Microsoft Excel LibreOffice Calc

United Technologies Corp. (UTX)


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 United Technologies Corp.’s common stock.


Rates of Return

United Technologies Corp., monthly rates of return

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United Technologies Corp. (UTX) Standard & Poor’s 500 (S&P 500)
t Date PriceUTX,t1 DividendUTX,t1 RUTX,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 114.02 1,782.59
1. Feb 28, 2014 117.02 0.59 3.15% 1,859.45 4.31%
2. Mar 31, 2014 116.84 -0.15% 1,872.34 0.69%
3. Apr 30, 2014 118.33 1.28% 1,883.95 0.62%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2018 121.84 0.735 -1.32% 2,760.17 1.79%
59. Dec 31, 2018 106.48 -12.61% 2,506.85 -9.18%
Average: 0.21% 0.63%
Standard deviation: 5.13% 3.13%
United Technologies Corp. (UTX) Standard & Poor’s 500 (S&P 500)
t Date PriceUTX,t1 DividendUTX,t1 RUTX,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2014 114.02 1,782.59
1. Feb 28, 2014 117.02 0.59 3.15% 1,859.45 4.31%
2. Mar 31, 2014 116.84 -0.15% 1,872.34 0.69%
3. Apr 30, 2014 118.33 1.28% 1,883.95 0.62%
4. May 31, 2014 116.22 0.59 -1.28% 1,923.57 2.10%
5. Jun 30, 2014 115.45 -0.66% 1,960.23 1.91%
6. Jul 31, 2014 105.15 -8.92% 1,930.67 -1.51%
7. Aug 31, 2014 107.98 0.59 3.25% 2,003.37 3.77%
8. Sep 30, 2014 105.60 -2.20% 1,972.29 -1.55%
9. Oct 31, 2014 107.00 1.33% 2,018.05 2.32%
10. Nov 30, 2014 110.08 0.59 3.43% 2,067.56 2.45%
11. Dec 31, 2014 115.00 4.47% 2,058.90 -0.42%
12. Jan 31, 2015 114.78 -0.19% 1,994.99 -3.10%
13. Feb 28, 2015 121.91 0.64 6.77% 2,104.50 5.49%
14. Mar 31, 2015 117.20 -3.86% 2,067.89 -1.74%
15. Apr 30, 2015 113.75 -2.94% 2,085.51 0.85%
16. May 31, 2015 117.17 0.64 3.57% 2,107.39 1.05%
17. Jun 30, 2015 110.93 -5.33% 2,063.11 -2.10%
18. Jul 31, 2015 100.31 -9.57% 2,103.84 1.97%
19. Aug 31, 2015 91.61 0.64 -8.04% 1,972.18 -6.26%
20. Sep 30, 2015 88.99 -2.86% 1,920.03 -2.64%
21. Oct 31, 2015 98.41 10.59% 2,079.36 8.30%
22. Nov 30, 2015 96.05 0.64 -1.75% 2,080.41 0.05%
23. Dec 31, 2015 96.07 0.02% 2,043.94 -1.75%
24. Jan 31, 2016 87.69 -8.72% 1,940.24 -5.07%
25. Feb 29, 2016 96.62 0.64 10.91% 1,932.23 -0.41%
26. Mar 31, 2016 100.10 3.60% 2,059.74 6.60%
27. Apr 30, 2016 104.37 4.27% 2,065.30 0.27%
28. May 31, 2016 100.58 0.66 -3.00% 2,096.95 1.53%
29. Jun 30, 2016 102.55 1.96% 2,098.86 0.09%
30. Jul 31, 2016 107.65 4.97% 2,173.60 3.56%
31. Aug 31, 2016 106.43 0.66 -0.52% 2,170.95 -0.12%
32. Sep 30, 2016 101.60 -4.54% 2,168.27 -0.12%
33. Oct 31, 2016 102.20 0.59% 2,126.15 -1.94%
34. Nov 30, 2016 107.72 0.66 6.05% 2,198.81 3.42%
35. Dec 31, 2016 109.62 1.76% 2,238.83 1.82%
36. Jan 31, 2017 109.67 0.05% 2,278.87 1.79%
37. Feb 28, 2017 112.55 0.66 3.23% 2,363.64 3.72%
38. Mar 31, 2017 112.21 -0.30% 2,362.72 -0.04%
39. Apr 30, 2017 118.99 6.04% 2,384.20 0.91%
40. May 31, 2017 121.28 0.66 2.48% 2,411.80 1.16%
41. Jun 30, 2017 122.11 0.68% 2,423.41 0.48%
42. Jul 31, 2017 118.57 -2.90% 2,470.30 1.93%
43. Aug 31, 2017 119.72 0.70 1.56% 2,471.65 0.05%
44. Sep 30, 2017 116.08 -3.04% 2,519.36 1.93%
45. Oct 31, 2017 119.76 3.17% 2,575.26 2.22%
46. Nov 30, 2017 121.45 0.70 2.00% 2,647.58 2.81%
47. Dec 31, 2017 127.57 5.04% 2,673.61 0.98%
48. Jan 31, 2018 138.01 8.18% 2,823.81 5.62%
49. Feb 28, 2018 134.74 0.70 -1.86% 2,713.83 -3.89%
50. Mar 31, 2018 125.82 -6.62% 2,640.87 -2.69%
51. Apr 30, 2018 120.15 -4.51% 2,648.05 0.27%
52. May 31, 2018 124.82 0.70 4.47% 2,705.27 2.16%
53. Jun 30, 2018 125.03 0.17% 2,718.37 0.48%
54. Jul 31, 2018 135.74 8.57% 2,816.29 3.60%
55. Aug 31, 2018 131.70 0.70 -2.46% 2,901.52 3.03%
56. Sep 30, 2018 139.81 6.16% 2,913.98 0.43%
57. Oct 31, 2018 124.21 -11.16% 2,711.74 -6.94%
58. Nov 30, 2018 121.84 0.735 -1.32% 2,760.17 1.79%
59. Dec 31, 2018 106.48 -12.61% 2,506.85 -9.18%
Average: 0.21% 0.63%
Standard deviation: 5.13% 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 UTX 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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VarianceUTX 26.29
VarianceS&P 500 9.77
CovarianceUTX, S&P 500 11.20
Correlation coefficientUTX, S&P 5001 0.70
βUTX2 1.15
αUTX3 -0.51

Calculations

1 Correlation coefficientUTX, S&P 500
= CovarianceUTX, S&P 500 ÷ (Standard deviationUTX × Standard deviationS&P 500)
= 11.20 ÷ (5.13 × 3.13)

2 βUTX
= CovarianceUTX, S&P 500 ÷ VarianceS&P 500
= 11.20 ÷ 9.77

3 αUTX
= AverageUTX – βUTX × AverageS&P 500
= 0.211.15 × 0.63


Expected Rate of Return

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Assumptions
Rate of return on LT Treasury Composite1 RF 2.28%
Expected rate of return on market portfolio2 E(RM) 11.55%
Systematic risk (β) of United Technologies Corp.’s common stock βUTX 1.15
 
Expected rate of return on United Technologies Corp.’s common stock3 E(RUTX) 12.91%

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(RUTX) = RF + βUTX [E(RM) – RF]
= 2.28% + 1.15 [11.55%2.28%]
= 12.91%