Stock Analysis on Net

Northrop Grumman Corp. (NYSE:NOC)

Capital Asset Pricing Model (CAPM) 

Microsoft Excel

Rates of Return

Northrop Grumman Corp., monthly rates of return

Microsoft Excel
Northrop Grumman Corp. (NOC) Standard & Poor’s 500 (S&P 500)
t Date PriceNOC,t1 DividendNOC,t1 RNOC,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2018 $340.53 2,823.81
1. Feb 28, 2018 $350.04 2.79% 2,713.83 -3.89%
2. Mar 31, 2018 $349.12 $1.10 0.05% 2,640.87 -2.69%
3. Apr 30, 2018 $322.04 -7.76% 2,648.05 0.27%
. . . . . . .
. . . . . . .
. . . . . . .
57. Oct 31, 2022 $549.01 16.73% 3,871.98 7.99%
58. Nov 30, 2022 $533.29 $1.73 -2.55% 4,080.11 5.38%
Average (R): 1.15% 0.78%
Standard deviation: 6.92% 5.38%
Northrop Grumman Corp. (NOC) Standard & Poor’s 500 (S&P 500)
t Date PriceNOC,t1 DividendNOC,t1 RNOC,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2018 $340.53 2,823.81
1. Feb 28, 2018 $350.04 2.79% 2,713.83 -3.89%
2. Mar 31, 2018 $349.12 $1.10 0.05% 2,640.87 -2.69%
3. Apr 30, 2018 $322.04 -7.76% 2,648.05 0.27%
4. May 31, 2018 $327.25 1.62% 2,705.27 2.16%
5. Jun 30, 2018 $307.70 $1.20 -5.61% 2,718.37 0.48%
6. Jul 31, 2018 $300.49 -2.34% 2,816.29 3.60%
7. Aug 31, 2018 $298.49 $1.20 -0.27% 2,901.52 3.03%
8. Sep 30, 2018 $317.37 6.33% 2,913.98 0.43%
9. Oct 31, 2018 $261.95 -17.46% 2,711.74 -6.94%
10. Nov 30, 2018 $259.88 $1.20 -0.33% 2,760.17 1.79%
11. Dec 31, 2018 $244.90 -5.76% 2,506.85 -9.18%
12. Jan 31, 2019 $275.55 12.52% 2,704.10 7.87%
13. Feb 28, 2019 $289.96 $1.20 5.67% 2,784.49 2.97%
14. Mar 31, 2019 $269.60 -7.02% 2,834.40 1.79%
15. Apr 30, 2019 $289.91 7.53% 2,945.83 3.93%
16. May 31, 2019 $303.25 $1.32 5.06% 2,752.06 -6.58%
17. Jun 30, 2019 $323.11 6.55% 2,941.76 6.89%
18. Jul 31, 2019 $345.57 6.95% 2,980.38 1.31%
19. Aug 31, 2019 $367.87 6.45% 2,926.46 -1.81%
20. Sep 30, 2019 $374.79 $1.32 2.24% 2,976.74 1.72%
21. Oct 31, 2019 $352.48 -5.95% 3,037.56 2.04%
22. Nov 30, 2019 $351.77 $1.32 0.17% 3,140.98 3.40%
23. Dec 31, 2019 $343.97 -2.22% 3,230.78 2.86%
24. Jan 31, 2020 $374.57 8.90% 3,225.52 -0.16%
25. Feb 29, 2020 $328.84 $1.32 -11.86% 2,954.22 -8.41%
26. Mar 31, 2020 $302.55 -7.99% 2,584.59 -12.51%
27. Apr 30, 2020 $330.67 9.29% 2,912.43 12.68%
28. May 31, 2020 $335.20 $1.45 1.81% 3,044.31 4.53%
29. Jun 30, 2020 $307.44 -8.28% 3,100.29 1.84%
30. Jul 31, 2020 $325.01 5.71% 3,271.12 5.51%
31. Aug 31, 2020 $342.61 $1.45 5.86% 3,500.31 7.01%
32. Sep 30, 2020 $315.49 -7.92% 3,363.00 -3.92%
33. Oct 31, 2020 $289.82 -8.14% 3,269.96 -2.77%
34. Nov 30, 2020 $302.26 $1.45 4.79% 3,621.63 10.75%
35. Dec 31, 2020 $304.72 0.81% 3,756.07 3.71%
36. Jan 31, 2021 $286.61 -5.94% 3,714.24 -1.11%
37. Feb 28, 2021 $291.66 $1.45 2.27% 3,811.15 2.61%
38. Mar 31, 2021 $323.64 10.96% 3,972.89 4.24%
39. Apr 30, 2021 $354.44 9.52% 4,181.17 5.24%
40. May 31, 2021 $365.87 $1.57 3.67% 4,204.11 0.55%
41. Jun 30, 2021 $363.43 -0.67% 4,297.50 2.22%
42. Jul 31, 2021 $363.02 -0.11% 4,395.26 2.27%
43. Aug 31, 2021 $367.70 $1.57 1.72% 4,522.68 2.90%
44. Sep 30, 2021 $360.15 -2.05% 4,307.54 -4.76%
45. Oct 31, 2021 $357.22 -0.81% 4,605.38 6.91%
46. Nov 30, 2021 $348.80 $1.57 -1.92% 4,567.00 -0.83%
47. Dec 31, 2021 $387.07 10.97% 4,766.18 4.36%
48. Jan 31, 2022 $369.90 -4.44% 4,515.55 -5.26%
49. Feb 28, 2022 $442.14 $1.57 19.95% 4,373.94 -3.14%
50. Mar 31, 2022 $447.22 1.15% 4,530.41 3.58%
51. Apr 30, 2022 $439.40 -1.75% 4,131.93 -8.80%
52. May 31, 2022 $467.97 $1.73 6.90% 4,132.15 0.01%
53. Jun 30, 2022 $478.57 2.27% 3,785.38 -8.39%
54. Jul 31, 2022 $478.90 0.07% 4,130.29 9.11%
55. Aug 31, 2022 $477.99 $1.73 0.17% 3,955.00 -4.24%
56. Sep 30, 2022 $470.32 -1.60% 3,585.62 -9.34%
57. Oct 31, 2022 $549.01 16.73% 3,871.98 7.99%
58. Nov 30, 2022 $533.29 $1.73 -2.55% 4,080.11 5.38%
Average (R): 1.15% 0.78%
Standard deviation: 6.92% 5.38%

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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 NOC during period t

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


Variance and Covariance

Northrop Grumman Corp., calculation of variance and covariance of returns

Microsoft Excel
t Date RNOC,t RS&P 500,t (RNOC,tRNOC)2 (RS&P 500,tRS&P 500)2 (RNOC,tRNOC)×(RS&P 500,tRS&P 500)
1. Feb 28, 2018 2.79% -3.89% 2.70 21.85 -7.68
2. Mar 31, 2018 0.05% -2.69% 1.21 12.03 3.81
3. Apr 30, 2018 -7.76% 0.27% 79.33 0.26 4.52
. . . . . . .
. . . . . . .
. . . . . . .
57. Oct 31, 2022 16.73% 7.99% 242.77 51.93 112.29
58. Nov 30, 2022 -2.55% 5.38% 13.68 21.12 -16.99
Total (Σ): 2,730.15 1,647.65 983.97
t Date RNOC,t RS&P 500,t (RNOC,tRNOC)2 (RS&P 500,tRS&P 500)2 (RNOC,tRNOC)×(RS&P 500,tRS&P 500)
1. Feb 28, 2018 2.79% -3.89% 2.70 21.85 -7.68
2. Mar 31, 2018 0.05% -2.69% 1.21 12.03 3.81
3. Apr 30, 2018 -7.76% 0.27% 79.33 0.26 4.52
4. May 31, 2018 1.62% 2.16% 0.22 1.91 0.65
5. Jun 30, 2018 -5.61% 0.48% 45.66 0.09 2.00
6. Jul 31, 2018 -2.34% 3.60% 12.20 7.97 -9.86
7. Aug 31, 2018 -0.27% 3.03% 2.01 5.05 -3.18
8. Sep 30, 2018 6.33% 0.43% 26.78 0.12 -1.81
9. Oct 31, 2018 -17.46% -6.94% 346.42 59.60 143.69
10. Nov 30, 2018 -0.33% 1.79% 2.20 1.01 -1.49
11. Dec 31, 2018 -5.76% -9.18% 47.81 99.15 68.85
12. Jan 31, 2019 12.52% 7.87% 129.17 50.25 80.56
13. Feb 28, 2019 5.67% 2.97% 20.39 4.81 9.90
14. Mar 31, 2019 -7.02% 1.79% 66.78 1.03 -8.27
15. Apr 30, 2019 7.53% 3.93% 40.75 9.93 20.12
16. May 31, 2019 5.06% -6.58% 15.26 54.13 -28.74
17. Jun 30, 2019 6.55% 6.89% 29.15 37.37 33.01
18. Jul 31, 2019 6.95% 1.31% 33.65 0.28 3.09
19. Aug 31, 2019 6.45% -1.81% 28.12 6.70 -13.73
20. Sep 30, 2019 2.24% 1.72% 1.19 0.88 1.02
21. Oct 31, 2019 -5.95% 2.04% 50.45 1.60 -8.97
22. Nov 30, 2019 0.17% 3.40% 0.95 6.89 -2.56
23. Dec 31, 2019 -2.22% 2.86% 11.34 4.32 -7.00
24. Jan 31, 2020 8.90% -0.16% 60.00 0.89 -7.30
25. Feb 29, 2020 -11.86% -8.41% 169.16 84.47 119.54
26. Mar 31, 2020 -7.99% -12.51% 83.63 176.67 121.55
27. Apr 30, 2020 9.29% 12.68% 66.33 141.72 96.96
28. May 31, 2020 1.81% 4.53% 0.43 14.05 2.47
29. Jun 30, 2020 -8.28% 1.84% 88.95 1.12 -9.99
30. Jul 31, 2020 5.71% 5.51% 20.84 22.38 21.59
31. Aug 31, 2020 5.86% 7.01% 22.20 38.77 29.34
32. Sep 30, 2020 -7.92% -3.92% 82.19 22.11 42.63
33. Oct 31, 2020 -8.14% -2.77% 86.24 12.58 32.93
34. Nov 30, 2020 4.79% 10.75% 13.27 99.50 36.33
35. Dec 31, 2020 0.81% 3.71% 0.11 8.60 -0.99
36. Jan 31, 2021 -5.94% -1.11% 50.31 3.59 13.43
37. Feb 28, 2021 2.27% 2.61% 1.25 3.35 2.05
38. Mar 31, 2021 10.96% 4.24% 96.33 12.00 34.00
39. Apr 30, 2021 9.52% 5.24% 70.00 19.92 37.34
40. May 31, 2021 3.67% 0.55% 6.34 0.05 -0.58
41. Jun 30, 2021 -0.67% 2.22% 3.30 2.08 -2.62
42. Jul 31, 2021 -0.11% 2.27% 1.59 2.24 -1.89
43. Aug 31, 2021 1.72% 2.90% 0.33 4.49 1.21
44. Sep 30, 2021 -2.05% -4.76% 10.26 30.66 17.74
45. Oct 31, 2021 -0.81% 6.91% 3.86 37.63 -12.05
46. Nov 30, 2021 -1.92% -0.83% 9.41 2.60 4.95
47. Dec 31, 2021 10.97% 4.36% 96.47 12.83 35.18
48. Jan 31, 2022 -4.44% -5.26% 31.20 36.46 33.73
49. Feb 28, 2022 19.95% -3.14% 353.59 15.33 -73.63
50. Mar 31, 2022 1.15% 3.58% 0.00 7.83 0.00
51. Apr 30, 2022 -1.75% -8.80% 8.40 91.69 27.76
52. May 31, 2022 6.90% 0.01% 33.01 0.60 -4.45
53. Jun 30, 2022 2.27% -8.39% 1.24 84.12 -10.23
54. Jul 31, 2022 0.07% 9.11% 1.17 69.42 -9.01
55. Aug 31, 2022 0.17% -4.24% 0.96 25.24 4.92
56. Sep 30, 2022 -1.60% -9.34% 7.59 102.40 27.87
57. Oct 31, 2022 16.73% 7.99% 242.77 51.93 112.29
58. Nov 30, 2022 -2.55% 5.38% 13.68 21.12 -16.99
Total (Σ): 2,730.15 1,647.65 983.97

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VarianceNOC = Σ(RNOC,tRNOC)2 ÷ (58 – 1)
= 2,730.15 ÷ (58 – 1)
= 47.90

VarianceS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (58 – 1)
= 1,647.65 ÷ (58 – 1)
= 28.91

CovarianceNOC, S&P 500 = Σ(RNOC,tRNOC)×(RS&P 500,tRS&P 500) ÷ (58 – 1)
= 983.97 ÷ (58 – 1)
= 17.26


Systematic Risk (β) Estimation

Microsoft Excel
VarianceNOC 47.90
VarianceS&P 500 28.91
CovarianceNOC, S&P 500 17.26
Correlation coefficientNOC, S&P 5001 0.46
βNOC2 0.60
αNOC3 0.68%

Calculations

1 Correlation coefficientNOC, S&P 500
= CovarianceNOC, S&P 500 ÷ (Standard deviationNOC × Standard deviationS&P 500)
= 17.26 ÷ (6.92% × 5.38%)
= 0.46

2 βNOC
= CovarianceNOC, S&P 500 ÷ VarianceS&P 500
= 17.26 ÷ 28.91
= 0.60

3 αNOC
= AverageNOC – βNOC × AverageS&P 500
= 1.15%0.60 × 0.78%
= 0.68%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 3.72%
Expected rate of return on market portfolio2 E(RM) 12.62%
Systematic risk (β) of Northrop Grumman Corp. common stock βNOC 0.60
 
Expected rate of return on Northrop Grumman Corp. common stock3 E(RNOC) 9.03%

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(RNOC) = RF + βNOC [E(RM) – RF]
= 3.72% + 0.60 [12.62%3.72%]
= 9.03%