Applied Materials Inc. (NASDAQ:AMAT)

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 Applied Materials Inc. common stock.

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

Rates of Return

Applied Materials Inc., monthly rates of return

		Applied Materials Inc. (AMAT)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_AMAT,t¹	Dividend_AMAT,t¹	R_AMAT,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Nov 30, 2017	$52.77			2,647.58
1.	Dec 31, 2017	$51.12		-3.13%	2,673.61	0.98%
2.	Jan 31, 2018	$53.63		4.91%	2,823.81	5.62%
3.	Feb 28, 2018	$57.59	$0.10	7.57%	2,713.83	-3.89%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Sep 30, 2023	$138.45		-9.37%	4,288.05	-4.87%
71.	Oct 31, 2023	$132.35		-4.41%	4,193.80	-2.20%
Average (R):				2.00%		0.78%
Standard deviation:				11.13%		5.13%

		Applied Materials Inc. (AMAT)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_AMAT,t¹	Dividend_AMAT,t¹	R_AMAT,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Nov 30, 2017	$52.77			2,647.58
1.	Dec 31, 2017	$51.12		-3.13%	2,673.61	0.98%
2.	Jan 31, 2018	$53.63		4.91%	2,823.81	5.62%
3.	Feb 28, 2018	$57.59	$0.10	7.57%	2,713.83	-3.89%
4.	Mar 31, 2018	$55.61		-3.44%	2,640.87	-2.69%
5.	Apr 30, 2018	$49.67		-10.68%	2,648.05	0.27%
6.	May 31, 2018	$50.78	$0.20	2.64%	2,705.27	2.16%
7.	Jun 30, 2018	$46.19		-9.04%	2,718.37	0.48%
8.	Jul 31, 2018	$48.63		5.28%	2,816.29	3.60%
9.	Aug 31, 2018	$43.02	$0.20	-11.12%	2,901.52	3.03%
10.	Sep 30, 2018	$38.65		-10.16%	2,913.98	0.43%
11.	Oct 31, 2018	$32.88		-14.93%	2,711.74	-6.94%
12.	Nov 30, 2018	$37.28	$0.20	13.99%	2,760.17	1.79%
13.	Dec 31, 2018	$32.74		-12.18%	2,506.85	-9.18%
14.	Jan 31, 2019	$39.08		19.36%	2,704.10	7.87%
15.	Feb 28, 2019	$38.34	$0.20	-1.38%	2,784.49	2.97%
16.	Mar 31, 2019	$39.66		3.44%	2,834.40	1.79%
17.	Apr 30, 2019	$44.07		11.12%	2,945.83	3.93%
18.	May 31, 2019	$38.69	$0.21	-11.73%	2,752.06	-6.58%
19.	Jun 30, 2019	$44.91		16.08%	2,941.76	6.89%
20.	Jul 31, 2019	$49.37		9.93%	2,980.38	1.31%
21.	Aug 31, 2019	$48.02	$0.21	-2.31%	2,926.46	-1.81%
22.	Sep 30, 2019	$49.90		3.92%	2,976.74	1.72%
23.	Oct 31, 2019	$54.26		8.74%	3,037.56	2.04%
24.	Nov 30, 2019	$57.90	$0.21	7.10%	3,140.98	3.40%
25.	Dec 31, 2019	$61.04		5.42%	3,230.78	2.86%
26.	Jan 31, 2020	$57.99		-5.00%	3,225.52	-0.16%
27.	Feb 29, 2020	$58.12	$0.21	0.59%	2,954.22	-8.41%
28.	Mar 31, 2020	$45.82		-21.16%	2,584.59	-12.51%
29.	Apr 30, 2020	$49.68		8.42%	2,912.43	12.68%
30.	May 31, 2020	$56.18	$0.22	13.53%	3,044.31	4.53%
31.	Jun 30, 2020	$60.45		7.60%	3,100.29	1.84%
32.	Jul 31, 2020	$64.33		6.42%	3,271.12	5.51%
33.	Aug 31, 2020	$61.60	$0.22	-3.90%	3,500.31	7.01%
34.	Sep 30, 2020	$59.45		-3.49%	3,363.00	-3.92%
35.	Oct 31, 2020	$59.23		-0.37%	3,269.96	-2.77%
36.	Nov 30, 2020	$82.48	$0.22	39.63%	3,621.63	10.75%
37.	Dec 31, 2020	$86.30		4.63%	3,756.07	3.71%
38.	Jan 31, 2021	$96.68		12.03%	3,714.24	-1.11%
39.	Feb 28, 2021	$118.19	$0.22	22.48%	3,811.15	2.61%
40.	Mar 31, 2021	$133.60		13.04%	3,972.89	4.24%
41.	Apr 30, 2021	$132.71		-0.67%	4,181.17	5.24%
42.	May 31, 2021	$138.13	$0.24	4.26%	4,204.11	0.55%
43.	Jun 30, 2021	$142.40		3.09%	4,297.50	2.22%
44.	Jul 31, 2021	$139.93		-1.73%	4,395.26	2.27%
45.	Aug 31, 2021	$135.13	$0.24	-3.26%	4,522.68	2.90%
46.	Sep 30, 2021	$128.73		-4.74%	4,307.54	-4.76%
47.	Oct 31, 2021	$136.65		6.15%	4,605.38	6.91%
48.	Nov 30, 2021	$147.19	$0.24	7.89%	4,567.00	-0.83%
49.	Dec 31, 2021	$157.36		6.91%	4,766.18	4.36%
50.	Jan 31, 2022	$138.18		-12.19%	4,515.55	-5.26%
51.	Feb 28, 2022	$134.20	$0.24	-2.71%	4,373.94	-3.14%
52.	Mar 31, 2022	$131.80		-1.79%	4,530.41	3.58%
53.	Apr 30, 2022	$110.35		-16.27%	4,131.93	-8.80%
54.	May 31, 2022	$117.29	$0.26	6.52%	4,132.15	0.01%
55.	Jun 30, 2022	$90.98		-22.43%	3,785.38	-8.39%
56.	Jul 31, 2022	$105.98		16.49%	4,130.29	9.11%
57.	Aug 31, 2022	$94.07	$0.26	-10.99%	3,955.00	-4.24%
58.	Sep 30, 2022	$81.93		-12.91%	3,585.62	-9.34%
59.	Oct 31, 2022	$88.29		7.76%	3,871.98	7.99%
60.	Nov 30, 2022	$109.60	$0.26	24.43%	4,080.11	5.38%
61.	Dec 31, 2022	$97.38		-11.15%	3,839.50	-5.90%
62.	Jan 31, 2023	$111.49		14.49%	4,076.60	6.18%
63.	Feb 28, 2023	$116.15	$0.26	4.41%	3,970.15	-2.61%
64.	Mar 31, 2023	$122.83		5.75%	4,109.31	3.51%
65.	Apr 30, 2023	$113.03		-7.98%	4,169.48	1.46%
66.	May 31, 2023	$133.30	$0.32	18.22%	4,179.83	0.25%
67.	Jun 30, 2023	$144.54		8.43%	4,376.86	4.71%
68.	Jul 31, 2023	$151.59		4.88%	4,588.96	4.85%
69.	Aug 31, 2023	$152.76	$0.32	0.98%	4,507.66	-1.77%
70.	Sep 30, 2023	$138.45		-9.37%	4,288.05	-4.87%
71.	Oct 31, 2023	$132.35		-4.41%	4,193.80	-2.20%
Average (R):				2.00%		0.78%
Standard deviation:				11.13%		5.13%

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 AMAT during period t

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

Variance and Covariance

Applied Materials Inc., calculation of variance and covariance of returns

t	Date	R_AMAT,t	R_{S&P 500,t}	(R_AMAT,t–R_AMAT)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_AMAT,t–R_AMAT)×(R_{S&P 500,t}–R_{S&P 500})
1.	Dec 31, 2017	-3.13%	0.98%	26.27	0.04	-1.04
2.	Jan 31, 2018	4.91%	5.62%	8.47	23.40	14.08
3.	Feb 28, 2018	7.57%	-3.89%	31.04	21.86	-26.05
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70.	Sep 30, 2023	-9.37%	-4.87%	129.20	31.95	64.25
71.	Oct 31, 2023	-4.41%	-2.20%	41.02	8.87	19.08
Total (Σ):				8,676.22	1,843.80	2,853.21

t	Date	R_AMAT,t	R_{S&P 500,t}	(R_AMAT,t–R_AMAT)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_AMAT,t–R_AMAT)×(R_{S&P 500,t}–R_{S&P 500})
1.	Dec 31, 2017	-3.13%	0.98%	26.27	0.04	-1.04
2.	Jan 31, 2018	4.91%	5.62%	8.47	23.40	14.08
3.	Feb 28, 2018	7.57%	-3.89%	31.04	21.86	-26.05
4.	Mar 31, 2018	-3.44%	-2.69%	29.56	12.04	18.86
5.	Apr 30, 2018	-10.68%	0.27%	160.79	0.26	6.45
6.	May 31, 2018	2.64%	2.16%	0.41	1.90	0.88
7.	Jun 30, 2018	-9.04%	0.48%	121.84	0.09	3.27
8.	Jul 31, 2018	5.28%	3.60%	10.78	7.96	9.26
9.	Aug 31, 2018	-11.12%	3.03%	172.23	5.04	-29.47
10.	Sep 30, 2018	-10.16%	0.43%	147.79	0.12	4.27
11.	Oct 31, 2018	-14.93%	-6.94%	286.55	59.62	130.70
12.	Nov 30, 2018	13.99%	1.79%	143.79	1.01	12.05
13.	Dec 31, 2018	-12.18%	-9.18%	200.99	99.17	141.18
14.	Jan 31, 2019	19.36%	7.87%	301.57	50.24	123.08
15.	Feb 28, 2019	-1.38%	2.97%	11.43	4.81	-7.41
16.	Mar 31, 2019	3.44%	1.79%	2.09	1.02	1.46
17.	Apr 30, 2019	11.12%	3.93%	83.19	9.93	28.74
18.	May 31, 2019	-11.73%	-6.58%	188.52	54.15	101.03
19.	Jun 30, 2019	16.08%	6.89%	198.18	37.36	86.05
20.	Jul 31, 2019	9.93%	1.31%	62.92	0.28	4.22
21.	Aug 31, 2019	-2.31%	-1.81%	18.56	6.71	11.16
22.	Sep 30, 2019	3.92%	1.72%	3.67	0.88	1.80
23.	Oct 31, 2019	8.74%	2.04%	45.41	1.59	8.51
24.	Nov 30, 2019	7.10%	3.40%	25.97	6.89	13.37
25.	Dec 31, 2019	5.42%	2.86%	11.73	4.32	7.12
26.	Jan 31, 2020	-5.00%	-0.16%	48.94	0.89	6.60
27.	Feb 29, 2020	0.59%	-8.41%	2.00	84.49	12.98
28.	Mar 31, 2020	-21.16%	-12.51%	536.48	176.70	307.89
29.	Apr 30, 2020	8.42%	12.68%	41.29	141.70	76.49
30.	May 31, 2020	13.53%	4.53%	132.89	14.04	43.20
31.	Jun 30, 2020	7.60%	1.84%	31.38	1.12	5.93
32.	Jul 31, 2020	6.42%	5.51%	19.53	22.37	20.90
33.	Aug 31, 2020	-3.90%	7.01%	34.82	38.76	-36.74
34.	Sep 30, 2020	-3.49%	-3.92%	30.13	22.12	25.82
35.	Oct 31, 2020	-0.37%	-2.77%	5.61	12.58	8.40
36.	Nov 30, 2020	39.63%	10.75%	1,415.74	99.48	375.28
37.	Dec 31, 2020	4.63%	3.71%	6.93	8.59	7.72
38.	Jan 31, 2021	12.03%	-1.11%	100.58	3.59	-19.00
39.	Feb 28, 2021	22.48%	2.61%	419.32	3.34	37.44
40.	Mar 31, 2021	13.04%	4.24%	121.87	11.99	38.23
41.	Apr 30, 2021	-0.67%	5.24%	7.10	19.91	-11.89
42.	May 31, 2021	4.26%	0.55%	5.13	0.05	-0.53
43.	Jun 30, 2021	3.09%	2.22%	1.19	2.08	1.57
44.	Jul 31, 2021	-1.73%	2.27%	13.94	2.23	-5.58
45.	Aug 31, 2021	-3.26%	2.90%	27.64	4.49	-11.14
46.	Sep 30, 2021	-4.74%	-4.76%	45.36	30.67	37.30
47.	Oct 31, 2021	6.15%	6.91%	17.25	37.62	25.48
48.	Nov 30, 2021	7.89%	-0.83%	34.69	2.61	-9.51
49.	Dec 31, 2021	6.91%	4.36%	24.11	12.82	17.58
50.	Jan 31, 2022	-12.19%	-5.26%	201.29	36.47	85.68
51.	Feb 28, 2022	-2.71%	-3.14%	22.14	15.34	18.43
52.	Mar 31, 2022	-1.79%	3.58%	14.34	7.82	-10.59
53.	Apr 30, 2022	-16.27%	-8.80%	333.92	91.71	175.00
54.	May 31, 2022	6.52%	0.01%	20.48	0.60	-3.51
55.	Jun 30, 2022	-22.43%	-8.39%	596.85	84.14	224.09
56.	Jul 31, 2022	16.49%	9.11%	209.91	69.40	120.70
57.	Aug 31, 2022	-10.99%	-4.24%	168.78	25.25	65.28
58.	Sep 30, 2022	-12.91%	-9.34%	222.13	102.42	150.84
59.	Oct 31, 2022	7.76%	7.99%	33.22	51.92	41.53
60.	Nov 30, 2022	24.43%	5.38%	503.19	21.11	103.06
61.	Dec 31, 2022	-11.15%	-5.90%	172.88	44.59	87.80
62.	Jan 31, 2023	14.49%	6.18%	156.02	29.10	67.38
63.	Feb 28, 2023	4.41%	-2.61%	5.83	11.51	-8.19
64.	Mar 31, 2023	5.75%	3.51%	14.08	7.42	10.22
65.	Apr 30, 2023	-7.98%	1.46%	99.55	0.47	-6.82
66.	May 31, 2023	18.22%	0.25%	263.01	0.28	-8.64
67.	Jun 30, 2023	8.43%	4.71%	41.39	15.47	25.30
68.	Jul 31, 2023	4.88%	4.85%	8.29	16.53	11.70
69.	Aug 31, 2023	0.98%	-1.77%	1.03	6.51	2.59
70.	Sep 30, 2023	-9.37%	-4.87%	129.20	31.95	64.25
71.	Oct 31, 2023	-4.41%	-2.20%	41.02	8.87	19.08
Total (Σ):				8,676.22	1,843.80	2,853.21

Show all

Variance_AMAT = Σ(R_AMAT,t–R_AMAT)² ÷ (71 – 1)
= 8,676.22 ÷ (71 – 1)
= 123.95

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,843.80 ÷ (71 – 1)
= 26.34

Covariance_{AMAT, S&P 500} = Σ(R_AMAT,t–R_AMAT)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 2,853.21 ÷ (71 – 1)
= 40.76

Systematic Risk (β) Estimation

Variance_AMAT	123.95
Variance_{S&P 500}	26.34
Covariance_{AMAT, S&P 500}	40.76
Correlation coefficient_{AMAT, S&P 500}¹	0.71
β_AMAT²	1.55
α_AMAT³	0.79%

Calculations

¹ Correlation coefficient_{AMAT, S&P 500}
= Covariance_{AMAT, S&P 500} ÷ (Standard deviation_AMAT × Standard deviation_{S&P 500})
= 40.76 ÷ (11.13% × 5.13%)
= 0.71

² β_AMAT
= Covariance_{AMAT, S&P 500} ÷ Variance_{S&P 500}
= 40.76 ÷ 26.34
= 1.55

³ α_AMAT
= Average_AMAT – β_AMAT × Average_{S&P 500}
= 2.00% – 1.55 × 0.78%
= 0.79%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.86%
Expected rate of return on market portfolio²	E(R_M)	13.52%
Systematic risk (β) of Applied Materials Inc. common stock	β_AMAT	1.55

Expected rate of return on Applied Materials Inc. common stock³	E(R_AMAT)	18.27%

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_AMAT) = R_F + β_AMAT [E(R_M) – R_F]
= 4.86% + 1.55 [13.52% – 4.86%]
= 18.27%