Vertex Pharmaceuticals Inc. (NASDAQ:VRTX)

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 Vertex Pharmaceuticals Inc. common stock.

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

Rates of Return

Vertex Pharmaceuticals Inc., monthly rates of return

		Vertex Pharmaceuticals Inc. (VRTX)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_VRTX,t¹	Dividend_VRTX,t¹	R_VRTX,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$190.91			2,704.10
1.	Feb 28, 2019	$188.75		-1.13%	2,784.49	2.97%
2.	Mar 31, 2019	$183.95		-2.54%	2,834.40	1.79%
3.	Apr 30, 2019	$168.98		-8.14%	2,945.83	3.93%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2023	$354.81		-2.02%	4,567.80	8.92%
59.	Dec 31, 2023	$406.89		14.68%	4,769.83	4.42%
Average (R):				1.58%		1.11%
Standard deviation:				7.63%		5.31%

		Vertex Pharmaceuticals Inc. (VRTX)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_VRTX,t¹	Dividend_VRTX,t¹	R_VRTX,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2019	$190.91			2,704.10
1.	Feb 28, 2019	$188.75		-1.13%	2,784.49	2.97%
2.	Mar 31, 2019	$183.95		-2.54%	2,834.40	1.79%
3.	Apr 30, 2019	$168.98		-8.14%	2,945.83	3.93%
4.	May 31, 2019	$166.18		-1.66%	2,752.06	-6.58%
5.	Jun 30, 2019	$183.38		10.35%	2,941.76	6.89%
6.	Jul 31, 2019	$166.62		-9.14%	2,980.38	1.31%
7.	Aug 31, 2019	$180.02		8.04%	2,926.46	-1.81%
8.	Sep 30, 2019	$169.42		-5.89%	2,976.74	1.72%
9.	Oct 31, 2019	$195.48		15.38%	3,037.56	2.04%
10.	Nov 30, 2019	$221.75		13.44%	3,140.98	3.40%
11.	Dec 31, 2019	$218.95		-1.26%	3,230.78	2.86%
12.	Jan 31, 2020	$227.05		3.70%	3,225.52	-0.16%
13.	Feb 29, 2020	$224.03		-1.33%	2,954.22	-8.41%
14.	Mar 31, 2020	$237.95		6.21%	2,584.59	-12.51%
15.	Apr 30, 2020	$251.20		5.57%	2,912.43	12.68%
16.	May 31, 2020	$287.96		14.63%	3,044.31	4.53%
17.	Jun 30, 2020	$290.31		0.82%	3,100.29	1.84%
18.	Jul 31, 2020	$272.00		-6.31%	3,271.12	5.51%
19.	Aug 31, 2020	$279.12		2.62%	3,500.31	7.01%
20.	Sep 30, 2020	$272.12		-2.51%	3,363.00	-3.92%
21.	Oct 31, 2020	$208.36		-23.43%	3,269.96	-2.77%
22.	Nov 30, 2020	$227.75		9.31%	3,621.63	10.75%
23.	Dec 31, 2020	$236.34		3.77%	3,756.07	3.71%
24.	Jan 31, 2021	$229.08		-3.07%	3,714.24	-1.11%
25.	Feb 28, 2021	$212.55		-7.22%	3,811.15	2.61%
26.	Mar 31, 2021	$214.89		1.10%	3,972.89	4.24%
27.	Apr 30, 2021	$218.20		1.54%	4,181.17	5.24%
28.	May 31, 2021	$208.63		-4.39%	4,204.11	0.55%
29.	Jun 30, 2021	$201.63		-3.36%	4,297.50	2.22%
30.	Jul 31, 2021	$201.58		-0.02%	4,395.26	2.27%
31.	Aug 31, 2021	$200.29		-0.64%	4,522.68	2.90%
32.	Sep 30, 2021	$181.39		-9.44%	4,307.54	-4.76%
33.	Oct 31, 2021	$184.93		1.95%	4,605.38	6.91%
34.	Nov 30, 2021	$186.94		1.09%	4,567.00	-0.83%
35.	Dec 31, 2021	$219.60		17.47%	4,766.18	4.36%
36.	Jan 31, 2022	$243.05		10.68%	4,515.55	-5.26%
37.	Feb 28, 2022	$230.02		-5.36%	4,373.94	-3.14%
38.	Mar 31, 2022	$260.97		13.46%	4,530.41	3.58%
39.	Apr 30, 2022	$273.22		4.69%	4,131.93	-8.80%
40.	May 31, 2022	$268.65		-1.67%	4,132.15	0.01%
41.	Jun 30, 2022	$281.79		4.89%	3,785.38	-8.39%
42.	Jul 31, 2022	$280.41		-0.49%	4,130.29	9.11%
43.	Aug 31, 2022	$281.76		0.48%	3,955.00	-4.24%
44.	Sep 30, 2022	$289.54		2.76%	3,585.62	-9.34%
45.	Oct 31, 2022	$312.00		7.76%	3,871.98	7.99%
46.	Nov 30, 2022	$316.40		1.41%	4,080.11	5.38%
47.	Dec 31, 2022	$288.78		-8.73%	3,839.50	-5.90%
48.	Jan 31, 2023	$323.10		11.88%	4,076.60	6.18%
49.	Feb 28, 2023	$290.29		-10.15%	3,970.15	-2.61%
50.	Mar 31, 2023	$315.07		8.54%	4,109.31	3.51%
51.	Apr 30, 2023	$340.73		8.14%	4,169.48	1.46%
52.	May 31, 2023	$323.57		-5.04%	4,179.83	0.25%
53.	Jun 30, 2023	$351.91		8.76%	4,376.86	4.71%
54.	Jul 31, 2023	$352.34		0.12%	4,588.96	4.85%
55.	Aug 31, 2023	$348.34		-1.14%	4,507.66	-1.77%
56.	Sep 30, 2023	$347.74		-0.17%	4,288.05	-4.87%
57.	Oct 31, 2023	$362.11		4.13%	4,193.80	-2.20%
58.	Nov 30, 2023	$354.81		-2.02%	4,567.80	8.92%
59.	Dec 31, 2023	$406.89		14.68%	4,769.83	4.42%
Average (R):				1.58%		1.11%
Standard deviation:				7.63%		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 VRTX during period t

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

Variance and Covariance

Vertex Pharmaceuticals Inc., calculation of variance and covariance of returns

t	Date	R_VRTX,t	R_{S&P 500,t}	(R_VRTX,t–R_VRTX)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_VRTX,t–R_VRTX)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	-1.13%	2.97%	7.34	3.49	-5.06
2.	Mar 31, 2019	-2.54%	1.79%	16.99	0.47	-2.83
3.	Apr 30, 2019	-8.14%	3.93%	94.42	7.98	-27.45
.	.	.	.	.	.	.
.	.	.	.	.	.	.
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58.	Nov 30, 2023	-2.02%	8.92%	12.92	61.03	-28.08
59.	Dec 31, 2023	14.68%	4.42%	171.60	11.00	43.45
Total (Σ):				3,378.96	1,634.30	577.31

t	Date	R_VRTX,t	R_{S&P 500,t}	(R_VRTX,t–R_VRTX)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_VRTX,t–R_VRTX)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2019	-1.13%	2.97%	7.34	3.49	-5.06
2.	Mar 31, 2019	-2.54%	1.79%	16.99	0.47	-2.83
3.	Apr 30, 2019	-8.14%	3.93%	94.42	7.98	-27.45
4.	May 31, 2019	-1.66%	-6.58%	10.47	59.04	24.86
5.	Jun 30, 2019	10.35%	6.89%	76.94	33.49	50.76
6.	Jul 31, 2019	-9.14%	1.31%	114.88	0.04	-2.22
7.	Aug 31, 2019	8.04%	-1.81%	41.78	8.50	-18.84
8.	Sep 30, 2019	-5.89%	1.72%	55.75	0.37	-4.57
9.	Oct 31, 2019	15.38%	2.04%	190.53	0.88	12.94
10.	Nov 30, 2019	13.44%	3.40%	140.66	5.28	27.26
11.	Dec 31, 2019	-1.26%	2.86%	8.07	3.07	-4.98
12.	Jan 31, 2020	3.70%	-0.16%	4.50	1.61	-2.69
13.	Feb 29, 2020	-1.33%	-8.41%	8.46	90.57	27.68
14.	Mar 31, 2020	6.21%	-12.51%	21.48	185.44	-63.12
15.	Apr 30, 2020	5.57%	12.68%	15.92	134.06	46.20
16.	May 31, 2020	14.63%	4.53%	170.43	11.71	44.68
17.	Jun 30, 2020	0.82%	1.84%	0.58	0.54	-0.56
18.	Jul 31, 2020	-6.31%	5.51%	62.18	19.40	-34.73
19.	Aug 31, 2020	2.62%	7.01%	1.08	34.82	6.13
20.	Sep 30, 2020	-2.51%	-3.92%	16.70	25.29	20.55
21.	Oct 31, 2020	-23.43%	-2.77%	625.48	15.00	96.85
22.	Nov 30, 2020	9.31%	10.75%	59.71	93.10	74.56
23.	Dec 31, 2020	3.77%	3.71%	4.81	6.79	5.72
24.	Jan 31, 2021	-3.07%	-1.11%	21.63	4.93	10.32
25.	Feb 28, 2021	-7.22%	2.61%	77.34	2.26	-13.22
26.	Mar 31, 2021	1.10%	4.24%	0.23	9.85	-1.50
27.	Apr 30, 2021	1.54%	5.24%	0.00	17.11	-0.16
28.	May 31, 2021	-4.39%	0.55%	35.58	0.31	3.32
29.	Jun 30, 2021	-3.36%	2.22%	24.34	1.24	-5.50
30.	Jul 31, 2021	-0.02%	2.27%	2.57	1.37	-1.87
31.	Aug 31, 2021	-0.64%	2.90%	4.92	3.22	-3.98
32.	Sep 30, 2021	-9.44%	-4.76%	121.33	34.37	64.58
33.	Oct 31, 2021	1.95%	6.91%	0.14	33.74	2.17
34.	Nov 30, 2021	1.09%	-0.83%	0.24	3.76	0.95
35.	Dec 31, 2021	17.47%	4.36%	252.56	10.60	51.74
36.	Jan 31, 2022	10.68%	-5.26%	82.81	40.51	-57.91
37.	Feb 28, 2022	-5.36%	-3.14%	48.16	17.99	29.44
38.	Mar 31, 2022	13.46%	3.58%	141.06	6.11	29.35
39.	Apr 30, 2022	4.69%	-8.80%	9.71	98.04	-30.85
40.	May 31, 2022	-1.67%	0.01%	10.57	1.21	3.58
41.	Jun 30, 2022	4.89%	-8.39%	10.97	90.21	-31.46
42.	Jul 31, 2022	-0.49%	9.11%	4.28	64.09	-16.56
43.	Aug 31, 2022	0.48%	-4.24%	1.20	28.62	5.87
44.	Sep 30, 2022	2.76%	-9.34%	1.40	109.11	-12.35
45.	Oct 31, 2022	7.76%	7.99%	38.17	47.34	42.51
46.	Nov 30, 2022	1.41%	5.38%	0.03	18.23	-0.72
47.	Dec 31, 2022	-8.73%	-5.90%	106.26	49.04	72.19
48.	Jan 31, 2023	11.88%	6.18%	106.21	25.70	52.24
49.	Feb 28, 2023	-10.15%	-2.61%	137.67	13.82	43.61
50.	Mar 31, 2023	8.54%	3.51%	48.41	5.76	16.69
51.	Apr 30, 2023	8.14%	1.46%	43.11	0.13	2.35
52.	May 31, 2023	-5.04%	0.25%	43.76	0.74	5.67
53.	Jun 30, 2023	8.76%	4.71%	51.55	13.02	25.90
54.	Jul 31, 2023	0.12%	4.85%	2.12	13.99	-5.45
55.	Aug 31, 2023	-1.14%	-1.77%	7.37	8.28	7.81
56.	Sep 30, 2023	-0.17%	-4.87%	3.07	35.73	10.47
57.	Oct 31, 2023	4.13%	-2.20%	6.52	10.92	-8.44
58.	Nov 30, 2023	-2.02%	8.92%	12.92	61.03	-28.08
59.	Dec 31, 2023	14.68%	4.42%	171.60	11.00	43.45
Total (Σ):				3,378.96	1,634.30	577.31

Show all

Variance_VRTX = Σ(R_VRTX,t–R_VRTX)² ÷ (59 – 1)
= 3,378.96 ÷ (59 – 1)
= 58.26

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_{VRTX, S&P 500} = Σ(R_VRTX,t–R_VRTX)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 577.31 ÷ (59 – 1)
= 9.95

Systematic Risk (β) Estimation

Variance_VRTX	58.26
Variance_{S&P 500}	28.18
Covariance_{VRTX, S&P 500}	9.95
Correlation coefficient_{VRTX, S&P 500}¹	0.25
β_VRTX²	0.35
α_VRTX³	1.19%

Calculations

¹ Correlation coefficient_{VRTX, S&P 500}
= Covariance_{VRTX, S&P 500} ÷ (Standard deviation_VRTX × Standard deviation_{S&P 500})
= 9.95 ÷ (7.63% × 5.31%)
= 0.25

² β_VRTX
= Covariance_{VRTX, S&P 500} ÷ Variance_{S&P 500}
= 9.95 ÷ 28.18
= 0.35

³ α_VRTX
= Average_VRTX – β_VRTX × Average_{S&P 500}
= 1.58% – 0.35 × 1.11%
= 1.19%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.81%
Expected rate of return on market portfolio²	E(R_M)	13.54%
Systematic risk (β) of Vertex Pharmaceuticals Inc. common stock	β_VRTX	0.35

Expected rate of return on Vertex Pharmaceuticals Inc. common stock³	E(R_VRTX)	7.89%

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_VRTX) = R_F + β_VRTX [E(R_M) – R_F]
= 4.81% + 0.35 [13.54% – 4.81%]
= 7.89%