, 2015 116.88 -7.95% 2,085.51 0.85%
42. May 31, 2015 148.07 26.69% 2,107.39 1.05%
43. Jun 30, 2015 132.93 0.40 -9.95% 2,063.11 -2.10%
44. Jul 31, 2015 125.14 -5.86% 2,103.84 1.97%
45. Aug 31, 2015 125.97 0.66% 1,972.18 -6.26%
46. Sep 30, 2015 125.01 0.42 -0.43% 1,920.03 -2.64%
47. Oct 31, 2015 123.13 -1.50% 2,079.36 8.30%
48. Nov 30, 2015 130.45 5.94% 2,080.41 0.05%
49. Dec 31, 2015 145.15 0.44 11.61% 2,043.94 -1.75%
50. Jan 31, 2016 133.71 -7.88% 1,940.24 -5.07%
51. Feb 29, 2016 133.97 0.19% 1,932.23 -0.41%
52. Mar 31, 2016 154.50 0.49 15.69% 2,059.74 6.60%
53. Apr 30, 2016 145.75 -5.66% 2,065.30 0.27%
54. May 31, 2016 154.36 5.91% 2,096.95 1.53%
55. Jun 30, 2016 155.40 0.50 1.00% 2,098.86 0.09%
56. Jul 31, 2016 161.98 4.23% 2,173.60 3.56%
57. Aug 31, 2016 176.42 8.91% 2,170.95 -0.12%
58. Sep 30, 2016 172.52 0.51 -1.92% 2,168.27 -0.12%
59. Oct 31, 2016 170.28 -1.30% 2,126.15 -1.94%
60. Nov 30, 2016 170.49 0.12% 2,198.81 3.42%
61. Dec 31, 2016 176.77 1.02 4.28% 2,238.83 1.82%
62. Jan 31, 2017 199.50 12.86% 2,278.87 1.79%
63. Feb 28, 2017 210.93 5.73% 2,363.64 3.72%
64. Mar 31, 2017 218.96 1.02 4.29% 2,362.72 -0.04%
65. Apr 30, 2017 220.81 0.84% 2,384.20 0.91%
66. May 31, 2017 239.48 8.46% 2,411.80 1.16%
67. Jun 30, 2017 233.05 1.02 -2.26% 2,423.41 0.48%
68. Jul 31, 2017 246.66 5.84% 2,470.30 1.93%
69. Aug 31, 2017 252.07 2.19% 2,471.65 0.05%
70. Sep 30, 2017 242.54 1.02 -3.38% 2,519.36 1.93%
71. Oct 31, 2017 263.91 8.81% 2,575.26 2.22%
Average: 3.57% 1.06%
Standard Deviation: 8.14% 2.78%

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1 Data in USD $ 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

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Systematic Risk (β) Estimation

 
VarianceAVGO 66.27
VarianceS&P 500 7.71
CovarianceAVGO, S&P 500 9.01
Correlation CoefficientAVGO, S&P 5001 0.40
βAVGO2 1.17
αAVGO3 2.32

Calculations

1 CovarianceAVGO, S&P 500 ÷ (Standard DeviationAVGO × Standard DeviationS&P 500)
= 9.01 ÷ (8.14 × 2.78)

2 CovarianceAVGO, S&P 500 ÷ VarianceS&P 500
= 9.01 ÷ 7.71

3 AverageAVGO – βAVGO × AverageS&P 500
= 3.57 – 1.17 × 1.06

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Expected Rate of Return

 
Assumptions
Rate of return on LT Treasury Composite1 RF 3.00%
Expected rate of return on market portfolio2 E(RM) 12.42%
Systematic risk (β) of Broadcom's common stock βAVGO 1.17
Expected rate of return on Broadcom's common stock3 E(RAVGO) 14.02%

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).

Calculations

2 See Details »

3 E(RAVGO) = RF + βAVGO [E(RM) – RF]
= 3.00% + 1.17 [12.42% – 3.00%]
= 14.02%

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