Stock Analysis on Net

UnitedHealth Group Inc. (NYSE:UNH)

Capital Asset Pricing Model (CAPM) 

Microsoft Excel

Rates of Return

UnitedHealth Group Inc., monthly rates of return

Microsoft Excel
UnitedHealth Group Inc. (UNH) Standard & Poor’s 500 (S&P 500)
t Date PriceUNH,t1 DividendUNH,t1 RUNH,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2020 $272.45 3,225.52
1. Feb 29, 2020 $254.96 -6.42% 2,954.22 -8.41%
2. Mar 31, 2020 $249.38 $1.08 -1.76% 2,584.59 -12.51%
3. Apr 30, 2020 $292.47 17.28% 2,912.43 12.68%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2024 $610.20 8.10% 6,032.38 5.73%
59. Dec 31, 2024 $505.86 $2.10 -16.76% 5,881.63 -2.50%
Average (R): 1.37% 1.16%
Standard deviation: 6.30% 5.28%
UnitedHealth Group Inc. (UNH) Standard & Poor’s 500 (S&P 500)
t Date PriceUNH,t1 DividendUNH,t1 RUNH,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2020 $272.45 3,225.52
1. Feb 29, 2020 $254.96 -6.42% 2,954.22 -8.41%
2. Mar 31, 2020 $249.38 $1.08 -1.76% 2,584.59 -12.51%
3. Apr 30, 2020 $292.47 17.28% 2,912.43 12.68%
4. May 31, 2020 $304.85 4.23% 3,044.31 4.53%
5. Jun 30, 2020 $294.95 $1.25 -2.84% 3,100.29 1.84%
6. Jul 31, 2020 $302.78 2.65% 3,271.12 5.51%
7. Aug 31, 2020 $312.55 3.23% 3,500.31 7.01%
8. Sep 30, 2020 $311.77 $1.25 0.15% 3,363.00 -3.92%
9. Oct 31, 2020 $305.14 -2.13% 3,269.96 -2.77%
10. Nov 30, 2020 $336.34 10.22% 3,621.63 10.75%
11. Dec 31, 2020 $350.68 $1.25 4.64% 3,756.07 3.71%
12. Jan 31, 2021 $333.58 -4.88% 3,714.24 -1.11%
13. Feb 28, 2021 $332.22 -0.41% 3,811.15 2.61%
14. Mar 31, 2021 $372.07 $1.25 12.37% 3,972.89 4.24%
15. Apr 30, 2021 $398.80 7.18% 4,181.17 5.24%
16. May 31, 2021 $411.92 3.29% 4,204.11 0.55%
17. Jun 30, 2021 $400.44 $1.45 -2.43% 4,297.50 2.22%
18. Jul 31, 2021 $412.22 2.94% 4,395.26 2.27%
19. Aug 31, 2021 $416.27 0.98% 4,522.68 2.90%
20. Sep 30, 2021 $390.74 $1.45 -5.78% 4,307.54 -4.76%
21. Oct 31, 2021 $460.47 17.85% 4,605.38 6.91%
22. Nov 30, 2021 $444.22 -3.53% 4,567.00 -0.83%
23. Dec 31, 2021 $502.14 $1.45 13.36% 4,766.18 4.36%
24. Jan 31, 2022 $472.57 -5.89% 4,515.55 -5.26%
25. Feb 28, 2022 $475.87 0.70% 4,373.94 -3.14%
26. Mar 31, 2022 $509.97 $1.45 7.47% 4,530.41 3.58%
27. Apr 30, 2022 $508.55 -0.28% 4,131.93 -8.80%
28. May 31, 2022 $496.78 -2.31% 4,132.15 0.01%
29. Jun 30, 2022 $513.63 $1.65 3.72% 3,785.38 -8.39%
30. Jul 31, 2022 $542.34 5.59% 4,130.29 9.11%
31. Aug 31, 2022 $519.33 -4.24% 3,955.00 -4.24%
32. Sep 30, 2022 $505.04 $1.65 -2.43% 3,585.62 -9.34%
33. Oct 31, 2022 $555.15 9.92% 3,871.98 7.99%
34. Nov 30, 2022 $547.76 -1.33% 4,080.11 5.38%
35. Dec 31, 2022 $530.18 $1.65 -2.91% 3,839.50 -5.90%
36. Jan 31, 2023 $499.19 -5.85% 4,076.60 6.18%
37. Feb 28, 2023 $475.94 -4.66% 3,970.15 -2.61%
38. Mar 31, 2023 $472.59 $1.65 -0.36% 4,109.31 3.51%
39. Apr 30, 2023 $492.09 4.13% 4,169.48 1.46%
40. May 31, 2023 $487.24 -0.99% 4,179.83 0.25%
41. Jun 30, 2023 $480.64 $1.88 -0.97% 4,376.86 4.71%
42. Jul 31, 2023 $506.37 5.35% 4,588.96 4.85%
43. Aug 31, 2023 $476.58 -5.88% 4,507.66 -1.77%
44. Sep 30, 2023 $504.19 $1.88 6.19% 4,288.05 -4.87%
45. Oct 31, 2023 $535.56 6.22% 4,193.80 -2.20%
46. Nov 30, 2023 $552.97 3.25% 4,567.80 8.92%
47. Dec 31, 2023 $526.47 $1.88 -4.45% 4,769.83 4.42%
48. Jan 31, 2024 $511.74 -2.80% 4,845.65 1.59%
49. Feb 29, 2024 $493.60 -3.54% 5,096.27 5.17%
50. Mar 31, 2024 $494.70 $1.88 0.60% 5,254.35 3.10%
51. Apr 30, 2024 $483.70 -2.22% 5,035.69 -4.16%
52. May 31, 2024 $495.37 2.41% 5,277.51 4.80%
53. Jun 30, 2024 $509.26 $2.10 3.23% 5,460.48 3.47%
54. Jul 31, 2024 $576.16 13.14% 5,522.30 1.13%
55. Aug 31, 2024 $590.20 2.44% 5,648.40 2.28%
56. Sep 30, 2024 $584.68 $2.10 -0.58% 5,762.48 2.02%
57. Oct 31, 2024 $564.50 -3.45% 5,705.45 -0.99%
58. Nov 30, 2024 $610.20 8.10% 6,032.38 5.73%
59. Dec 31, 2024 $505.86 $2.10 -16.76% 5,881.63 -2.50%
Average (R): 1.37% 1.16%
Standard deviation: 6.30% 5.28%

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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 UNH during period t

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


Variance and Covariance

UnitedHealth Group Inc., calculation of variance and covariance of returns

Microsoft Excel
t Date RUNH,t RS&P 500,t (RUNH,tRUNH)2 (RS&P 500,tRS&P 500)2 (RUNH,tRUNH)×(RS&P 500,tRS&P 500)
1. Feb 29, 2020 -6.42% -8.41% 60.66 91.63 74.55
2. Mar 31, 2020 -1.76% -12.51% 9.82 186.96 42.85
3. Apr 30, 2020 17.28% 12.68% 253.13 132.78 183.33
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2024 8.10% 5.73% 45.25 20.87 30.73
59. Dec 31, 2024 -16.76% -2.50% 328.48 13.40 66.34
Total (Σ): 2,303.00 1,618.62 1,005.26
t Date RUNH,t RS&P 500,t (RUNH,tRUNH)2 (RS&P 500,tRS&P 500)2 (RUNH,tRUNH)×(RS&P 500,tRS&P 500)
1. Feb 29, 2020 -6.42% -8.41% 60.66 91.63 74.55
2. Mar 31, 2020 -1.76% -12.51% 9.82 186.96 42.85
3. Apr 30, 2020 17.28% 12.68% 253.13 132.78 183.33
4. May 31, 2020 4.23% 4.53% 8.20 11.34 9.64
5. Jun 30, 2020 -2.84% 1.84% 17.69 0.46 -2.85
6. Jul 31, 2020 2.65% 5.51% 1.65 18.91 5.59
7. Aug 31, 2020 3.23% 7.01% 3.45 34.17 10.86
8. Sep 30, 2020 0.15% -3.92% 1.48 25.85 6.19
9. Oct 31, 2020 -2.13% -2.77% 12.22 15.43 13.73
10. Nov 30, 2020 10.22% 10.75% 78.43 92.03 84.96
11. Dec 31, 2020 4.64% 3.71% 10.67 6.51 8.33
12. Jan 31, 2021 -4.88% -1.11% 39.00 5.18 14.21
13. Feb 28, 2021 -0.41% 2.61% 3.16 2.10 -2.57
14. Mar 31, 2021 12.37% 4.24% 121.05 9.50 33.92
15. Apr 30, 2021 7.18% 5.24% 33.82 16.66 23.73
16. May 31, 2021 3.29% 0.55% 3.69 0.38 -1.18
17. Jun 30, 2021 -2.43% 2.22% 14.47 1.12 -4.03
18. Jul 31, 2021 2.94% 2.27% 2.47 1.24 1.75
19. Aug 31, 2021 0.98% 2.90% 0.15 3.02 -0.67
20. Sep 30, 2021 -5.78% -4.76% 51.17 35.02 42.34
21. Oct 31, 2021 17.85% 6.91% 271.48 33.10 94.79
22. Nov 30, 2021 -3.53% -0.83% 23.99 3.98 9.77
23. Dec 31, 2021 13.36% 4.36% 143.91 10.24 38.39
24. Jan 31, 2022 -5.89% -5.26% 52.67 41.21 46.59
25. Feb 28, 2022 0.70% -3.14% 0.45 18.47 2.88
26. Mar 31, 2022 7.47% 3.58% 37.23 5.84 14.74
27. Apr 30, 2022 -0.28% -8.80% 2.71 99.14 16.40
28. May 31, 2022 -2.31% 0.01% 13.57 1.34 4.26
29. Jun 30, 2022 3.72% -8.39% 5.55 91.26 -22.50
30. Jul 31, 2022 5.59% 9.11% 17.82 63.21 33.56
31. Aug 31, 2022 -4.24% -4.24% 31.49 29.22 30.33
32. Sep 30, 2022 -2.43% -9.34% 14.46 110.27 39.93
33. Oct 31, 2022 9.92% 7.99% 73.16 46.58 58.38
34. Nov 30, 2022 -1.33% 5.38% 7.29 17.76 -11.38
35. Dec 31, 2022 -2.91% -5.90% 18.29 49.82 30.19
36. Jan 31, 2023 -5.85% 6.18% 52.04 25.14 -36.17
37. Feb 28, 2023 -4.66% -2.61% 36.32 14.23 22.73
38. Mar 31, 2023 -0.36% 3.51% 2.98 5.49 -4.05
39. Apr 30, 2023 4.13% 1.46% 7.60 0.09 0.84
40. May 31, 2023 -0.99% 0.25% 5.54 0.83 2.15
41. Jun 30, 2023 -0.97% 4.71% 5.46 12.62 -8.30
42. Jul 31, 2023 5.35% 4.85% 15.88 13.58 14.68
43. Aug 31, 2023 -5.88% -1.77% 52.59 8.60 21.27
44. Sep 30, 2023 6.19% -4.87% 23.22 36.40 -29.07
45. Oct 31, 2023 6.22% -2.20% 23.55 11.28 -16.30
46. Nov 30, 2023 3.25% 8.92% 3.54 60.17 14.60
47. Dec 31, 2023 -4.45% 4.42% 33.89 10.64 -18.99
48. Jan 31, 2024 -2.80% 1.59% 17.36 0.18 -1.78
49. Feb 29, 2024 -3.54% 5.17% 24.14 16.09 -19.71
50. Mar 31, 2024 0.60% 3.10% 0.59 3.77 -1.48
51. Apr 30, 2024 -2.22% -4.16% 12.91 28.33 19.12
52. May 31, 2024 2.41% 4.80% 1.09 13.26 3.80
53. Jun 30, 2024 3.23% 3.47% 3.46 5.32 4.29
54. Jul 31, 2024 13.14% 1.13% 138.48 0.00 -0.34
55. Aug 31, 2024 2.44% 2.28% 1.14 1.26 1.20
56. Sep 30, 2024 -0.58% 2.02% 3.80 0.74 -1.67
57. Oct 31, 2024 -3.45% -0.99% 23.24 4.63 10.37
58. Nov 30, 2024 8.10% 5.73% 45.25 20.87 30.73
59. Dec 31, 2024 -16.76% -2.50% 328.48 13.40 66.34
Total (Σ): 2,303.00 1,618.62 1,005.26

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VarianceUNH = Σ(RUNH,tRUNH)2 ÷ (59 – 1)
= 2,303.00 ÷ (59 – 1)
= 39.71

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91

CovarianceUNH, S&P 500 = Σ(RUNH,tRUNH)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,005.26 ÷ (59 – 1)
= 17.33


Systematic Risk (β) Estimation

Microsoft Excel
VarianceUNH 39.71
VarianceS&P 500 27.91
CovarianceUNH, S&P 500 17.33
Correlation coefficientUNH, S&P 5001 0.52
βUNH2 0.62
αUNH3 0.65%

Calculations

1 Correlation coefficientUNH, S&P 500
= CovarianceUNH, S&P 500 ÷ (Standard deviationUNH × Standard deviationS&P 500)
= 17.33 ÷ (6.30% × 5.28%)
= 0.52

2 βUNH
= CovarianceUNH, S&P 500 ÷ VarianceS&P 500
= 17.33 ÷ 27.91
= 0.62

3 αUNH
= AverageUNH – βUNH × AverageS&P 500
= 1.37%0.62 × 1.16%
= 0.65%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.64%
Expected rate of return on market portfolio2 E(RM) 14.89%
Systematic risk (β) of UnitedHealth Group Inc. common stock βUNH 0.62
 
Expected rate of return on UnitedHealth Group Inc. common stock3 E(RUNH) 11.01%

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(RUNH) = RF + βUNH [E(RM) – RF]
= 4.64% + 0.62 [14.89%4.64%]
= 11.01%