Thermo Fisher Scientific Inc. (NYSE:TMO)

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 Thermo Fisher Scientific Inc. common stock.

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

Rates of Return

Thermo Fisher Scientific Inc., monthly rates of return

		Thermo Fisher Scientific Inc. (TMO)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_TMO,t¹	Dividend_TMO,t¹	R_TMO,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$245.67			2,704.10
1.	Feb 28, 2019	$259.57		5.66%	2,784.49	2.97%
2.	Mar 31, 2019	$273.72	$0.19	5.52%	2,834.40	1.79%
3.	Apr 30, 2019	$277.45		1.36%	2,945.83	3.93%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2023	$495.76		11.46%	4,567.80	8.92%
59.	Dec 31, 2023	$530.79	$0.35	7.14%	4,769.83	4.42%
Average (R):				1.55%		1.11%
Standard deviation:				6.71%		5.31%

		Thermo Fisher Scientific Inc. (TMO)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_TMO,t¹	Dividend_TMO,t¹	R_TMO,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$245.67			2,704.10
1.	Feb 28, 2019	$259.57		5.66%	2,784.49	2.97%
2.	Mar 31, 2019	$273.72	$0.19	5.52%	2,834.40	1.79%
3.	Apr 30, 2019	$277.45		1.36%	2,945.83	3.93%
4.	May 31, 2019	$266.98		-3.77%	2,752.06	-6.58%
5.	Jun 30, 2019	$293.68	$0.19	10.07%	2,941.76	6.89%
6.	Jul 31, 2019	$277.68		-5.45%	2,980.38	1.31%
7.	Aug 31, 2019	$287.06		3.38%	2,926.46	-1.81%
8.	Sep 30, 2019	$291.27	$0.19	1.53%	2,976.74	1.72%
9.	Oct 31, 2019	$301.98		3.68%	3,037.56	2.04%
10.	Nov 30, 2019	$313.95		3.96%	3,140.98	3.40%
11.	Dec 31, 2019	$324.87	$0.19	3.54%	3,230.78	2.86%
12.	Jan 31, 2020	$313.19		-3.60%	3,225.52	-0.16%
13.	Feb 29, 2020	$290.80		-7.15%	2,954.22	-8.41%
14.	Mar 31, 2020	$283.60	$0.22	-2.40%	2,584.59	-12.51%
15.	Apr 30, 2020	$334.68		18.01%	2,912.43	12.68%
16.	May 31, 2020	$349.19		4.34%	3,044.31	4.53%
17.	Jun 30, 2020	$362.34	$0.22	3.83%	3,100.29	1.84%
18.	Jul 31, 2020	$413.95		14.24%	3,271.12	5.51%
19.	Aug 31, 2020	$428.98		3.63%	3,500.31	7.01%
20.	Sep 30, 2020	$441.52	$0.22	2.97%	3,363.00	-3.92%
21.	Oct 31, 2020	$473.12		7.16%	3,269.96	-2.77%
22.	Nov 30, 2020	$464.98		-1.72%	3,621.63	10.75%
23.	Dec 31, 2020	$465.78	$0.22	0.22%	3,756.07	3.71%
24.	Jan 31, 2021	$509.70		9.43%	3,714.24	-1.11%
25.	Feb 28, 2021	$450.08		-11.70%	3,811.15	2.61%
26.	Mar 31, 2021	$456.38	$0.26	1.46%	3,972.89	4.24%
27.	Apr 30, 2021	$470.23		3.03%	4,181.17	5.24%
28.	May 31, 2021	$469.50		-0.16%	4,204.11	0.55%
29.	Jun 30, 2021	$504.47	$0.26	7.50%	4,297.50	2.22%
30.	Jul 31, 2021	$540.01		7.05%	4,395.26	2.27%
31.	Aug 31, 2021	$554.95		2.77%	4,522.68	2.90%
32.	Sep 30, 2021	$571.33	$0.26	3.00%	4,307.54	-4.76%
33.	Oct 31, 2021	$633.07		10.81%	4,605.38	6.91%
34.	Nov 30, 2021	$632.83		-0.04%	4,567.00	-0.83%
35.	Dec 31, 2021	$667.24	$0.26	5.48%	4,766.18	4.36%
36.	Jan 31, 2022	$581.30		-12.88%	4,515.55	-5.26%
37.	Feb 28, 2022	$544.00		-6.42%	4,373.94	-3.14%
38.	Mar 31, 2022	$590.65	$0.30	8.63%	4,530.41	3.58%
39.	Apr 30, 2022	$552.92		-6.39%	4,131.93	-8.80%
40.	May 31, 2022	$567.57		2.65%	4,132.15	0.01%
41.	Jun 30, 2022	$543.28	$0.30	-4.23%	3,785.38	-8.39%
42.	Jul 31, 2022	$598.41		10.15%	4,130.29	9.11%
43.	Aug 31, 2022	$545.32		-8.87%	3,955.00	-4.24%
44.	Sep 30, 2022	$507.19	$0.30	-6.94%	3,585.62	-9.34%
45.	Oct 31, 2022	$513.97		1.34%	3,871.98	7.99%
46.	Nov 30, 2022	$560.22		9.00%	4,080.11	5.38%
47.	Dec 31, 2022	$550.69	$0.30	-1.65%	3,839.50	-5.90%
48.	Jan 31, 2023	$570.33		3.57%	4,076.60	6.18%
49.	Feb 28, 2023	$541.76		-5.01%	3,970.15	-2.61%
50.	Mar 31, 2023	$576.37	$0.35	6.45%	4,109.31	3.51%
51.	Apr 30, 2023	$554.90		-3.73%	4,169.48	1.46%
52.	May 31, 2023	$508.46		-8.37%	4,179.83	0.25%
53.	Jun 30, 2023	$521.75	$0.35	2.68%	4,376.86	4.71%
54.	Jul 31, 2023	$548.66		5.16%	4,588.96	4.85%
55.	Aug 31, 2023	$557.10		1.54%	4,507.66	-1.77%
56.	Sep 30, 2023	$506.17	$0.35	-9.08%	4,288.05	-4.87%
57.	Oct 31, 2023	$444.77		-12.13%	4,193.80	-2.20%
58.	Nov 30, 2023	$495.76		11.46%	4,567.80	8.92%
59.	Dec 31, 2023	$530.79	$0.35	7.14%	4,769.83	4.42%
Average (R):				1.55%		1.11%
Standard deviation:				6.71%		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 TMO during period t

³ Rate of return on S&P 500 (the market portfolio proxy) during period t

Variance and Covariance

Thermo Fisher Scientific Inc., calculation of variance and covariance of returns

t	Date	R_TMO,t	R_{S&P 500,t}	(R_TMO,t–R_TMO)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_TMO,t–R_TMO)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	5.66%	2.97%	16.84	3.49	7.66
2.	Mar 31, 2019	5.52%	1.79%	15.76	0.47	2.73
3.	Apr 30, 2019	1.36%	3.93%	0.04	7.98	-0.54
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2023	11.46%	8.92%	98.20	61.03	77.41
59.	Dec 31, 2023	7.14%	4.42%	31.16	11.00	18.51
Total (Σ):				2,609.92	1,634.30	1,315.98

t	Date	R_TMO,t	R_{S&P 500,t}	(R_TMO,t–R_TMO)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_TMO,t–R_TMO)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	5.66%	2.97%	16.84	3.49	7.66
2.	Mar 31, 2019	5.52%	1.79%	15.76	0.47	2.73
3.	Apr 30, 2019	1.36%	3.93%	0.04	7.98	-0.54
4.	May 31, 2019	-3.77%	-6.58%	28.39	59.04	40.94
5.	Jun 30, 2019	10.07%	6.89%	72.54	33.49	49.29
6.	Jul 31, 2019	-5.45%	1.31%	49.04	0.04	-1.45
7.	Aug 31, 2019	3.38%	-1.81%	3.32	8.50	-5.31
8.	Sep 30, 2019	1.53%	1.72%	0.00	0.37	-0.01
9.	Oct 31, 2019	3.68%	2.04%	4.50	0.88	1.99
10.	Nov 30, 2019	3.96%	3.40%	5.80	5.28	5.54
11.	Dec 31, 2019	3.54%	2.86%	3.94	3.07	3.48
12.	Jan 31, 2020	-3.60%	-0.16%	26.52	1.61	6.53
13.	Feb 29, 2020	-7.15%	-8.41%	75.76	90.57	82.83
14.	Mar 31, 2020	-2.40%	-12.51%	15.64	185.44	53.86
15.	Apr 30, 2020	18.01%	12.68%	270.82	134.06	190.54
16.	May 31, 2020	4.34%	4.53%	7.73	11.71	9.52
17.	Jun 30, 2020	3.83%	1.84%	5.17	0.54	1.67
18.	Jul 31, 2020	14.24%	5.51%	161.00	19.40	55.88
19.	Aug 31, 2020	3.63%	7.01%	4.31	34.82	12.25
20.	Sep 30, 2020	2.97%	-3.92%	2.02	25.29	-7.14
21.	Oct 31, 2020	7.16%	-2.77%	31.39	15.00	-21.69
22.	Nov 30, 2020	-1.72%	10.75%	10.73	93.10	-31.60
23.	Dec 31, 2020	0.22%	3.71%	1.78	6.79	-3.48
24.	Jan 31, 2021	9.43%	-1.11%	62.01	4.93	-17.48
25.	Feb 28, 2021	-11.70%	2.61%	175.61	2.26	-19.92
26.	Mar 31, 2021	1.46%	4.24%	0.01	9.85	-0.31
27.	Apr 30, 2021	3.03%	5.24%	2.19	17.11	6.12
28.	May 31, 2021	-0.16%	0.55%	2.92	0.31	0.95
29.	Jun 30, 2021	7.50%	2.22%	35.39	1.24	6.64
30.	Jul 31, 2021	7.05%	2.27%	30.14	1.37	6.42
31.	Aug 31, 2021	2.77%	2.90%	1.47	3.22	2.17
32.	Sep 30, 2021	3.00%	-4.76%	2.08	34.37	-8.46
33.	Oct 31, 2021	10.81%	6.91%	85.59	33.74	53.74
34.	Nov 30, 2021	-0.04%	-0.83%	2.54	3.76	3.09
35.	Dec 31, 2021	5.48%	4.36%	15.40	10.60	12.77
36.	Jan 31, 2022	-12.88%	-5.26%	208.36	40.51	91.87
37.	Feb 28, 2022	-6.42%	-3.14%	63.54	17.99	33.81
38.	Mar 31, 2022	8.63%	3.58%	50.07	6.11	17.49
39.	Apr 30, 2022	-6.39%	-8.80%	63.09	98.04	78.64
40.	May 31, 2022	2.65%	0.01%	1.20	1.21	-1.20
41.	Jun 30, 2022	-4.23%	-8.39%	33.43	90.21	54.91
42.	Jul 31, 2022	10.15%	9.11%	73.84	64.09	68.79
43.	Aug 31, 2022	-8.87%	-4.24%	108.71	28.62	55.78
44.	Sep 30, 2022	-6.94%	-9.34%	72.11	109.11	88.70
45.	Oct 31, 2022	1.34%	7.99%	0.05	47.34	-1.50
46.	Nov 30, 2022	9.00%	5.38%	55.41	18.23	31.78
47.	Dec 31, 2022	-1.65%	-5.90%	10.26	49.04	22.43
48.	Jan 31, 2023	3.57%	6.18%	4.05	25.70	10.20
49.	Feb 28, 2023	-5.01%	-2.61%	43.09	13.82	24.40
50.	Mar 31, 2023	6.45%	3.51%	23.99	5.76	11.75
51.	Apr 30, 2023	-3.73%	1.46%	27.88	0.13	-1.89
52.	May 31, 2023	-8.37%	0.25%	98.48	0.74	8.51
53.	Jun 30, 2023	2.68%	4.71%	1.27	13.02	4.07
54.	Jul 31, 2023	5.16%	4.85%	12.98	13.99	13.47
55.	Aug 31, 2023	1.54%	-1.77%	0.00	8.28	0.05
56.	Sep 30, 2023	-9.08%	-4.87%	113.08	35.73	63.57
57.	Oct 31, 2023	-12.13%	-2.20%	187.28	10.92	45.21
58.	Nov 30, 2023	11.46%	8.92%	98.20	61.03	77.41
59.	Dec 31, 2023	7.14%	4.42%	31.16	11.00	18.51
Total (Σ):				2,609.92	1,634.30	1,315.98

Show all

Variance_TMO = Σ(R_TMO,t–R_TMO)² ÷ (59 – 1)
= 2,609.92 ÷ (59 – 1)
= 45.00

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18

Covariance_{TMO, S&P 500} = Σ(R_TMO,t–R_TMO)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 1,315.98 ÷ (59 – 1)
= 22.69

Systematic Risk (β) Estimation

Variance_TMO	45.00
Variance_{S&P 500}	28.18
Covariance_{TMO, S&P 500}	22.69
Correlation coefficient_{TMO, S&P 500}¹	0.64
β_TMO²	0.81
α_TMO³	0.66%

Calculations

¹ Correlation coefficient_{TMO, S&P 500}
= Covariance_{TMO, S&P 500} ÷ (Standard deviation_TMO × Standard deviation_{S&P 500})
= 22.69 ÷ (6.71% × 5.31%)
= 0.64

² β_TMO
= Covariance_{TMO, S&P 500} ÷ Variance_{S&P 500}
= 22.69 ÷ 28.18
= 0.81

³ α_TMO
= Average_TMO – β_TMO × Average_{S&P 500}
= 1.55% – 0.81 × 1.11%
= 0.66%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.67%
Expected rate of return on market portfolio²	E(R_M)	13.79%
Systematic risk (β) of Thermo Fisher Scientific Inc. common stock	β_TMO	0.81

Expected rate of return on Thermo Fisher Scientific Inc. common stock³	E(R_TMO)	12.01%

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_TMO) = R_F + β_TMO [E(R_M) – R_F]
= 4.67% + 0.81 [13.79% – 4.67%]
= 12.01%