Stock Analysis on Net

UnitedHealth Group Inc. (NYSE:UNH)

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 UnitedHealth Group Inc. common stock.


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%

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 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

Show all

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 4.82%
Expected rate of return on market portfolio2 E(RM) 15.01%
Systematic risk (β) of UnitedHealth Group Inc. common stock βUNH 0.62
 
Expected rate of return on UnitedHealth Group Inc. common stock3 E(RUNH) 11.15%

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]
= 4.82% + 0.62 [15.01%4.82%]
= 11.15%