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T-Mobile US Inc. (TMUS)
Capital Asset Pricing Model (CAPM)
Intermediate level
Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like T-Mobile US Inc.’s 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) | |||||
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| t | Date | PriceTMUS,t1 | DividendTMUS,t1 | RTMUS,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2014 | |
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| 1. | Feb 28, 2014 | |
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| 2. | Mar 31, 2014 | |
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| 3. | Apr 30, 2014 | |
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| 58. | Nov 30, 2018 | |
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| 59. | Dec 31, 2018 | |
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| Average: | |
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| Standard deviation: | |
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| T-Mobile US Inc. (TMUS) | Standard & Poor’s 500 (S&P 500) | |||||
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| t | Date | PriceTMUS,t1 | DividendTMUS,t1 | RTMUS,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2014 | |
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| 1. | Feb 28, 2014 | |
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| 2. | Mar 31, 2014 | |
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| 3. | Apr 30, 2014 | |
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| 4. | May 31, 2014 | |
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| 5. | Jun 30, 2014 | |
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| 6. | Jul 31, 2014 | |
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| 7. | Aug 31, 2014 | |
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| 8. | Sep 30, 2014 | |
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| 9. | Oct 31, 2014 | |
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| 10. | Nov 30, 2014 | |
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| 11. | Dec 31, 2014 | |
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| 12. | Jan 31, 2015 | |
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| 13. | Feb 28, 2015 | |
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| 14. | Mar 31, 2015 | |
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| 15. | Apr 30, 2015 | |
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| 16. | May 31, 2015 | |
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| 17. | Jun 30, 2015 | |
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| 18. | Jul 31, 2015 | |
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| 19. | Aug 31, 2015 | |
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| 20. | Sep 30, 2015 | |
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| 21. | Oct 31, 2015 | |
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| 22. | Nov 30, 2015 | |
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| 23. | Dec 31, 2015 | |
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| 24. | Jan 31, 2016 | |
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| 25. | Feb 29, 2016 | |
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| 26. | Mar 31, 2016 | |
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| 27. | Apr 30, 2016 | |
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| 28. | May 31, 2016 | |
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| 29. | Jun 30, 2016 | |
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| 30. | Jul 31, 2016 | |
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| 31. | Aug 31, 2016 | |
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| 32. | Sep 30, 2016 | |
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| 33. | Oct 31, 2016 | |
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| 34. | Nov 30, 2016 | |
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| 35. | Dec 31, 2016 | |
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| 36. | Jan 31, 2017 | |
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| 37. | Feb 28, 2017 | |
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| 38. | Mar 31, 2017 | |
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| 39. | Apr 30, 2017 | |
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| 40. | May 31, 2017 | |
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| 41. | Jun 30, 2017 | |
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| 42. | Jul 31, 2017 | |
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| 43. | Aug 31, 2017 | |
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| 44. | Sep 30, 2017 | |
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| 45. | Oct 31, 2017 | |
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| 46. | Nov 30, 2017 | |
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| 47. | Dec 31, 2017 | |
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| 48. | Jan 31, 2018 | |
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| 49. | Feb 28, 2018 | |
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| 50. | Mar 31, 2018 | |
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| 51. | Apr 30, 2018 | |
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| 52. | May 31, 2018 | |
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| 53. | Jun 30, 2018 | |
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| 54. | Jul 31, 2018 | |
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| 55. | Aug 31, 2018 | |
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| 56. | Sep 30, 2018 | |
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| 57. | Oct 31, 2018 | |
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| 58. | Nov 30, 2018 | |
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| 59. | Dec 31, 2018 | |
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| Average: | |
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| Standard deviation: | |
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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
Systematic Risk (β) Estimation
| VarianceTMUS | |
| VarianceS&P 500 | |
| CovarianceTMUS, S&P 500 | |
| Correlation coefficientTMUS, S&P 5001 | |
| βTMUS2 | |
| αTMUS3 | |
Calculations
1 Correlation coefficientTMUS, S&P 500
= CovarianceTMUS, S&P 500 ÷ (Standard deviationTMUS × Standard deviationS&P 500)
= ÷ ( × )
2 βTMUS
= CovarianceTMUS, S&P 500 ÷ VarianceS&P 500
= ÷
3 αTMUS
= AverageTMUS – βTMUS × AverageS&P 500
= – ×
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | |
| Expected rate of return on market portfolio2 | E(RM) | |
| Systematic risk (β) of T-Mobile US Inc.’s common stock | βTMUS | |
| Expected rate of return on T-Mobile US Inc.’s common stock3 | E(RTMUS) | |
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]
= + [ – ]
=