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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 General Motors Co.’s common stock.


Rates of Return

General Motors Co., monthly rates of return

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General Motors Co. (GM) Standard & Poor’s 500 (S&P 500)
t Date PriceGM,t1 DividendGM,t1 RGM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 36.08 1,782.59
1. Feb 28, 2014 36.20 0.33% 1,859.45 4.31%
2. Mar 31, 2014 34.42 0.30 -4.09% 1,872.34 0.69%
3. Apr 30, 2014 34.48 0.17% 1,883.95 0.62%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2018 37.95 3.72% 2,760.17 1.79%
59. Dec 31, 2018 33.45 0.38 -10.86% 2,506.85 -9.18%
Average: 0.42% 0.63%
Standard Deviation: 6.48% 3.13%
General Motors Co. (GM) Standard & Poor’s 500 (S&P 500)
t Date PriceGM,t1 DividendGM,t1 RGM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 36.08 1,782.59
1. Feb 28, 2014 36.20 0.33% 1,859.45 4.31%
2. Mar 31, 2014 34.42 0.30 -4.09% 1,872.34 0.69%
3. Apr 30, 2014 34.48 0.17% 1,883.95 0.62%
4. May 31, 2014 34.58 0.29% 1,923.57 2.10%
5. Jun 30, 2014 36.30 0.30 5.84% 1,960.23 1.91%
6. Jul 31, 2014 33.82 -6.83% 1,930.67 -1.51%
7. Aug 31, 2014 34.80 2.90% 2,003.37 3.77%
8. Sep 30, 2014 31.94 0.30 -7.36% 1,972.29 -1.55%
9. Oct 31, 2014 31.40 -1.69% 2,018.05 2.32%
10. Nov 30, 2014 33.43 6.46% 2,067.56 2.45%
11. Dec 31, 2014 34.91 0.30 5.32% 2,058.90 -0.42%
12. Jan 31, 2015 32.62 -6.56% 1,994.99 -3.10%
13. Feb 28, 2015 37.31 14.38% 2,104.50 5.49%
14. Mar 31, 2015 37.50 0.30 1.31% 2,067.89 -1.74%
15. Apr 30, 2015 35.06 -6.51% 2,085.51 0.85%
16. May 31, 2015 35.97 2.60% 2,107.39 1.05%
17. Jun 30, 2015 33.33 0.36 -6.34% 2,063.11 -2.10%
18. Jul 31, 2015 31.51 -5.46% 2,103.84 1.97%
19. Aug 31, 2015 29.44 -6.57% 1,972.18 -6.26%
20. Sep 30, 2015 30.02 0.36 3.19% 1,920.03 -2.64%
21. Oct 31, 2015 34.91 16.29% 2,079.36 8.30%
22. Nov 30, 2015 36.20 3.70% 2,080.41 0.05%
23. Dec 31, 2015 34.01 0.36 -5.06% 2,043.94 -1.75%
24. Jan 31, 2016 29.64 -12.85% 1,940.24 -5.07%
25. Feb 29, 2016 29.44 -0.67% 1,932.23 -0.41%
26. Mar 31, 2016 31.43 0.38 8.05% 2,059.74 6.60%
27. Apr 30, 2016 31.80 1.18% 2,065.30 0.27%
28. May 31, 2016 31.28 -1.64% 2,096.95 1.53%
29. Jun 30, 2016 28.30 0.38 -8.31% 2,098.86 0.09%
30. Jul 31, 2016 31.54 11.45% 2,173.60 3.56%
31. Aug 31, 2016 31.92 1.20% 2,170.95 -0.12%
32. Sep 30, 2016 31.77 0.38 0.72% 2,168.27 -0.12%
33. Oct 31, 2016 31.60 -0.54% 2,126.15 -1.94%
34. Nov 30, 2016 34.53 9.27% 2,198.81 3.42%
35. Dec 31, 2016 34.84 0.38 2.00% 2,238.83 1.82%
36. Jan 31, 2017 36.61 5.08% 2,278.87 1.79%
37. Feb 28, 2017 36.84 0.63% 2,363.64 3.72%
38. Mar 31, 2017 35.36 0.38 -2.99% 2,362.72 -0.04%
39. Apr 30, 2017 34.64 -2.04% 2,384.20 0.91%
40. May 31, 2017 33.93 -2.05% 2,411.80 1.16%
41. Jun 30, 2017 34.93 0.38 4.07% 2,423.41 0.48%
42. Jul 31, 2017 35.98 3.01% 2,470.30 1.93%
43. Aug 31, 2017 36.54 1.56% 2,471.65 0.05%
44. Sep 30, 2017 40.38 0.38 11.55% 2,519.36 1.93%
45. Oct 31, 2017 42.98 6.44% 2,575.26 2.22%
46. Nov 30, 2017 43.09 0.26% 2,647.58 2.81%
47. Dec 31, 2017 40.99 0.38 -3.99% 2,673.61 0.98%
48. Jan 31, 2018 42.41 3.46% 2,823.81 5.62%
49. Feb 28, 2018 39.35 -7.22% 2,713.83 -3.89%
50. Mar 31, 2018 36.34 0.38 -6.68% 2,640.87 -2.69%
51. Apr 30, 2018 36.74 1.10% 2,648.05 0.27%
52. May 31, 2018 42.70 16.22% 2,705.27 2.16%
53. Jun 30, 2018 39.40 0.38 -6.84% 2,718.37 0.48%
54. Jul 31, 2018 37.91 -3.78% 2,816.29 3.60%
55. Aug 31, 2018 36.05 -4.91% 2,901.52 3.03%
56. Sep 30, 2018 33.67 0.38 -5.55% 2,913.98 0.43%
57. Oct 31, 2018 36.59 8.67% 2,711.74 -6.94%
58. Nov 30, 2018 37.95 3.72% 2,760.17 1.79%
59. Dec 31, 2018 33.45 0.38 -10.86% 2,506.85 -9.18%
Average: 0.42% 0.63%
Standard Deviation: 6.48% 3.13%

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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 GM 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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VarianceGM 42.00
VarianceS&P 500 9.77
CovarianceGM, S&P 500 11.46
Correlation CoefficientGM, S&P 5001 0.57
βGM2 1.17
αGM3 -0.31

Calculations

1 CovarianceGM, S&P 500 ÷ (Standard DeviationGM × Standard DeviationS&P 500)
= 11.46 ÷ (6.48 × 3.13)

2 CovarianceGM, S&P 500 ÷ VarianceS&P 500
= 11.46 ÷ 9.77

3 AverageGM – βGM × AverageS&P 500
= 0.421.17 × 0.63


Expected Rate of Return

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Assumptions
Rate of return on LT Treasury Composite1 RF 2.94%
Expected rate of return on market portfolio2 E(RM) 11.63%
Systematic risk (β) of General Motors Co.’s common stock βGM 1.17
Expected rate of return on General Motors Co.’s common stock3 E(RGM) 13.13%

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(RGM) = RF + βGM [E(RM) – RF]
= 2.94% + 1.17 [11.63%2.94%]
= 13.13%