Microsoft Excel LibreOffice Calc

Stryker Corp. (SYK)


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 Stryker Corp.’s common stock.


Rates of Return

Stryker Corp., monthly rates of return

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Stryker Corp. (SYK) Standard & Poor’s 500 (S&P 500)
t Date PriceSYK,t1 DividendSYK,t1 RSYK,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 77.60 1,782.59
1. Feb 28, 2014 80.24 3.40% 1,859.45 4.31%
2. Mar 31, 2014 81.47 0.305 1.91% 1,872.34 0.69%
3. Apr 30, 2014 77.75 -4.57% 1,883.95 0.62%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2018 175.46 8.16% 2,760.17 1.79%
59. Dec 31, 2018 156.75 0.52 -10.37% 2,506.85 -9.18%
Average: 1.41% 0.63%
Standard deviation: 4.41% 3.13%
Stryker Corp. (SYK) Standard & Poor’s 500 (S&P 500)
t Date PriceSYK,t1 DividendSYK,t1 RSYK,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 77.60 1,782.59
1. Feb 28, 2014 80.24 3.40% 1,859.45 4.31%
2. Mar 31, 2014 81.47 0.305 1.91% 1,872.34 0.69%
3. Apr 30, 2014 77.75 -4.57% 1,883.95 0.62%
4. May 31, 2014 84.49 8.67% 1,923.57 2.10%
5. Jun 30, 2014 84.32 0.305 0.16% 1,960.23 1.91%
6. Jul 31, 2014 79.77 -5.40% 1,930.67 -1.51%
7. Aug 31, 2014 83.31 4.44% 2,003.37 3.77%
8. Sep 30, 2014 80.75 0.305 -2.71% 1,972.29 -1.55%
9. Oct 31, 2014 87.53 8.40% 2,018.05 2.32%
10. Nov 30, 2014 92.91 6.15% 2,067.56 2.45%
11. Dec 31, 2014 94.33 0.345 1.90% 2,058.90 -0.42%
12. Jan 31, 2015 91.05 -3.48% 1,994.99 -3.10%
13. Feb 28, 2015 94.75 4.06% 2,104.50 5.49%
14. Mar 31, 2015 92.25 0.345 -2.27% 2,067.89 -1.74%
15. Apr 30, 2015 92.24 -0.01% 2,085.51 0.85%
16. May 31, 2015 96.13 4.22% 2,107.39 1.05%
17. Jun 30, 2015 95.57 0.345 -0.22% 2,063.11 -2.10%
18. Jul 31, 2015 102.27 7.01% 2,103.84 1.97%
19. Aug 31, 2015 98.65 -3.54% 1,972.18 -6.26%
20. Sep 30, 2015 94.10 0.345 -4.26% 1,920.03 -2.64%
21. Oct 31, 2015 95.62 1.62% 2,079.36 8.30%
22. Nov 30, 2015 96.46 0.88% 2,080.41 0.05%
23. Dec 31, 2015 92.94 0.38 -3.26% 2,043.94 -1.75%
24. Jan 31, 2016 99.15 6.68% 1,940.24 -5.07%
25. Feb 29, 2016 99.88 0.74% 1,932.23 -0.41%
26. Mar 31, 2016 107.29 0.38 7.80% 2,059.74 6.60%
27. Apr 30, 2016 109.01 1.60% 2,065.30 0.27%
28. May 31, 2016 111.16 1.97% 2,096.95 1.53%
29. Jun 30, 2016 119.83 0.38 8.14% 2,098.86 0.09%
30. Jul 31, 2016 116.28 -2.96% 2,173.60 3.56%
31. Aug 31, 2016 115.66 -0.53% 2,170.95 -0.12%
32. Sep 30, 2016 116.41 0.38 0.98% 2,168.27 -0.12%
33. Oct 31, 2016 115.35 -0.91% 2,126.15 -1.94%
34. Nov 30, 2016 113.66 -1.47% 2,198.81 3.42%
35. Dec 31, 2016 119.81 0.425 5.78% 2,238.83 1.82%
36. Jan 31, 2017 123.53 3.10% 2,278.87 1.79%
37. Feb 28, 2017 128.56 4.07% 2,363.64 3.72%
38. Mar 31, 2017 131.65 0.425 2.73% 2,362.72 -0.04%
39. Apr 30, 2017 136.37 3.59% 2,384.20 0.91%
40. May 31, 2017 142.96 4.83% 2,411.80 1.16%
41. Jun 30, 2017 138.78 0.425 -2.63% 2,423.41 0.48%
42. Jul 31, 2017 147.10 6.00% 2,470.30 1.93%
43. Aug 31, 2017 141.37 -3.90% 2,471.65 0.05%
44. Sep 30, 2017 142.02 0.425 0.76% 2,519.36 1.93%
45. Oct 31, 2017 154.87 9.05% 2,575.26 2.22%
46. Nov 30, 2017 156.00 0.73% 2,647.58 2.81%
47. Dec 31, 2017 154.84 0.47 -0.44% 2,673.61 0.98%
48. Jan 31, 2018 164.38 6.16% 2,823.81 5.62%
49. Feb 28, 2018 162.16 -1.35% 2,713.83 -3.89%
50. Mar 31, 2018 160.92 0.47 -0.47% 2,640.87 -2.69%
51. Apr 30, 2018 169.42 5.28% 2,648.05 0.27%
52. May 31, 2018 174.02 2.72% 2,705.27 2.16%
53. Jun 30, 2018 168.86 0.47 -2.70% 2,718.37 0.48%
54. Jul 31, 2018 163.25 -3.32% 2,816.29 3.60%
55. Aug 31, 2018 169.43 3.79% 2,901.52 3.03%
56. Sep 30, 2018 177.68 0.47 5.15% 2,913.98 0.43%
57. Oct 31, 2018 162.22 -8.70% 2,711.74 -6.94%
58. Nov 30, 2018 175.46 8.16% 2,760.17 1.79%
59. Dec 31, 2018 156.75 0.52 -10.37% 2,506.85 -9.18%
Average: 1.41% 0.63%
Standard deviation: 4.41% 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 SYK 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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VarianceSYK 19.45
VarianceS&P 500 9.77
CovarianceSYK, S&P 500 7.77
Correlation coefficientSYK, S&P 5001 0.56
βSYK2 0.80
αSYK3 0.91

Calculations

1 Correlation coefficientSYK, S&P 500
= CovarianceSYK, S&P 500 ÷ (Standard deviationSYK × Standard deviationS&P 500)
= 7.77 ÷ (4.41 × 3.13)

2 βSYK
= CovarianceSYK, S&P 500 ÷ VarianceS&P 500
= 7.77 ÷ 9.77

3 αSYK
= AverageSYK – βSYK × AverageS&P 500
= 1.410.80 × 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 Stryker Corp.’s common stock βSYK 0.80
 
Expected rate of return on Stryker Corp.’s common stock3 E(RSYK) 9.64%

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(RSYK) = RF + βSYK [E(RM) – RF]
= 2.23% + 0.80 [11.55%2.23%]
= 9.64%