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Microsoft Excel LibreOffice Calc


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

Microsoft Excel LibreOffice Calc
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, 2013 hidden hidden
1. Feb 28, 2013 hidden hidden hidden% hidden hidden%
2. Mar 31, 2013 hidden hidden% hidden hidden%
3. Apr 30, 2013 hidden hidden% hidden hidden%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2017 hidden hidden hidden% hidden hidden%
59. Dec 31, 2017 hidden hidden% hidden hidden%
Average: hidden% hidden%
Standard Deviation: hidden% hidden%
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, 2013 hidden hidden
1. Feb 28, 2013 hidden hidden hidden% hidden hidden%
2. Mar 31, 2013 hidden hidden% hidden hidden%
3. Apr 30, 2013 hidden hidden% hidden hidden%
4. May 31, 2013 hidden hidden hidden% hidden hidden%
5. Jun 30, 2013 hidden hidden% hidden hidden%
6. Jul 31, 2013 hidden hidden% hidden hidden%
7. Aug 31, 2013 hidden hidden hidden% hidden hidden%
8. Sep 30, 2013 hidden hidden% hidden hidden%
9. Oct 31, 2013 hidden hidden% hidden hidden%
10. Nov 30, 2013 hidden hidden hidden% hidden hidden%
11. Dec 31, 2013 hidden hidden% hidden hidden%
12. Jan 31, 2014 hidden hidden% hidden hidden%
13. Feb 28, 2014 hidden hidden hidden% hidden hidden%
14. Mar 31, 2014 hidden hidden% hidden hidden%
15. Apr 30, 2014 hidden hidden% hidden hidden%
16. May 31, 2014 hidden hidden hidden% hidden hidden%
17. Jun 30, 2014 hidden hidden% hidden hidden%
18. Jul 31, 2014 hidden hidden% hidden hidden%
19. Aug 31, 2014 hidden hidden hidden% hidden hidden%
20. Sep 30, 2014 hidden hidden% hidden hidden%
21. Oct 31, 2014 hidden hidden% hidden hidden%
22. Nov 30, 2014 hidden hidden hidden% hidden hidden%
23. Dec 31, 2014 hidden hidden% hidden hidden%
24. Jan 31, 2015 hidden hidden% hidden hidden%
25. Feb 28, 2015 hidden hidden hidden% hidden hidden%
26. Mar 31, 2015 hidden hidden% hidden hidden%
27. Apr 30, 2015 hidden hidden% hidden hidden%
28. May 31, 2015 hidden hidden hidden% hidden hidden%
29. Jun 30, 2015 hidden hidden% hidden hidden%
30. Jul 31, 2015 hidden hidden% hidden hidden%
31. Aug 31, 2015 hidden hidden hidden% hidden hidden%
32. Sep 30, 2015 hidden hidden% hidden hidden%
33. Oct 31, 2015 hidden hidden% hidden hidden%
34. Nov 30, 2015 hidden hidden hidden% hidden hidden%
35. Dec 31, 2015 hidden hidden% hidden hidden%
36. Jan 31, 2016 hidden hidden% hidden hidden%
37. Feb 29, 2016 hidden hidden hidden% hidden hidden%
38. Mar 31, 2016 hidden hidden% hidden hidden%
39. Apr 30, 2016 hidden hidden% hidden hidden%
40. May 31, 2016 hidden hidden hidden% hidden hidden%
41. Jun 30, 2016 hidden hidden% hidden hidden%
42. Jul 31, 2016 hidden hidden% hidden hidden%
43. Aug 31, 2016 hidden hidden hidden% hidden hidden%
44. Sep 30, 2016 hidden hidden% hidden hidden%
45. Oct 31, 2016 hidden hidden% hidden hidden%
46. Nov 30, 2016 hidden hidden hidden% hidden hidden%
47. Dec 31, 2016 hidden hidden% hidden hidden%
48. Jan 31, 2017 hidden hidden% hidden hidden%
49. Feb 28, 2017 hidden hidden hidden% hidden hidden%
50. Mar 31, 2017 hidden hidden% hidden hidden%
51. Apr 30, 2017 hidden hidden% hidden hidden%
52. May 31, 2017 hidden hidden hidden% hidden hidden%
53. Jun 30, 2017 hidden hidden% hidden hidden%
54. Jul 31, 2017 hidden hidden% hidden hidden%
55. Aug 31, 2017 hidden hidden hidden% hidden hidden%
56. Sep 30, 2017 hidden hidden% hidden hidden%
57. Oct 31, 2017 hidden hidden% hidden hidden%
58. Nov 30, 2017 hidden hidden hidden% hidden hidden%
59. Dec 31, 2017 hidden hidden% hidden hidden%
Average: hidden% hidden%
Standard Deviation: hidden% hidden%

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


Systematic Risk (β) Estimation

Microsoft Excel LibreOffice Calc
VarianceIBM hidden
VarianceS&P 500 hidden
CovarianceIBM, S&P 500 hidden
Correlation CoefficientIBM, S&P 5001 hidden
βIBM2 hidden
αIBM3 hidden

Calculations

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

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

3 AverageIBM – βIBM × AverageS&P 500
= hiddenhidden × hidden


Expected Rate of Return

Microsoft Excel LibreOffice Calc
Assumptions
Rate of return on LT Treasury Composite1 RF hidden%
Expected rate of return on market portfolio2 E(RM) hidden%
Systematic risk (β) of IBM's common stock βIBM hidden
Expected rate of return on IBM's common stock3 E(RIBM) hidden%

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]
= hidden% + hidden [hidden% – hidden%]
= hidden%