Merck & Co. Inc. (NYSE:MRK)

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 Merck & Co. Inc. common stock.

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

Rates of Return

Merck & Co. Inc., monthly rates of return

		Merck & Co. Inc. (MRK)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_MRK,t¹	Dividend_MRK,t¹	R_MRK,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2020	$85.44			3,225.52
1.	Feb 29, 2020	$76.56		-10.39%	2,954.22	-8.41%
2.	Mar 31, 2020	$76.94	$0.61	1.29%	2,584.59	-12.51%
3.	Apr 30, 2020	$79.34		3.12%	2,912.43	12.68%
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58.	Nov 30, 2024	$101.64		-0.66%	6,032.38	5.73%
59.	Dec 31, 2024	$99.48	$0.81	-1.33%	5,881.63	-2.50%
Average (R):				0.77%		1.16%
Standard deviation:				6.30%		5.28%

		Merck & Co. Inc. (MRK)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_MRK,t¹	Dividend_MRK,t¹	R_MRK,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2020	$85.44			3,225.52
1.	Feb 29, 2020	$76.56		-10.39%	2,954.22	-8.41%
2.	Mar 31, 2020	$76.94	$0.61	1.29%	2,584.59	-12.51%
3.	Apr 30, 2020	$79.34		3.12%	2,912.43	12.68%
4.	May 31, 2020	$80.72		1.74%	3,044.31	4.53%
5.	Jun 30, 2020	$77.33	$0.61	-3.44%	3,100.29	1.84%
6.	Jul 31, 2020	$80.24		3.76%	3,271.12	5.51%
7.	Aug 31, 2020	$85.27		6.27%	3,500.31	7.01%
8.	Sep 30, 2020	$82.95	$0.61	-2.01%	3,363.00	-3.92%
9.	Oct 31, 2020	$75.21		-9.33%	3,269.96	-2.77%
10.	Nov 30, 2020	$80.39		6.89%	3,621.63	10.75%
11.	Dec 31, 2020	$81.80	$0.65	2.56%	3,756.07	3.71%
12.	Jan 31, 2021	$77.07		-5.78%	3,714.24	-1.11%
13.	Feb 28, 2021	$72.62		-5.77%	3,811.15	2.61%
14.	Mar 31, 2021	$77.09	$0.65	7.05%	3,972.89	4.24%
15.	Apr 30, 2021	$74.50		-3.36%	4,181.17	5.24%
16.	May 31, 2021	$75.89		1.87%	4,204.11	0.55%
17.	Jun 30, 2021	$77.77	$3.75	7.42%	4,297.50	2.22%
18.	Jul 31, 2021	$76.87		-1.16%	4,395.26	2.27%
19.	Aug 31, 2021	$76.29		-0.75%	4,522.68	2.90%
20.	Sep 30, 2021	$75.11	$0.65	-0.69%	4,307.54	-4.76%
21.	Oct 31, 2021	$88.05		17.23%	4,605.38	6.91%
22.	Nov 30, 2021	$74.91		-14.92%	4,567.00	-0.83%
23.	Dec 31, 2021	$76.64	$0.69	3.23%	4,766.18	4.36%
24.	Jan 31, 2022	$81.48		6.32%	4,515.55	-5.26%
25.	Feb 28, 2022	$76.58		-6.01%	4,373.94	-3.14%
26.	Mar 31, 2022	$82.05	$0.69	8.04%	4,530.41	3.58%
27.	Apr 30, 2022	$88.69		8.09%	4,131.93	-8.80%
28.	May 31, 2022	$92.03		3.77%	4,132.15	0.01%
29.	Jun 30, 2022	$91.17	$0.69	-0.18%	3,785.38	-8.39%
30.	Jul 31, 2022	$89.34		-2.01%	4,130.29	9.11%
31.	Aug 31, 2022	$85.36		-4.45%	3,955.00	-4.24%
32.	Sep 30, 2022	$86.12	$0.69	1.70%	3,585.62	-9.34%
33.	Oct 31, 2022	$101.20		17.51%	3,871.98	7.99%
34.	Nov 30, 2022	$110.12		8.81%	4,080.11	5.38%
35.	Dec 31, 2022	$110.95	$0.73	1.42%	3,839.50	-5.90%
36.	Jan 31, 2023	$107.41		-3.19%	4,076.60	6.18%
37.	Feb 28, 2023	$106.24		-1.09%	3,970.15	-2.61%
38.	Mar 31, 2023	$106.39	$0.73	0.83%	4,109.31	3.51%
39.	Apr 30, 2023	$115.47		8.53%	4,169.48	1.46%
40.	May 31, 2023	$110.41		-4.38%	4,179.83	0.25%
41.	Jun 30, 2023	$115.39	$0.73	5.17%	4,376.86	4.71%
42.	Jul 31, 2023	$106.65		-7.57%	4,588.96	4.85%
43.	Aug 31, 2023	$108.98		2.18%	4,507.66	-1.77%
44.	Sep 30, 2023	$102.95	$0.73	-4.86%	4,288.05	-4.87%
45.	Oct 31, 2023	$102.70		-0.24%	4,193.80	-2.20%
46.	Nov 30, 2023	$102.48		-0.21%	4,567.80	8.92%
47.	Dec 31, 2023	$109.02	$0.77	7.13%	4,769.83	4.42%
48.	Jan 31, 2024	$120.78		10.79%	4,845.65	1.59%
49.	Feb 29, 2024	$127.15		5.27%	5,096.27	5.17%
50.	Mar 31, 2024	$131.95	$0.77	4.38%	5,254.35	3.10%
51.	Apr 30, 2024	$129.22		-2.07%	5,035.69	-4.16%
52.	May 31, 2024	$125.54		-2.85%	5,277.51	4.80%
53.	Jun 30, 2024	$123.80	$0.77	-0.77%	5,460.48	3.47%
54.	Jul 31, 2024	$113.13		-8.62%	5,522.30	1.13%
55.	Aug 31, 2024	$118.45		4.70%	5,648.40	2.28%
56.	Sep 30, 2024	$113.56	$0.77	-3.48%	5,762.48	2.02%
57.	Oct 31, 2024	$102.32		-9.90%	5,705.45	-0.99%
58.	Nov 30, 2024	$101.64		-0.66%	6,032.38	5.73%
59.	Dec 31, 2024	$99.48	$0.81	-1.33%	5,881.63	-2.50%
Average (R):				0.77%		1.16%
Standard deviation:				6.30%		5.28%

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¹ Data in US$ per share of common stock, adjusted for splits and stock dividends.

² Rate of return on common stock of MRK during period t

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

Variance and Covariance

Merck & Co. Inc., calculation of variance and covariance of returns

t	Date	R_MRK,t	R_{S&P 500,t}	(R_MRK,t–R_MRK)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_MRK,t–R_MRK)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2020	-10.39%	-8.41%	124.67	91.63	106.88
2.	Mar 31, 2020	1.29%	-12.51%	0.27	186.96	-7.12
3.	Apr 30, 2020	3.12%	12.68%	5.51	132.78	27.04
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58.	Nov 30, 2024	-0.66%	5.73%	2.06	20.87	-6.57
59.	Dec 31, 2024	-1.33%	-2.50%	4.41	13.40	7.69
Total (Σ):				2,302.47	1,618.62	603.76

t	Date	R_MRK,t	R_{S&P 500,t}	(R_MRK,t–R_MRK)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_MRK,t–R_MRK)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2020	-10.39%	-8.41%	124.67	91.63	106.88
2.	Mar 31, 2020	1.29%	-12.51%	0.27	186.96	-7.12
3.	Apr 30, 2020	3.12%	12.68%	5.51	132.78	27.04
4.	May 31, 2020	1.74%	4.53%	0.94	11.34	3.26
5.	Jun 30, 2020	-3.44%	1.84%	17.78	0.46	-2.86
6.	Jul 31, 2020	3.76%	5.51%	8.94	18.91	13.01
7.	Aug 31, 2020	6.27%	7.01%	30.21	34.17	32.13
8.	Sep 30, 2020	-2.01%	-3.92%	7.72	25.85	14.12
9.	Oct 31, 2020	-9.33%	-2.77%	102.08	15.43	39.68
10.	Nov 30, 2020	6.89%	10.75%	37.39	92.03	58.66
11.	Dec 31, 2020	2.56%	3.71%	3.20	6.51	4.57
12.	Jan 31, 2021	-5.78%	-1.11%	42.96	5.18	14.91
13.	Feb 28, 2021	-5.77%	2.61%	42.85	2.10	-9.48
14.	Mar 31, 2021	7.05%	4.24%	39.41	9.50	19.35
15.	Apr 30, 2021	-3.36%	5.24%	17.07	16.66	-16.86
16.	May 31, 2021	1.87%	0.55%	1.20	0.38	-0.67
17.	Jun 30, 2021	7.42%	2.22%	44.17	1.12	7.05
18.	Jul 31, 2021	-1.16%	2.27%	3.72	1.24	-2.15
19.	Aug 31, 2021	-0.75%	2.90%	2.33	3.02	-2.65
20.	Sep 30, 2021	-0.69%	-4.76%	2.15	35.02	8.68
21.	Oct 31, 2021	17.23%	6.91%	270.79	33.10	94.67
22.	Nov 30, 2021	-14.92%	-0.83%	246.35	3.98	31.31
23.	Dec 31, 2021	3.23%	4.36%	6.04	10.24	7.87
24.	Jan 31, 2022	6.32%	-5.26%	30.72	41.21	-35.58
25.	Feb 28, 2022	-6.01%	-3.14%	46.05	18.47	29.16
26.	Mar 31, 2022	8.04%	3.58%	52.88	5.84	17.57
27.	Apr 30, 2022	8.09%	-8.80%	53.59	99.14	-72.89
28.	May 31, 2022	3.77%	0.01%	8.96	1.34	-3.46
29.	Jun 30, 2022	-0.18%	-8.39%	0.92	91.26	9.14
30.	Jul 31, 2022	-2.01%	9.11%	7.73	63.21	-22.10
31.	Aug 31, 2022	-4.45%	-4.24%	27.32	29.22	28.25
32.	Sep 30, 2022	1.70%	-9.34%	0.86	110.27	-9.73
33.	Oct 31, 2022	17.51%	7.99%	280.16	46.58	114.24
34.	Nov 30, 2022	8.81%	5.38%	64.67	17.76	33.89
35.	Dec 31, 2022	1.42%	-5.90%	0.42	49.82	-4.55
36.	Jan 31, 2023	-3.19%	6.18%	15.71	25.14	-19.87
37.	Feb 28, 2023	-1.09%	-2.61%	3.47	14.23	7.02
38.	Mar 31, 2023	0.83%	3.51%	0.00	5.49	0.13
39.	Apr 30, 2023	8.53%	1.46%	60.25	0.09	2.35
40.	May 31, 2023	-4.38%	0.25%	26.57	0.83	4.71
41.	Jun 30, 2023	5.17%	4.71%	19.35	12.62	15.63
42.	Jul 31, 2023	-7.57%	4.85%	69.67	13.58	-30.75
43.	Aug 31, 2023	2.18%	-1.77%	1.99	8.60	-4.14
44.	Sep 30, 2023	-4.86%	-4.87%	31.76	36.40	34.00
45.	Oct 31, 2023	-0.24%	-2.20%	1.03	11.28	3.41
46.	Nov 30, 2023	-0.21%	8.92%	0.97	60.17	-7.65
47.	Dec 31, 2023	7.13%	4.42%	40.46	10.64	20.75
48.	Jan 31, 2024	10.79%	1.59%	100.29	0.18	4.29
49.	Feb 29, 2024	5.27%	5.17%	20.27	16.09	18.06
50.	Mar 31, 2024	4.38%	3.10%	13.02	3.77	7.00
51.	Apr 30, 2024	-2.07%	-4.16%	8.07	28.33	15.12
52.	May 31, 2024	-2.85%	4.80%	13.11	13.26	-13.18
53.	Jun 30, 2024	-0.77%	3.47%	2.39	5.32	-3.56
54.	Jul 31, 2024	-8.62%	1.13%	88.19	0.00	0.27
55.	Aug 31, 2024	4.70%	2.28%	15.45	1.26	4.41
56.	Sep 30, 2024	-3.48%	2.02%	18.07	0.74	-3.65
57.	Oct 31, 2024	-9.90%	-0.99%	113.85	4.63	22.95
58.	Nov 30, 2024	-0.66%	5.73%	2.06	20.87	-6.57
59.	Dec 31, 2024	-1.33%	-2.50%	4.41	13.40	7.69
Total (Σ):				2,302.47	1,618.62	603.76

Show all

Variance_MRK = Σ(R_MRK,t–R_MRK)² ÷ (59 – 1)
= 2,302.47 ÷ (59 – 1)
= 39.70

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_{MRK, S&P 500} = Σ(R_MRK,t–R_MRK)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 603.76 ÷ (59 – 1)
= 10.41

Systematic Risk (β) Estimation

Variance_MRK	39.70
Variance_{S&P 500}	27.91
Covariance_{MRK, S&P 500}	10.41
Correlation coefficient_{MRK, S&P 500}¹	0.31
β_MRK²	0.37
α_MRK³	0.34%

Calculations

¹ Correlation coefficient_{MRK, S&P 500}
= Covariance_{MRK, S&P 500} ÷ (Standard deviation_MRK × Standard deviation_{S&P 500})
= 10.41 ÷ (6.30% × 5.28%)
= 0.31

² β_MRK
= Covariance_{MRK, S&P 500} ÷ Variance_{S&P 500}
= 10.41 ÷ 27.91
= 0.37

³ α_MRK
= Average_MRK – β_MRK × Average_{S&P 500}
= 0.77% – 0.37 × 1.16%
= 0.34%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.48%
Expected rate of return on market portfolio²	E(R_M)	14.85%
Systematic risk (β) of Merck & Co. Inc. common stock	β_MRK	0.37

Expected rate of return on Merck & Co. Inc. common stock³	E(R_MRK)	8.35%

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_MRK) = R_F + β_MRK [E(R_M) – R_F]
= 4.48% + 0.37 [14.85% – 4.48%]
= 8.35%