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T-Mobile US Inc. (TMUS)
Capital Asset Pricing Model (CAPM)
Difficulty: Intermediate
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]
= + [ – ]
=