Microsoft Excel LibreOffice Calc

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 UPS's common stock.


Rates of Return

United Parcel Service Inc., monthly rates of return

Microsoft Excel LibreOffice Calc
United Parcel Service Inc. (UPS) Standard & Poor's 500 (S&P 500)
t Date PriceUPS,t1 DividendUPS,t1 RUPS,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2013 79.29 1,498.11
1. Feb 28, 2013 82.65 0.62 5.02% 1,514.68 1.11%
2. Mar 31, 2013 85.90 3.93% 1,569.19 3.60%
3. Apr 30, 2013 85.84 -0.07% 1,597.57 1.81%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2017 121.45 0.83 4.04% 2,647.58 2.81%
59. Dec 31, 2017 119.15 -1.89% 2,673.61 0.98%
Average: 1.02% 1.02%
Standard Deviation: 4.10% 2.71%
United Parcel Service Inc. (UPS) Standard & Poor's 500 (S&P 500)
t Date PriceUPS,t1 DividendUPS,t1 RUPS,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2013 79.29 1,498.11
1. Feb 28, 2013 82.65 0.62 5.02% 1,514.68 1.11%
2. Mar 31, 2013 85.90 3.93% 1,569.19 3.60%
3. Apr 30, 2013 85.84 -0.07% 1,597.57 1.81%
4. May 31, 2013 85.90 0.62 0.79% 1,630.74 2.08%
5. Jun 30, 2013 86.48 0.68% 1,606.28 -1.50%
6. Jul 31, 2013 86.80 0.37% 1,685.73 4.95%
7. Aug 31, 2013 85.58 0.62 -0.69% 1,632.97 -3.13%
8. Sep 30, 2013 91.37 6.77% 1,681.55 2.97%
9. Oct 31, 2013 98.24 7.52% 1,756.54 4.46%
10. Nov 30, 2013 102.38 0.62 4.85% 1,805.81 2.80%
11. Dec 31, 2013 105.08 2.64% 1,848.36 2.36%
12. Jan 31, 2014 95.23 -9.37% 1,782.59 -3.56%
13. Feb 28, 2014 95.77 0.67 1.27% 1,859.45 4.31%
14. Mar 31, 2014 97.38 1.68% 1,872.34 0.69%
15. Apr 30, 2014 98.50 1.15% 1,883.95 0.62%
16. May 31, 2014 103.88 0.67 6.14% 1,923.57 2.10%
17. Jun 30, 2014 102.66 -1.17% 1,960.23 1.91%
18. Jul 31, 2014 97.09 -5.43% 1,930.67 -1.51%
19. Aug 31, 2014 97.33 0.67 0.94% 2,003.37 3.77%
20. Sep 30, 2014 98.29 0.99% 1,972.29 -1.55%
21. Oct 31, 2014 104.91 6.74% 2,018.05 2.32%
22. Nov 30, 2014 109.92 0.67 5.41% 2,067.56 2.45%
23. Dec 31, 2014 111.17 1.14% 2,058.90 -0.42%
24. Jan 31, 2015 98.84 -11.09% 1,994.99 -3.10%
25. Feb 28, 2015 101.73 0.73 3.66% 2,104.50 5.49%
26. Mar 31, 2015 96.94 -4.71% 2,067.89 -1.74%
27. Apr 30, 2015 100.53 3.70% 2,085.51 0.85%
28. May 31, 2015 99.22 0.73 -0.58% 2,107.39 1.05%
29. Jun 30, 2015 96.91 -2.33% 2,063.11 -2.10%
30. Jul 31, 2015 102.36 5.62% 2,103.84 1.97%
31. Aug 31, 2015 97.65 0.73 -3.89% 1,972.18 -6.26%
32. Sep 30, 2015 98.69 1.07% 1,920.03 -2.64%
33. Oct 31, 2015 103.02 4.39% 2,079.36 8.30%
34. Nov 30, 2015 103.01 0.73 0.70% 2,080.41 0.05%
35. Dec 31, 2015 96.23 -6.58% 2,043.94 -1.75%
36. Jan 31, 2016 93.20 -3.15% 1,940.24 -5.07%
37. Feb 29, 2016 96.55 0.78 4.43% 1,932.23 -0.41%
38. Mar 31, 2016 105.47 9.24% 2,059.74 6.60%
39. Apr 30, 2016 105.07 -0.38% 2,065.30 0.27%
40. May 31, 2016 103.09 0.78 -1.14% 2,096.95 1.53%
41. Jun 30, 2016 107.72 4.49% 2,098.86 0.09%
42. Jul 31, 2016 108.10 0.35% 2,173.60 3.56%
43. Aug 31, 2016 109.22 0.78 1.76% 2,170.95 -0.12%
44. Sep 30, 2016 109.36 0.13% 2,168.27 -0.12%
45. Oct 31, 2016 107.76 -1.46% 2,126.15 -1.94%
46. Nov 30, 2016 115.92 0.78 8.30% 2,198.81 3.42%
47. Dec 31, 2016 114.64 -1.10% 2,238.83 1.82%
48. Jan 31, 2017 109.13 -4.81% 2,278.87 1.79%
49. Feb 28, 2017 105.76 0.83 -2.33% 2,363.64 3.72%
50. Mar 31, 2017 107.30 1.46% 2,362.72 -0.04%
51. Apr 30, 2017 107.46 0.15% 2,384.20 0.91%
52. May 31, 2017 105.97 0.83 -0.61% 2,411.80 1.16%
53. Jun 30, 2017 110.59 4.36% 2,423.41 0.48%
54. Jul 31, 2017 110.29 -0.27% 2,470.30 1.93%
55. Aug 31, 2017 114.36 0.83 4.44% 2,471.65 0.05%
56. Sep 30, 2017 120.09 5.01% 2,519.36 1.93%
57. Oct 31, 2017 117.53 -2.13% 2,575.26 2.22%
58. Nov 30, 2017 121.45 0.83 4.04% 2,647.58 2.81%
59. Dec 31, 2017 119.15 -1.89% 2,673.61 0.98%
Average: 1.02% 1.02%
Standard Deviation: 4.10% 2.71%

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 UPS during period t

3 Rate of return on S&P 500 (the market portfolio proxy) during period t


Systematic Risk (β) Estimation

Microsoft Excel LibreOffice Calc
VarianceUPS 16.80
VarianceS&P 500 7.32
CovarianceUPS, S&P 500 6.54
Correlation CoefficientUPS, S&P 5001 0.59
βUPS2 0.89
αUPS3 0.11

Calculations

1 CovarianceUPS, S&P 500 ÷ (Standard DeviationUPS × Standard DeviationS&P 500)
= 6.54 ÷ (4.10 × 2.71)

2 CovarianceUPS, S&P 500 ÷ VarianceS&P 500
= 6.54 ÷ 7.32

3 AverageUPS – βUPS × AverageS&P 500
= 1.020.89 × 1.02


Expected Rate of Return

Microsoft Excel LibreOffice Calc
Assumptions
Rate of return on LT Treasury Composite1 RF 3.29%
Expected rate of return on market portfolio2 E(RM) 12.28%
Systematic risk (β) of UPS's common stock βUPS 0.89
Expected rate of return on UPS's common stock3 E(RUPS) 11.32%

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(RUPS) = RF + βUPS [E(RM) – RF]
= 3.29% + 0.89 [12.28% – 3.29%]
= 11.32%