Stock Analysis on Net

Union Pacific Corp. (NYSE:UNP)

Capital Asset Pricing Model (CAPM)

Microsoft Excel

Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like Union Pacific Corp. common stock.


Rates of Return

Union Pacific Corp., monthly rates of return

Microsoft Excel
Union Pacific Corp. (UNP) Standard & Poor’s 500 (S&P 500)
t Date PriceUNP,t1 DividendUNP,t1 RUNP,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2019 $159.07 2,704.10
1. Feb 28, 2019 $167.70 $0.88 5.98% 2,784.49 2.97%
2. Mar 31, 2019 $167.20 -0.30% 2,834.40 1.79%
3. Apr 30, 2019 $177.04 5.89% 2,945.83 3.93%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 $225.27 8.51% 4,567.80 8.92%
59. Dec 31, 2023 $245.62 $1.30 9.61% 4,769.83 4.42%
Average (R): 1.19% 1.11%
Standard deviation: 7.41% 5.31%
Union Pacific Corp. (UNP) Standard & Poor’s 500 (S&P 500)
t Date PriceUNP,t1 DividendUNP,t1 RUNP,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2019 $159.07 2,704.10
1. Feb 28, 2019 $167.70 $0.88 5.98% 2,784.49 2.97%
2. Mar 31, 2019 $167.20 -0.30% 2,834.40 1.79%
3. Apr 30, 2019 $177.04 5.89% 2,945.83 3.93%
4. May 31, 2019 $166.78 $0.88 -5.30% 2,752.06 -6.58%
5. Jun 30, 2019 $169.11 1.40% 2,941.76 6.89%
6. Jul 31, 2019 $179.95 6.41% 2,980.38 1.31%
7. Aug 31, 2019 $161.96 $0.97 -9.46% 2,926.46 -1.81%
8. Sep 30, 2019 $161.98 0.01% 2,976.74 1.72%
9. Oct 31, 2019 $165.46 2.15% 3,037.56 2.04%
10. Nov 30, 2019 $175.99 $0.97 6.95% 3,140.98 3.40%
11. Dec 31, 2019 $180.79 2.73% 3,230.78 2.86%
12. Jan 31, 2020 $179.42 -0.76% 3,225.52 -0.16%
13. Feb 29, 2020 $159.81 $0.97 -10.39% 2,954.22 -8.41%
14. Mar 31, 2020 $141.04 -11.75% 2,584.59 -12.51%
15. Apr 30, 2020 $159.79 13.29% 2,912.43 12.68%
16. May 31, 2020 $169.86 $0.97 6.91% 3,044.31 4.53%
17. Jun 30, 2020 $169.07 -0.47% 3,100.29 1.84%
18. Jul 31, 2020 $173.35 2.53% 3,271.12 5.51%
19. Aug 31, 2020 $192.44 $0.97 11.57% 3,500.31 7.01%
20. Sep 30, 2020 $196.87 2.30% 3,363.00 -3.92%
21. Oct 31, 2020 $177.19 -10.00% 3,269.96 -2.77%
22. Nov 30, 2020 $204.08 $0.97 15.72% 3,621.63 10.75%
23. Dec 31, 2020 $208.22 2.03% 3,756.07 3.71%
24. Jan 31, 2021 $197.47 -5.16% 3,714.24 -1.11%
25. Feb 28, 2021 $205.96 $0.97 4.79% 3,811.15 2.61%
26. Mar 31, 2021 $220.41 7.02% 3,972.89 4.24%
27. Apr 30, 2021 $222.09 0.76% 4,181.17 5.24%
28. May 31, 2021 $224.73 $1.07 1.67% 4,204.11 0.55%
29. Jun 30, 2021 $219.93 -2.14% 4,297.50 2.22%
30. Jul 31, 2021 $218.76 -0.53% 4,395.26 2.27%
31. Aug 31, 2021 $216.84 $1.07 -0.39% 4,522.68 2.90%
32. Sep 30, 2021 $196.01 -9.61% 4,307.54 -4.76%
33. Oct 31, 2021 $241.40 23.16% 4,605.38 6.91%
34. Nov 30, 2021 $235.64 -2.39% 4,567.00 -0.83%
35. Dec 31, 2021 $251.93 $1.18 7.41% 4,766.18 4.36%
36. Jan 31, 2022 $244.55 -2.93% 4,515.55 -5.26%
37. Feb 28, 2022 $245.95 $1.18 1.05% 4,373.94 -3.14%
38. Mar 31, 2022 $273.21 11.08% 4,530.41 3.58%
39. Apr 30, 2022 $234.29 -14.25% 4,131.93 -8.80%
40. May 31, 2022 $219.78 $1.30 -5.64% 4,132.15 0.01%
41. Jun 30, 2022 $213.28 -2.96% 3,785.38 -8.39%
42. Jul 31, 2022 $227.30 6.57% 4,130.29 9.11%
43. Aug 31, 2022 $224.51 $1.30 -0.66% 3,955.00 -4.24%
44. Sep 30, 2022 $194.82 -13.22% 3,585.62 -9.34%
45. Oct 31, 2022 $197.14 1.19% 3,871.98 7.99%
46. Nov 30, 2022 $217.43 10.29% 4,080.11 5.38%
47. Dec 31, 2022 $207.07 $1.30 -4.17% 3,839.50 -5.90%
48. Jan 31, 2023 $204.19 -1.39% 4,076.60 6.18%
49. Feb 28, 2023 $207.28 $1.30 2.15% 3,970.15 -2.61%
50. Mar 31, 2023 $201.26 -2.90% 4,109.31 3.51%
51. Apr 30, 2023 $195.70 -2.76% 4,169.48 1.46%
52. May 31, 2023 $192.52 $1.30 -0.96% 4,179.83 0.25%
53. Jun 30, 2023 $204.62 6.29% 4,376.86 4.71%
54. Jul 31, 2023 $232.02 13.39% 4,588.96 4.85%
55. Aug 31, 2023 $220.57 $1.30 -4.37% 4,507.66 -1.77%
56. Sep 30, 2023 $203.63 -7.68% 4,288.05 -4.87%
57. Oct 31, 2023 $207.61 1.95% 4,193.80 -2.20%
58. Nov 30, 2023 $225.27 8.51% 4,567.80 8.92%
59. Dec 31, 2023 $245.62 $1.30 9.61% 4,769.83 4.42%
Average (R): 1.19% 1.11%
Standard deviation: 7.41% 5.31%

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1 Data in US$ per share of common stock, adjusted for splits and stock dividends.

2 Rate of return on common stock of UNP during period t

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


Variance and Covariance

Union Pacific Corp., calculation of variance and covariance of returns

Microsoft Excel
t Date RUNP,t RS&P 500,t (RUNP,tRUNP)2 (RS&P 500,tRS&P 500)2 (RUNP,tRUNP)×(RS&P 500,tRS&P 500)
1. Feb 28, 2019 5.98% 2.97% 22.92 3.49 8.94
2. Mar 31, 2019 -0.30% 1.79% 2.22 0.47 -1.02
3. Apr 30, 2019 5.89% 3.93% 22.04 7.98 13.26
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 8.51% 8.92% 53.52 61.03 57.15
59. Dec 31, 2023 9.61% 4.42% 70.89 11.00 27.93
Total (Σ): 3,180.39 1,634.30 1,780.86
t Date RUNP,t RS&P 500,t (RUNP,tRUNP)2 (RS&P 500,tRS&P 500)2 (RUNP,tRUNP)×(RS&P 500,tRS&P 500)
1. Feb 28, 2019 5.98% 2.97% 22.92 3.49 8.94
2. Mar 31, 2019 -0.30% 1.79% 2.22 0.47 -1.02
3. Apr 30, 2019 5.89% 3.93% 22.04 7.98 13.26
4. May 31, 2019 -5.30% -6.58% 42.11 59.04 49.86
5. Jun 30, 2019 1.40% 6.89% 0.04 33.49 1.19
6. Jul 31, 2019 6.41% 1.31% 27.24 0.04 1.08
7. Aug 31, 2019 -9.46% -1.81% 113.40 8.50 31.04
8. Sep 30, 2019 0.01% 1.72% 1.39 0.37 -0.72
9. Oct 31, 2019 2.15% 2.04% 0.92 0.88 0.90
10. Nov 30, 2019 6.95% 3.40% 33.17 5.28 13.24
11. Dec 31, 2019 2.73% 2.86% 2.36 3.07 2.69
12. Jan 31, 2020 -0.76% -0.16% 3.80 1.61 2.47
13. Feb 29, 2020 -10.39% -8.41% 134.09 90.57 110.20
14. Mar 31, 2020 -11.75% -12.51% 167.34 185.44 176.16
15. Apr 30, 2020 13.29% 12.68% 146.49 134.06 140.14
16. May 31, 2020 6.91% 4.53% 32.70 11.71 19.57
17. Jun 30, 2020 -0.47% 1.84% 2.74 0.54 -1.21
18. Jul 31, 2020 2.53% 5.51% 1.80 19.40 5.90
19. Aug 31, 2020 11.57% 7.01% 107.77 34.82 61.25
20. Sep 30, 2020 2.30% -3.92% 1.23 25.29 -5.59
21. Oct 31, 2020 -10.00% -2.77% 125.16 15.00 43.32
22. Nov 30, 2020 15.72% 10.75% 211.19 93.10 140.22
23. Dec 31, 2020 2.03% 3.71% 0.70 6.79 2.18
24. Jan 31, 2021 -5.16% -1.11% 40.37 4.93 14.10
25. Feb 28, 2021 4.79% 2.61% 12.96 2.26 5.41
26. Mar 31, 2021 7.02% 4.24% 33.93 9.85 18.28
27. Apr 30, 2021 0.76% 5.24% 0.18 17.11 -1.77
28. May 31, 2021 1.67% 0.55% 0.23 0.31 -0.27
29. Jun 30, 2021 -2.14% 2.22% 11.07 1.24 -3.71
30. Jul 31, 2021 -0.53% 2.27% 2.97 1.37 -2.01
31. Aug 31, 2021 -0.39% 2.90% 2.49 3.22 -2.83
32. Sep 30, 2021 -9.61% -4.76% 116.58 34.37 63.30
33. Oct 31, 2021 23.16% 6.91% 482.51 33.74 127.59
34. Nov 30, 2021 -2.39% -0.83% 12.79 3.76 6.94
35. Dec 31, 2021 7.41% 4.36% 38.73 10.60 20.26
36. Jan 31, 2022 -2.93% -5.26% 16.98 40.51 26.22
37. Feb 28, 2022 1.05% -3.14% 0.02 17.99 0.58
38. Mar 31, 2022 11.08% 3.58% 97.86 6.11 24.45
39. Apr 30, 2022 -14.25% -8.80% 238.28 98.04 152.84
40. May 31, 2022 -5.64% 0.01% 46.64 1.21 7.52
41. Jun 30, 2022 -2.96% -8.39% 17.21 90.21 39.40
42. Jul 31, 2022 6.57% 9.11% 28.97 64.09 43.09
43. Aug 31, 2022 -0.66% -4.24% 3.41 28.62 9.88
44. Sep 30, 2022 -13.22% -9.34% 207.80 109.11 150.57
45. Oct 31, 2022 1.19% 7.99% 0.00 47.34 0.00
46. Nov 30, 2022 10.29% 5.38% 82.83 18.23 38.86
47. Dec 31, 2022 -4.17% -5.90% 28.71 49.04 37.52
48. Jan 31, 2023 -1.39% 6.18% 6.67 25.70 -13.09
49. Feb 28, 2023 2.15% -2.61% 0.92 13.82 -3.56
50. Mar 31, 2023 -2.90% 3.51% 16.77 5.76 -9.83
51. Apr 30, 2023 -2.76% 1.46% 15.63 0.13 -1.42
52. May 31, 2023 -0.96% 0.25% 4.63 0.74 1.85
53. Jun 30, 2023 6.29% 4.71% 25.95 13.02 18.38
54. Jul 31, 2023 13.39% 4.85% 148.83 13.99 45.63
55. Aug 31, 2023 -4.37% -1.77% 30.97 8.28 16.01
56. Sep 30, 2023 -7.68% -4.87% 78.69 35.73 53.03
57. Oct 31, 2023 1.95% -2.20% 0.58 10.92 -2.52
58. Nov 30, 2023 8.51% 8.92% 53.52 61.03 57.15
59. Dec 31, 2023 9.61% 4.42% 70.89 11.00 27.93
Total (Σ): 3,180.39 1,634.30 1,780.86

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VarianceUNP = Σ(RUNP,tRUNP)2 ÷ (59 – 1)
= 3,180.39 ÷ (59 – 1)
= 54.83

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18

CovarianceUNP, S&P 500 = Σ(RUNP,tRUNP)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,780.86 ÷ (59 – 1)
= 30.70


Systematic Risk (β) Estimation

Microsoft Excel
VarianceUNP 54.83
VarianceS&P 500 28.18
CovarianceUNP, S&P 500 30.70
Correlation coefficientUNP, S&P 5001 0.78
βUNP2 1.09
αUNP3 -0.01%

Calculations

1 Correlation coefficientUNP, S&P 500
= CovarianceUNP, S&P 500 ÷ (Standard deviationUNP × Standard deviationS&P 500)
= 30.70 ÷ (7.41% × 5.31%)
= 0.78

2 βUNP
= CovarianceUNP, S&P 500 ÷ VarianceS&P 500
= 30.70 ÷ 28.18
= 1.09

3 αUNP
= AverageUNP – βUNP × AverageS&P 500
= 1.19%1.09 × 1.11%
= -0.01%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.86%
Expected rate of return on market portfolio2 E(RM) 13.52%
Systematic risk (β) of Union Pacific Corp. common stock βUNP 1.09
 
Expected rate of return on Union Pacific Corp. common stock3 E(RUNP) 14.30%

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(RUNP) = RF + βUNP [E(RM) – RF]
= 4.86% + 1.09 [13.52%4.86%]
= 14.30%