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Capital Asset Pricing Model (CAPM)

Difficulty: Intermediate

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like IBM's common stock.


Rates of Return

International Business Machines Corp., monthly rates of return

 
International Business Machines Corp. (IBM) Standard & Poor's 500 (S&P 500)
t Date PriceIBM,t1 DividendIBM,t1 RIBM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2012
1. Feb 29, 2012 % %
2. Mar 31, 2012 % %
3. Apr 30, 2012 % %
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2016 % %
59. Dec 31, 2016 % %
Average: % %
Standard Deviation: % %
International Business Machines Corp. (IBM) Standard & Poor's 500 (S&P 500)
t Date PriceIBM,t1 DividendIBM,t1 RIBM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2012
1. Feb 29, 2012 % %
2. Mar 31, 2012 % %
3. Apr 30, 2012 % %
4. May 31, 2012 % %
5. Jun 30, 2012 % %
6. Jul 31, 2012 % %
7. Aug 31, 2012 % %
8. Sep 30, 2012 % %
9. Oct 31, 2012 % %
10. Nov 30, 2012 % %
11. Dec 31, 2012 % %
12. Jan 31, 2013 % %
13. Feb 28, 2013 % %
14. Mar 31, 2013 % %
15. Apr 30, 2013 % %
16. May 31, 2013 % %
17. Jun 30, 2013 % %
18. Jul 31, 2013 % %
19. Aug 31, 2013 % %
20. Sep 30, 2013 % %
21. Oct 31, 2013 % %
22. Nov 30, 2013 % %
23. Dec 31, 2013 % %
24. Jan 31, 2014 % %
25. Feb 28, 2014 % %
26. Mar 31, 2014 % %
27. Apr 30, 2014 % %
28. May 31, 2014 % %
29. Jun 30, 2014 % %
30. Jul 31, 2014 % %
31. Aug 31, 2014 % %
32. Sep 30, 2014 % %
33. Oct 31, 2014 % %
34. Nov 30, 2014 % %
35. Dec 31, 2014 % %
36. Jan 31, 2015 % %
37. Feb 28, 2015 % %
38. Mar 31, 2015 % %
39. Apr 30, 2015 % %
40. May 31, 2015 % %
41. Jun 30, 2015 % %
42. Jul 31, 2015 % %
43. Aug 31, 2015 % %
44. Sep 30, 2015 % %
45. Oct 31, 2015 % %
46. Nov 30, 2015 % %
47. Dec 31, 2015 % %
48. Jan 31, 2016 % %
49. Feb 29, 2016 % %
50. Mar 31, 2016 % %
51. Apr 30, 2016 % %
52. May 31, 2016 % %
53. Jun 30, 2016 % %
54. Jul 31, 2016 % %
55. Aug 31, 2016 % %
56. Sep 30, 2016 % %
57. Oct 31, 2016 % %
58. Nov 30, 2016 % %
59. Dec 31, 2016 % %
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 IBM 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

 
VarianceIBM
VarianceS&P 500
CovarianceIBM, S&P 500
Correlation CoefficientIBM, S&P 5001
βIBM2
αIBM3

Calculations

1 CovarianceIBM, S&P 500 ÷ (Standard DeviationIBM × Standard DeviationS&P 500)
= ÷ ( × )

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

3 AverageIBM – βIBM × 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 IBM's common stock βIBM
Expected rate of return on IBM's common stock3 E(RIBM) %

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(RIBM) = RF + βIBM [E(RM) – RF]
= % + [% – %]
= %

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