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, 2019 | $69.62 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $72.21 | 3.72% | 2,784.49 | 2.97% | |
| 2. | Mar 31, 2019 | $69.10 | -4.31% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $72.99 | 5.63% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | $150.45 | $0.65 | 5.03% | 4,567.80 | 8.92% |
| 59. | Dec 31, 2023 | $160.33 | 6.57% | 4,769.83 | 4.42% | |
| Average (R): | 1.62% | 1.11% | ||||
| Standard deviation: | 6.30% | 5.31% | ||||
| 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, 2019 | $69.62 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $72.21 | 3.72% | 2,784.49 | 2.97% | |
| 2. | Mar 31, 2019 | $69.10 | -4.31% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $72.99 | 5.63% | 2,945.83 | 3.93% | |
| 4. | May 31, 2019 | $73.44 | 0.62% | 2,752.06 | -6.58% | |
| 5. | Jun 30, 2019 | $74.14 | 0.95% | 2,941.76 | 6.89% | |
| 6. | Jul 31, 2019 | $79.73 | 7.54% | 2,980.38 | 1.31% | |
| 7. | Aug 31, 2019 | $78.05 | -2.11% | 2,926.46 | -1.81% | |
| 8. | Sep 30, 2019 | $78.77 | 0.92% | 2,976.74 | 1.72% | |
| 9. | Oct 31, 2019 | $82.66 | 4.94% | 3,037.56 | 2.04% | |
| 10. | Nov 30, 2019 | $78.55 | -4.97% | 3,140.98 | 3.40% | |
| 11. | Dec 31, 2019 | $78.42 | -0.17% | 3,230.78 | 2.86% | |
| 12. | Jan 31, 2020 | $79.19 | 0.98% | 3,225.52 | -0.16% | |
| 13. | Feb 29, 2020 | $90.16 | 13.85% | 2,954.22 | -8.41% | |
| 14. | Mar 31, 2020 | $83.90 | -6.94% | 2,584.59 | -12.51% | |
| 15. | Apr 30, 2020 | $87.80 | 4.65% | 2,912.43 | 12.68% | |
| 16. | May 31, 2020 | $100.04 | 13.94% | 3,044.31 | 4.53% | |
| 17. | Jun 30, 2020 | $104.15 | 4.11% | 3,100.29 | 1.84% | |
| 18. | Jul 31, 2020 | $107.38 | 3.10% | 3,271.12 | 5.51% | |
| 19. | Aug 31, 2020 | $116.68 | 8.66% | 3,500.31 | 7.01% | |
| 20. | Sep 30, 2020 | $114.36 | -1.99% | 3,363.00 | -3.92% | |
| 21. | Oct 31, 2020 | $109.57 | -4.19% | 3,269.96 | -2.77% | |
| 22. | Nov 30, 2020 | $132.94 | 21.33% | 3,621.63 | 10.75% | |
| 23. | Dec 31, 2020 | $134.85 | 1.44% | 3,756.07 | 3.71% | |
| 24. | Jan 31, 2021 | $126.08 | -6.50% | 3,714.24 | -1.11% | |
| 25. | Feb 28, 2021 | $119.97 | -4.85% | 3,811.15 | 2.61% | |
| 26. | Mar 31, 2021 | $125.29 | 4.43% | 3,972.89 | 4.24% | |
| 27. | Apr 30, 2021 | $132.13 | 5.46% | 4,181.17 | 5.24% | |
| 28. | May 31, 2021 | $141.45 | 7.05% | 4,204.11 | 0.55% | |
| 29. | Jun 30, 2021 | $144.83 | 2.39% | 4,297.50 | 2.22% | |
| 30. | Jul 31, 2021 | $144.02 | -0.56% | 4,395.26 | 2.27% | |
| 31. | Aug 31, 2021 | $137.02 | -4.86% | 4,522.68 | 2.90% | |
| 32. | Sep 30, 2021 | $127.76 | -6.76% | 4,307.54 | -4.76% | |
| 33. | Oct 31, 2021 | $115.03 | -9.96% | 4,605.38 | 6.91% | |
| 34. | Nov 30, 2021 | $108.81 | -5.41% | 4,567.00 | -0.83% | |
| 35. | Dec 31, 2021 | $115.98 | 6.59% | 4,766.18 | 4.36% | |
| 36. | Jan 31, 2022 | $108.17 | -6.73% | 4,515.55 | -5.26% | |
| 37. | Feb 28, 2022 | $123.21 | 13.90% | 4,373.94 | -3.14% | |
| 38. | Mar 31, 2022 | $128.35 | 4.17% | 4,530.41 | 3.58% | |
| 39. | Apr 30, 2022 | $123.14 | -4.06% | 4,131.93 | -8.80% | |
| 40. | May 31, 2022 | $133.29 | 8.24% | 4,132.15 | 0.01% | |
| 41. | Jun 30, 2022 | $134.54 | 0.94% | 3,785.38 | -8.39% | |
| 42. | Jul 31, 2022 | $143.06 | 6.33% | 4,130.29 | 9.11% | |
| 43. | Aug 31, 2022 | $143.96 | 0.63% | 3,955.00 | -4.24% | |
| 44. | Sep 30, 2022 | $134.17 | -6.80% | 3,585.62 | -9.34% | |
| 45. | Oct 31, 2022 | $151.56 | 12.96% | 3,871.98 | 7.99% | |
| 46. | Nov 30, 2022 | $151.46 | -0.07% | 4,080.11 | 5.38% | |
| 47. | Dec 31, 2022 | $140.00 | -7.57% | 3,839.50 | -5.90% | |
| 48. | Jan 31, 2023 | $149.31 | 6.65% | 4,076.60 | 6.18% | |
| 49. | Feb 28, 2023 | $142.18 | -4.78% | 3,970.15 | -2.61% | |
| 50. | Mar 31, 2023 | $144.84 | 1.87% | 4,109.31 | 3.51% | |
| 51. | Apr 30, 2023 | $143.90 | -0.65% | 4,169.48 | 1.46% | |
| 52. | May 31, 2023 | $137.25 | -4.62% | 4,179.83 | 0.25% | |
| 53. | Jun 30, 2023 | $138.90 | 1.20% | 4,376.86 | 4.71% | |
| 54. | Jul 31, 2023 | $137.77 | -0.81% | 4,588.96 | 4.85% | |
| 55. | Aug 31, 2023 | $136.25 | -1.10% | 4,507.66 | -1.77% | |
| 56. | Sep 30, 2023 | $140.05 | 2.79% | 4,288.05 | -4.87% | |
| 57. | Oct 31, 2023 | $143.86 | 2.72% | 4,193.80 | -2.20% | |
| 58. | Nov 30, 2023 | $150.45 | $0.65 | 5.03% | 4,567.80 | 8.92% |
| 59. | Dec 31, 2023 | $160.33 | 6.57% | 4,769.83 | 4.42% | |
| Average (R): | 1.62% | 1.11% | ||||
| Standard deviation: | 6.30% | 5.31% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of 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, 2019 | 3.72% | 2.97% | 4.41 | 3.49 | 3.92 |
| 2. | Mar 31, 2019 | -4.31% | 1.79% | 35.12 | 0.47 | -4.07 |
| 3. | Apr 30, 2019 | 5.63% | 3.93% | 16.08 | 7.98 | 11.33 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | 5.03% | 8.92% | 11.65 | 61.03 | 26.66 |
| 59. | Dec 31, 2023 | 6.57% | 4.42% | 24.48 | 11.00 | 16.41 |
| Total (Σ): | 2,303.77 | 1,634.30 | 811.33 | |||
| 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, 2019 | 3.72% | 2.97% | 4.41 | 3.49 | 3.92 |
| 2. | Mar 31, 2019 | -4.31% | 1.79% | 35.12 | 0.47 | -4.07 |
| 3. | Apr 30, 2019 | 5.63% | 3.93% | 16.08 | 7.98 | 11.33 |
| 4. | May 31, 2019 | 0.62% | -6.58% | 1.01 | 59.04 | 7.71 |
| 5. | Jun 30, 2019 | 0.95% | 6.89% | 0.44 | 33.49 | -3.86 |
| 6. | Jul 31, 2019 | 7.54% | 1.31% | 35.05 | 0.04 | 1.23 |
| 7. | Aug 31, 2019 | -2.11% | -1.81% | 13.89 | 8.50 | 10.86 |
| 8. | Sep 30, 2019 | 0.92% | 1.72% | 0.49 | 0.37 | -0.43 |
| 9. | Oct 31, 2019 | 4.94% | 2.04% | 11.01 | 0.88 | 3.11 |
| 10. | Nov 30, 2019 | -4.97% | 3.40% | 43.45 | 5.28 | -15.15 |
| 11. | Dec 31, 2019 | -0.17% | 2.86% | 3.19 | 3.07 | -3.13 |
| 12. | Jan 31, 2020 | 0.98% | -0.16% | 0.41 | 1.61 | 0.81 |
| 13. | Feb 29, 2020 | 13.85% | -8.41% | 149.65 | 90.57 | -116.42 |
| 14. | Mar 31, 2020 | -6.94% | -12.51% | 73.32 | 185.44 | 116.61 |
| 15. | Apr 30, 2020 | 4.65% | 12.68% | 9.17 | 134.06 | 35.07 |
| 16. | May 31, 2020 | 13.94% | 4.53% | 151.81 | 11.71 | 42.17 |
| 17. | Jun 30, 2020 | 4.11% | 1.84% | 6.19 | 0.54 | 1.82 |
| 18. | Jul 31, 2020 | 3.10% | 5.51% | 2.20 | 19.40 | 6.53 |
| 19. | Aug 31, 2020 | 8.66% | 7.01% | 49.58 | 34.82 | 41.55 |
| 20. | Sep 30, 2020 | -1.99% | -3.92% | 13.02 | 25.29 | 18.14 |
| 21. | Oct 31, 2020 | -4.19% | -2.77% | 33.73 | 15.00 | 22.49 |
| 22. | Nov 30, 2020 | 21.33% | 10.75% | 388.45 | 93.10 | 190.17 |
| 23. | Dec 31, 2020 | 1.44% | 3.71% | 0.03 | 6.79 | -0.48 |
| 24. | Jan 31, 2021 | -6.50% | -1.11% | 65.99 | 4.93 | 18.03 |
| 25. | Feb 28, 2021 | -4.85% | 2.61% | 41.81 | 2.26 | -9.72 |
| 26. | Mar 31, 2021 | 4.43% | 4.24% | 7.92 | 9.85 | 8.83 |
| 27. | Apr 30, 2021 | 5.46% | 5.24% | 14.74 | 17.11 | 15.88 |
| 28. | May 31, 2021 | 7.05% | 0.55% | 29.53 | 0.31 | -3.03 |
| 29. | Jun 30, 2021 | 2.39% | 2.22% | 0.59 | 1.24 | 0.86 |
| 30. | Jul 31, 2021 | -0.56% | 2.27% | 4.75 | 1.37 | -2.55 |
| 31. | Aug 31, 2021 | -4.86% | 2.90% | 41.99 | 3.22 | -11.62 |
| 32. | Sep 30, 2021 | -6.76% | -4.76% | 70.19 | 34.37 | 49.12 |
| 33. | Oct 31, 2021 | -9.96% | 6.91% | 134.18 | 33.74 | -67.28 |
| 34. | Nov 30, 2021 | -5.41% | -0.83% | 49.38 | 3.76 | 13.63 |
| 35. | Dec 31, 2021 | 6.59% | 4.36% | 24.70 | 10.60 | 16.18 |
| 36. | Jan 31, 2022 | -6.73% | -5.26% | 69.78 | 40.51 | 53.17 |
| 37. | Feb 28, 2022 | 13.90% | -3.14% | 150.91 | 17.99 | -52.11 |
| 38. | Mar 31, 2022 | 4.17% | 3.58% | 6.51 | 6.11 | 6.31 |
| 39. | Apr 30, 2022 | -4.06% | -8.80% | 32.25 | 98.04 | 56.23 |
| 40. | May 31, 2022 | 8.24% | 0.01% | 43.86 | 1.21 | -7.29 |
| 41. | Jun 30, 2022 | 0.94% | -8.39% | 0.46 | 90.21 | 6.48 |
| 42. | Jul 31, 2022 | 6.33% | 9.11% | 22.21 | 64.09 | 37.73 |
| 43. | Aug 31, 2022 | 0.63% | -4.24% | 0.98 | 28.62 | 5.30 |
| 44. | Sep 30, 2022 | -6.80% | -9.34% | 70.90 | 109.11 | 87.95 |
| 45. | Oct 31, 2022 | 12.96% | 7.99% | 128.63 | 47.34 | 78.04 |
| 46. | Nov 30, 2022 | -0.07% | 5.38% | 2.84 | 18.23 | -7.20 |
| 47. | Dec 31, 2022 | -7.57% | -5.90% | 84.38 | 49.04 | 64.33 |
| 48. | Jan 31, 2023 | 6.65% | 6.18% | 25.30 | 25.70 | 25.50 |
| 49. | Feb 28, 2023 | -4.78% | -2.61% | 40.90 | 13.82 | 23.77 |
| 50. | Mar 31, 2023 | 1.87% | 3.51% | 0.06 | 5.76 | 0.60 |
| 51. | Apr 30, 2023 | -0.65% | 1.46% | 5.15 | 0.13 | -0.81 |
| 52. | May 31, 2023 | -4.62% | 0.25% | 38.95 | 0.74 | 5.35 |
| 53. | Jun 30, 2023 | 1.20% | 4.71% | 0.17 | 13.02 | -1.51 |
| 54. | Jul 31, 2023 | -0.81% | 4.85% | 5.92 | 13.99 | -9.10 |
| 55. | Aug 31, 2023 | -1.10% | -1.77% | 7.41 | 8.28 | 7.84 |
| 56. | Sep 30, 2023 | 2.79% | -4.87% | 1.37 | 35.73 | -6.99 |
| 57. | Oct 31, 2023 | 2.72% | -2.20% | 1.21 | 10.92 | -3.64 |
| 58. | Nov 30, 2023 | 5.03% | 8.92% | 11.65 | 61.03 | 26.66 |
| 59. | Dec 31, 2023 | 6.57% | 4.42% | 24.48 | 11.00 | 16.41 |
| Total (Σ): | 2,303.77 | 1,634.30 | 811.33 | |||
Show all
VarianceTMUS = Σ(RTMUS,t–RTMUS)2 ÷ (59 – 1)
= 2,303.77 ÷ (59 – 1)
= 39.72
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceTMUS, S&P 500 = Σ(RTMUS,t–RTMUS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 811.33 ÷ (59 – 1)
= 13.99
Systematic Risk (β) Estimation
| VarianceTMUS | 39.72 |
| VarianceS&P 500 | 28.18 |
| CovarianceTMUS, S&P 500 | 13.99 |
| Correlation coefficientTMUS, S&P 5001 | 0.42 |
| βTMUS2 | 0.50 |
| αTMUS3 | 1.07% |
Calculations
1 Correlation coefficientTMUS, S&P 500
= CovarianceTMUS, S&P 500 ÷ (Standard deviationTMUS × Standard deviationS&P 500)
= 13.99 ÷ (6.30% × 5.31%)
= 0.42
2 βTMUS
= CovarianceTMUS, S&P 500 ÷ VarianceS&P 500
= 13.99 ÷ 28.18
= 0.50
3 αTMUS
= AverageTMUS – βTMUS × AverageS&P 500
= 1.62% – 0.50 × 1.11%
= 1.07%
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 T-Mobile US Inc. common stock | βTMUS | 0.50 |
| Expected rate of return on T-Mobile US Inc. common stock3 | E(RTMUS) | 9.19% |
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]
= 4.65% + 0.50 [13.79% – 4.65%]
= 9.19%