Stock Analysis on Net
Stock Analysis on Net

United Rentals Inc. (NYSE:URI)

This company has been moved to the archive! The financial data has not been updated since January 25, 2023.

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 United Rentals Inc. common stock.

Rates of Return

United Rentals Inc., monthly rates of return

Microsoft Excel
United Rentals Inc. (URI) Standard & Poor’s 500 (S&P 500)
t Date PriceURI,t1 DividendURI,t1 RURI,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2018 $181.11 2,823.81
1. Feb 28, 2018 $175.09 -3.32% 2,713.83 -3.89%
2. Mar 31, 2018 $172.73 -1.35% 2,640.87 -2.69%
3. Apr 30, 2018 $150.00 -13.16% 2,648.05 0.27%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2022 $353.03 11.82% 4,080.11 5.38%
59. Dec 31, 2022 $355.42 0.68% 3,839.50 -5.90%
Average (R): 1.95% 0.67%
Standard deviation: 12.83% 5.40%
United Rentals Inc. (URI) Standard & Poor’s 500 (S&P 500)
t Date PriceURI,t1 DividendURI,t1 RURI,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2018 $181.11 2,823.81
1. Feb 28, 2018 $175.09 -3.32% 2,713.83 -3.89%
2. Mar 31, 2018 $172.73 -1.35% 2,640.87 -2.69%
3. Apr 30, 2018 $150.00 -13.16% 2,648.05 0.27%
4. May 31, 2018 $159.57 6.38% 2,705.27 2.16%
5. Jun 30, 2018 $147.62 -7.49% 2,718.37 0.48%
6. Jul 31, 2018 $148.80 0.80% 2,816.29 3.60%
7. Aug 31, 2018 $155.87 4.75% 2,901.52 3.03%
8. Sep 30, 2018 $163.60 4.96% 2,913.98 0.43%
9. Oct 31, 2018 $120.07 -26.61% 2,711.74 -6.94%
10. Nov 30, 2018 $117.13 -2.45% 2,760.17 1.79%
11. Dec 31, 2018 $102.53 -12.46% 2,506.85 -9.18%
12. Jan 31, 2019 $125.26 22.17% 2,704.10 7.87%
13. Feb 28, 2019 $134.59 7.45% 2,784.49 2.97%
14. Mar 31, 2019 $114.25 -15.11% 2,834.40 1.79%
15. Apr 30, 2019 $140.92 23.34% 2,945.83 3.93%
16. May 31, 2019 $110.10 -21.87% 2,752.06 -6.58%
17. Jun 30, 2019 $132.63 20.46% 2,941.76 6.89%
18. Jul 31, 2019 $126.55 -4.58% 2,980.38 1.31%
19. Aug 31, 2019 $112.56 -11.05% 2,926.46 -1.81%
20. Sep 30, 2019 $124.64 10.73% 2,976.74 1.72%
21. Oct 31, 2019 $133.57 7.16% 3,037.56 2.04%
22. Nov 30, 2019 $153.05 14.58% 3,140.98 3.40%
23. Dec 31, 2019 $166.77 8.96% 3,230.78 2.86%
24. Jan 31, 2020 $135.69 -18.64% 3,225.52 -0.16%
25. Feb 29, 2020 $132.48 -2.37% 2,954.22 -8.41%
26. Mar 31, 2020 $102.90 -22.33% 2,584.59 -12.51%
27. Apr 30, 2020 $128.50 24.88% 2,912.43 12.68%
28. May 31, 2020 $138.89 8.09% 3,044.31 4.53%
29. Jun 30, 2020 $149.04 7.31% 3,100.29 1.84%
30. Jul 31, 2020 $155.37 4.25% 3,271.12 5.51%
31. Aug 31, 2020 $177.05 13.95% 3,500.31 7.01%
32. Sep 30, 2020 $174.50 -1.44% 3,363.00 -3.92%
33. Oct 31, 2020 $178.29 2.17% 3,269.96 -2.77%
34. Nov 30, 2020 $226.98 27.31% 3,621.63 10.75%
35. Dec 31, 2020 $231.91 2.17% 3,756.07 3.71%
36. Jan 31, 2021 $243.01 4.79% 3,714.24 -1.11%
37. Feb 28, 2021 $297.38 22.37% 3,811.15 2.61%
38. Mar 31, 2021 $329.31 10.74% 3,972.89 4.24%
39. Apr 30, 2021 $319.95 -2.84% 4,181.17 5.24%
40. May 31, 2021 $333.96 4.38% 4,204.11 0.55%
41. Jun 30, 2021 $319.01 -4.48% 4,297.50 2.22%
42. Jul 31, 2021 $329.55 3.30% 4,395.26 2.27%
43. Aug 31, 2021 $352.65 7.01% 4,522.68 2.90%
44. Sep 30, 2021 $350.93 -0.49% 4,307.54 -4.76%
45. Oct 31, 2021 $379.11 8.03% 4,605.38 6.91%
46. Nov 30, 2021 $338.74 -10.65% 4,567.00 -0.83%
47. Dec 31, 2021 $332.29 -1.90% 4,766.18 4.36%
48. Jan 31, 2022 $320.12 -3.66% 4,515.55 -5.26%
49. Feb 28, 2022 $321.62 0.47% 4,373.94 -3.14%
50. Mar 31, 2022 $355.21 10.44% 4,530.41 3.58%
51. Apr 30, 2022 $316.52 -10.89% 4,131.93 -8.80%
52. May 31, 2022 $298.18 -5.79% 4,132.15 0.01%
53. Jun 30, 2022 $242.91 -18.54% 3,785.38 -8.39%
54. Jul 31, 2022 $322.67 32.84% 4,130.29 9.11%
55. Aug 31, 2022 $292.04 -9.49% 3,955.00 -4.24%
56. Sep 30, 2022 $270.12 -7.51% 3,585.62 -9.34%
57. Oct 31, 2022 $315.71 16.88% 3,871.98 7.99%
58. Nov 30, 2022 $353.03 11.82% 4,080.11 5.38%
59. Dec 31, 2022 $355.42 0.68% 3,839.50 -5.90%
Average (R): 1.95% 0.67%
Standard deviation: 12.83% 5.40%

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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 URI during period t

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

Variance and Covariance

United Rentals Inc., calculation of variance and covariance of returns

Microsoft Excel
t Date RURI,t RS&P 500,t (RURI,t–RURI)2 (RS&P 500,t–RS&P 500)2 (RURI,t–RURI)×(RS&P 500,t–RS&P 500)
1. Feb 28, 2018 -3.32% -3.89% 27.83 20.81 24.06
2. Mar 31, 2018 -1.35% -2.69% 10.89 11.26 11.07
3. Apr 30, 2018 -13.16% 0.27% 228.34 0.16 5.97
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2022 11.82% 5.38% 97.40 22.17 46.47
59. Dec 31, 2022 0.68% -5.90% 1.62 43.08 8.37
Total (Σ): 9,550.56 1,691.48 3,092.28
t Date RURI,t RS&P 500,t (RURI,t–RURI)2 (RS&P 500,t–RS&P 500)2 (RURI,t–RURI)×(RS&P 500,t–RS&P 500)
1. Feb 28, 2018 -3.32% -3.89% 27.83 20.81 24.06
2. Mar 31, 2018 -1.35% -2.69% 10.89 11.26 11.07
3. Apr 30, 2018 -13.16% 0.27% 228.34 0.16 5.97
4. May 31, 2018 6.38% 2.16% 19.61 2.23 6.62
5. Jun 30, 2018 -7.49% 0.48% 89.13 0.03 1.72
6. Jul 31, 2018 0.80% 3.60% 1.33 8.62 -3.38
7. Aug 31, 2018 4.75% 3.03% 7.84 5.57 6.61
8. Sep 30, 2018 4.96% 0.43% 9.05 0.06 -0.71
9. Oct 31, 2018 -26.61% -6.94% 815.63 57.87 217.25
10. Nov 30, 2018 -2.45% 1.79% 19.36 1.25 -4.93
11. Dec 31, 2018 -12.46% -9.18% 207.84 96.91 141.92
12. Jan 31, 2019 22.17% 7.87% 408.74 51.87 145.60
13. Feb 28, 2019 7.45% 2.97% 30.21 5.32 12.68
14. Mar 31, 2019 -15.11% 1.79% 291.19 1.27 -19.21
15. Apr 30, 2019 23.34% 3.93% 457.61 10.66 69.84
16. May 31, 2019 -21.87% -6.58% 567.50 52.48 172.58
17. Jun 30, 2019 20.46% 6.89% 342.67 38.77 115.26
18. Jul 31, 2019 -4.58% 1.31% 42.72 0.42 -4.22
19. Aug 31, 2019 -11.05% -1.81% 169.17 6.13 32.20
20. Sep 30, 2019 10.73% 1.72% 77.09 1.11 9.23
21. Oct 31, 2019 7.16% 2.04% 27.17 1.89 7.18
22. Nov 30, 2019 14.58% 3.40% 159.58 7.50 34.59
23. Dec 31, 2019 8.96% 2.86% 49.18 4.81 15.37
24. Jan 31, 2020 -18.64% -0.16% 423.87 0.69 17.08
25. Feb 29, 2020 -2.37% -8.41% 18.64 82.40 39.19
26. Mar 31, 2020 -22.33% -12.51% 589.50 173.67 319.97
27. Apr 30, 2020 24.88% 12.68% 525.64 144.43 275.53
28. May 31, 2020 8.09% 4.53% 37.62 14.91 23.69
29. Jun 30, 2020 7.31% 1.84% 28.69 1.37 6.28
30. Jul 31, 2020 4.25% 5.51% 5.27 23.46 11.12
31. Aug 31, 2020 13.95% 7.01% 144.05 40.19 76.09
32. Sep 30, 2020 -1.44% -3.92% 11.51 21.06 15.57
33. Oct 31, 2020 2.17% -2.77% 0.05 11.79 -0.76
34. Nov 30, 2020 27.31% 10.75% 643.01 101.77 255.81
35. Dec 31, 2020 2.17% 3.71% 0.05 9.28 0.67
36. Jan 31, 2021 4.79% -1.11% 8.03 3.17 -5.05
37. Feb 28, 2021 22.37% 2.61% 417.05 3.77 39.67
38. Mar 31, 2021 10.74% 4.24% 77.18 12.80 31.43
39. Apr 30, 2021 -2.84% 5.24% 22.98 20.94 -21.94
40. May 31, 2021 4.38% 0.55% 5.89 0.01 -0.29
41. Jun 30, 2021 -4.48% 2.22% 41.32 2.42 -9.99
42. Jul 31, 2021 3.30% 2.27% 1.83 2.59 2.17
43. Aug 31, 2021 7.01% 2.90% 25.58 4.98 11.29
44. Sep 30, 2021 -0.49% -4.76% 5.95 29.42 13.23
45. Oct 31, 2021 8.03% 6.91% 36.95 39.03 37.98
46. Nov 30, 2021 -10.65% -0.83% 158.77 2.25 18.90
47. Dec 31, 2021 -1.90% 4.36% 14.87 13.65 -14.25
48. Jan 31, 2022 -3.66% -5.26% 31.52 35.11 33.27
49. Feb 28, 2022 0.47% -3.14% 2.20 14.46 5.64
50. Mar 31, 2022 10.44% 3.58% 72.12 8.47 24.72
51. Apr 30, 2022 -10.89% -8.80% 164.97 89.54 121.53
52. May 31, 2022 -5.79% 0.01% 60.00 0.44 5.12
53. Jun 30, 2022 -18.54% -8.39% 419.74 82.06 185.59
54. Jul 31, 2022 32.84% 9.11% 953.79 71.32 260.81
55. Aug 31, 2022 -9.49% -4.24% 130.97 24.11 56.20
56. Sep 30, 2022 -7.51% -9.34% 89.45 100.12 94.63
57. Oct 31, 2022 16.88% 7.99% 222.78 53.58 109.25
58. Nov 30, 2022 11.82% 5.38% 97.40 22.17 46.47
59. Dec 31, 2022 0.68% -5.90% 1.62 43.08 8.37
Total (Σ): 9,550.56 1,691.48 3,092.28

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VarianceURI = Σ(RURI,t–RURI)2 ÷ (59 – 1)
= 9,550.56 ÷ (59 – 1)
= 164.66

VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16

CovarianceURI, S&P 500 = Σ(RURI,t–RURI)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,092.28 ÷ (59 – 1)
= 53.32

Systematic Risk (β) Estimation

Microsoft Excel
VarianceURI 164.66
VarianceS&P 500 29.16
CovarianceURI, S&P 500 53.32
Correlation coefficientURI, S&P 5001 0.77
βURI2 1.83
αURI3 0.73%

Calculations

1 Correlation coefficientURI, S&P 500
= CovarianceURI, S&P 500 ÷ (Standard deviationURI × Standard deviationS&P 500)
= 53.32 ÷ (12.83% × 5.40%)
= 0.77

2 βURI
= CovarianceURI, S&P 500 ÷ VarianceS&P 500
= 53.32 ÷ 29.16
= 1.83

3 αURI
= AverageURI – βURI × AverageS&P 500
= 1.95% – 1.83 × 0.67%
= 0.73%

Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.83%
Expected rate of return on market portfolio2 E(RM) 14.44%
Systematic risk (β) of United Rentals Inc. common stock βURI 1.83
 
Expected rate of return on United Rentals Inc. common stock3 E(RURI) 22.39%

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(RURI) = RF + βURI [E(RM) – RF]
= 4.83% + 1.83 [14.44% – 4.83%]
= 22.39%