Microsoft Excel LibreOffice Calc

International Business Machines Corp. (IBM)


Capital Asset Pricing Model (CAPM)

Medium level of difficulty

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like International Business Machines Corp.’s common stock.


Rates of Return

International Business Machines Corp., monthly rates of return

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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, 2014 176.68 1,782.59
1. Feb 28, 2014 185.17 0.95 5.34% 1,859.45 4.31%
2. Mar 31, 2014 192.49 3.95% 1,872.34 0.69%
3. Apr 30, 2014 196.47 2.07% 1,883.95 0.62%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2018 124.27 1.57 9.02% 2,760.17 1.79%
59. Dec 31, 2018 113.67 -8.53% 2,506.85 -9.18%
Average: -0.27% 0.63%
Standard deviation: 5.95% 3.13%
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, 2014 176.68 1,782.59
1. Feb 28, 2014 185.17 0.95 5.34% 1,859.45 4.31%
2. Mar 31, 2014 192.49 3.95% 1,872.34 0.69%
3. Apr 30, 2014 196.47 2.07% 1,883.95 0.62%
4. May 31, 2014 184.36 1.10 -5.60% 1,923.57 2.10%
5. Jun 30, 2014 181.27 -1.68% 1,960.23 1.91%
6. Jul 31, 2014 191.67 5.74% 1,930.67 -1.51%
7. Aug 31, 2014 192.30 1.10 0.90% 2,003.37 3.77%
8. Sep 30, 2014 189.83 -1.28% 1,972.29 -1.55%
9. Oct 31, 2014 164.40 -13.40% 2,018.05 2.32%
10. Nov 30, 2014 162.17 1.10 -0.69% 2,067.56 2.45%
11. Dec 31, 2014 160.44 -1.07% 2,058.90 -0.42%
12. Jan 31, 2015 153.31 -4.44% 1,994.99 -3.10%
13. Feb 28, 2015 161.94 1.10 6.35% 2,104.50 5.49%
14. Mar 31, 2015 160.50 -0.89% 2,067.89 -1.74%
15. Apr 30, 2015 171.29 6.72% 2,085.51 0.85%
16. May 31, 2015 169.65 1.30 -0.20% 2,107.39 1.05%
17. Jun 30, 2015 162.66 -4.12% 2,063.11 -2.10%
18. Jul 31, 2015 161.99 -0.41% 2,103.84 1.97%
19. Aug 31, 2015 147.89 1.30 -7.90% 1,972.18 -6.26%
20. Sep 30, 2015 144.97 -1.97% 1,920.03 -2.64%
21. Oct 31, 2015 140.08 -3.37% 2,079.36 8.30%
22. Nov 30, 2015 139.42 1.30 0.46% 2,080.41 0.05%
23. Dec 31, 2015 137.62 -1.29% 2,043.94 -1.75%
24. Jan 31, 2016 124.79 -9.32% 1,940.24 -5.07%
25. Feb 29, 2016 131.03 1.30 6.04% 1,932.23 -0.41%
26. Mar 31, 2016 151.45 15.58% 2,059.74 6.60%
27. Apr 30, 2016 145.94 -3.64% 2,065.30 0.27%
28. May 31, 2016 153.74 1.40 6.30% 2,096.95 1.53%
29. Jun 30, 2016 151.78 -1.27% 2,098.86 0.09%
30. Jul 31, 2016 160.62 5.82% 2,173.60 3.56%
31. Aug 31, 2016 158.88 1.40 -0.21% 2,170.95 -0.12%
32. Sep 30, 2016 158.85 -0.02% 2,168.27 -0.12%
33. Oct 31, 2016 153.69 -3.25% 2,126.15 -1.94%
34. Nov 30, 2016 162.22 1.40 6.46% 2,198.81 3.42%
35. Dec 31, 2016 165.99 2.32% 2,238.83 1.82%
36. Jan 31, 2017 174.52 5.14% 2,278.87 1.79%
37. Feb 28, 2017 179.82 1.40 3.84% 2,363.64 3.72%
38. Mar 31, 2017 174.14 -3.16% 2,362.72 -0.04%
39. Apr 30, 2017 160.29 -7.95% 2,384.20 0.91%
40. May 31, 2017 152.63 1.50 -3.84% 2,411.80 1.16%
41. Jun 30, 2017 153.83 0.79% 2,423.41 0.48%
42. Jul 31, 2017 144.67 -5.95% 2,470.30 1.93%
43. Aug 31, 2017 143.03 1.50 -0.10% 2,471.65 0.05%
44. Sep 30, 2017 145.08 1.43% 2,519.36 1.93%
45. Oct 31, 2017 154.06 6.19% 2,575.26 2.22%
46. Nov 30, 2017 153.97 1.50 0.92% 2,647.58 2.81%
47. Dec 31, 2017 153.42 -0.36% 2,673.61 0.98%
48. Jan 31, 2018 163.70 6.70% 2,823.81 5.62%
49. Feb 28, 2018 155.83 1.50 -3.89% 2,713.83 -3.89%
50. Mar 31, 2018 153.43 -1.54% 2,640.87 -2.69%
51. Apr 30, 2018 144.96 -5.52% 2,648.05 0.27%
52. May 31, 2018 141.31 1.57 -1.43% 2,705.27 2.16%
53. Jun 30, 2018 139.70 -1.14% 2,718.37 0.48%
54. Jul 31, 2018 144.93 3.74% 2,816.29 3.60%
55. Aug 31, 2018 146.48 1.57 2.15% 2,901.52 3.03%
56. Sep 30, 2018 151.21 3.23% 2,913.98 0.43%
57. Oct 31, 2018 115.43 -23.66% 2,711.74 -6.94%
58. Nov 30, 2018 124.27 1.57 9.02% 2,760.17 1.79%
59. Dec 31, 2018 113.67 -8.53% 2,506.85 -9.18%
Average: -0.27% 0.63%
Standard deviation: 5.95% 3.13%

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 IBM during period t

3 Rate of return on S&P 500 (the market portfolio proxy) during period t


Systematic Risk (β) Estimation

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VarianceIBM 35.45
VarianceS&P 500 9.77
CovarianceIBM, S&P 500 11.03
Correlation coefficientIBM, S&P 5001 0.59
βIBM2 1.13
αIBM3 -0.98

Calculations

1 Correlation coefficientIBM, S&P 500
= CovarianceIBM, S&P 500 ÷ (Standard deviationIBM × Standard deviationS&P 500)
= 11.03 ÷ (5.95 × 3.13)

2 βIBM
= CovarianceIBM, S&P 500 ÷ VarianceS&P 500
= 11.03 ÷ 9.77

3 αIBM
= AverageIBM – βIBM × AverageS&P 500
= -0.271.13 × 0.63


Expected Rate of Return

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Assumptions
Rate of return on LT Treasury Composite1 RF 2.23%
Expected rate of return on market portfolio2 E(RM) 11.55%
Systematic risk (β) of International Business Machines Corp.’s common stock βIBM 1.13
 
Expected rate of return on International Business Machines Corp.’s common stock3 E(RIBM) 12.76%

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).

2 See details »

3 E(RIBM) = RF + βIBM [E(RM) – RF]
= 2.23% + 1.13 [11.55%2.23%]
= 12.76%