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 Dollar General Corp. common stock.
Rates of Return
Dollar General Corp., monthly rates of return
| Dollar General Corp. (DG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceDG,t1 | DividendDG,t1 | RDG,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Feb 28, 2017 | $73.02 | 2,363.64 | ||||
| 1. | Mar 31, 2017 | $69.73 | -4.51% | 2,362.72 | -0.04% | |
| 2. | Apr 30, 2017 | $72.71 | $0.26 | 4.65% | 2,384.20 | 0.91% |
| 3. | May 31, 2017 | $73.39 | 0.94% | 2,411.80 | 1.16% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Dec 31, 2022 | $246.25 | $0.55 | -3.47% | 3,839.50 | -5.90% |
| 71. | Jan 31, 2023 | $233.60 | -5.14% | 4,076.60 | 6.18% | |
| Average (R): | 1.91% | 0.90% | ||||
| Standard deviation: | 6.00% | 5.01% | ||||
| Dollar General Corp. (DG) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceDG,t1 | DividendDG,t1 | RDG,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Feb 28, 2017 | $73.02 | 2,363.64 | ||||
| 1. | Mar 31, 2017 | $69.73 | -4.51% | 2,362.72 | -0.04% | |
| 2. | Apr 30, 2017 | $72.71 | $0.26 | 4.65% | 2,384.20 | 0.91% |
| 3. | May 31, 2017 | $73.39 | 0.94% | 2,411.80 | 1.16% | |
| 4. | Jun 30, 2017 | $72.09 | -1.77% | 2,423.41 | 0.48% | |
| 5. | Jul 31, 2017 | $75.16 | $0.26 | 4.62% | 2,470.30 | 1.93% |
| 6. | Aug 31, 2017 | $72.56 | -3.46% | 2,471.65 | 0.05% | |
| 7. | Sep 30, 2017 | $81.05 | 11.70% | 2,519.36 | 1.93% | |
| 8. | Oct 31, 2017 | $80.84 | $0.26 | 0.06% | 2,575.26 | 2.22% |
| 9. | Nov 30, 2017 | $88.08 | 8.96% | 2,647.58 | 2.81% | |
| 10. | Dec 31, 2017 | $93.01 | 5.60% | 2,673.61 | 0.98% | |
| 11. | Jan 31, 2018 | $103.12 | $0.26 | 11.15% | 2,823.81 | 5.62% |
| 12. | Feb 28, 2018 | $94.59 | -8.27% | 2,713.83 | -3.89% | |
| 13. | Mar 31, 2018 | $93.55 | -1.10% | 2,640.87 | -2.69% | |
| 14. | Apr 30, 2018 | $96.53 | $0.29 | 3.50% | 2,648.05 | 0.27% |
| 15. | May 31, 2018 | $87.48 | -9.38% | 2,705.27 | 2.16% | |
| 16. | Jun 30, 2018 | $98.60 | 12.71% | 2,718.37 | 0.48% | |
| 17. | Jul 31, 2018 | $98.15 | $0.29 | -0.16% | 2,816.29 | 3.60% |
| 18. | Aug 31, 2018 | $107.73 | 9.76% | 2,901.52 | 3.03% | |
| 19. | Sep 30, 2018 | $109.30 | 1.46% | 2,913.98 | 0.43% | |
| 20. | Oct 31, 2018 | $111.38 | $0.29 | 2.17% | 2,711.74 | -6.94% |
| 21. | Nov 30, 2018 | $110.99 | -0.35% | 2,760.17 | 1.79% | |
| 22. | Dec 31, 2018 | $108.08 | -2.62% | 2,506.85 | -9.18% | |
| 23. | Jan 31, 2019 | $115.43 | $0.29 | 7.07% | 2,704.10 | 7.87% |
| 24. | Feb 28, 2019 | $118.46 | 2.62% | 2,784.49 | 2.97% | |
| 25. | Mar 31, 2019 | $119.30 | 0.71% | 2,834.40 | 1.79% | |
| 26. | Apr 30, 2019 | $126.09 | $0.32 | 5.96% | 2,945.83 | 3.93% |
| 27. | May 31, 2019 | $127.28 | 0.94% | 2,752.06 | -6.58% | |
| 28. | Jun 30, 2019 | $135.16 | 6.19% | 2,941.76 | 6.89% | |
| 29. | Jul 31, 2019 | $134.02 | $0.32 | -0.61% | 2,980.38 | 1.31% |
| 30. | Aug 31, 2019 | $156.09 | 16.47% | 2,926.46 | -1.81% | |
| 31. | Sep 30, 2019 | $158.94 | 1.83% | 2,976.74 | 1.72% | |
| 32. | Oct 31, 2019 | $160.34 | $0.32 | 1.08% | 3,037.56 | 2.04% |
| 33. | Nov 30, 2019 | $157.36 | -1.86% | 3,140.98 | 3.40% | |
| 34. | Dec 31, 2019 | $155.98 | -0.88% | 3,230.78 | 2.86% | |
| 35. | Jan 31, 2020 | $153.41 | $0.32 | -1.44% | 3,225.52 | -0.16% |
| 36. | Feb 29, 2020 | $150.30 | -2.03% | 2,954.22 | -8.41% | |
| 37. | Mar 31, 2020 | $151.01 | 0.47% | 2,584.59 | -12.51% | |
| 38. | Apr 30, 2020 | $175.30 | $0.36 | 16.32% | 2,912.43 | 12.68% |
| 39. | May 31, 2020 | $191.51 | 9.25% | 3,044.31 | 4.53% | |
| 40. | Jun 30, 2020 | $190.51 | -0.52% | 3,100.29 | 1.84% | |
| 41. | Jul 31, 2020 | $190.40 | $0.36 | 0.13% | 3,271.12 | 5.51% |
| 42. | Aug 31, 2020 | $201.88 | 6.03% | 3,500.31 | 7.01% | |
| 43. | Sep 30, 2020 | $209.62 | 3.83% | 3,363.00 | -3.92% | |
| 44. | Oct 31, 2020 | $208.71 | $0.36 | -0.26% | 3,269.96 | -2.77% |
| 45. | Nov 30, 2020 | $218.58 | 4.73% | 3,621.63 | 10.75% | |
| 46. | Dec 31, 2020 | $210.30 | -3.79% | 3,756.07 | 3.71% | |
| 47. | Jan 31, 2021 | $194.61 | $0.36 | -7.29% | 3,714.24 | -1.11% |
| 48. | Feb 28, 2021 | $188.99 | -2.89% | 3,811.15 | 2.61% | |
| 49. | Mar 31, 2021 | $202.62 | 7.21% | 3,972.89 | 4.24% | |
| 50. | Apr 30, 2021 | $214.75 | $0.42 | 6.19% | 4,181.17 | 5.24% |
| 51. | May 31, 2021 | $202.96 | -5.49% | 4,204.11 | 0.55% | |
| 52. | Jun 30, 2021 | $216.39 | 6.62% | 4,297.50 | 2.22% | |
| 53. | Jul 31, 2021 | $232.64 | $0.42 | 7.70% | 4,395.26 | 2.27% |
| 54. | Aug 31, 2021 | $222.91 | -4.18% | 4,522.68 | 2.90% | |
| 55. | Sep 30, 2021 | $212.14 | -4.83% | 4,307.54 | -4.76% | |
| 56. | Oct 31, 2021 | $221.52 | $0.42 | 4.62% | 4,605.38 | 6.91% |
| 57. | Nov 30, 2021 | $221.30 | -0.10% | 4,567.00 | -0.83% | |
| 58. | Dec 31, 2021 | $235.83 | 6.57% | 4,766.18 | 4.36% | |
| 59. | Jan 31, 2022 | $208.48 | $0.42 | -11.42% | 4,515.55 | -5.26% |
| 60. | Feb 28, 2022 | $198.34 | -4.86% | 4,373.94 | -3.14% | |
| 61. | Mar 31, 2022 | $222.63 | 12.25% | 4,530.41 | 3.58% | |
| 62. | Apr 30, 2022 | $237.53 | $0.55 | 6.94% | 4,131.93 | -8.80% |
| 63. | May 31, 2022 | $220.34 | -7.24% | 4,132.15 | 0.01% | |
| 64. | Jun 30, 2022 | $245.44 | 11.39% | 3,785.38 | -8.39% | |
| 65. | Jul 31, 2022 | $248.43 | $0.55 | 1.44% | 4,130.29 | 9.11% |
| 66. | Aug 31, 2022 | $237.42 | -4.43% | 3,955.00 | -4.24% | |
| 67. | Sep 30, 2022 | $239.86 | 1.03% | 3,585.62 | -9.34% | |
| 68. | Oct 31, 2022 | $255.05 | $0.55 | 6.56% | 3,871.98 | 7.99% |
| 69. | Nov 30, 2022 | $255.68 | 0.25% | 4,080.11 | 5.38% | |
| 70. | Dec 31, 2022 | $246.25 | $0.55 | -3.47% | 3,839.50 | -5.90% |
| 71. | Jan 31, 2023 | $233.60 | -5.14% | 4,076.60 | 6.18% | |
| Average (R): | 1.91% | 0.90% | ||||
| Standard deviation: | 6.00% | 5.01% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of DG during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Dollar General Corp., calculation of variance and covariance of returns
| t | Date | RDG,t | RS&P 500,t | (RDG,t–RDG)2 | (RS&P 500,t–RS&P 500)2 | (RDG,t–RDG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Mar 31, 2017 | -4.51% | -0.04% | 41.11 | 0.87 | 5.99 |
| 2. | Apr 30, 2017 | 4.65% | 0.91% | 7.51 | 0.00 | 0.04 |
| 3. | May 31, 2017 | 0.94% | 1.16% | 0.94 | 0.07 | -0.25 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Dec 31, 2022 | -3.47% | -5.90% | 28.93 | 46.14 | 36.54 |
| 71. | Jan 31, 2023 | -5.14% | 6.18% | 49.60 | 27.88 | -37.19 |
| Total (Σ): | 2,522.48 | 1,754.14 | 675.21 | |||
| t | Date | RDG,t | RS&P 500,t | (RDG,t–RDG)2 | (RS&P 500,t–RS&P 500)2 | (RDG,t–RDG)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Mar 31, 2017 | -4.51% | -0.04% | 41.11 | 0.87 | 5.99 |
| 2. | Apr 30, 2017 | 4.65% | 0.91% | 7.51 | 0.00 | 0.04 |
| 3. | May 31, 2017 | 0.94% | 1.16% | 0.94 | 0.07 | -0.25 |
| 4. | Jun 30, 2017 | -1.77% | 0.48% | 13.52 | 0.17 | 1.52 |
| 5. | Jul 31, 2017 | 4.62% | 1.93% | 7.36 | 1.08 | 2.82 |
| 6. | Aug 31, 2017 | -3.46% | 0.05% | 28.79 | 0.71 | 4.51 |
| 7. | Sep 30, 2017 | 11.70% | 1.93% | 95.94 | 1.07 | 10.14 |
| 8. | Oct 31, 2017 | 0.06% | 2.22% | 3.40 | 1.75 | -2.44 |
| 9. | Nov 30, 2017 | 8.96% | 2.81% | 49.70 | 3.66 | 13.49 |
| 10. | Dec 31, 2017 | 5.60% | 0.98% | 13.63 | 0.01 | 0.32 |
| 11. | Jan 31, 2018 | 11.15% | 5.62% | 85.44 | 22.30 | 43.65 |
| 12. | Feb 28, 2018 | -8.27% | -3.89% | 103.59 | 22.94 | 48.75 |
| 13. | Mar 31, 2018 | -1.10% | -2.69% | 9.03 | 12.84 | 10.77 |
| 14. | Apr 30, 2018 | 3.50% | 0.27% | 2.53 | 0.39 | -0.99 |
| 15. | May 31, 2018 | -9.38% | 2.16% | 127.27 | 1.60 | -14.28 |
| 16. | Jun 30, 2018 | 12.71% | 0.48% | 116.76 | 0.17 | -4.44 |
| 17. | Jul 31, 2018 | -0.16% | 3.60% | 4.28 | 7.33 | -5.60 |
| 18. | Aug 31, 2018 | 9.76% | 3.03% | 61.69 | 4.54 | 16.74 |
| 19. | Sep 30, 2018 | 1.46% | 0.43% | 0.20 | 0.22 | 0.21 |
| 20. | Oct 31, 2018 | 2.17% | -6.94% | 0.07 | 61.40 | -2.06 |
| 21. | Nov 30, 2018 | -0.35% | 1.79% | 5.09 | 0.79 | -2.01 |
| 22. | Dec 31, 2018 | -2.62% | -9.18% | 20.50 | 101.46 | 45.61 |
| 23. | Jan 31, 2019 | 7.07% | 7.87% | 26.66 | 48.63 | 36.00 |
| 24. | Feb 28, 2019 | 2.62% | 2.97% | 0.52 | 4.32 | 1.49 |
| 25. | Mar 31, 2019 | 0.71% | 1.79% | 1.43 | 0.80 | -1.07 |
| 26. | Apr 30, 2019 | 5.96% | 3.93% | 16.43 | 9.22 | 12.31 |
| 27. | May 31, 2019 | 0.94% | -6.58% | 0.93 | 55.85 | 7.19 |
| 28. | Jun 30, 2019 | 6.19% | 6.89% | 18.36 | 35.97 | 25.70 |
| 29. | Jul 31, 2019 | -0.61% | 1.31% | 6.31 | 0.17 | -1.05 |
| 30. | Aug 31, 2019 | 16.47% | -1.81% | 212.04 | 7.31 | -39.38 |
| 31. | Sep 30, 2019 | 1.83% | 1.72% | 0.01 | 0.68 | -0.07 |
| 32. | Oct 31, 2019 | 1.08% | 2.04% | 0.68 | 1.32 | -0.95 |
| 33. | Nov 30, 2019 | -1.86% | 3.40% | 14.17 | 6.30 | -9.45 |
| 34. | Dec 31, 2019 | -0.88% | 2.86% | 7.74 | 3.86 | -5.46 |
| 35. | Jan 31, 2020 | -1.44% | -0.16% | 11.21 | 1.12 | 3.54 |
| 36. | Feb 29, 2020 | -2.03% | -8.41% | 15.47 | 86.61 | 36.60 |
| 37. | Mar 31, 2020 | 0.47% | -12.51% | 2.06 | 179.75 | 19.22 |
| 38. | Apr 30, 2020 | 16.32% | 12.68% | 207.86 | 138.98 | 169.97 |
| 39. | May 31, 2020 | 9.25% | 4.53% | 53.89 | 13.20 | 26.67 |
| 40. | Jun 30, 2020 | -0.52% | 1.84% | 5.90 | 0.89 | -2.29 |
| 41. | Jul 31, 2020 | 0.13% | 5.51% | 3.15 | 21.30 | -8.19 |
| 42. | Aug 31, 2020 | 6.03% | 7.01% | 17.00 | 37.35 | 25.20 |
| 43. | Sep 30, 2020 | 3.83% | -3.92% | 3.72 | 23.21 | -9.29 |
| 44. | Oct 31, 2020 | -0.26% | -2.77% | 4.70 | 13.41 | 7.94 |
| 45. | Nov 30, 2020 | 4.73% | 10.75% | 7.97 | 97.21 | 27.83 |
| 46. | Dec 31, 2020 | -3.79% | 3.71% | 32.42 | 7.93 | -16.04 |
| 47. | Jan 31, 2021 | -7.29% | -1.11% | 84.56 | 4.04 | 18.47 |
| 48. | Feb 28, 2021 | -2.89% | 2.61% | 22.98 | 2.94 | -8.22 |
| 49. | Mar 31, 2021 | 7.21% | 4.24% | 28.15 | 11.21 | 17.77 |
| 50. | Apr 30, 2021 | 6.19% | 5.24% | 18.39 | 18.90 | 18.64 |
| 51. | May 31, 2021 | -5.49% | 0.55% | 54.70 | 0.12 | 2.56 |
| 52. | Jun 30, 2021 | 6.62% | 2.22% | 22.19 | 1.76 | 6.25 |
| 53. | Jul 31, 2021 | 7.70% | 2.27% | 33.61 | 1.90 | 8.00 |
| 54. | Aug 31, 2021 | -4.18% | 2.90% | 37.07 | 4.02 | -12.20 |
| 55. | Sep 30, 2021 | -4.83% | -4.76% | 45.39 | 31.95 | 38.08 |
| 56. | Oct 31, 2021 | 4.62% | 6.91% | 7.36 | 36.23 | 16.33 |
| 57. | Nov 30, 2021 | -0.10% | -0.83% | 4.02 | 2.99 | 3.47 |
| 58. | Dec 31, 2021 | 6.57% | 4.36% | 21.71 | 12.01 | 16.15 |
| 59. | Jan 31, 2022 | -11.42% | -5.26% | 177.56 | 37.87 | 82.00 |
| 60. | Feb 28, 2022 | -4.86% | -3.14% | 45.83 | 16.25 | 27.29 |
| 61. | Mar 31, 2022 | 12.25% | 3.58% | 106.93 | 7.19 | 27.73 |
| 62. | Apr 30, 2022 | 6.94% | -8.80% | 25.34 | 93.91 | -48.78 |
| 63. | May 31, 2022 | -7.24% | 0.01% | 83.59 | 0.79 | 8.14 |
| 64. | Jun 30, 2022 | 11.39% | -8.39% | 89.98 | 86.25 | -88.09 |
| 65. | Jul 31, 2022 | 1.44% | 9.11% | 0.21 | 67.51 | -3.81 |
| 66. | Aug 31, 2022 | -4.43% | -4.24% | 40.17 | 26.41 | 32.57 |
| 67. | Sep 30, 2022 | 1.03% | -9.34% | 0.77 | 104.75 | 8.99 |
| 68. | Oct 31, 2022 | 6.56% | 7.99% | 21.68 | 50.28 | 33.02 |
| 69. | Nov 30, 2022 | 0.25% | 5.38% | 2.75 | 20.07 | -7.43 |
| 70. | Dec 31, 2022 | -3.47% | -5.90% | 28.93 | 46.14 | 36.54 |
| 71. | Jan 31, 2023 | -5.14% | 6.18% | 49.60 | 27.88 | -37.19 |
| Total (Σ): | 2,522.48 | 1,754.14 | 675.21 | |||
Show all
VarianceDG = Σ(RDG,t–RDG)2 ÷ (71 – 1)
= 2,522.48 ÷ (71 – 1)
= 36.04
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,754.14 ÷ (71 – 1)
= 25.06
CovarianceDG, S&P 500 = Σ(RDG,t–RDG)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 675.21 ÷ (71 – 1)
= 9.65
Systematic Risk (β) Estimation
| VarianceDG | 36.04 |
| VarianceS&P 500 | 25.06 |
| CovarianceDG, S&P 500 | 9.65 |
| Correlation coefficientDG, S&P 5001 | 0.32 |
| βDG2 | 0.38 |
| αDG3 | 1.56% |
Calculations
1 Correlation coefficientDG, S&P 500
= CovarianceDG, S&P 500 ÷ (Standard deviationDG × Standard deviationS&P 500)
= 9.65 ÷ (6.00% × 5.01%)
= 0.32
2 βDG
= CovarianceDG, S&P 500 ÷ VarianceS&P 500
= 9.65 ÷ 25.06
= 0.38
3 αDG
= AverageDG – βDG × AverageS&P 500
= 1.91% – 0.38 × 0.90%
= 1.56%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.86% |
| Expected rate of return on market portfolio2 | E(RM) | 13.54% |
| Systematic risk (β) of Dollar General Corp. common stock | βDG | 0.38 |
| Expected rate of return on Dollar General Corp. common stock3 | E(RDG) | 8.20% |
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(RDG) = RF + βDG [E(RM) – RF]
= 4.86% + 0.38 [13.54% – 4.86%]
= 8.20%