T-Mobile US Inc. (NASDAQ:TMUS)

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
Variance and Covariance
Systematic Risk (β) Estimation
Expected Rate of Return

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	Price_TMUS,t¹	Dividend_TMUS,t¹	R_TMUS,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2020	$79.19			3,225.52
1.	Feb 29, 2020	$90.16		13.85%	2,954.22	-8.41%
2.	Mar 31, 2020	$83.90		-6.94%	2,584.59	-12.51%
3.	Apr 30, 2020	$87.80		4.65%	2,912.43	12.68%
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58.	Nov 30, 2024	$246.94	$0.88	11.05%	6,032.38	5.73%
59.	Dec 31, 2024	$220.73		-10.61%	5,881.63	-2.50%
Average (R):				1.99%		1.16%
Standard deviation:				6.59%		5.28%

		T-Mobile US Inc. (TMUS)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_TMUS,t¹	Dividend_TMUS,t¹	R_TMUS,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2020	$79.19			3,225.52
1.	Feb 29, 2020	$90.16		13.85%	2,954.22	-8.41%
2.	Mar 31, 2020	$83.90		-6.94%	2,584.59	-12.51%
3.	Apr 30, 2020	$87.80		4.65%	2,912.43	12.68%
4.	May 31, 2020	$100.04		13.94%	3,044.31	4.53%
5.	Jun 30, 2020	$104.15		4.11%	3,100.29	1.84%
6.	Jul 31, 2020	$107.38		3.10%	3,271.12	5.51%
7.	Aug 31, 2020	$116.68		8.66%	3,500.31	7.01%
8.	Sep 30, 2020	$114.36		-1.99%	3,363.00	-3.92%
9.	Oct 31, 2020	$109.57		-4.19%	3,269.96	-2.77%
10.	Nov 30, 2020	$132.94		21.33%	3,621.63	10.75%
11.	Dec 31, 2020	$134.85		1.44%	3,756.07	3.71%
12.	Jan 31, 2021	$126.08		-6.50%	3,714.24	-1.11%
13.	Feb 28, 2021	$119.97		-4.85%	3,811.15	2.61%
14.	Mar 31, 2021	$125.29		4.43%	3,972.89	4.24%
15.	Apr 30, 2021	$132.13		5.46%	4,181.17	5.24%
16.	May 31, 2021	$141.45		7.05%	4,204.11	0.55%
17.	Jun 30, 2021	$144.83		2.39%	4,297.50	2.22%
18.	Jul 31, 2021	$144.02		-0.56%	4,395.26	2.27%
19.	Aug 31, 2021	$137.02		-4.86%	4,522.68	2.90%
20.	Sep 30, 2021	$127.76		-6.76%	4,307.54	-4.76%
21.	Oct 31, 2021	$115.03		-9.96%	4,605.38	6.91%
22.	Nov 30, 2021	$108.81		-5.41%	4,567.00	-0.83%
23.	Dec 31, 2021	$115.98		6.59%	4,766.18	4.36%
24.	Jan 31, 2022	$108.17		-6.73%	4,515.55	-5.26%
25.	Feb 28, 2022	$123.21		13.90%	4,373.94	-3.14%
26.	Mar 31, 2022	$128.35		4.17%	4,530.41	3.58%
27.	Apr 30, 2022	$123.14		-4.06%	4,131.93	-8.80%
28.	May 31, 2022	$133.29		8.24%	4,132.15	0.01%
29.	Jun 30, 2022	$134.54		0.94%	3,785.38	-8.39%
30.	Jul 31, 2022	$143.06		6.33%	4,130.29	9.11%
31.	Aug 31, 2022	$143.96		0.63%	3,955.00	-4.24%
32.	Sep 30, 2022	$134.17		-6.80%	3,585.62	-9.34%
33.	Oct 31, 2022	$151.56		12.96%	3,871.98	7.99%
34.	Nov 30, 2022	$151.46		-0.07%	4,080.11	5.38%
35.	Dec 31, 2022	$140.00		-7.57%	3,839.50	-5.90%
36.	Jan 31, 2023	$149.31		6.65%	4,076.60	6.18%
37.	Feb 28, 2023	$142.18		-4.78%	3,970.15	-2.61%
38.	Mar 31, 2023	$144.84		1.87%	4,109.31	3.51%
39.	Apr 30, 2023	$143.90		-0.65%	4,169.48	1.46%
40.	May 31, 2023	$137.25		-4.62%	4,179.83	0.25%
41.	Jun 30, 2023	$138.90		1.20%	4,376.86	4.71%
42.	Jul 31, 2023	$137.77		-0.81%	4,588.96	4.85%
43.	Aug 31, 2023	$136.25		-1.10%	4,507.66	-1.77%
44.	Sep 30, 2023	$140.05		2.79%	4,288.05	-4.87%
45.	Oct 31, 2023	$143.86		2.72%	4,193.80	-2.20%
46.	Nov 30, 2023	$150.45	$0.65	5.03%	4,567.80	8.92%
47.	Dec 31, 2023	$160.33		6.57%	4,769.83	4.42%
48.	Jan 31, 2024	$161.23		0.56%	4,845.65	1.59%
49.	Feb 29, 2024	$163.30	$0.65	1.69%	5,096.27	5.17%
50.	Mar 31, 2024	$163.22		-0.05%	5,254.35	3.10%
51.	Apr 30, 2024	$164.17		0.58%	5,035.69	-4.16%
52.	May 31, 2024	$174.96	$0.65	6.97%	5,277.51	4.80%
53.	Jun 30, 2024	$176.18		0.70%	5,460.48	3.47%
54.	Jul 31, 2024	$182.28		3.46%	5,522.30	1.13%
55.	Aug 31, 2024	$198.72	$0.65	9.38%	5,648.40	2.28%
56.	Sep 30, 2024	$206.36		3.84%	5,762.48	2.02%
57.	Oct 31, 2024	$223.16		8.14%	5,705.45	-0.99%
58.	Nov 30, 2024	$246.94	$0.88	11.05%	6,032.38	5.73%
59.	Dec 31, 2024	$220.73		-10.61%	5,881.63	-2.50%
Average (R):				1.99%		1.16%
Standard deviation:				6.59%		5.28%

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	R_TMUS,t	R_{S&P 500,t}	(R_TMUS,t–R_TMUS)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_TMUS,t–R_TMUS)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2020	13.85%	-8.41%	140.68	91.63	-113.54
2.	Mar 31, 2020	-6.94%	-12.51%	79.83	186.96	122.17
3.	Apr 30, 2020	4.65%	12.68%	7.06	132.78	30.61
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58.	Nov 30, 2024	11.05%	5.73%	82.06	20.87	41.39
59.	Dec 31, 2024	-10.61%	-2.50%	158.90	13.40	46.14
Total (Σ):				2,515.13	1,618.62	902.53

t	Date	R_TMUS,t	R_{S&P 500,t}	(R_TMUS,t–R_TMUS)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_TMUS,t–R_TMUS)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2020	13.85%	-8.41%	140.68	91.63	-113.54
2.	Mar 31, 2020	-6.94%	-12.51%	79.83	186.96	122.17
3.	Apr 30, 2020	4.65%	12.68%	7.06	132.78	30.61
4.	May 31, 2020	13.94%	4.53%	142.78	11.34	40.23
5.	Jun 30, 2020	4.11%	1.84%	4.48	0.46	1.43
6.	Jul 31, 2020	3.10%	5.51%	1.23	18.91	4.83
7.	Aug 31, 2020	8.66%	7.01%	44.48	34.17	38.98
8.	Sep 30, 2020	-1.99%	-3.92%	15.84	25.85	20.24
9.	Oct 31, 2020	-4.19%	-2.77%	38.20	15.43	24.28
10.	Nov 30, 2020	21.33%	10.75%	373.92	92.03	185.51
11.	Dec 31, 2020	1.44%	3.71%	0.31	6.51	-1.42
12.	Jan 31, 2021	-6.50%	-1.11%	72.17	5.18	19.33
13.	Feb 28, 2021	-4.85%	2.61%	46.76	2.10	-9.90
14.	Mar 31, 2021	4.43%	4.24%	5.97	9.50	7.53
15.	Apr 30, 2021	5.46%	5.24%	12.02	16.66	14.15
16.	May 31, 2021	7.05%	0.55%	25.62	0.38	-3.10
17.	Jun 30, 2021	2.39%	2.22%	0.16	1.12	0.42
18.	Jul 31, 2021	-0.56%	2.27%	6.51	1.24	-2.84
19.	Aug 31, 2021	-4.86%	2.90%	46.95	3.02	-11.91
20.	Sep 30, 2021	-6.76%	-4.76%	76.56	35.02	51.78
21.	Oct 31, 2021	-9.96%	6.91%	142.94	33.10	-68.78
22.	Nov 30, 2021	-5.41%	-0.83%	54.75	3.98	14.76
23.	Dec 31, 2021	6.59%	4.36%	21.14	10.24	14.71
24.	Jan 31, 2022	-6.73%	-5.26%	76.14	41.21	56.02
25.	Feb 28, 2022	13.90%	-3.14%	141.90	18.47	-51.19
26.	Mar 31, 2022	4.17%	3.58%	4.75	5.84	5.27
27.	Apr 30, 2022	-4.06%	-8.80%	36.61	99.14	60.25
28.	May 31, 2022	8.24%	0.01%	39.07	1.34	-7.23
29.	Jun 30, 2022	0.94%	-8.39%	1.11	91.26	10.07
30.	Jul 31, 2022	6.33%	9.11%	18.84	63.21	34.51
31.	Aug 31, 2022	0.63%	-4.24%	1.86	29.22	7.37
32.	Sep 30, 2022	-6.80%	-9.34%	77.30	110.27	92.33
33.	Oct 31, 2022	12.96%	7.99%	120.33	46.58	74.87
34.	Nov 30, 2022	-0.07%	5.38%	4.23	17.76	-8.67
35.	Dec 31, 2022	-7.57%	-5.90%	91.36	49.82	67.47
36.	Jan 31, 2023	6.65%	6.18%	21.70	25.14	23.36
37.	Feb 28, 2023	-4.78%	-2.61%	45.79	14.23	25.53
38.	Mar 31, 2023	1.87%	3.51%	0.01	5.49	-0.28
39.	Apr 30, 2023	-0.65%	1.46%	6.97	0.09	-0.80
40.	May 31, 2023	-4.62%	0.25%	43.73	0.83	6.04
41.	Jun 30, 2023	1.20%	4.71%	0.62	12.62	-2.81
42.	Jul 31, 2023	-0.81%	4.85%	7.87	13.58	-10.34
43.	Aug 31, 2023	-1.10%	-1.77%	9.58	8.60	9.08
44.	Sep 30, 2023	2.79%	-4.87%	0.64	36.40	-4.81
45.	Oct 31, 2023	2.72%	-2.20%	0.53	11.28	-2.45
46.	Nov 30, 2023	5.03%	8.92%	9.25	60.17	23.59
47.	Dec 31, 2023	6.57%	4.42%	20.93	10.64	14.92
48.	Jan 31, 2024	0.56%	1.59%	2.05	0.18	-0.61
49.	Feb 29, 2024	1.69%	5.17%	0.09	16.09	-1.22
50.	Mar 31, 2024	-0.05%	3.10%	4.16	3.77	-3.96
51.	Apr 30, 2024	0.58%	-4.16%	1.99	28.33	7.50
52.	May 31, 2024	6.97%	4.80%	24.77	13.26	18.12
53.	Jun 30, 2024	0.70%	3.47%	1.68	5.32	-2.98
54.	Jul 31, 2024	3.46%	1.13%	2.16	0.00	-0.04
55.	Aug 31, 2024	9.38%	2.28%	54.52	1.26	8.29
56.	Sep 30, 2024	3.84%	2.02%	3.43	0.74	1.59
57.	Oct 31, 2024	8.14%	-0.99%	37.81	4.63	-13.23
58.	Nov 30, 2024	11.05%	5.73%	82.06	20.87	41.39
59.	Dec 31, 2024	-10.61%	-2.50%	158.90	13.40	46.14
Total (Σ):				2,515.13	1,618.62	902.53

Show all

Variance_TMUS = Σ(R_TMUS,t–R_TMUS)² ÷ (59 – 1)
= 2,515.13 ÷ (59 – 1)
= 43.36

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91

Covariance_{TMUS, S&P 500} = Σ(R_TMUS,t–R_TMUS)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 902.53 ÷ (59 – 1)
= 15.56

Systematic Risk (β) Estimation

Variance_TMUS	43.36
Variance_{S&P 500}	27.91
Covariance_{TMUS, S&P 500}	15.56
Correlation coefficient_{TMUS, S&P 500}¹	0.45
β_TMUS²	0.56
α_TMUS³	1.34%

Calculations

¹ Correlation coefficient_{TMUS, S&P 500}
= Covariance_{TMUS, S&P 500} ÷ (Standard deviation_TMUS × Standard deviation_{S&P 500})
= 15.56 ÷ (6.59% × 5.28%)
= 0.45

² β_TMUS
= Covariance_{TMUS, S&P 500} ÷ Variance_{S&P 500}
= 15.56 ÷ 27.91
= 0.56

³ α_TMUS
= Average_TMUS – β_TMUS × Average_{S&P 500}
= 1.99% – 0.56 × 1.16%
= 1.34%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.78%
Expected rate of return on market portfolio²	E(R_M)	14.43%
Systematic risk (β) of T-Mobile US Inc. common stock	β_TMUS	0.56

Expected rate of return on T-Mobile US Inc. common stock³	E(R_TMUS)	10.16%

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).

² See details »

³ E(R_TMUS) = R_F + β_TMUS [E(R_M) – R_F]
= 4.78% + 0.56 [14.43% – 4.78%]
= 10.16%