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, 2019 $270.20 2,704.10
1. Feb 28, 2019 $242.22 -10.36% 2,784.49 2.97%
2. Mar 31, 2019 $247.26 $0.90 2.45% 2,834.40 1.79%
3. Apr 30, 2019 $233.07 -5.74% 2,945.83 3.93%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 $552.97 3.25% 4,567.80 8.92%
59. Dec 31, 2023 $526.47 $1.88 -4.45% 4,769.83 4.42%
Average (R): 1.46% 1.11%
Standard deviation: 6.46% 5.31%
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, 2019 $270.20 2,704.10
1. Feb 28, 2019 $242.22 -10.36% 2,784.49 2.97%
2. Mar 31, 2019 $247.26 $0.90 2.45% 2,834.40 1.79%
3. Apr 30, 2019 $233.07 -5.74% 2,945.83 3.93%
4. May 31, 2019 $241.80 3.75% 2,752.06 -6.58%
5. Jun 30, 2019 $244.01 $1.08 1.36% 2,941.76 6.89%
6. Jul 31, 2019 $249.01 2.05% 2,980.38 1.31%
7. Aug 31, 2019 $234.00 -6.03% 2,926.46 -1.81%
8. Sep 30, 2019 $217.32 $1.08 -6.67% 2,976.74 1.72%
9. Oct 31, 2019 $252.70 16.28% 3,037.56 2.04%
10. Nov 30, 2019 $279.87 10.75% 3,140.98 3.40%
11. Dec 31, 2019 $293.98 $1.08 5.43% 3,230.78 2.86%
12. Jan 31, 2020 $272.45 -7.32% 3,225.52 -0.16%
13. Feb 29, 2020 $254.96 -6.42% 2,954.22 -8.41%
14. Mar 31, 2020 $249.38 $1.08 -1.76% 2,584.59 -12.51%
15. Apr 30, 2020 $292.47 17.28% 2,912.43 12.68%
16. May 31, 2020 $304.85 4.23% 3,044.31 4.53%
17. Jun 30, 2020 $294.95 $1.25 -2.84% 3,100.29 1.84%
18. Jul 31, 2020 $302.78 2.65% 3,271.12 5.51%
19. Aug 31, 2020 $312.55 3.23% 3,500.31 7.01%
20. Sep 30, 2020 $311.77 $1.25 0.15% 3,363.00 -3.92%
21. Oct 31, 2020 $305.14 -2.13% 3,269.96 -2.77%
22. Nov 30, 2020 $336.34 10.22% 3,621.63 10.75%
23. Dec 31, 2020 $350.68 $1.25 4.64% 3,756.07 3.71%
24. Jan 31, 2021 $333.58 -4.88% 3,714.24 -1.11%
25. Feb 28, 2021 $332.22 -0.41% 3,811.15 2.61%
26. Mar 31, 2021 $372.07 $1.25 12.37% 3,972.89 4.24%
27. Apr 30, 2021 $398.80 7.18% 4,181.17 5.24%
28. May 31, 2021 $411.92 3.29% 4,204.11 0.55%
29. Jun 30, 2021 $400.44 $1.45 -2.43% 4,297.50 2.22%
30. Jul 31, 2021 $412.22 2.94% 4,395.26 2.27%
31. Aug 31, 2021 $416.27 0.98% 4,522.68 2.90%
32. Sep 30, 2021 $390.74 $1.45 -5.78% 4,307.54 -4.76%
33. Oct 31, 2021 $460.47 17.85% 4,605.38 6.91%
34. Nov 30, 2021 $444.22 -3.53% 4,567.00 -0.83%
35. Dec 31, 2021 $502.14 $1.45 13.36% 4,766.18 4.36%
36. Jan 31, 2022 $472.57 -5.89% 4,515.55 -5.26%
37. Feb 28, 2022 $475.87 0.70% 4,373.94 -3.14%
38. Mar 31, 2022 $509.97 $1.45 7.47% 4,530.41 3.58%
39. Apr 30, 2022 $508.55 -0.28% 4,131.93 -8.80%
40. May 31, 2022 $496.78 -2.31% 4,132.15 0.01%
41. Jun 30, 2022 $513.63 $1.65 3.72% 3,785.38 -8.39%
42. Jul 31, 2022 $542.34 5.59% 4,130.29 9.11%
43. Aug 31, 2022 $519.33 -4.24% 3,955.00 -4.24%
44. Sep 30, 2022 $505.04 $1.65 -2.43% 3,585.62 -9.34%
45. Oct 31, 2022 $555.15 9.92% 3,871.98 7.99%
46. Nov 30, 2022 $547.76 -1.33% 4,080.11 5.38%
47. Dec 31, 2022 $530.18 $1.65 -2.91% 3,839.50 -5.90%
48. Jan 31, 2023 $499.19 -5.85% 4,076.60 6.18%
49. Feb 28, 2023 $475.94 -4.66% 3,970.15 -2.61%
50. Mar 31, 2023 $472.59 $1.65 -0.36% 4,109.31 3.51%
51. Apr 30, 2023 $492.09 4.13% 4,169.48 1.46%
52. May 31, 2023 $487.24 -0.99% 4,179.83 0.25%
53. Jun 30, 2023 $480.64 $1.88 -0.97% 4,376.86 4.71%
54. Jul 31, 2023 $506.37 5.35% 4,588.96 4.85%
55. Aug 31, 2023 $476.58 -5.88% 4,507.66 -1.77%
56. Sep 30, 2023 $504.19 $1.88 6.19% 4,288.05 -4.87%
57. Oct 31, 2023 $535.56 6.22% 4,193.80 -2.20%
58. Nov 30, 2023 $552.97 3.25% 4,567.80 8.92%
59. Dec 31, 2023 $526.47 $1.88 -4.45% 4,769.83 4.42%
Average (R): 1.46% 1.11%
Standard deviation: 6.46% 5.31%

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 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 28, 2019 -10.36% 2.97% 139.61 3.49 -22.06
2. Mar 31, 2019 2.45% 1.79% 0.98 0.47 0.68
3. Apr 30, 2019 -5.74% 3.93% 51.83 7.98 -20.34
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 3.25% 8.92% 3.21 61.03 13.99
59. Dec 31, 2023 -4.45% 4.42% 34.96 11.00 -19.61
Total (Σ): 2,419.55 1,634.30 906.22
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 28, 2019 -10.36% 2.97% 139.61 3.49 -22.06
2. Mar 31, 2019 2.45% 1.79% 0.98 0.47 0.68
3. Apr 30, 2019 -5.74% 3.93% 51.83 7.98 -20.34
4. May 31, 2019 3.75% -6.58% 5.22 59.04 -17.56
5. Jun 30, 2019 1.36% 6.89% 0.01 33.49 -0.58
6. Jul 31, 2019 2.05% 1.31% 0.35 0.04 0.12
7. Aug 31, 2019 -6.03% -1.81% 56.07 8.50 21.83
8. Sep 30, 2019 -6.67% 1.72% 66.05 0.37 -4.98
9. Oct 31, 2019 16.28% 2.04% 219.63 0.88 13.89
10. Nov 30, 2019 10.75% 3.40% 86.33 5.28 21.36
11. Dec 31, 2019 5.43% 2.86% 15.74 3.07 6.96
12. Jan 31, 2020 -7.32% -0.16% 77.16 1.61 11.14
13. Feb 29, 2020 -6.42% -8.41% 62.09 90.57 74.99
14. Mar 31, 2020 -1.76% -12.51% 10.40 185.44 43.92
15. Apr 30, 2020 17.28% 12.68% 250.23 134.06 183.16
16. May 31, 2020 4.23% 4.53% 7.69 11.71 9.49
17. Jun 30, 2020 -2.84% 1.84% 18.47 0.54 -3.15
18. Jul 31, 2020 2.65% 5.51% 1.43 19.40 5.26
19. Aug 31, 2020 3.23% 7.01% 3.12 34.82 10.42
20. Sep 30, 2020 0.15% -3.92% 1.72 25.29 6.59
21. Oct 31, 2020 -2.13% -2.77% 12.87 15.00 13.89
22. Nov 30, 2020 10.22% 10.75% 76.82 93.10 84.57
23. Dec 31, 2020 4.64% 3.71% 10.08 6.79 8.27
24. Jan 31, 2021 -4.88% -1.11% 40.15 4.93 14.06
25. Feb 28, 2021 -0.41% 2.61% 3.49 2.26 -2.81
26. Mar 31, 2021 12.37% 4.24% 119.05 9.85 34.24
27. Apr 30, 2021 7.18% 5.24% 32.76 17.11 23.68
28. May 31, 2021 3.29% 0.55% 3.35 0.31 -1.02
29. Jun 30, 2021 -2.43% 2.22% 15.17 1.24 -4.35
30. Jul 31, 2021 2.94% 2.27% 2.19 1.37 1.73
31. Aug 31, 2021 0.98% 2.90% 0.23 3.22 -0.86
32. Sep 30, 2021 -5.78% -4.76% 52.49 34.37 42.48
33. Oct 31, 2021 17.85% 6.91% 268.48 33.74 95.18
34. Nov 30, 2021 -3.53% -0.83% 24.89 3.76 9.68
35. Dec 31, 2021 13.36% 4.36% 141.72 10.60 38.76
36. Jan 31, 2022 -5.89% -5.26% 54.01 40.51 46.77
37. Feb 28, 2022 0.70% -3.14% 0.58 17.99 3.23
38. Mar 31, 2022 7.47% 3.58% 36.12 6.11 14.85
39. Apr 30, 2022 -0.28% -8.80% 3.02 98.04 17.22
40. May 31, 2022 -2.31% 0.01% 14.25 1.21 4.15
41. Jun 30, 2022 3.72% -8.39% 5.12 90.21 -21.50
42. Jul 31, 2022 5.59% 9.11% 17.05 64.09 33.06
43. Aug 31, 2022 -4.24% -4.24% 32.52 28.62 30.51
44. Sep 30, 2022 -2.43% -9.34% 15.16 109.11 40.68
45. Oct 31, 2022 9.92% 7.99% 71.60 47.34 58.22
46. Nov 30, 2022 -1.33% 5.38% 7.79 18.23 -11.92
47. Dec 31, 2022 -2.91% -5.90% 19.08 49.04 30.59
48. Jan 31, 2023 -5.85% 6.18% 53.37 25.70 -37.03
49. Feb 28, 2023 -4.66% -2.61% 37.43 13.82 22.74
50. Mar 31, 2023 -0.36% 3.51% 3.30 5.76 -4.36
51. Apr 30, 2023 4.13% 1.46% 7.11 0.13 0.96
52. May 31, 2023 -0.99% 0.25% 5.98 0.74 2.10
53. Jun 30, 2023 -0.97% 4.71% 5.90 13.02 -8.76
54. Jul 31, 2023 5.35% 4.85% 15.16 13.99 14.56
55. Aug 31, 2023 -5.88% -1.77% 53.92 8.28 21.13
56. Sep 30, 2023 6.19% -4.87% 22.35 35.73 -28.26
57. Oct 31, 2023 6.22% -2.20% 22.67 10.92 -15.73
58. Nov 30, 2023 3.25% 8.92% 3.21 61.03 13.99
59. Dec 31, 2023 -4.45% 4.42% 34.96 11.00 -19.61
Total (Σ): 2,419.55 1,634.30 906.22

Show all

VarianceUNH = Σ(RUNH,tRUNH)2 ÷ (59 – 1)
= 2,419.55 ÷ (59 – 1)
= 41.72

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

CovarianceUNH, S&P 500 = Σ(RUNH,tRUNH)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 906.22 ÷ (59 – 1)
= 15.62


Systematic Risk (β) Estimation

Microsoft Excel
VarianceUNH 41.72
VarianceS&P 500 28.18
CovarianceUNH, S&P 500 15.62
Correlation coefficientUNH, S&P 5001 0.46
βUNH2 0.55
αUNH3 0.85%

Calculations

1 Correlation coefficientUNH, S&P 500
= CovarianceUNH, S&P 500 ÷ (Standard deviationUNH × Standard deviationS&P 500)
= 15.62 ÷ (6.46% × 5.31%)
= 0.46

2 βUNH
= CovarianceUNH, S&P 500 ÷ VarianceS&P 500
= 15.62 ÷ 28.18
= 0.55

3 αUNH
= AverageUNH – βUNH × AverageS&P 500
= 1.46%0.55 × 1.11%
= 0.85%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.67%
Expected rate of return on market portfolio2 E(RM) 13.79%
Systematic risk (β) of UnitedHealth Group Inc. common stock βUNH 0.55
 
Expected rate of return on UnitedHealth Group Inc. common stock3 E(RUNH) 9.73%

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]
= 4.67% + 0.55 [13.79%4.67%]
= 9.73%