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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 Ford's common stock.


Rates of Return

Ford Motor Co., monthly rates of return

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Ford Motor Co. (F) Standard & Poor's 500 (S&P 500)
t Date PriceF,t1 DividendF,t1 RF,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2013 12.95 1,498.11
1. Feb 28, 2013 12.61 -2.63% 1,514.68 1.11%
2. Mar 31, 2013 13.15 4.28% 1,569.19 3.60%
3. Apr 30, 2013 13.71 4.26% 1,597.57 1.81%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2017 12.52 2.04% 2,647.58 2.81%
59. Dec 31, 2017 12.49 -0.24% 2,673.61 0.98%
Average: 0.45% 1.02%
Standard Deviation: 5.49% 2.71%
Ford Motor Co. (F) Standard & Poor's 500 (S&P 500)
t Date PriceF,t1 DividendF,t1 RF,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2013 12.95 1,498.11
1. Feb 28, 2013 12.61 -2.63% 1,514.68 1.11%
2. Mar 31, 2013 13.15 4.28% 1,569.19 3.60%
3. Apr 30, 2013 13.71 4.26% 1,597.57 1.81%
4. May 31, 2013 15.68 0.10 15.10% 1,630.74 2.08%
5. Jun 30, 2013 15.47 -1.34% 1,606.28 -1.50%
6. Jul 31, 2013 16.88 0.10 9.76% 1,685.73 4.95%
7. Aug 31, 2013 16.19 -4.09% 1,632.97 -3.13%
8. Sep 30, 2013 16.87 4.20% 1,681.55 2.97%
9. Oct 31, 2013 17.11 0.10 2.02% 1,756.54 4.46%
10. Nov 30, 2013 17.08 -0.18% 1,805.81 2.80%
11. Dec 31, 2013 15.43 -9.66% 1,848.36 2.36%
12. Jan 31, 2014 14.96 0.125 -2.24% 1,782.59 -3.56%
13. Feb 28, 2014 15.39 2.87% 1,859.45 4.31%
14. Mar 31, 2014 15.60 1.36% 1,872.34 0.69%
15. Apr 30, 2014 16.15 0.125 4.33% 1,883.95 0.62%
16. May 31, 2014 16.44 1.80% 1,923.57 2.10%
17. Jun 30, 2014 17.24 4.87% 1,960.23 1.91%
18. Jul 31, 2014 17.02 0.125 -0.55% 1,930.67 -1.51%
19. Aug 31, 2014 17.41 2.29% 2,003.37 3.77%
20. Sep 30, 2014 14.79 -15.05% 1,972.29 -1.55%
21. Oct 31, 2014 14.09 0.125 -3.89% 2,018.05 2.32%
22. Nov 30, 2014 15.73 11.64% 2,067.56 2.45%
23. Dec 31, 2014 15.50 -1.46% 2,058.90 -0.42%
24. Jan 31, 2015 14.71 0.15 -4.13% 1,994.99 -3.10%
25. Feb 28, 2015 16.34 11.08% 2,104.50 5.49%
26. Mar 31, 2015 16.14 -1.22% 2,067.89 -1.74%
27. Apr 30, 2015 15.80 0.15 -1.18% 2,085.51 0.85%
28. May 31, 2015 15.17 -3.99% 2,107.39 1.05%
29. Jun 30, 2015 15.01 -1.05% 2,063.11 -2.10%
30. Jul 31, 2015 14.83 0.15 -0.20% 2,103.84 1.97%
31. Aug 31, 2015 13.87 -6.47% 1,972.18 -6.26%
32. Sep 30, 2015 13.57 -2.16% 1,920.03 -2.64%
33. Oct 31, 2015 14.81 0.15 10.24% 2,079.36 8.30%
34. Nov 30, 2015 14.33 -3.24% 2,080.41 0.05%
35. Dec 31, 2015 14.09 -1.67% 2,043.94 -1.75%
36. Jan 31, 2016 11.94 0.40 -12.42% 1,940.24 -5.07%
37. Feb 29, 2016 12.51 4.77% 1,932.23 -0.41%
38. Mar 31, 2016 13.50 7.91% 2,059.74 6.60%
39. Apr 30, 2016 13.56 0.15 1.56% 2,065.30 0.27%
40. May 31, 2016 13.49 -0.52% 2,096.95 1.53%
41. Jun 30, 2016 12.57 -6.82% 2,098.86 0.09%
42. Jul 31, 2016 12.66 0.15 1.91% 2,173.60 3.56%
43. Aug 31, 2016 12.60 -0.47% 2,170.95 -0.12%
44. Sep 30, 2016 12.07 -4.21% 2,168.27 -0.12%
45. Oct 31, 2016 11.74 0.15 -1.49% 2,126.15 -1.94%
46. Nov 30, 2016 11.96 1.87% 2,198.81 3.42%
47. Dec 31, 2016 12.13 1.42% 2,238.83 1.82%
48. Jan 31, 2017 12.36 0.20 3.54% 2,278.87 1.79%
49. Feb 28, 2017 12.53 1.38% 2,363.64 3.72%
50. Mar 31, 2017 11.64 -7.10% 2,362.72 -0.04%
51. Apr 30, 2017 11.47 0.15 -0.17% 2,384.20 0.91%
52. May 31, 2017 11.12 -3.05% 2,411.80 1.16%
53. Jun 30, 2017 11.19 0.63% 2,423.41 0.48%
54. Jul 31, 2017 11.22 0.15 1.61% 2,470.30 1.93%
55. Aug 31, 2017 11.03 -1.69% 2,471.65 0.05%
56. Sep 30, 2017 11.97 8.52% 2,519.36 1.93%
57. Oct 31, 2017 12.27 0.15 3.76% 2,575.26 2.22%
58. Nov 30, 2017 12.52 2.04% 2,647.58 2.81%
59. Dec 31, 2017 12.49 -0.24% 2,673.61 0.98%
Average: 0.45% 1.02%
Standard Deviation: 5.49% 2.71%

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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 F 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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VarianceF 30.13
VarianceS&P 500 7.32
CovarianceF, S&P 500 9.58
Correlation CoefficientF, S&P 5001 0.64
βF2 1.31
αF3 -0.89

Calculations

1 CovarianceF, S&P 500 ÷ (Standard DeviationF × Standard DeviationS&P 500)
= 9.58 ÷ (5.49 × 2.71)

2 CovarianceF, S&P 500 ÷ VarianceS&P 500
= 9.58 ÷ 7.32

3 AverageF – βF × AverageS&P 500
= 0.451.31 × 1.02


Expected Rate of Return

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Assumptions
Rate of return on LT Treasury Composite1 RF 3.29%
Expected rate of return on market portfolio2 E(RM) 12.36%
Systematic risk (β) of Ford's common stock βF 1.31
Expected rate of return on Ford's common stock3 E(RF) 15.16%

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(RF) = RF + βF [E(RM) – RF]
= 3.29% + 1.31 [12.36%3.29%]
= 15.16%