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Capital Asset Pricing Model (CAPM)

Difficulty: Intermediate


Rates of Return

Apple Inc., monthly rates of return

 
Apple Inc. (AAPL) Standard & Poor's 500 (S&P 500)
t Date PriceAAPL,t1 DividendAAPL,t1 RAAPL,t2 PriceS&P 500,t RS&P 500,t3
Oct 31, 2011
1. Nov 30, 2011 % %
2. Dec 31, 2011 % %
3. Jan 31, 2012 % %
. . . . . . .
. . . . . . .
. . . . . . .
70. Aug 31, 2017 % %
71. Sep 30, 2017 % %
Average: % %
Standard Deviation: % %
Apple Inc. (AAPL) Standard & Poor's 500 (S&P 500)
t Date PriceAAPL,t1 DividendAAPL,t1 RAAPL,t2 PriceS&P 500,t RS&P 500,t3
Oct 31, 2011
1. Nov 30, 2011 % %
2. Dec 31, 2011 % %
3. Jan 31, 2012 % %
4. Feb 29, 2012 % %
5. Mar 31, 2012 % %
6. Apr 30, 2012 % %
7. May 31, 2012 % %
8. Jun 30, 2012 % %
9. Jul 31, 2012 % %
10. Aug 31, 2012 % %
11. Sep 30, 2012 % %
12. Oct 31, 2012 % %
13. Nov 30, 2012 % %
14. Dec 31, 2012 % %
15. Jan 31, 2013 % %
16. Feb 28, 2013 % %
17. Mar 31, 2013 % %
18. Apr 30, 2013 % %
19. May 31, 2013 % %
20. Jun 30, 2013 % %
21. Jul 31, 2013 % %
22. Aug 31, 2013 % %
23. Sep 30, 2013 % %
24. Oct 31, 2013 % %
25. Nov 30, 2013 % %
26. Dec 31, 2013 % %
27. Jan 31, 2014 % %
28. Feb 28, 2014 % %
29. Mar 31, 2014 % %
30. Apr 30, 2014 % %
31. May 31, 2014 % %
32. Jun 30, 2014 % %
33. Jul 31, 2014 % %
34. Aug 31, 2014 % %
35. Sep 30, 2014 % %
36. Oct 31, 2014 % %
37. Nov 30, 2014 % %
38. Dec 31, 2014 % %
39. Jan 31, 2015 % %
40. Feb 28, 2015 % %
41. Mar 31, 2015 % %
42. Apr 30, 2015 % %
43. May 31, 2015 % %
44. Jun 30, 2015 % %
45. Jul 31, 2015 % %
46. Aug 31, 2015 % %
47. Sep 30, 2015 % %
48. Oct 31, 2015 % %
49. Nov 30, 2015 % %
50. Dec 31, 2015 % %
51. Jan 31, 2016 % %
52. Feb 29, 2016 % %
53. Mar 31, 2016 % %
54. Apr 30, 2016 % %
55. May 31, 2016 % %
56. Jun 30, 2016 % %
57. Jul 31, 2016 % %
58. Aug 31, 2016 % %
59. Sep 30, 2016 % %
60. Oct 31, 2016 % %
61. Nov 30, 2016 % %
62. Dec 31, 2016 % %
63. Jan 31, 2017 % %
64. Feb 28, 2017 % %
65. Mar 31, 2017 % %
66. Apr 30, 2017 % %
67. May 31, 2017 % %
68. Jun 30, 2017 % %
69. Jul 31, 2017 % %
70. Aug 31, 2017 % %
71. Sep 30, 2017 % %
Average: % %
Standard Deviation: % %

Show All

1 Data in USD $ per share of common stock, adjusted for splits and stock dividends.

2 Rate of return on common stock of AAPL 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

 
VarianceAAPL
VarianceS&P 500
CovarianceAAPL, S&P 500
Correlation CoefficientAAPL, S&P 5001
βAAPL2
αAAPL3

Calculations

1 CovarianceAAPL, S&P 500 ÷ (Standard DeviationAAPL × Standard DeviationS&P 500)
= ÷ ( × )

2 CovarianceAAPL, S&P 500 ÷ VarianceS&P 500
= ÷

3 AverageAAPL – βAAPL × AverageS&P 500
= ×

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Expected Rate of Return

 
Assumptions
Rate of return on LT Treasury Composite1 RF %
Expected rate of return on market portfolio2 E(RM) %
Systematic risk (β) of Apple's common stock βAAPL
Expected rate of return on Apple's common stock3 E(RAAPL) %

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(RAAPL) = RF + βAAPL [E(RM) – RF]
= % + [% – %]
= %

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