Capital Asset Pricing Model (CAPM)
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
| 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 | $35.92 | 13.67% | 4,769.83 | 4.42% | |
| Average (R): | 0.66% | 1.11% | ||||
| Standard deviation: | 11.68% | 5.31% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of 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
| t | Date | RGM,t | RS&P 500,t | (RGM,t–RGM)2 | (RS&P 500,t–RS&P 500)2 | (RGM,t–RGM)×(RS&P 500,t–RS&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,t–RGM)2 | (RS&P 500,t–RS&P 500)2 | (RGM,t–RGM)×(RS&P 500,t–RS&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 | |||
Show all
VarianceGM = Σ(RGM,t–RGM)2 ÷ (59 – 1)
= 7,916.60 ÷ (59 – 1)
= 136.49
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceGM, S&P 500 = Σ(RGM,t–RGM)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,416.18 ÷ (59 – 1)
= 41.66
Systematic Risk (β) Estimation
| 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
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.65% |
| Expected rate of return on market portfolio2 | E(RM) | 13.79% |
| Systematic risk (β) of General Motors Co. common stock | βGM | 1.48 |
| Expected rate of return on General Motors Co. common stock3 | E(RGM) | 18.16% |
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).
3 E(RGM) = RF + βGM [E(RM) – RF]
= 4.65% + 1.48 [13.79% – 4.65%]
= 18.16%