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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.’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) | |||||
---|---|---|---|---|---|---|
t | Date | PriceTMUS,t1 | DividendTMUS,t1 | RTMUS,t2 | PriceS&P 500,t | RS&P 500,t3 |
Jan 31, 2015 | ||||||
1. | Feb 28, 2015 | |||||
2. | Mar 31, 2015 | |||||
3. | Apr 30, 2015 | |||||
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
58. | Nov 30, 2019 | |||||
59. | Dec 31, 2019 | |||||
Average (R): | ||||||
Standard deviation: |
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, 2015 | ||||||
1. | Feb 28, 2015 | |||||
2. | Mar 31, 2015 | |||||
3. | Apr 30, 2015 | |||||
4. | May 31, 2015 | |||||
5. | Jun 30, 2015 | |||||
6. | Jul 31, 2015 | |||||
7. | Aug 31, 2015 | |||||
8. | Sep 30, 2015 | |||||
9. | Oct 31, 2015 | |||||
10. | Nov 30, 2015 | |||||
11. | Dec 31, 2015 | |||||
12. | Jan 31, 2016 | |||||
13. | Feb 29, 2016 | |||||
14. | Mar 31, 2016 | |||||
15. | Apr 30, 2016 | |||||
16. | May 31, 2016 | |||||
17. | Jun 30, 2016 | |||||
18. | Jul 31, 2016 | |||||
19. | Aug 31, 2016 | |||||
20. | Sep 30, 2016 | |||||
21. | Oct 31, 2016 | |||||
22. | Nov 30, 2016 | |||||
23. | Dec 31, 2016 | |||||
24. | Jan 31, 2017 | |||||
25. | Feb 28, 2017 | |||||
26. | Mar 31, 2017 | |||||
27. | Apr 30, 2017 | |||||
28. | May 31, 2017 | |||||
29. | Jun 30, 2017 | |||||
30. | Jul 31, 2017 | |||||
31. | Aug 31, 2017 | |||||
32. | Sep 30, 2017 | |||||
33. | Oct 31, 2017 | |||||
34. | Nov 30, 2017 | |||||
35. | Dec 31, 2017 | |||||
36. | Jan 31, 2018 | |||||
37. | Feb 28, 2018 | |||||
38. | Mar 31, 2018 | |||||
39. | Apr 30, 2018 | |||||
40. | May 31, 2018 | |||||
41. | Jun 30, 2018 | |||||
42. | Jul 31, 2018 | |||||
43. | Aug 31, 2018 | |||||
44. | Sep 30, 2018 | |||||
45. | Oct 31, 2018 | |||||
46. | Nov 30, 2018 | |||||
47. | Dec 31, 2018 | |||||
48. | Jan 31, 2019 | |||||
49. | Feb 28, 2019 | |||||
50. | Mar 31, 2019 | |||||
51. | Apr 30, 2019 | |||||
52. | May 31, 2019 | |||||
53. | Jun 30, 2019 | |||||
54. | Jul 31, 2019 | |||||
55. | Aug 31, 2019 | |||||
56. | Sep 30, 2019 | |||||
57. | Oct 31, 2019 | |||||
58. | Nov 30, 2019 | |||||
59. | Dec 31, 2019 | |||||
Average (R): | ||||||
Standard deviation: |
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, 2015 | |||||
2. | Mar 31, 2015 | |||||
3. | Apr 30, 2015 | |||||
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
58. | Nov 30, 2019 | |||||
59. | Dec 31, 2019 | |||||
Total (Σ): |
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, 2015 | |||||
2. | Mar 31, 2015 | |||||
3. | Apr 30, 2015 | |||||
4. | May 31, 2015 | |||||
5. | Jun 30, 2015 | |||||
6. | Jul 31, 2015 | |||||
7. | Aug 31, 2015 | |||||
8. | Sep 30, 2015 | |||||
9. | Oct 31, 2015 | |||||
10. | Nov 30, 2015 | |||||
11. | Dec 31, 2015 | |||||
12. | Jan 31, 2016 | |||||
13. | Feb 29, 2016 | |||||
14. | Mar 31, 2016 | |||||
15. | Apr 30, 2016 | |||||
16. | May 31, 2016 | |||||
17. | Jun 30, 2016 | |||||
18. | Jul 31, 2016 | |||||
19. | Aug 31, 2016 | |||||
20. | Sep 30, 2016 | |||||
21. | Oct 31, 2016 | |||||
22. | Nov 30, 2016 | |||||
23. | Dec 31, 2016 | |||||
24. | Jan 31, 2017 | |||||
25. | Feb 28, 2017 | |||||
26. | Mar 31, 2017 | |||||
27. | Apr 30, 2017 | |||||
28. | May 31, 2017 | |||||
29. | Jun 30, 2017 | |||||
30. | Jul 31, 2017 | |||||
31. | Aug 31, 2017 | |||||
32. | Sep 30, 2017 | |||||
33. | Oct 31, 2017 | |||||
34. | Nov 30, 2017 | |||||
35. | Dec 31, 2017 | |||||
36. | Jan 31, 2018 | |||||
37. | Feb 28, 2018 | |||||
38. | Mar 31, 2018 | |||||
39. | Apr 30, 2018 | |||||
40. | May 31, 2018 | |||||
41. | Jun 30, 2018 | |||||
42. | Jul 31, 2018 | |||||
43. | Aug 31, 2018 | |||||
44. | Sep 30, 2018 | |||||
45. | Oct 31, 2018 | |||||
46. | Nov 30, 2018 | |||||
47. | Dec 31, 2018 | |||||
48. | Jan 31, 2019 | |||||
49. | Feb 28, 2019 | |||||
50. | Mar 31, 2019 | |||||
51. | Apr 30, 2019 | |||||
52. | May 31, 2019 | |||||
53. | Jun 30, 2019 | |||||
54. | Jul 31, 2019 | |||||
55. | Aug 31, 2019 | |||||
56. | Sep 30, 2019 | |||||
57. | Oct 31, 2019 | |||||
58. | Nov 30, 2019 | |||||
59. | Dec 31, 2019 | |||||
Total (Σ): |
Show all
VarianceTMUS = Σ(RTMUS,t–RTMUS)2 ÷ (59 – 1)
= ÷ (59 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= ÷ (59 – 1)
=
CovarianceTMUS, S&P 500 = Σ(RTMUS,t–RTMUS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= ÷ (59 – 1)
=
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]
= + [ – ]
=