Stock Analysis on Net

General Motors Co. (NYSE:GM)

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 General Motors Co. common stock.


Rates of Return

General Motors Co., monthly rates of return

Microsoft Excel
General Motors Co. (GM) Standard & Poor’s 500 (S&P 500)
t Date PriceGM,t1 DividendGM,t1 RGM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2019 $39.02 2,704.10
1. Feb 28, 2019 $39.48 1.18% 2,784.49 2.97%
2. Mar 31, 2019 $37.10 $0.38 -5.07% 2,834.40 1.79%
3. Apr 30, 2019 $38.95 4.99% 2,945.83 3.93%
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 $31.60 $0.09 12.38% 4,567.80 8.92%
59. Dec 31, 2023 $35.92 13.67% 4,769.83 4.42%
Average (R): 0.66% 1.11%
Standard deviation: 11.68% 5.31%
General Motors Co. (GM) Standard & Poor’s 500 (S&P 500)
t Date PriceGM,t1 DividendGM,t1 RGM,t2 PriceS&P 500,t RS&P 500,t3
Jan 31, 2019 $39.02 2,704.10
1. Feb 28, 2019 $39.48 1.18% 2,784.49 2.97%
2. Mar 31, 2019 $37.10 $0.38 -5.07% 2,834.40 1.79%
3. Apr 30, 2019 $38.95 4.99% 2,945.83 3.93%
4. May 31, 2019 $33.34 -14.40% 2,752.06 -6.58%
5. Jun 30, 2019 $38.53 $0.38 16.71% 2,941.76 6.89%
6. Jul 31, 2019 $40.34 4.70% 2,980.38 1.31%
7. Aug 31, 2019 $37.09 -8.06% 2,926.46 -1.81%
8. Sep 30, 2019 $37.48 $0.38 2.08% 2,976.74 1.72%
9. Oct 31, 2019 $37.16 -0.85% 3,037.56 2.04%
10. Nov 30, 2019 $36.00 -3.12% 3,140.98 3.40%
11. Dec 31, 2019 $36.60 $0.38 2.72% 3,230.78 2.86%
12. Jan 31, 2020 $33.39 -8.77% 3,225.52 -0.16%
13. Feb 29, 2020 $30.50 -8.66% 2,954.22 -8.41%
14. Mar 31, 2020 $20.78 $0.38 -30.62% 2,584.59 -12.51%
15. Apr 30, 2020 $22.29 7.27% 2,912.43 12.68%
16. May 31, 2020 $25.88 16.11% 3,044.31 4.53%
17. Jun 30, 2020 $25.30 -2.24% 3,100.29 1.84%
18. Jul 31, 2020 $24.89 -1.62% 3,271.12 5.51%
19. Aug 31, 2020 $29.63 19.04% 3,500.31 7.01%
20. Sep 30, 2020 $29.59 -0.13% 3,363.00 -3.92%
21. Oct 31, 2020 $34.53 16.69% 3,269.96 -2.77%
22. Nov 30, 2020 $43.84 26.96% 3,621.63 10.75%
23. Dec 31, 2020 $41.64 -5.02% 3,756.07 3.71%
24. Jan 31, 2021 $50.68 21.71% 3,714.24 -1.11%
25. Feb 28, 2021 $51.33 1.28% 3,811.15 2.61%
26. Mar 31, 2021 $57.46 11.94% 3,972.89 4.24%
27. Apr 30, 2021 $57.22 -0.42% 4,181.17 5.24%
28. May 31, 2021 $59.31 3.65% 4,204.11 0.55%
29. Jun 30, 2021 $59.17 -0.24% 4,297.50 2.22%
30. Jul 31, 2021 $56.84 -3.94% 4,395.26 2.27%
31. Aug 31, 2021 $49.01 -13.78% 4,522.68 2.90%
32. Sep 30, 2021 $52.71 7.55% 4,307.54 -4.76%
33. Oct 31, 2021 $54.43 3.26% 4,605.38 6.91%
34. Nov 30, 2021 $57.87 6.32% 4,567.00 -0.83%
35. Dec 31, 2021 $58.63 1.31% 4,766.18 4.36%
36. Jan 31, 2022 $52.73 -10.06% 4,515.55 -5.26%
37. Feb 28, 2022 $46.72 -11.40% 4,373.94 -3.14%
38. Mar 31, 2022 $43.74 -6.38% 4,530.41 3.58%
39. Apr 30, 2022 $37.91 -13.33% 4,131.93 -8.80%
40. May 31, 2022 $38.68 2.03% 4,132.15 0.01%
41. Jun 30, 2022 $31.76 -17.89% 3,785.38 -8.39%
42. Jul 31, 2022 $36.26 14.17% 4,130.29 9.11%
43. Aug 31, 2022 $38.21 $0.09 5.63% 3,955.00 -4.24%
44. Sep 30, 2022 $32.09 -16.02% 3,585.62 -9.34%
45. Oct 31, 2022 $39.25 22.31% 3,871.98 7.99%
46. Nov 30, 2022 $40.56 3.34% 4,080.11 5.38%
47. Dec 31, 2022 $33.64 $0.09 -16.84% 3,839.50 -5.90%
48. Jan 31, 2023 $39.32 16.88% 4,076.60 6.18%
49. Feb 28, 2023 $38.74 -1.48% 3,970.15 -2.61%
50. Mar 31, 2023 $36.68 $0.09 -5.09% 4,109.31 3.51%
51. Apr 30, 2023 $33.04 -9.92% 4,169.48 1.46%
52. May 31, 2023 $32.41 -1.91% 4,179.83 0.25%
53. Jun 30, 2023 $38.56 $0.09 19.25% 4,376.86 4.71%
54. Jul 31, 2023 $38.37 -0.49% 4,588.96 4.85%
55. Aug 31, 2023 $33.51 $0.09 -12.43% 4,507.66 -1.77%
56. Sep 30, 2023 $32.97 -1.61% 4,288.05 -4.87%
57. Oct 31, 2023 $28.20 -14.47% 4,193.80 -2.20%
58. Nov 30, 2023 $31.60 $0.09 12.38% 4,567.80 8.92%
59. Dec 31, 2023 $35.92 13.67% 4,769.83 4.42%
Average (R): 0.66% 1.11%
Standard deviation: 11.68% 5.31%

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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 GM during period t

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


Variance and Covariance

General Motors Co., calculation of variance and covariance of returns

Microsoft Excel
t Date RGM,t RS&P 500,t (RGM,tRGM)2 (RS&P 500,tRS&P 500)2 (RGM,tRGM)×(RS&P 500,tRS&P 500)
1. Feb 28, 2019 1.18% 2.97% 0.27 3.49 0.97
2. Mar 31, 2019 -5.07% 1.79% 32.78 0.47 -3.93
3. Apr 30, 2019 4.99% 3.93% 18.73 7.98 12.23
. . . . . . .
. . . . . . .
. . . . . . .
58. Nov 30, 2023 12.38% 8.92% 137.28 61.03 91.53
59. Dec 31, 2023 13.67% 4.42% 169.30 11.00 43.16
Total (Σ): 7,916.60 1,634.30 2,416.18
t Date RGM,t RS&P 500,t (RGM,tRGM)2 (RS&P 500,tRS&P 500)2 (RGM,tRGM)×(RS&P 500,tRS&P 500)
1. Feb 28, 2019 1.18% 2.97% 0.27 3.49 0.97
2. Mar 31, 2019 -5.07% 1.79% 32.78 0.47 -3.93
3. Apr 30, 2019 4.99% 3.93% 18.73 7.98 12.23
4. May 31, 2019 -14.40% -6.58% 226.87 59.04 115.73
5. Jun 30, 2019 16.71% 6.89% 257.52 33.49 92.87
6. Jul 31, 2019 4.70% 1.31% 16.31 0.04 0.84
7. Aug 31, 2019 -8.06% -1.81% 75.96 8.50 25.41
8. Sep 30, 2019 2.08% 1.72% 2.01 0.37 0.87
9. Oct 31, 2019 -0.85% 2.04% 2.29 0.88 -1.42
10. Nov 30, 2019 -3.12% 3.40% 14.29 5.28 -8.69
11. Dec 31, 2019 2.72% 2.86% 4.26 3.07 3.62
12. Jan 31, 2020 -8.77% -0.16% 88.92 1.61 11.96
13. Feb 29, 2020 -8.66% -8.41% 86.76 90.57 88.65
14. Mar 31, 2020 -30.62% -12.51% 978.58 185.44 425.99
15. Apr 30, 2020 7.27% 12.68% 43.66 134.06 76.50
16. May 31, 2020 16.11% 4.53% 238.60 11.71 52.86
17. Jun 30, 2020 -2.24% 1.84% 8.41 0.54 -2.13
18. Jul 31, 2020 -1.62% 5.51% 5.20 19.40 -10.04
19. Aug 31, 2020 19.04% 7.01% 337.99 34.82 108.48
20. Sep 30, 2020 -0.13% -3.92% 0.63 25.29 3.99
21. Oct 31, 2020 16.69% -2.77% 257.14 15.00 -62.10
22. Nov 30, 2020 26.96% 10.75% 691.84 93.10 253.79
23. Dec 31, 2020 -5.02% 3.71% 32.23 6.79 -14.80
24. Jan 31, 2021 21.71% -1.11% 443.13 4.93 -46.72
25. Feb 28, 2021 1.28% 2.61% 0.39 2.26 0.94
26. Mar 31, 2021 11.94% 4.24% 127.31 9.85 35.41
27. Apr 30, 2021 -0.42% 5.24% 1.16 17.11 -4.45
28. May 31, 2021 3.65% 0.55% 8.96 0.31 -1.67
29. Jun 30, 2021 -0.24% 2.22% 0.80 1.24 -1.00
30. Jul 31, 2021 -3.94% 2.27% 21.13 1.37 -5.37
31. Aug 31, 2021 -13.78% 2.90% 208.36 3.22 -25.88
32. Sep 30, 2021 7.55% -4.76% 47.48 34.37 -40.40
33. Oct 31, 2021 3.26% 6.91% 6.78 33.74 15.12
34. Nov 30, 2021 6.32% -0.83% 32.04 3.76 -10.98
35. Dec 31, 2021 1.31% 4.36% 0.43 10.60 2.13
36. Jan 31, 2022 -10.06% -5.26% 114.97 40.51 68.24
37. Feb 28, 2022 -11.40% -3.14% 145.37 17.99 51.14
38. Mar 31, 2022 -6.38% 3.58% 49.53 6.11 -17.39
39. Apr 30, 2022 -13.33% -8.80% 195.66 98.04 138.50
40. May 31, 2022 2.03% 0.01% 1.88 1.21 -1.51
41. Jun 30, 2022 -17.89% -8.39% 344.09 90.21 176.18
42. Jul 31, 2022 14.17% 9.11% 182.51 64.09 108.15
43. Aug 31, 2022 5.63% -4.24% 24.67 28.62 -26.57
44. Sep 30, 2022 -16.02% -9.34% 278.09 109.11 174.19
45. Oct 31, 2022 22.31% 7.99% 468.85 47.34 148.98
46. Nov 30, 2022 3.34% 5.38% 7.17 18.23 11.44
47. Dec 31, 2022 -16.84% -5.90% 306.20 49.04 122.54
48. Jan 31, 2023 16.88% 6.18% 263.26 25.70 82.25
49. Feb 28, 2023 -1.48% -2.61% 4.56 13.82 7.93
50. Mar 31, 2023 -5.09% 3.51% 33.00 5.76 -13.78
51. Apr 30, 2023 -9.92% 1.46% 112.00 0.13 -3.79
52. May 31, 2023 -1.91% 0.25% 6.58 0.74 2.20
53. Jun 30, 2023 19.25% 4.71% 345.74 13.02 67.09
54. Jul 31, 2023 -0.49% 4.85% 1.33 13.99 -4.31
55. Aug 31, 2023 -12.43% -1.77% 171.37 8.28 37.67
56. Sep 30, 2023 -1.61% -4.87% 5.16 35.73 13.57
57. Oct 31, 2023 -14.47% -2.20% 228.82 10.92 49.98
58. Nov 30, 2023 12.38% 8.92% 137.28 61.03 91.53
59. Dec 31, 2023 13.67% 4.42% 169.30 11.00 43.16
Total (Σ): 7,916.60 1,634.30 2,416.18

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VarianceGM = Σ(RGM,tRGM)2 ÷ (59 – 1)
= 7,916.60 ÷ (59 – 1)
= 136.49

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

CovarianceGM, S&P 500 = Σ(RGM,tRGM)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 2,416.18 ÷ (59 – 1)
= 41.66


Systematic Risk (β) Estimation

Microsoft Excel
VarianceGM 136.49
VarianceS&P 500 28.18
CovarianceGM, S&P 500 41.66
Correlation coefficientGM, S&P 5001 0.67
βGM2 1.48
αGM3 -0.98%

Calculations

1 Correlation coefficientGM, S&P 500
= CovarianceGM, S&P 500 ÷ (Standard deviationGM × Standard deviationS&P 500)
= 41.66 ÷ (11.68% × 5.31%)
= 0.67

2 βGM
= CovarianceGM, S&P 500 ÷ VarianceS&P 500
= 41.66 ÷ 28.18
= 1.48

3 αGM
= AverageGM – βGM × AverageS&P 500
= 0.66%1.48 × 1.11%
= -0.98%


Expected Rate of Return

Microsoft Excel
Assumptions
Rate of return on LT Treasury Composite1 RF 4.43%
Expected rate of return on market portfolio2 E(RM) 13.60%
Systematic risk (β) of General Motors Co. common stock βGM 1.48
 
Expected rate of return on General Motors Co. common stock3 E(RGM) 17.99%

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(RGM) = RF + βGM [E(RM) – RF]
= 4.43% + 1.48 [13.60%4.43%]
= 17.99%