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, 2019	$74.43			2,704.10
1.	Feb 28, 2019	$81.29		9.22%	2,784.49	2.97%
2.	Mar 31, 2019	$83.17	$0.55	2.99%	2,834.40	1.79%
3.	Apr 30, 2019	$78.71		-5.36%	2,945.83	3.93%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2023	$102.48		-0.21%	4,567.80	8.92%
59.	Dec 31, 2023	$109.02	$0.77	7.13%	4,769.83	4.42%
Average (R):				1.15%		1.11%
Standard deviation:				6.07%		5.31%

		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, 2019	$74.43			2,704.10
1.	Feb 28, 2019	$81.29		9.22%	2,784.49	2.97%
2.	Mar 31, 2019	$83.17	$0.55	2.99%	2,834.40	1.79%
3.	Apr 30, 2019	$78.71		-5.36%	2,945.83	3.93%
4.	May 31, 2019	$79.21		0.64%	2,752.06	-6.58%
5.	Jun 30, 2019	$83.85	$0.55	6.55%	2,941.76	6.89%
6.	Jul 31, 2019	$82.99		-1.03%	2,980.38	1.31%
7.	Aug 31, 2019	$86.47		4.19%	2,926.46	-1.81%
8.	Sep 30, 2019	$84.18	$0.55	-2.01%	2,976.74	1.72%
9.	Oct 31, 2019	$86.66		2.95%	3,037.56	2.04%
10.	Nov 30, 2019	$87.18		0.60%	3,140.98	3.40%
11.	Dec 31, 2019	$90.95	$0.61	5.02%	3,230.78	2.86%
12.	Jan 31, 2020	$85.44		-6.06%	3,225.52	-0.16%
13.	Feb 29, 2020	$76.56		-10.39%	2,954.22	-8.41%
14.	Mar 31, 2020	$76.94	$0.61	1.29%	2,584.59	-12.51%
15.	Apr 30, 2020	$79.34		3.12%	2,912.43	12.68%
16.	May 31, 2020	$80.72		1.74%	3,044.31	4.53%
17.	Jun 30, 2020	$77.33	$0.61	-3.44%	3,100.29	1.84%
18.	Jul 31, 2020	$80.24		3.76%	3,271.12	5.51%
19.	Aug 31, 2020	$85.27		6.27%	3,500.31	7.01%
20.	Sep 30, 2020	$82.95	$0.61	-2.01%	3,363.00	-3.92%
21.	Oct 31, 2020	$75.21		-9.33%	3,269.96	-2.77%
22.	Nov 30, 2020	$80.39		6.89%	3,621.63	10.75%
23.	Dec 31, 2020	$81.80	$0.65	2.56%	3,756.07	3.71%
24.	Jan 31, 2021	$77.07		-5.78%	3,714.24	-1.11%
25.	Feb 28, 2021	$72.62		-5.77%	3,811.15	2.61%
26.	Mar 31, 2021	$77.09	$0.65	7.05%	3,972.89	4.24%
27.	Apr 30, 2021	$74.50		-3.36%	4,181.17	5.24%
28.	May 31, 2021	$75.89		1.87%	4,204.11	0.55%
29.	Jun 30, 2021	$77.77	$3.75	7.42%	4,297.50	2.22%
30.	Jul 31, 2021	$76.87		-1.16%	4,395.26	2.27%
31.	Aug 31, 2021	$76.29		-0.75%	4,522.68	2.90%
32.	Sep 30, 2021	$75.11	$0.65	-0.69%	4,307.54	-4.76%
33.	Oct 31, 2021	$88.05		17.23%	4,605.38	6.91%
34.	Nov 30, 2021	$74.91		-14.92%	4,567.00	-0.83%
35.	Dec 31, 2021	$76.64	$0.69	3.23%	4,766.18	4.36%
36.	Jan 31, 2022	$81.48		6.32%	4,515.55	-5.26%
37.	Feb 28, 2022	$76.58		-6.01%	4,373.94	-3.14%
38.	Mar 31, 2022	$82.05	$0.69	8.04%	4,530.41	3.58%
39.	Apr 30, 2022	$88.69		8.09%	4,131.93	-8.80%
40.	May 31, 2022	$92.03		3.77%	4,132.15	0.01%
41.	Jun 30, 2022	$91.17	$0.69	-0.18%	3,785.38	-8.39%
42.	Jul 31, 2022	$89.34		-2.01%	4,130.29	9.11%
43.	Aug 31, 2022	$85.36		-4.45%	3,955.00	-4.24%
44.	Sep 30, 2022	$86.12	$0.69	1.70%	3,585.62	-9.34%
45.	Oct 31, 2022	$101.20		17.51%	3,871.98	7.99%
46.	Nov 30, 2022	$110.12		8.81%	4,080.11	5.38%
47.	Dec 31, 2022	$110.95	$0.73	1.42%	3,839.50	-5.90%
48.	Jan 31, 2023	$107.41		-3.19%	4,076.60	6.18%
49.	Feb 28, 2023	$106.24		-1.09%	3,970.15	-2.61%
50.	Mar 31, 2023	$106.39	$0.73	0.83%	4,109.31	3.51%
51.	Apr 30, 2023	$115.47		8.53%	4,169.48	1.46%
52.	May 31, 2023	$110.41		-4.38%	4,179.83	0.25%
53.	Jun 30, 2023	$115.39	$0.73	5.17%	4,376.86	4.71%
54.	Jul 31, 2023	$106.65		-7.57%	4,588.96	4.85%
55.	Aug 31, 2023	$108.98		2.18%	4,507.66	-1.77%
56.	Sep 30, 2023	$102.95	$0.73	-4.86%	4,288.05	-4.87%
57.	Oct 31, 2023	$102.70		-0.24%	4,193.80	-2.20%
58.	Nov 30, 2023	$102.48		-0.21%	4,567.80	8.92%
59.	Dec 31, 2023	$109.02	$0.77	7.13%	4,769.83	4.42%
Average (R):				1.15%		1.11%
Standard deviation:				6.07%		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 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 28, 2019	9.22%	2.97%	65.09	3.49	15.06
2.	Mar 31, 2019	2.99%	1.79%	3.39	0.47	1.26
3.	Apr 30, 2019	-5.36%	3.93%	42.40	7.98	-18.40
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2023	-0.21%	8.92%	1.86	61.03	-10.65
59.	Dec 31, 2023	7.13%	4.42%	35.81	11.00	19.85
Total (Σ):				2,134.37	1,634.30	591.86

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 28, 2019	9.22%	2.97%	65.09	3.49	15.06
2.	Mar 31, 2019	2.99%	1.79%	3.39	0.47	1.26
3.	Apr 30, 2019	-5.36%	3.93%	42.40	7.98	-18.40
4.	May 31, 2019	0.64%	-6.58%	0.26	59.04	3.95
5.	Jun 30, 2019	6.55%	6.89%	29.19	33.49	31.27
6.	Jul 31, 2019	-1.03%	1.31%	4.73	0.04	-0.45
7.	Aug 31, 2019	4.19%	-1.81%	9.27	8.50	-8.87
8.	Sep 30, 2019	-2.01%	1.72%	9.99	0.37	-1.94
9.	Oct 31, 2019	2.95%	2.04%	3.23	0.88	1.68
10.	Nov 30, 2019	0.60%	3.40%	0.30	5.28	-1.26
11.	Dec 31, 2019	5.02%	2.86%	15.02	3.07	6.79
12.	Jan 31, 2020	-6.06%	-0.16%	51.95	1.61	9.14
13.	Feb 29, 2020	-10.39%	-8.41%	133.23	90.57	109.85
14.	Mar 31, 2020	1.29%	-12.51%	0.02	185.44	-1.96
15.	Apr 30, 2020	3.12%	12.68%	3.88	134.06	22.81
16.	May 31, 2020	1.74%	4.53%	0.35	11.71	2.02
17.	Jun 30, 2020	-3.44%	1.84%	21.10	0.54	-3.37
18.	Jul 31, 2020	3.76%	5.51%	6.83	19.40	11.51
19.	Aug 31, 2020	6.27%	7.01%	26.21	34.82	30.21
20.	Sep 30, 2020	-2.01%	-3.92%	9.95	25.29	15.86
21.	Oct 31, 2020	-9.33%	-2.77%	109.83	15.00	40.58
22.	Nov 30, 2020	6.89%	10.75%	32.93	93.10	55.37
23.	Dec 31, 2020	2.56%	3.71%	2.00	6.79	3.68
24.	Jan 31, 2021	-5.78%	-1.11%	48.05	4.93	15.38
25.	Feb 28, 2021	-5.77%	2.61%	47.93	2.26	-10.41
26.	Mar 31, 2021	7.05%	4.24%	34.83	9.85	18.52
27.	Apr 30, 2021	-3.36%	5.24%	20.33	17.11	-18.65
28.	May 31, 2021	1.87%	0.55%	0.51	0.31	-0.40
29.	Jun 30, 2021	7.42%	2.22%	39.31	1.24	6.99
30.	Jul 31, 2021	-1.16%	2.27%	5.32	1.37	-2.70
31.	Aug 31, 2021	-0.75%	2.90%	3.62	3.22	-3.41
32.	Sep 30, 2021	-0.69%	-4.76%	3.40	34.37	10.81
33.	Oct 31, 2021	17.23%	6.91%	258.53	33.74	93.40
34.	Nov 30, 2021	-14.92%	-0.83%	258.32	3.76	31.17
35.	Dec 31, 2021	3.23%	4.36%	4.33	10.60	6.78
36.	Jan 31, 2022	6.32%	-5.26%	26.69	40.51	-32.88
37.	Feb 28, 2022	-6.01%	-3.14%	51.31	17.99	30.38
38.	Mar 31, 2022	8.04%	3.58%	47.54	6.11	17.04
39.	Apr 30, 2022	8.09%	-8.80%	48.21	98.04	-68.75
40.	May 31, 2022	3.77%	0.01%	6.85	1.21	-2.88
41.	Jun 30, 2022	-0.18%	-8.39%	1.78	90.21	12.67
42.	Jul 31, 2022	-2.01%	9.11%	9.96	64.09	-25.27
43.	Aug 31, 2022	-4.45%	-4.24%	31.41	28.62	29.98
44.	Sep 30, 2022	1.70%	-9.34%	0.30	109.11	-5.74
45.	Oct 31, 2022	17.51%	7.99%	267.69	47.34	112.57
46.	Nov 30, 2022	8.81%	5.38%	58.75	18.23	32.73
47.	Dec 31, 2022	1.42%	-5.90%	0.07	49.04	-1.87
48.	Jan 31, 2023	-3.19%	6.18%	18.83	25.70	-22.00
49.	Feb 28, 2023	-1.09%	-2.61%	5.01	13.82	8.32
50.	Mar 31, 2023	0.83%	3.51%	0.10	5.76	-0.77
51.	Apr 30, 2023	8.53%	1.46%	54.55	0.13	2.65
52.	May 31, 2023	-4.38%	0.25%	30.59	0.74	4.74
53.	Jun 30, 2023	5.17%	4.71%	16.18	13.02	14.51
54.	Jul 31, 2023	-7.57%	4.85%	76.10	13.99	-32.63
55.	Aug 31, 2023	2.18%	-1.77%	1.07	8.28	-2.98
56.	Sep 30, 2023	-4.86%	-4.87%	36.15	35.73	35.94
57.	Oct 31, 2023	-0.24%	-2.20%	1.94	10.92	4.60
58.	Nov 30, 2023	-0.21%	8.92%	1.86	61.03	-10.65
59.	Dec 31, 2023	7.13%	4.42%	35.81	11.00	19.85
Total (Σ):				2,134.37	1,634.30	591.86

Show all

Variance_MRK = Σ(R_MRK,t–R_MRK)² ÷ (59 – 1)
= 2,134.37 ÷ (59 – 1)
= 36.80

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_{MRK, S&P 500} = Σ(R_MRK,t–R_MRK)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 591.86 ÷ (59 – 1)
= 10.20

Systematic Risk (β) Estimation

Variance_MRK	36.80
Variance_{S&P 500}	28.18
Covariance_{MRK, S&P 500}	10.20
Correlation coefficient_{MRK, S&P 500}¹	0.32
β_MRK²	0.36
α_MRK³	0.75%

Calculations

¹ Correlation coefficient_{MRK, S&P 500}
= Covariance_{MRK, S&P 500} ÷ (Standard deviation_MRK × Standard deviation_{S&P 500})
= 10.20 ÷ (6.07% × 5.31%)
= 0.32

² β_MRK
= Covariance_{MRK, S&P 500} ÷ Variance_{S&P 500}
= 10.20 ÷ 28.18
= 0.36

³ α_MRK
= Average_MRK – β_MRK × Average_{S&P 500}
= 1.15% – 0.36 × 1.11%
= 0.75%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.57%
Expected rate of return on market portfolio²	E(R_M)	13.82%
Systematic risk (β) of Merck & Co. Inc. common stock	β_MRK	0.36

Expected rate of return on Merck & Co. Inc. common stock³	E(R_MRK)	7.92%

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]
= 4.57% + 0.36 [13.82% – 4.57%]
= 7.92%