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 T-Mobile US Inc. common stock.
Rates of Return
T-Mobile US Inc., monthly rates of return
| T-Mobile US Inc. (TMUS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceTMUS,t1 | DividendTMUS,t1 | RTMUS,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2021 | $126.08 | 3,714.24 | ||||
| 1. | Feb 28, 2021 | $119.97 | -4.85% | 3,811.15 | 2.61% | |
| 2. | Mar 31, 2021 | $125.29 | 4.43% | 3,972.89 | 4.24% | |
| 3. | Apr 30, 2021 | $132.13 | 5.46% | 4,181.17 | 5.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2025 | $209.01 | $1.02 | -0.01% | 6,849.09 | 0.13% |
| 59. | Dec 31, 2025 | $203.04 | -2.86% | 6,845.50 | -0.05% | |
| Average (R): | 1.05% | 1.14% | ||||
| Standard deviation: | 6.13% | 4.37% | ||||
| T-Mobile US Inc. (TMUS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceTMUS,t1 | DividendTMUS,t1 | RTMUS,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2021 | $126.08 | 3,714.24 | ||||
| 1. | Feb 28, 2021 | $119.97 | -4.85% | 3,811.15 | 2.61% | |
| 2. | Mar 31, 2021 | $125.29 | 4.43% | 3,972.89 | 4.24% | |
| 3. | Apr 30, 2021 | $132.13 | 5.46% | 4,181.17 | 5.24% | |
| 4. | May 31, 2021 | $141.45 | 7.05% | 4,204.11 | 0.55% | |
| 5. | Jun 30, 2021 | $144.83 | 2.39% | 4,297.50 | 2.22% | |
| 6. | Jul 31, 2021 | $144.02 | -0.56% | 4,395.26 | 2.27% | |
| 7. | Aug 31, 2021 | $137.02 | -4.86% | 4,522.68 | 2.90% | |
| 8. | Sep 30, 2021 | $127.76 | -6.76% | 4,307.54 | -4.76% | |
| 9. | Oct 31, 2021 | $115.03 | -9.96% | 4,605.38 | 6.91% | |
| 10. | Nov 30, 2021 | $108.81 | -5.41% | 4,567.00 | -0.83% | |
| 11. | Dec 31, 2021 | $115.98 | 6.59% | 4,766.18 | 4.36% | |
| 12. | Jan 31, 2022 | $108.17 | -6.73% | 4,515.55 | -5.26% | |
| 13. | Feb 28, 2022 | $123.21 | 13.90% | 4,373.94 | -3.14% | |
| 14. | Mar 31, 2022 | $128.35 | 4.17% | 4,530.41 | 3.58% | |
| 15. | Apr 30, 2022 | $123.14 | -4.06% | 4,131.93 | -8.80% | |
| 16. | May 31, 2022 | $133.29 | 8.24% | 4,132.15 | 0.01% | |
| 17. | Jun 30, 2022 | $134.54 | 0.94% | 3,785.38 | -8.39% | |
| 18. | Jul 31, 2022 | $143.06 | 6.33% | 4,130.29 | 9.11% | |
| 19. | Aug 31, 2022 | $143.96 | 0.63% | 3,955.00 | -4.24% | |
| 20. | Sep 30, 2022 | $134.17 | -6.80% | 3,585.62 | -9.34% | |
| 21. | Oct 31, 2022 | $151.56 | 12.96% | 3,871.98 | 7.99% | |
| 22. | Nov 30, 2022 | $151.46 | -0.07% | 4,080.11 | 5.38% | |
| 23. | Dec 31, 2022 | $140.00 | -7.57% | 3,839.50 | -5.90% | |
| 24. | Jan 31, 2023 | $149.31 | 6.65% | 4,076.60 | 6.18% | |
| 25. | Feb 28, 2023 | $142.18 | -4.78% | 3,970.15 | -2.61% | |
| 26. | Mar 31, 2023 | $144.84 | 1.87% | 4,109.31 | 3.51% | |
| 27. | Apr 30, 2023 | $143.90 | -0.65% | 4,169.48 | 1.46% | |
| 28. | May 31, 2023 | $137.25 | -4.62% | 4,179.83 | 0.25% | |
| 29. | Jun 30, 2023 | $138.90 | 1.20% | 4,376.86 | 4.71% | |
| 30. | Jul 31, 2023 | $137.77 | -0.81% | 4,588.96 | 4.85% | |
| 31. | Aug 31, 2023 | $136.25 | -1.10% | 4,507.66 | -1.77% | |
| 32. | Sep 30, 2023 | $140.05 | 2.79% | 4,288.05 | -4.87% | |
| 33. | Oct 31, 2023 | $143.86 | 2.72% | 4,193.80 | -2.20% | |
| 34. | Nov 30, 2023 | $150.45 | $0.65 | 5.03% | 4,567.80 | 8.92% |
| 35. | Dec 31, 2023 | $160.33 | 6.57% | 4,769.83 | 4.42% | |
| 36. | Jan 31, 2024 | $161.23 | 0.56% | 4,845.65 | 1.59% | |
| 37. | Feb 29, 2024 | $163.30 | $0.65 | 1.69% | 5,096.27 | 5.17% |
| 38. | Mar 31, 2024 | $163.22 | -0.05% | 5,254.35 | 3.10% | |
| 39. | Apr 30, 2024 | $164.17 | 0.58% | 5,035.69 | -4.16% | |
| 40. | May 31, 2024 | $174.96 | $0.65 | 6.97% | 5,277.51 | 4.80% |
| 41. | Jun 30, 2024 | $176.18 | 0.70% | 5,460.48 | 3.47% | |
| 42. | Jul 31, 2024 | $182.28 | 3.46% | 5,522.30 | 1.13% | |
| 43. | Aug 31, 2024 | $198.72 | $0.65 | 9.38% | 5,648.40 | 2.28% |
| 44. | Sep 30, 2024 | $206.36 | 3.84% | 5,762.48 | 2.02% | |
| 45. | Oct 31, 2024 | $223.16 | 8.14% | 5,705.45 | -0.99% | |
| 46. | Nov 30, 2024 | $246.94 | $0.88 | 11.05% | 6,032.38 | 5.73% |
| 47. | Dec 31, 2024 | $220.73 | -10.61% | 5,881.63 | -2.50% | |
| 48. | Jan 31, 2025 | $232.97 | 5.55% | 6,040.53 | 2.70% | |
| 49. | Feb 28, 2025 | $269.69 | $0.88 | 16.14% | 5,954.50 | -1.42% |
| 50. | Mar 31, 2025 | $266.71 | -1.10% | 5,611.85 | -5.75% | |
| 51. | Apr 30, 2025 | $246.95 | -7.41% | 5,569.06 | -0.76% | |
| 52. | May 31, 2025 | $242.20 | $0.88 | -1.57% | 5,911.69 | 6.15% |
| 53. | Jun 30, 2025 | $238.26 | -1.63% | 6,204.95 | 4.96% | |
| 54. | Jul 31, 2025 | $238.41 | 0.06% | 6,339.39 | 2.17% | |
| 55. | Aug 31, 2025 | $251.99 | $0.88 | 6.07% | 6,460.26 | 1.91% |
| 56. | Sep 30, 2025 | $239.38 | -5.00% | 6,688.46 | 3.53% | |
| 57. | Oct 31, 2025 | $210.05 | -12.25% | 6,840.20 | 2.27% | |
| 58. | Nov 30, 2025 | $209.01 | $1.02 | -0.01% | 6,849.09 | 0.13% |
| 59. | Dec 31, 2025 | $203.04 | -2.86% | 6,845.50 | -0.05% | |
| Average (R): | 1.05% | 1.14% | ||||
| Standard deviation: | 6.13% | 4.37% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of TMUS during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
T-Mobile US Inc., calculation of variance and covariance of returns
| t | Date | RTMUS,t | RS&P 500,t | (RTMUS,t–RTMUS)2 | (RS&P 500,t–RS&P 500)2 | (RTMUS,t–RTMUS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2021 | -4.85% | 2.61% | 34.78 | 2.17 | -8.69 |
| 2. | Mar 31, 2021 | 4.43% | 4.24% | 11.44 | 9.66 | 10.51 |
| 3. | Apr 30, 2021 | 5.46% | 5.24% | 19.43 | 16.86 | 18.10 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2025 | -0.01% | 0.13% | 1.13 | 1.01 | 1.07 |
| 59. | Dec 31, 2025 | -2.86% | -0.05% | 15.27 | 1.41 | 4.64 |
| Total (Σ): | 2,178.16 | 1,108.23 | 482.05 | |||
| t | Date | RTMUS,t | RS&P 500,t | (RTMUS,t–RTMUS)2 | (RS&P 500,t–RS&P 500)2 | (RTMUS,t–RTMUS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2021 | -4.85% | 2.61% | 34.78 | 2.17 | -8.69 |
| 2. | Mar 31, 2021 | 4.43% | 4.24% | 11.44 | 9.66 | 10.51 |
| 3. | Apr 30, 2021 | 5.46% | 5.24% | 19.43 | 16.86 | 18.10 |
| 4. | May 31, 2021 | 7.05% | 0.55% | 36.02 | 0.35 | -3.53 |
| 5. | Jun 30, 2021 | 2.39% | 2.22% | 1.79 | 1.18 | 1.45 |
| 6. | Jul 31, 2021 | -0.56% | 2.27% | 2.59 | 1.30 | -1.83 |
| 7. | Aug 31, 2021 | -4.86% | 2.90% | 34.95 | 3.11 | -10.42 |
| 8. | Sep 30, 2021 | -6.76% | -4.76% | 60.99 | 34.73 | 46.02 |
| 9. | Oct 31, 2021 | -9.96% | 6.91% | 121.34 | 33.39 | -63.65 |
| 10. | Nov 30, 2021 | -5.41% | -0.83% | 41.72 | 3.88 | 12.72 |
| 11. | Dec 31, 2021 | 6.59% | 4.36% | 30.67 | 10.40 | 17.86 |
| 12. | Jan 31, 2022 | -6.73% | -5.26% | 60.61 | 40.89 | 49.79 |
| 13. | Feb 28, 2022 | 13.90% | -3.14% | 165.19 | 18.25 | -54.91 |
| 14. | Mar 31, 2022 | 4.17% | 3.58% | 9.74 | 5.96 | 7.62 |
| 15. | Apr 30, 2022 | -4.06% | -8.80% | 26.12 | 98.64 | 50.76 |
| 16. | May 31, 2022 | 8.24% | 0.01% | 51.71 | 1.28 | -8.13 |
| 17. | Jun 30, 2022 | 0.94% | -8.39% | 0.01 | 90.79 | 1.08 |
| 18. | Jul 31, 2022 | 6.33% | 9.11% | 27.89 | 63.61 | 42.12 |
| 19. | Aug 31, 2022 | 0.63% | -4.24% | 0.18 | 28.95 | 2.27 |
| 20. | Sep 30, 2022 | -6.80% | -9.34% | 61.66 | 109.74 | 82.26 |
| 21. | Oct 31, 2022 | 12.96% | 7.99% | 141.84 | 46.93 | 81.58 |
| 22. | Nov 30, 2022 | -0.07% | 5.38% | 1.25 | 17.97 | -4.74 |
| 23. | Dec 31, 2022 | -7.57% | -5.90% | 74.27 | 49.47 | 60.61 |
| 24. | Jan 31, 2023 | 6.65% | 6.18% | 31.34 | 25.39 | 28.21 |
| 25. | Feb 28, 2023 | -4.78% | -2.61% | 33.95 | 14.04 | 21.84 |
| 26. | Mar 31, 2023 | 1.87% | 3.51% | 0.67 | 5.61 | 1.94 |
| 27. | Apr 30, 2023 | -0.65% | 1.46% | 2.89 | 0.11 | -0.56 |
| 28. | May 31, 2023 | -4.62% | 0.25% | 32.18 | 0.79 | 5.04 |
| 29. | Jun 30, 2023 | 1.20% | 4.71% | 0.02 | 12.80 | 0.54 |
| 30. | Jul 31, 2023 | -0.81% | 4.85% | 3.48 | 13.76 | -6.92 |
| 31. | Aug 31, 2023 | -1.10% | -1.77% | 4.64 | 8.46 | 6.27 |
| 32. | Sep 30, 2023 | 2.79% | -4.87% | 3.02 | 36.10 | -10.44 |
| 33. | Oct 31, 2023 | 2.72% | -2.20% | 2.79 | 11.12 | -5.56 |
| 34. | Nov 30, 2023 | 5.03% | 8.92% | 15.85 | 60.56 | 30.98 |
| 35. | Dec 31, 2023 | 6.57% | 4.42% | 30.42 | 10.80 | 18.13 |
| 36. | Jan 31, 2024 | 0.56% | 1.59% | 0.24 | 0.21 | -0.22 |
| 37. | Feb 29, 2024 | 1.69% | 5.17% | 0.40 | 16.29 | 2.56 |
| 38. | Mar 31, 2024 | -0.05% | 3.10% | 1.21 | 3.86 | -2.16 |
| 39. | Apr 30, 2024 | 0.58% | -4.16% | 0.22 | 28.06 | 2.49 |
| 40. | May 31, 2024 | 6.97% | 4.80% | 35.01 | 13.44 | 21.69 |
| 41. | Jun 30, 2024 | 0.70% | 3.47% | 0.13 | 5.43 | -0.83 |
| 42. | Jul 31, 2024 | 3.46% | 1.13% | 5.81 | 0.00 | -0.01 |
| 43. | Aug 31, 2024 | 9.38% | 2.28% | 69.29 | 1.32 | 9.55 |
| 44. | Sep 30, 2024 | 3.84% | 2.02% | 7.80 | 0.78 | 2.47 |
| 45. | Oct 31, 2024 | 8.14% | -0.99% | 50.26 | 4.52 | -15.07 |
| 46. | Nov 30, 2024 | 11.05% | 5.73% | 99.98 | 21.10 | 45.93 |
| 47. | Dec 31, 2024 | -10.61% | -2.50% | 136.08 | 13.21 | 42.41 |
| 48. | Jan 31, 2025 | 5.55% | 2.70% | 20.19 | 2.45 | 7.03 |
| 49. | Feb 28, 2025 | 16.14% | -1.42% | 227.64 | 6.56 | -38.63 |
| 50. | Mar 31, 2025 | -1.10% | -5.75% | 4.65 | 47.48 | 14.86 |
| 51. | Apr 30, 2025 | -7.41% | -0.76% | 71.58 | 3.60 | 16.06 |
| 52. | May 31, 2025 | -1.57% | 6.15% | 6.86 | 25.16 | -13.14 |
| 53. | Jun 30, 2025 | -1.63% | 4.96% | 7.17 | 14.63 | -10.24 |
| 54. | Jul 31, 2025 | 0.06% | 2.17% | 0.98 | 1.06 | -1.02 |
| 55. | Aug 31, 2025 | 6.07% | 1.91% | 25.14 | 0.59 | 3.86 |
| 56. | Sep 30, 2025 | -5.00% | 3.53% | 36.67 | 5.74 | -14.51 |
| 57. | Oct 31, 2025 | -12.25% | 2.27% | 177.00 | 1.28 | -15.07 |
| 58. | Nov 30, 2025 | -0.01% | 0.13% | 1.13 | 1.01 | 1.07 |
| 59. | Dec 31, 2025 | -2.86% | -0.05% | 15.27 | 1.41 | 4.64 |
| Total (Σ): | 2,178.16 | 1,108.23 | 482.05 | |||
Show all
VarianceTMUS = Σ(RTMUS,t–RTMUS)2 ÷ (59 – 1)
= 2,178.16 ÷ (59 – 1)
= 37.55
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,108.23 ÷ (59 – 1)
= 19.11
CovarianceTMUS, S&P 500 = Σ(RTMUS,t–RTMUS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 482.05 ÷ (59 – 1)
= 8.31
Systematic Risk (β) Estimation
| VarianceTMUS | 37.55 |
| VarianceS&P 500 | 19.11 |
| CovarianceTMUS, S&P 500 | 8.31 |
| Correlation coefficientTMUS, S&P 5001 | 0.31 |
| βTMUS2 | 0.43 |
| αTMUS3 | 0.56% |
Calculations
1 Correlation coefficientTMUS, S&P 500
= CovarianceTMUS, S&P 500 ÷ (Standard deviationTMUS × Standard deviationS&P 500)
= 8.31 ÷ (6.13% × 4.37%)
= 0.31
2 βTMUS
= CovarianceTMUS, S&P 500 ÷ VarianceS&P 500
= 8.31 ÷ 19.11
= 0.43
3 αTMUS
= AverageTMUS – βTMUS × AverageS&P 500
= 1.05% – 0.43 × 1.14%
= 0.56%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.54% |
| Expected rate of return on market portfolio2 | E(RM) | 17.37% |
| Systematic risk (β) of T-Mobile US Inc. common stock | βTMUS | 0.43 |
| Expected rate of return on T-Mobile US Inc. common stock3 | E(RTMUS) | 10.12% |
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(RTMUS) = RF + βTMUS [E(RM) – RF]
= 4.54% + 0.43 [17.37% – 4.54%]
= 10.12%