Analog Devices Inc. (NASDAQ:ADI)

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 Analog Devices Inc. common stock.

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

Rates of Return

Analog Devices Inc., monthly rates of return

		Analog Devices Inc. (ADI)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_ADI,t¹	Dividend_ADI,t¹	R_ADI,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Nov 30, 2018	$91.92			2,760.17
1.	Dec 31, 2018	$85.83		-6.63%	2,506.85	-9.18%
2.	Jan 31, 2019	$98.86		15.18%	2,704.10	7.87%
3.	Feb 28, 2019	$106.96	$0.54	8.74%	2,784.49	2.97%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Sep 30, 2024	$230.17	$0.92	-1.60%	5,762.48	2.02%
71.	Oct 31, 2024	$223.11		-3.07%	5,705.45	-0.99%
Average (R):				1.75%		1.16%
Standard deviation:				8.44%		5.15%

		Analog Devices Inc. (ADI)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_ADI,t¹	Dividend_ADI,t¹	R_ADI,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Nov 30, 2018	$91.92			2,760.17
1.	Dec 31, 2018	$85.83		-6.63%	2,506.85	-9.18%
2.	Jan 31, 2019	$98.86		15.18%	2,704.10	7.87%
3.	Feb 28, 2019	$106.96	$0.54	8.74%	2,784.49	2.97%
4.	Mar 31, 2019	$105.27		-1.58%	2,834.40	1.79%
5.	Apr 30, 2019	$116.24		10.42%	2,945.83	3.93%
6.	May 31, 2019	$96.62	$0.54	-16.41%	2,752.06	-6.58%
7.	Jun 30, 2019	$112.87		16.82%	2,941.76	6.89%
8.	Jul 31, 2019	$117.46		4.07%	2,980.38	1.31%
9.	Aug 31, 2019	$109.83	$0.54	-6.04%	2,926.46	-1.81%
10.	Sep 30, 2019	$111.73		1.73%	2,976.74	1.72%
11.	Oct 31, 2019	$106.63		-4.56%	3,037.56	2.04%
12.	Nov 30, 2019	$112.95		5.93%	3,140.98	3.40%
13.	Dec 31, 2019	$118.84	$0.54	5.69%	3,230.78	2.86%
14.	Jan 31, 2020	$109.75		-7.65%	3,225.52	-0.16%
15.	Feb 29, 2020	$109.05	$0.62	-0.07%	2,954.22	-8.41%
16.	Mar 31, 2020	$89.65		-17.79%	2,584.59	-12.51%
17.	Apr 30, 2020	$109.60		22.25%	2,912.43	12.68%
18.	May 31, 2020	$112.95	$0.62	3.62%	3,044.31	4.53%
19.	Jun 30, 2020	$122.64		8.58%	3,100.29	1.84%
20.	Jul 31, 2020	$114.85		-6.35%	3,271.12	5.51%
21.	Aug 31, 2020	$116.88	$0.62	2.31%	3,500.31	7.01%
22.	Sep 30, 2020	$116.74		-0.12%	3,363.00	-3.92%
23.	Oct 31, 2020	$118.53		1.53%	3,269.96	-2.77%
24.	Nov 30, 2020	$139.08		17.34%	3,621.63	10.75%
25.	Dec 31, 2020	$147.73	$0.62	6.67%	3,756.07	3.71%
26.	Jan 31, 2021	$147.33		-0.27%	3,714.24	-1.11%
27.	Feb 28, 2021	$155.82	$0.69	6.23%	3,811.15	2.61%
28.	Mar 31, 2021	$155.08		-0.47%	3,972.89	4.24%
29.	Apr 30, 2021	$153.16		-1.24%	4,181.17	5.24%
30.	May 31, 2021	$164.60	$0.69	7.92%	4,204.11	0.55%
31.	Jun 30, 2021	$172.16		4.59%	4,297.50	2.22%
32.	Jul 31, 2021	$167.42		-2.75%	4,395.26	2.27%
33.	Aug 31, 2021	$162.95	$0.69	-2.26%	4,522.68	2.90%
34.	Sep 30, 2021	$167.48		2.78%	4,307.54	-4.76%
35.	Oct 31, 2021	$173.49		3.59%	4,605.38	6.91%
36.	Nov 30, 2021	$180.25		3.90%	4,567.00	-0.83%
37.	Dec 31, 2021	$175.77	$0.69	-2.10%	4,766.18	4.36%
38.	Jan 31, 2022	$163.97		-6.71%	4,515.55	-5.26%
39.	Feb 28, 2022	$160.29	$0.76	-1.78%	4,373.94	-3.14%
40.	Mar 31, 2022	$165.18		3.05%	4,530.41	3.58%
41.	Apr 30, 2022	$154.38		-6.54%	4,131.93	-8.80%
42.	May 31, 2022	$168.40	$0.76	9.57%	4,132.15	0.01%
43.	Jun 30, 2022	$146.09		-13.25%	3,785.38	-8.39%
44.	Jul 31, 2022	$171.96		17.71%	4,130.29	9.11%
45.	Aug 31, 2022	$151.53	$0.76	-11.44%	3,955.00	-4.24%
46.	Sep 30, 2022	$139.34		-8.04%	3,585.62	-9.34%
47.	Oct 31, 2022	$142.62		2.35%	3,871.98	7.99%
48.	Nov 30, 2022	$171.91		20.54%	4,080.11	5.38%
49.	Dec 31, 2022	$164.03	$0.76	-4.14%	3,839.50	-5.90%
50.	Jan 31, 2023	$171.47		4.54%	4,076.60	6.18%
51.	Feb 28, 2023	$183.47	$0.86	7.50%	3,970.15	-2.61%
52.	Mar 31, 2023	$197.22		7.49%	4,109.31	3.51%
53.	Apr 30, 2023	$179.88		-8.79%	4,169.48	1.46%
54.	May 31, 2023	$177.69		-1.22%	4,179.83	0.25%
55.	Jun 30, 2023	$194.81	$0.86	10.12%	4,376.86	4.71%
56.	Jul 31, 2023	$199.53		2.42%	4,588.96	4.85%
57.	Aug 31, 2023	$181.78		-8.90%	4,507.66	-1.77%
58.	Sep 30, 2023	$175.09	$0.86	-3.21%	4,288.05	-4.87%
59.	Oct 31, 2023	$157.33		-10.14%	4,193.80	-2.20%
60.	Nov 30, 2023	$183.38		16.56%	4,567.80	8.92%
61.	Dec 31, 2023	$198.56	$0.86	8.75%	4,769.83	4.42%
62.	Jan 31, 2024	$192.36		-3.12%	4,845.65	1.59%
63.	Feb 29, 2024	$191.82		-0.28%	5,096.27	5.17%
64.	Mar 31, 2024	$197.79	$0.92	3.59%	5,254.35	3.10%
65.	Apr 30, 2024	$200.61		1.43%	5,035.69	-4.16%
66.	May 31, 2024	$234.49		16.89%	5,277.51	4.80%
67.	Jun 30, 2024	$228.26	$0.92	-2.26%	5,460.48	3.47%
68.	Jul 31, 2024	$231.38		1.37%	5,522.30	1.13%
69.	Aug 31, 2024	$234.84		1.50%	5,648.40	2.28%
70.	Sep 30, 2024	$230.17	$0.92	-1.60%	5,762.48	2.02%
71.	Oct 31, 2024	$223.11		-3.07%	5,705.45	-0.99%
Average (R):				1.75%		1.16%
Standard deviation:				8.44%		5.15%

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 ADI during period t

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

Variance and Covariance

Analog Devices Inc., calculation of variance and covariance of returns

t	Date	R_ADI,t	R_{S&P 500,t}	(R_ADI,t–R_ADI)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ADI,t–R_ADI)×(R_{S&P 500,t}–R_{S&P 500})
1.	Dec 31, 2018	-6.63%	-9.18%	70.19	106.87	86.61
2.	Jan 31, 2019	15.18%	7.87%	180.32	45.00	90.08
3.	Feb 28, 2019	8.74%	2.97%	48.81	3.29	12.67
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Sep 30, 2024	-1.60%	2.02%	11.22	0.74	-2.88
71.	Oct 31, 2024	-3.07%	-0.99%	23.23	4.62	10.36
Total (Σ):				4,982.89	1,859.93	2,163.71

t	Date	R_ADI,t	R_{S&P 500,t}	(R_ADI,t–R_ADI)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ADI,t–R_ADI)×(R_{S&P 500,t}–R_{S&P 500})
1.	Dec 31, 2018	-6.63%	-9.18%	70.19	106.87	86.61
2.	Jan 31, 2019	15.18%	7.87%	180.32	45.00	90.08
3.	Feb 28, 2019	8.74%	2.97%	48.81	3.29	12.67
4.	Mar 31, 2019	-1.58%	1.79%	11.11	0.40	-2.11
5.	Apr 30, 2019	10.42%	3.93%	75.13	7.68	24.02
6.	May 31, 2019	-16.41%	-6.58%	330.05	59.87	140.57
7.	Jun 30, 2019	16.82%	6.89%	226.97	32.87	86.37
8.	Jul 31, 2019	4.07%	1.31%	5.35	0.02	0.35
9.	Aug 31, 2019	-6.04%	-1.81%	60.67	8.82	23.13
10.	Sep 30, 2019	1.73%	1.72%	0.00	0.31	-0.01
11.	Oct 31, 2019	-4.56%	2.04%	39.91	0.78	-5.58
12.	Nov 30, 2019	5.93%	3.40%	17.42	5.04	9.37
13.	Dec 31, 2019	5.69%	2.86%	15.52	2.89	6.69
14.	Jan 31, 2020	-7.65%	-0.16%	88.39	1.75	12.44
15.	Feb 29, 2020	-0.07%	-8.41%	3.33	91.60	17.47
16.	Mar 31, 2020	-17.79%	-12.51%	381.93	186.92	267.19
17.	Apr 30, 2020	22.25%	12.68%	420.26	132.81	236.26
18.	May 31, 2020	3.62%	4.53%	3.49	11.35	6.30
19.	Jun 30, 2020	8.58%	1.84%	46.60	0.46	4.63
20.	Jul 31, 2020	-6.35%	5.51%	65.69	18.92	-35.26
21.	Aug 31, 2020	2.31%	7.01%	0.31	34.18	3.24
22.	Sep 30, 2020	-0.12%	-3.92%	3.51	25.83	9.52
23.	Oct 31, 2020	1.53%	-2.77%	0.05	15.42	0.86
24.	Nov 30, 2020	17.34%	10.75%	242.88	92.06	149.53
25.	Dec 31, 2020	6.67%	3.71%	24.13	6.51	12.54
26.	Jan 31, 2021	-0.27%	-1.11%	4.10	5.17	4.60
27.	Feb 28, 2021	6.23%	2.61%	20.05	2.10	6.49
28.	Mar 31, 2021	-0.47%	4.24%	4.96	9.51	-6.87
29.	Apr 30, 2021	-1.24%	5.24%	8.95	16.67	-12.21
30.	May 31, 2021	7.92%	0.55%	38.03	0.37	-3.77
31.	Jun 30, 2021	4.59%	2.22%	8.07	1.13	3.01
32.	Jul 31, 2021	-2.75%	2.27%	20.31	1.24	-5.02
33.	Aug 31, 2021	-2.26%	2.90%	16.09	3.02	-6.98
34.	Sep 30, 2021	2.78%	-4.76%	1.05	35.01	-6.08
35.	Oct 31, 2021	3.59%	6.91%	3.37	33.11	10.56
36.	Nov 30, 2021	3.90%	-0.83%	4.59	3.97	-4.27
37.	Dec 31, 2021	-2.10%	4.36%	14.87	10.25	-12.34
38.	Jan 31, 2022	-6.71%	-5.26%	71.68	41.20	54.34
39.	Feb 28, 2022	-1.78%	-3.14%	12.49	18.46	15.18
40.	Mar 31, 2022	3.05%	3.58%	1.68	5.84	3.14
41.	Apr 30, 2022	-6.54%	-8.80%	68.74	99.11	82.54
42.	May 31, 2022	9.57%	0.01%	61.17	1.33	-9.03
43.	Jun 30, 2022	-13.25%	-8.39%	225.03	91.24	143.29
44.	Jul 31, 2022	17.71%	9.11%	254.57	63.23	126.87
45.	Aug 31, 2022	-11.44%	-4.24%	174.02	29.20	71.29
46.	Sep 30, 2022	-8.04%	-9.34%	95.99	110.24	102.87
47.	Oct 31, 2022	2.35%	7.99%	0.36	46.60	4.10
48.	Nov 30, 2022	20.54%	5.38%	352.85	17.77	79.18
49.	Dec 31, 2022	-4.14%	-5.90%	34.75	49.80	41.60
50.	Jan 31, 2023	4.54%	6.18%	7.74	25.15	13.96
51.	Feb 28, 2023	7.50%	-2.61%	33.03	14.22	-21.67
52.	Mar 31, 2023	7.49%	3.51%	32.96	5.50	13.47
53.	Apr 30, 2023	-8.79%	1.46%	111.20	0.09	-3.21
54.	May 31, 2023	-1.22%	0.25%	8.82	0.83	2.71
55.	Jun 30, 2023	10.12%	4.71%	69.99	12.63	29.73
56.	Jul 31, 2023	2.42%	4.85%	0.45	13.59	2.47
57.	Aug 31, 2023	-8.90%	-1.77%	113.40	8.59	31.22
58.	Sep 30, 2023	-3.21%	-4.87%	24.60	36.38	29.92
59.	Oct 31, 2023	-10.14%	-2.20%	141.52	11.28	39.95
60.	Nov 30, 2023	16.56%	8.92%	219.18	60.19	114.85
61.	Dec 31, 2023	8.75%	4.42%	48.92	10.65	22.82
62.	Jan 31, 2024	-3.12%	1.59%	23.77	0.18	-2.09
63.	Feb 29, 2024	-0.28%	5.17%	4.14	16.10	-8.16
64.	Mar 31, 2024	3.59%	3.10%	3.38	3.77	3.57
65.	Apr 30, 2024	1.43%	-4.16%	0.11	28.32	1.74
66.	May 31, 2024	16.89%	4.80%	229.09	13.27	55.13
67.	Jun 30, 2024	-2.26%	3.47%	16.14	5.32	-9.27
68.	Jul 31, 2024	1.37%	1.13%	0.15	0.00	0.01
69.	Aug 31, 2024	1.50%	2.28%	0.07	1.26	-0.29
70.	Sep 30, 2024	-1.60%	2.02%	11.22	0.74	-2.88
71.	Oct 31, 2024	-3.07%	-0.99%	23.23	4.62	10.36
Total (Σ):				4,982.89	1,859.93	2,163.71

Show all

Variance_ADI = Σ(R_ADI,t–R_ADI)² ÷ (71 – 1)
= 4,982.89 ÷ (71 – 1)
= 71.18

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,859.93 ÷ (71 – 1)
= 26.57

Covariance_{ADI, S&P 500} = Σ(R_ADI,t–R_ADI)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 2,163.71 ÷ (71 – 1)
= 30.91

Systematic Risk (β) Estimation

Variance_ADI	71.18
Variance_{S&P 500}	26.57
Covariance_{ADI, S&P 500}	30.91
Correlation coefficient_{ADI, S&P 500}¹	0.71
β_ADI²	1.16
α_ADI³	0.40%

Calculations

¹ Correlation coefficient_{ADI, S&P 500}
= Covariance_{ADI, S&P 500} ÷ (Standard deviation_ADI × Standard deviation_{S&P 500})
= 30.91 ÷ (8.44% × 5.15%)
= 0.71

² β_ADI
= Covariance_{ADI, S&P 500} ÷ Variance_{S&P 500}
= 30.91 ÷ 26.57
= 1.16

³ α_ADI
= Average_ADI – β_ADI × Average_{S&P 500}
= 1.75% – 1.16 × 1.16%
= 0.40%

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 Analog Devices Inc. common stock	β_ADI	1.16

Expected rate of return on Analog Devices Inc. common stock³	E(R_ADI)	16.00%

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_ADI) = R_F + β_ADI [E(R_M) – R_F]
= 4.78% + 1.16 [14.43% – 4.78%]
= 16.00%