Capital Asset Pricing Model (CAPM)

Difficulty level: Medium


Rates of Return

Johnson & Johnson, monthly rates of return

 
Johnson & Johnson (JNJ) Standard & Poor's 500 (S&P 500)
t Date PriceJNJ,t1 DividendJNJ,t1 RJNJ,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2010 62.86 1,073.87
1. Feb 28, 2010 63.00 0.49 1.00% 1,104.49 2.85%
2. Mar 31, 2010 65.20 3.49% 1,169.43 5.88%
3. Apr 30, 2010 64.30 -1.38% 1,186.69 1.48%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2014 108.25 0.70 1.09% 2,067.56 2.45%
59. Dec 31, 2014 104.57 -3.40% 2,058.90 -0.42%
Average: 1.22% 1.18%
Standard Deviation: 3.86% 3.73%
Johnson & Johnson (JNJ) Standard & Poor's 500 (S&P 500)
t Date PriceJNJ,t1 DividendJNJ,t1 RJNJ,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2010 62.86 1,073.87
1. Feb 28, 2010 63.00 0.49 1.00% 1,104.49 2.85%
2. Mar 31, 2010 65.20 3.49% 1,169.43 5.88%
3. Apr 30, 2010 64.30 -1.38% 1,186.69 1.48%
4. May 31, 2010 58.30 0.54 -8.49% 1,089.41 -8.20%
5. Jun 30, 2010 59.06 1.30% 1,030.71 -5.39%
6. Jul 31, 2010 58.09 -1.64% 1,101.60 6.88%
7. Aug 31, 2010 57.02 0.54 -0.91% 1,049.33 -4.74%
8. Sep 30, 2010 61.96 8.66% 1,141.20 8.76%
9. Oct 31, 2010 63.74 2.87% 1,183.26 3.69%
10. Nov 30, 2010 61.55 0.54 -2.59% 1,180.55 -0.23%
11. Dec 31, 2010 61.85 0.49% 1,257.64 6.53%
12. Jan 31, 2011 59.77 -3.36% 1,286.12 2.26%
13. Feb 28, 2011 61.44 0.54 3.70% 1,327.22 3.20%
14. Mar 31, 2011 59.25 -3.56% 1,325.83 -0.10%
15. Apr 30, 2011 65.72 10.92% 1,363.61 2.85%
16. May 31, 2011 67.29 0.57 3.26% 1,345.20 -1.35%
17. Jun 30, 2011 66.52 -1.14% 1,320.64 -1.83%
18. Jul 31, 2011 64.79 -2.60% 1,292.28 -2.15%
19. Aug 31, 2011 65.80 0.57 2.44% 1,218.89 -5.68%
20. Sep 30, 2011 63.69 -3.21% 1,131.42 -7.18%
21. Oct 31, 2011 64.39 1.10% 1,253.30 10.77%
22. Nov 30, 2011 64.72 0.57 1.40% 1,246.96 -0.51%
23. Dec 31, 2011 65.58 1.33% 1,257.60 0.85%
24. Jan 31, 2012 65.91 0.50% 1,312.41 4.36%
25. Feb 29, 2012 65.08 0.57 -0.39% 1,365.68 4.06%
26. Mar 31, 2012 65.96 1.35% 1,408.47 3.13%
27. Apr 30, 2012 65.10 -1.30% 1,397.91 -0.75%
28. May 31, 2012 62.43 0.61 -3.16% 1,310.33 -6.27%
29. Jun 30, 2012 67.56 8.22% 1,362.16 3.96%
30. Jul 31, 2012 69.22 2.46% 1,379.32 1.26%
31. Aug 31, 2012 67.43 0.61 -1.70% 1,406.58 1.98%
32. Sep 30, 2012 68.91 2.19% 1,440.67 2.42%
33. Oct 31, 2012 70.82 2.77% 1,412.16 -1.98%
34. Nov 30, 2012 69.73 0.61 -0.68% 1,416.18 0.28%
35. Dec 31, 2012 70.10 0.53% 1,426.19 0.71%
36. Jan 31, 2013 73.92 5.45% 1,498.11 5.04%
37. Feb 28, 2013 76.11 0.61 3.79% 1,514.68 1.11%
38. Mar 31, 2013 81.53 7.12% 1,569.19 3.60%
39. Apr 30, 2013 85.23 4.54% 1,597.57 1.81%
40. May 31, 2013 84.18 0.66 -0.46% 1,630.74 2.08%
41. Jun 30, 2013 85.86 2.00% 1,606.28 -1.50%
42. Jul 31, 2013 93.50 8.90% 1,685.73 4.95%
43. Aug 31, 2013 86.41 0.66 -6.88% 1,632.97 -3.13%
44. Sep 30, 2013 86.69 0.32% 1,681.55 2.97%
45. Oct 31, 2013 92.61 6.83% 1,756.54 4.46%
46. Nov 30, 2013 94.66 0.66 2.93% 1,805.81 2.80%
47. Dec 31, 2013 91.59 -3.24% 1,848.36 2.36%
48. Jan 31, 2014 88.47 -3.41% 1,782.59 -3.56%
49. Feb 28, 2014 92.12 0.66 4.87% 1,859.45 4.31%
50. Mar 31, 2014 98.23 6.63% 1,872.34 0.69%
51. Apr 30, 2014 101.29 3.12% 1,883.95 0.62%
52. May 31, 2014 101.46 0.70 0.86% 1,923.57 2.10%
53. Jun 30, 2014 104.62 3.11% 1,960.23 1.91%
54. Jul 31, 2014 100.09 -4.33% 1,930.67 -1.51%
55. Aug 31, 2014 103.73 0.70 4.34% 2,003.37 3.77%
56. Sep 30, 2014 106.59 2.76% 1,972.29 -1.55%
57. Oct 31, 2014 107.78 1.12% 2,018.05 2.32%
58. Nov 30, 2014 108.25 0.70 1.09% 2,067.56 2.45%
59. Dec 31, 2014 104.57 -3.40% 2,058.90 -0.42%
Average: 1.22% 1.18%
Standard Deviation: 3.86% 3.73%

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 JNJ 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

 
VarianceJNJ 14.93
VarianceS&P 500 13.95
CovarianceJNJ, S&P 500 7.46
Correlation CoefficientJNJ, S&P 5001 0.52
βJNJ2 0.53
αJNJ3 0.59

Calculations

1 CovarianceJNJ, S&P 500 ÷ (Standard DeviationJNJ × Standard DeviationS&P 500)
= 7.46 ÷ (3.86 × 3.73)

2 CovarianceJNJ, S&P 500 ÷ VarianceS&P 500
= 7.46 ÷ 13.95

3 AverageJNJ – βJNJ × AverageS&P 500
= 1.22 – 0.53 × 1.18

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Expected Rate of Return

 
Assumptions
Rate of return on LT Treasury Composite1 RF 2.36%
Expected rate of return on market portfolio2 E(RM) 14.00%
Systematic risk (β) of Johnson & Johnson's common stock βJNJ 0.53
Expected rate of return on Johnson & Johnson's common stock3 E(RJNJ) 8.58%

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(RJNJ) = RF + βJNJ [E(RM) – RF]
= 2.36% + 0.53 [14.00% – 2.36%]
= 8.58%

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