Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like GameStop Corp. common stock.
Rates of Return
GameStop Corp. (GME) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceGME,t1 | DividendGME,t1 | RGME,t2 | PriceS&P 500,t | RS&P 500,t3 |
Feb 29, 2016 | $7.71 | 1,932.23 | ||||
1. | Mar 31, 2016 | $7.93 | $0.0925 | 4.05% | 2,059.74 | 6.60% |
2. | Apr 30, 2016 | $8.20 | 3.40% | 2,065.30 | 0.27% | |
3. | May 31, 2016 | $7.28 | -11.22% | 2,096.95 | 1.53% | |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Dec 31, 2021 | $37.10 | -24.36% | 4,766.18 | 4.36% | |
71. | Jan 31, 2022 | $27.23 | -26.60% | 4,515.55 | -5.26% | |
Average (R): | 23.78% | 1.29% | ||||
Standard deviation: | 194.23% | 4.25% |
GameStop Corp. (GME) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceGME,t1 | DividendGME,t1 | RGME,t2 | PriceS&P 500,t | RS&P 500,t3 |
Feb 29, 2016 | $7.71 | 1,932.23 | ||||
1. | Mar 31, 2016 | $7.93 | $0.0925 | 4.05% | 2,059.74 | 6.60% |
2. | Apr 30, 2016 | $8.20 | 3.40% | 2,065.30 | 0.27% | |
3. | May 31, 2016 | $7.28 | -11.22% | 2,096.95 | 1.53% | |
4. | Jun 30, 2016 | $6.65 | $0.0925 | -7.38% | 2,098.86 | 0.09% |
5. | Jul 31, 2016 | $7.74 | 16.39% | 2,173.60 | 3.56% | |
6. | Aug 31, 2016 | $7.10 | -8.27% | 2,170.95 | -0.12% | |
7. | Sep 30, 2016 | $6.90 | $0.0925 | -1.51% | 2,168.27 | -0.12% |
8. | Oct 31, 2016 | $6.01 | -12.90% | 2,126.15 | -1.94% | |
9. | Nov 30, 2016 | $6.17 | $0.0925 | 4.20% | 2,198.81 | 3.42% |
10. | Dec 31, 2016 | $6.32 | 2.43% | 2,238.83 | 1.82% | |
11. | Jan 31, 2017 | $6.12 | -3.16% | 2,278.87 | 1.79% | |
12. | Feb 28, 2017 | $6.11 | -0.16% | 2,363.64 | 3.72% | |
13. | Mar 31, 2017 | $5.64 | $0.095 | -6.14% | 2,362.72 | -0.04% |
14. | Apr 30, 2017 | $5.67 | 0.53% | 2,384.20 | 0.91% | |
15. | May 31, 2017 | $5.54 | -2.29% | 2,411.80 | 1.16% | |
16. | Jun 30, 2017 | $5.40 | $0.095 | -0.81% | 2,423.41 | 0.48% |
17. | Jul 31, 2017 | $5.42 | 0.37% | 2,470.30 | 1.93% | |
18. | Aug 31, 2017 | $4.63 | -14.58% | 2,471.65 | 0.05% | |
19. | Sep 30, 2017 | $5.17 | $0.095 | 13.71% | 2,519.36 | 1.93% |
20. | Oct 31, 2017 | $4.67 | -9.67% | 2,575.26 | 2.22% | |
21. | Nov 30, 2017 | $4.69 | $0.095 | 2.46% | 2,647.58 | 2.81% |
22. | Dec 31, 2017 | $4.49 | -4.26% | 2,673.61 | 0.98% | |
23. | Jan 31, 2018 | $4.20 | -6.46% | 2,823.81 | 5.62% | |
24. | Feb 28, 2018 | $3.92 | -6.67% | 2,713.83 | -3.89% | |
25. | Mar 31, 2018 | $3.16 | $0.095 | -16.96% | 2,640.87 | -2.69% |
26. | Apr 30, 2018 | $3.41 | 7.91% | 2,648.05 | 0.27% | |
27. | May 31, 2018 | $3.30 | -3.23% | 2,705.27 | 2.16% | |
28. | Jun 30, 2018 | $3.64 | $0.095 | 13.18% | 2,718.37 | 0.48% |
29. | Jul 31, 2018 | $3.60 | -1.10% | 2,816.29 | 3.60% | |
30. | Aug 31, 2018 | $3.32 | -7.78% | 2,901.52 | 3.03% | |
31. | Sep 30, 2018 | $3.82 | $0.095 | 17.92% | 2,913.98 | 0.43% |
32. | Oct 31, 2018 | $3.65 | -4.45% | 2,711.74 | -6.94% | |
33. | Nov 30, 2018 | $3.42 | -6.30% | 2,760.17 | 1.79% | |
34. | Dec 31, 2018 | $3.16 | $0.095 | -4.82% | 2,506.85 | -9.18% |
35. | Jan 31, 2019 | $2.84 | -10.13% | 2,704.10 | 7.87% | |
36. | Feb 28, 2019 | $2.93 | 3.17% | 2,784.49 | 2.97% | |
37. | Mar 31, 2019 | $2.54 | $0.095 | -10.07% | 2,834.40 | 1.79% |
38. | Apr 30, 2019 | $2.16 | -14.96% | 2,945.83 | 3.93% | |
39. | May 31, 2019 | $1.90 | -12.04% | 2,752.06 | -6.58% | |
40. | Jun 30, 2019 | $1.37 | -27.89% | 2,941.76 | 6.89% | |
41. | Jul 31, 2019 | $1.01 | -26.28% | 2,980.38 | 1.31% | |
42. | Aug 31, 2019 | $0.99 | -1.98% | 2,926.46 | -1.81% | |
43. | Sep 30, 2019 | $1.38 | 39.39% | 2,976.74 | 1.72% | |
44. | Oct 31, 2019 | $1.36 | -1.45% | 3,037.56 | 2.04% | |
45. | Nov 30, 2019 | $1.59 | 16.91% | 3,140.98 | 3.40% | |
46. | Dec 31, 2019 | $1.52 | -4.40% | 3,230.78 | 2.86% | |
47. | Jan 31, 2020 | $0.96 | -36.84% | 3,225.52 | -0.16% | |
48. | Feb 29, 2020 | $0.90 | -6.25% | 2,954.22 | -8.41% | |
49. | Mar 31, 2020 | $0.88 | -2.22% | 2,584.59 | -12.51% | |
50. | Apr 30, 2020 | $1.43 | 62.50% | 2,912.43 | 12.68% | |
51. | May 31, 2020 | $1.02 | -28.67% | 3,044.31 | 4.53% | |
52. | Jun 30, 2020 | $1.09 | 6.86% | 3,100.29 | 1.84% | |
53. | Jul 31, 2020 | $1.00 | -8.26% | 3,271.12 | 5.51% | |
54. | Aug 31, 2020 | $1.67 | 67.00% | 3,500.31 | 7.01% | |
55. | Sep 30, 2020 | $2.55 | 52.69% | 3,363.00 | -3.92% | |
56. | Oct 31, 2020 | $2.62 | 2.75% | 3,269.96 | -2.77% | |
57. | Nov 30, 2020 | $4.14 | 58.02% | 3,621.63 | 10.75% | |
58. | Dec 31, 2020 | $4.71 | 13.77% | 3,756.07 | 3.71% | |
59. | Jan 31, 2021 | $81.25 | 1,625.05% | 3,714.24 | -1.11% | |
60. | Feb 28, 2021 | $25.44 | -68.69% | 3,811.15 | 2.61% | |
61. | Mar 31, 2021 | $47.46 | 86.56% | 3,972.89 | 4.24% | |
62. | Apr 30, 2021 | $43.40 | -8.55% | 4,181.17 | 5.24% | |
63. | May 31, 2021 | $55.50 | 27.88% | 4,204.11 | 0.55% | |
64. | Jun 30, 2021 | $53.54 | -3.53% | 4,297.50 | 2.22% | |
65. | Jul 31, 2021 | $40.28 | -24.77% | 4,395.26 | 2.27% | |
66. | Aug 31, 2021 | $54.56 | 35.45% | 4,522.68 | 2.90% | |
67. | Sep 30, 2021 | $43.87 | -19.59% | 4,307.54 | -4.76% | |
68. | Oct 31, 2021 | $45.88 | 4.58% | 4,605.38 | 6.91% | |
69. | Nov 30, 2021 | $49.05 | 6.91% | 4,567.00 | -0.83% | |
70. | Dec 31, 2021 | $37.10 | -24.36% | 4,766.18 | 4.36% | |
71. | Jan 31, 2022 | $27.23 | -26.60% | 4,515.55 | -5.26% | |
Average (R): | 23.78% | 1.29% | ||||
Standard deviation: | 194.23% | 4.25% |
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of GME during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RGME,t | RS&P 500,t | (RGME,t–RGME)2 | (RS&P 500,t–RS&P 500)2 | (RGME,t–RGME)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Mar 31, 2016 | 4.05% | 6.60% | 389.16 | 28.16 | -104.69 |
2. | Apr 30, 2016 | 3.40% | 0.27% | 415.16 | 1.05 | 20.83 |
3. | May 31, 2016 | -11.22% | 1.53% | 1,224.98 | 0.06 | -8.41 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Dec 31, 2021 | -24.36% | 4.36% | 2,317.76 | 9.42 | -147.75 |
71. | Jan 31, 2022 | -26.60% | -5.26% | 2,538.54 | 42.91 | 330.05 |
Total (Σ): | 2,640,729.02 | 1,262.70 | -1,983.24 |
t | Date | RGME,t | RS&P 500,t | (RGME,t–RGME)2 | (RS&P 500,t–RS&P 500)2 | (RGME,t–RGME)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Mar 31, 2016 | 4.05% | 6.60% | 389.16 | 28.16 | -104.69 |
2. | Apr 30, 2016 | 3.40% | 0.27% | 415.16 | 1.05 | 20.83 |
3. | May 31, 2016 | -11.22% | 1.53% | 1,224.98 | 0.06 | -8.41 |
4. | Jun 30, 2016 | -7.38% | 0.09% | 971.16 | 1.44 | 37.43 |
5. | Jul 31, 2016 | 16.39% | 3.56% | 54.60 | 5.15 | -16.76 |
6. | Aug 31, 2016 | -8.27% | -0.12% | 1,027.13 | 2.00 | 45.32 |
7. | Sep 30, 2016 | -1.51% | -0.12% | 639.80 | 2.00 | 35.81 |
8. | Oct 31, 2016 | -12.90% | -1.94% | 1,345.33 | 10.46 | 118.65 |
9. | Nov 30, 2016 | 4.20% | 3.42% | 383.33 | 4.52 | -41.61 |
10. | Dec 31, 2016 | 2.43% | 1.82% | 455.78 | 0.28 | -11.27 |
11. | Jan 31, 2017 | -3.16% | 1.79% | 726.02 | 0.25 | -13.37 |
12. | Feb 28, 2017 | -0.16% | 3.72% | 573.30 | 5.89 | -58.13 |
13. | Mar 31, 2017 | -6.14% | -0.04% | 895.07 | 1.77 | 39.83 |
14. | Apr 30, 2017 | 0.53% | 0.91% | 540.48 | 0.15 | 8.91 |
15. | May 31, 2017 | -2.29% | 1.16% | 679.80 | 0.02 | 3.51 |
16. | Jun 30, 2017 | -0.81% | 0.48% | 604.79 | 0.66 | 19.94 |
17. | Jul 31, 2017 | 0.37% | 1.93% | 548.02 | 0.41 | -15.04 |
18. | Aug 31, 2017 | -14.58% | 0.05% | 1,471.17 | 1.53 | 47.47 |
19. | Sep 30, 2017 | 13.71% | 1.93% | 101.31 | 0.41 | -6.42 |
20. | Oct 31, 2017 | -9.67% | 2.22% | 1,118.99 | 0.86 | -31.00 |
21. | Nov 30, 2017 | 2.46% | 2.81% | 454.44 | 2.30 | -32.32 |
22. | Dec 31, 2017 | -4.26% | 0.98% | 786.50 | 0.10 | 8.67 |
23. | Jan 31, 2018 | -6.46% | 5.62% | 914.40 | 18.71 | -130.80 |
24. | Feb 28, 2018 | -6.67% | -3.89% | 927.01 | 26.90 | 157.93 |
25. | Mar 31, 2018 | -16.96% | -2.69% | 1,660.11 | 15.85 | 162.19 |
26. | Apr 30, 2018 | 7.91% | 0.27% | 251.82 | 1.04 | 16.19 |
27. | May 31, 2018 | -3.23% | 2.16% | 729.32 | 0.75 | -23.46 |
28. | Jun 30, 2018 | 13.18% | 0.48% | 112.33 | 0.65 | 8.56 |
29. | Jul 31, 2018 | -1.10% | 3.60% | 618.97 | 5.34 | -57.47 |
30. | Aug 31, 2018 | -7.78% | 3.03% | 995.91 | 3.01 | -54.72 |
31. | Sep 30, 2018 | 17.92% | 0.43% | 34.32 | 0.74 | 5.05 |
32. | Oct 31, 2018 | -4.45% | -6.94% | 796.96 | 67.78 | 232.41 |
33. | Nov 30, 2018 | -6.30% | 1.79% | 904.90 | 0.24 | -14.85 |
34. | Dec 31, 2018 | -4.82% | -9.18% | 818.23 | 109.62 | 299.49 |
35. | Jan 31, 2019 | -10.13% | 7.87% | 1,149.67 | 43.25 | -222.98 |
36. | Feb 28, 2019 | 3.17% | 2.97% | 424.82 | 2.82 | -34.64 |
37. | Mar 31, 2019 | -10.07% | 1.79% | 1,145.72 | 0.25 | -16.93 |
38. | Apr 30, 2019 | -14.96% | 3.93% | 1,500.85 | 6.96 | -102.24 |
39. | May 31, 2019 | -12.04% | -6.58% | 1,282.87 | 61.94 | 281.88 |
40. | Jun 30, 2019 | -27.89% | 6.89% | 2,670.30 | 31.37 | -289.42 |
41. | Jul 31, 2019 | -26.28% | 1.31% | 2,505.76 | 0.00 | -1.03 |
42. | Aug 31, 2019 | -1.98% | -1.81% | 663.60 | 9.62 | 79.89 |
43. | Sep 30, 2019 | 39.39% | 1.72% | 243.79 | 0.18 | 6.65 |
44. | Oct 31, 2019 | -1.45% | 2.04% | 636.53 | 0.56 | -18.95 |
45. | Nov 30, 2019 | 16.91% | 3.40% | 47.18 | 4.46 | -14.51 |
46. | Dec 31, 2019 | -4.40% | 2.86% | 794.27 | 2.45 | -44.15 |
47. | Jan 31, 2020 | -36.84% | -0.16% | 3,675.06 | 2.12 | 88.21 |
48. | Feb 29, 2020 | -6.25% | -8.41% | 901.81 | 94.15 | 291.39 |
49. | Mar 31, 2020 | -2.22% | -12.51% | 676.13 | 190.56 | 358.94 |
50. | Apr 30, 2020 | 62.50% | 12.68% | 1,499.22 | 129.78 | 441.10 |
51. | May 31, 2020 | -28.67% | 4.53% | 2,751.16 | 10.47 | -169.73 |
52. | Jun 30, 2020 | 6.86% | 1.84% | 286.20 | 0.30 | -9.25 |
53. | Jul 31, 2020 | -8.26% | 5.51% | 1,026.37 | 17.79 | -135.13 |
54. | Aug 31, 2020 | 67.00% | 7.01% | 1,867.95 | 32.65 | 246.97 |
55. | Sep 30, 2020 | 52.69% | -3.92% | 836.04 | 27.20 | -150.79 |
56. | Oct 31, 2020 | 2.75% | -2.77% | 442.48 | 16.47 | 85.38 |
57. | Nov 30, 2020 | 58.02% | 10.75% | 1,172.04 | 89.54 | 323.94 |
58. | Dec 31, 2020 | 13.77% | 3.71% | 100.24 | 5.86 | -24.23 |
59. | Jan 31, 2021 | 1,625.05% | -1.11% | 2,564,074.83 | 5.79 | -3,852.52 |
60. | Feb 28, 2021 | -68.69% | 2.61% | 8,550.60 | 1.73 | -121.77 |
61. | Mar 31, 2021 | 86.56% | 4.24% | 3,940.88 | 8.71 | 185.29 |
62. | Apr 30, 2021 | -8.55% | 5.24% | 1,045.54 | 15.60 | -127.73 |
63. | May 31, 2021 | 27.88% | 0.55% | 16.81 | 0.55 | -3.05 |
64. | Jun 30, 2021 | -3.53% | 2.22% | 745.93 | 0.86 | -25.38 |
65. | Jul 31, 2021 | -24.77% | 2.27% | 2,356.79 | 0.97 | -47.70 |
66. | Aug 31, 2021 | 35.45% | 2.90% | 136.23 | 2.58 | 18.75 |
67. | Sep 30, 2021 | -19.59% | -4.76% | 1,881.24 | 36.59 | 262.37 |
68. | Oct 31, 2021 | 4.58% | 6.91% | 368.58 | 31.61 | -107.94 |
69. | Nov 30, 2021 | 6.91% | -0.83% | 284.63 | 4.52 | 35.86 |
70. | Dec 31, 2021 | -24.36% | 4.36% | 2,317.76 | 9.42 | -147.75 |
71. | Jan 31, 2022 | -26.60% | -5.26% | 2,538.54 | 42.91 | 330.05 |
Total (Σ): | 2,640,729.02 | 1,262.70 | -1,983.24 |
Show all
VarianceGME = Σ(RGME,t–RGME)2 ÷ (71 – 1)
= 2,640,729.02 ÷ (71 – 1)
= 37,724.70
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,262.70 ÷ (71 – 1)
= 18.04
CovarianceGME, S&P 500 = Σ(RGME,t–RGME)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= -1,983.24 ÷ (71 – 1)
= -28.33
Systematic Risk (β) Estimation
VarianceGME | 37,724.70 |
VarianceS&P 500 | 18.04 |
CovarianceGME, S&P 500 | -28.33 |
Correlation coefficientGME, S&P 5001 | -0.03 |
βGME2 | -1.57 |
αGME3 | 25.81% |
Calculations
1 Correlation coefficientGME, S&P 500
= CovarianceGME, S&P 500 ÷ (Standard deviationGME × Standard deviationS&P 500)
= -28.33 ÷ (194.23% × 4.25%)
= -0.03
2 βGME
= CovarianceGME, S&P 500 ÷ VarianceS&P 500
= -28.33 ÷ 18.04
= -1.57
3 αGME
= AverageGME – βGME × AverageS&P 500
= 23.78% – -1.57 × 1.29%
= 25.81%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.42% |
Expected rate of return on market portfolio2 | E(RM) | 13.61% |
Systematic risk (β) of GameStop Corp. common stock | βGME | -1.57 |
Expected rate of return on GameStop Corp. common stock3 | E(RGME) | -10.01% |
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(RGME) = RF + βGME [E(RM) – RF]
= 4.42% + -1.57 [13.61% – 4.42%]
= -10.01%