Stock Analysis on Net

Fiserv Inc. (NASDAQ:FISV)

Capital Asset Pricing Model (CAPM)

Microsoft Excel LibreOffice Calc

Rates of Return

Fiserv Inc., monthly rates of return

Microsoft Excel LibreOffice Calc
Fiserv Inc. (FISV) Standard & Poor’s 500 (S&P 500)
t Date PriceFISV,t1 DividendFISV,t1 RFISV,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2016 $47.28 1,940.24
1. Feb 29, 2016 $47.81 1.12% 1,932.23 -0.41%
2. Mar 31, 2016 $51.29 7.28% 2,059.74 6.60%
3. Apr 30, 2016 $48.86 -4.74% 2,065.30 0.27%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2020 $115.18 20.65% 3,621.63 10.75%
59. Dec 31, 2020 $113.86 -1.15% 3,756.07 3.71%
Average (R): 1.66% 1.22%
Standard deviation: 5.74% 4.36%
Fiserv Inc. (FISV) Standard & Poor’s 500 (S&P 500)
t Date PriceFISV,t1 DividendFISV,t1 RFISV,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2016 $47.28 1,940.24
1. Feb 29, 2016 $47.81 1.12% 1,932.23 -0.41%
2. Mar 31, 2016 $51.29 7.28% 2,059.74 6.60%
3. Apr 30, 2016 $48.86 -4.74% 2,065.30 0.27%
4. May 31, 2016 $52.67 7.80% 2,096.95 1.53%
5. Jun 30, 2016 $54.37 3.23% 2,098.86 0.09%
6. Jul 31, 2016 $55.18 1.49% 2,173.60 3.56%
7. Aug 31, 2016 $51.53 -6.61% 2,170.95 -0.12%
8. Sep 30, 2016 $49.74 -3.47% 2,168.27 -0.12%
9. Oct 31, 2016 $49.24 -1.01% 2,126.15 -1.94%
10. Nov 30, 2016 $52.31 6.23% 2,198.81 3.42%
11. Dec 31, 2016 $53.14 1.59% 2,238.83 1.82%
12. Jan 31, 2017 $53.72 1.09% 2,278.87 1.79%
13. Feb 28, 2017 $57.70 7.41% 2,363.64 3.72%
14. Mar 31, 2017 $57.65 -0.09% 2,362.72 -0.04%
15. Apr 30, 2017 $59.57 3.33% 2,384.20 0.91%
16. May 31, 2017 $62.64 5.15% 2,411.80 1.16%
17. Jun 30, 2017 $61.17 -2.35% 2,423.41 0.48%
18. Jul 31, 2017 $64.25 5.04% 2,470.30 1.93%
19. Aug 31, 2017 $61.86 -3.72% 2,471.65 0.05%
20. Sep 30, 2017 $64.48 4.24% 2,519.36 1.93%
21. Oct 31, 2017 $64.71 0.36% 2,575.26 2.22%
22. Nov 30, 2017 $65.72 1.56% 2,647.58 2.81%
23. Dec 31, 2017 $65.57 -0.23% 2,673.61 0.98%
24. Jan 31, 2018 $70.42 7.40% 2,823.81 5.62%
25. Feb 28, 2018 $71.70 1.82% 2,713.83 -3.89%
26. Mar 31, 2018 $71.31 -0.54% 2,640.87 -2.69%
27. Apr 30, 2018 $70.86 -0.63% 2,648.05 0.27%
28. May 31, 2018 $72.60 2.46% 2,705.27 2.16%
29. Jun 30, 2018 $74.09 2.05% 2,718.37 0.48%
30. Jul 31, 2018 $75.48 1.88% 2,816.29 3.60%
31. Aug 31, 2018 $80.07 6.08% 2,901.52 3.03%
32. Sep 30, 2018 $82.38 2.88% 2,913.98 0.43%
33. Oct 31, 2018 $79.30 -3.74% 2,711.74 -6.94%
34. Nov 30, 2018 $79.13 -0.21% 2,760.17 1.79%
35. Dec 31, 2018 $73.49 -7.13% 2,506.85 -9.18%
36. Jan 31, 2019 $82.93 12.85% 2,704.10 7.87%
37. Feb 28, 2019 $84.69 2.12% 2,784.49 2.97%
38. Mar 31, 2019 $88.28 4.24% 2,834.40 1.79%
39. Apr 30, 2019 $87.24 -1.18% 2,945.83 3.93%
40. May 31, 2019 $85.86 -1.58% 2,752.06 -6.58%
41. Jun 30, 2019 $91.16 6.17% 2,941.76 6.89%
42. Jul 31, 2019 $105.43 15.65% 2,980.38 1.31%
43. Aug 31, 2019 $106.94 1.43% 2,926.46 -1.81%
44. Sep 30, 2019 $103.59 -3.13% 2,976.74 1.72%
45. Oct 31, 2019 $106.14 2.46% 3,037.56 2.04%
46. Nov 30, 2019 $116.24 9.52% 3,140.98 3.40%
47. Dec 31, 2019 $115.63 -0.52% 3,230.78 2.86%
48. Jan 31, 2020 $118.61 2.58% 3,225.52 -0.16%
49. Feb 29, 2020 $109.36 -7.80% 2,954.22 -8.41%
50. Mar 31, 2020 $94.99 -13.14% 2,584.59 -12.51%
51. Apr 30, 2020 $103.06 8.50% 2,912.43 12.68%
52. May 31, 2020 $106.77 3.60% 3,044.31 4.53%
53. Jun 30, 2020 $97.62 -8.57% 3,100.29 1.84%
54. Jul 31, 2020 $99.79 2.22% 3,271.12 5.51%
55. Aug 31, 2020 $99.58 -0.21% 3,500.31 7.01%
56. Sep 30, 2020 $103.05 3.48% 3,363.00 -3.92%
57. Oct 31, 2020 $95.47 -7.36% 3,269.96 -2.77%
58. Nov 30, 2020 $115.18 20.65% 3,621.63 10.75%
59. Dec 31, 2020 $113.86 -1.15% 3,756.07 3.71%
Average (R): 1.66% 1.22%
Standard deviation: 5.74% 4.36%

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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 FISV during period t

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


Variance and Covariance

Fiserv Inc., calculation of variance and covariance of returns

Microsoft Excel LibreOffice Calc
t Date RFISV,t RS&P 500,t (RFISV,tRFISV)2 (RS&P 500,tRS&P 500)2 (RFISV,tRFISV)×(RS&P 500,tRS&P 500)
1. Feb 29, 2016 1.12% -0.41% 0.29 2.67 0.88
2. Mar 31, 2016 7.28% 6.60% 31.59 28.93 30.23
3. Apr 30, 2016 -4.74% 0.27% 40.91 0.90 6.08
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2020 20.65% 10.75% 360.51 90.91 181.03
59. Dec 31, 2020 -1.15% 3.71% 7.86 6.21 -6.99
Total (Σ): 1,908.44 1,103.45 976.27
t Date RFISV,t RS&P 500,t (RFISV,tRFISV)2 (RS&P 500,tRS&P 500)2 (RFISV,tRFISV)×(RS&P 500,tRS&P 500)
1. Feb 29, 2016 1.12% -0.41% 0.29 2.67 0.88
2. Mar 31, 2016 7.28% 6.60% 31.59 28.93 30.23
3. Apr 30, 2016 -4.74% 0.27% 40.91 0.90 6.08
4. May 31, 2016 7.80% 1.53% 37.69 0.10 1.92
5. Jun 30, 2016 3.23% 0.09% 2.46 1.27 -1.77
6. Jul 31, 2016 1.49% 3.56% 0.03 5.48 -0.39
7. Aug 31, 2016 -6.61% -0.12% 68.44 1.80 11.10
8. Sep 30, 2016 -3.47% -0.12% 26.34 1.81 6.89
9. Oct 31, 2016 -1.01% -1.94% 7.09 10.00 8.42
10. Nov 30, 2016 6.23% 3.42% 20.94 4.83 10.06
11. Dec 31, 2016 1.59% 1.82% 0.01 0.36 -0.04
12. Jan 31, 2017 1.09% 1.79% 0.32 0.32 -0.32
13. Feb 28, 2017 7.41% 3.72% 33.07 6.25 14.38
14. Mar 31, 2017 -0.09% -0.04% 3.04 1.59 2.20
15. Apr 30, 2017 3.33% 0.91% 2.80 0.10 -0.52
16. May 31, 2017 5.15% 1.16% 12.22 0.00 -0.22
17. Jun 30, 2017 -2.35% 0.48% 16.04 0.55 2.96
18. Jul 31, 2017 5.04% 1.93% 11.40 0.51 2.41
19. Aug 31, 2017 -3.72% 0.05% 28.92 1.36 6.27
20. Sep 30, 2017 4.24% 1.93% 6.64 0.50 1.83
21. Oct 31, 2017 0.36% 2.22% 1.69 1.00 -1.30
22. Nov 30, 2017 1.56% 2.81% 0.01 2.52 -0.15
23. Dec 31, 2017 -0.23% 0.98% 3.56 0.06 0.45
24. Jan 31, 2018 7.40% 5.62% 32.93 19.34 25.24
25. Feb 28, 2018 1.82% -3.89% 0.03 26.16 -0.82
26. Mar 31, 2018 -0.54% -2.69% 4.85 15.28 8.61
27. Apr 30, 2018 -0.63% 0.27% 5.24 0.90 2.17
28. May 31, 2018 2.46% 2.16% 0.64 0.89 0.75
29. Jun 30, 2018 2.05% 0.48% 0.16 0.54 -0.29
30. Jul 31, 2018 1.88% 3.60% 0.05 5.67 0.52
31. Aug 31, 2018 6.08% 3.03% 19.56 3.26 7.99
32. Sep 30, 2018 2.88% 0.43% 1.50 0.63 -0.97
33. Oct 31, 2018 -3.74% -6.94% 29.13 66.59 44.04
34. Nov 30, 2018 -0.21% 1.79% 3.51 0.32 -1.06
35. Dec 31, 2018 -7.13% -9.18% 77.19 108.11 91.35
36. Jan 31, 2019 12.85% 7.87% 125.15 44.20 74.38
37. Feb 28, 2019 2.12% 2.97% 0.22 3.07 0.81
38. Mar 31, 2019 4.24% 1.79% 6.66 0.33 1.48
39. Apr 30, 2019 -1.18% 3.93% 8.04 7.35 -7.69
40. May 31, 2019 -1.58% -6.58% 10.50 60.81 25.27
41. Jun 30, 2019 6.17% 6.89% 20.38 32.18 25.61
42. Jul 31, 2019 15.65% 1.31% 195.88 0.01 1.30
43. Aug 31, 2019 1.43% -1.81% 0.05 9.18 0.68
44. Sep 30, 2019 -3.13% 1.72% 22.95 0.25 -2.39
45. Oct 31, 2019 2.46% 2.04% 0.65 0.68 0.66
46. Nov 30, 2019 9.52% 3.40% 61.74 4.77 17.17
47. Dec 31, 2019 -0.52% 2.86% 4.77 2.69 -3.58
48. Jan 31, 2020 2.58% -0.16% 0.84 1.91 -1.27
49. Feb 29, 2020 -7.80% -8.41% 89.43 92.76 91.08
50. Mar 31, 2020 -13.14% -12.51% 218.99 188.57 203.21
51. Apr 30, 2020 8.50% 12.68% 46.75 131.43 78.39
52. May 31, 2020 3.60% 4.53% 3.77 10.94 6.42
53. Jun 30, 2020 -8.57% 1.84% 104.61 0.38 -6.33
54. Jul 31, 2020 2.22% 5.51% 0.32 18.40 2.42
55. Aug 31, 2020 -0.21% 7.01% 3.49 33.48 -10.81
56. Sep 30, 2020 3.48% -3.92% 3.34 26.45 -9.39
57. Oct 31, 2020 -7.36% -2.77% 81.25 15.89 35.94
58. Nov 30, 2020 20.65% 10.75% 360.51 90.91 181.03
59. Dec 31, 2020 -1.15% 3.71% 7.86 6.21 -6.99
Total (Σ): 1,908.44 1,103.45 976.27

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VarianceFISV = Σ(RFISV,tRFISV)2 ÷ (59 – 1)
= 1,908.44 ÷ (59 – 1)
= 32.90

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,103.45 ÷ (59 – 1)
= 19.02

CovarianceFISV, S&P 500 = Σ(RFISV,tRFISV)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 976.27 ÷ (59 – 1)
= 16.83


Systematic Risk (β) Estimation

Microsoft Excel LibreOffice Calc
VarianceFISV 32.90
VarianceS&P 500 19.02
CovarianceFISV, S&P 500 16.83
Correlation coefficientFISV, S&P 5001 0.67
βFISV2 0.88
αFISV3 0.58%

Calculations

1 Correlation coefficientFISV, S&P 500
= CovarianceFISV, S&P 500 ÷ (Standard deviationFISV × Standard deviationS&P 500)
= 16.83 ÷ (5.74% × 4.36%)
= 0.67

2 βFISV
= CovarianceFISV, S&P 500 ÷ VarianceS&P 500
= 16.83 ÷ 19.02
= 0.88

3 αFISV
= AverageFISV – βFISV × AverageS&P 500
= 1.66%0.88 × 1.22%
= 0.58%


Expected Rate of Return

Microsoft Excel LibreOffice Calc
Assumptions
Rate of return on LT Treasury Composite1 RF 2.08%
Expected rate of return on market portfolio2 E(RM) 11.60%
Systematic risk (β) of Fiserv Inc. common stock βFISV 0.88
 
Expected rate of return on Fiserv Inc. common stock3 E(RFISV) 10.50%

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(RFISV) = RF + βFISV [E(RM) – RF]
= 2.08% + 0.88 [11.60%2.08%]
= 10.50%