Lam Research Corp. (NASDAQ:LRCX)

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 Lam Research Corp. common stock.

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

Rates of Return

Lam Research Corp., monthly rates of return

		Lam Research Corp. (LRCX)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_LRCX,t¹	Dividend_LRCX,t¹	R_LRCX,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jul 31, 2018	$19.06			2,816.29
1.	Aug 31, 2018	$17.31		-9.18%	2,901.52	3.03%
2.	Sep 30, 2018	$15.17	$0.11	-11.73%	2,913.98	0.43%
3.	Oct 31, 2018	$14.17		-6.59%	2,711.74	-6.94%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	May 31, 2024	$93.24		4.25%	5,277.51	4.80%
71.	Jun 30, 2024	$106.49	$0.20	14.43%	5,460.48	3.47%
Average (R):				3.21%		1.07%
Standard deviation:				11.42%		5.24%

		Lam Research Corp. (LRCX)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_LRCX,t¹	Dividend_LRCX,t¹	R_LRCX,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jul 31, 2018	$19.06			2,816.29
1.	Aug 31, 2018	$17.31		-9.18%	2,901.52	3.03%
2.	Sep 30, 2018	$15.17	$0.11	-11.73%	2,913.98	0.43%
3.	Oct 31, 2018	$14.17		-6.59%	2,711.74	-6.94%
4.	Nov 30, 2018	$15.70		10.80%	2,760.17	1.79%
5.	Dec 31, 2018	$13.62	$0.11	-12.55%	2,506.85	-9.18%
6.	Jan 31, 2019	$16.96		24.52%	2,704.10	7.87%
7.	Feb 28, 2019	$17.61		3.83%	2,784.49	2.97%
8.	Mar 31, 2019	$17.90	$0.11	2.27%	2,834.40	1.79%
9.	Apr 30, 2019	$20.74		15.87%	2,945.83	3.93%
10.	May 31, 2019	$17.46		-15.81%	2,752.06	-6.58%
11.	Jun 30, 2019	$18.78	$0.11	8.19%	2,941.76	6.89%
12.	Jul 31, 2019	$20.86		11.08%	2,980.38	1.31%
13.	Aug 31, 2019	$21.05		0.91%	2,926.46	-1.81%
14.	Sep 30, 2019	$23.11	$0.115	10.33%	2,976.74	1.72%
15.	Oct 31, 2019	$27.10		17.27%	3,037.56	2.04%
16.	Nov 30, 2019	$26.68		-1.55%	3,140.98	3.40%
17.	Dec 31, 2019	$29.24	$0.115	10.03%	3,230.78	2.86%
18.	Jan 31, 2020	$29.82		1.98%	3,225.52	-0.16%
19.	Feb 29, 2020	$29.34		-1.61%	2,954.22	-8.41%
20.	Mar 31, 2020	$24.00	$0.115	-17.81%	2,584.59	-12.51%
21.	Apr 30, 2020	$25.53		6.38%	2,912.43	12.68%
22.	May 31, 2020	$27.37		7.21%	3,044.31	4.53%
23.	Jun 30, 2020	$32.35	$0.115	18.62%	3,100.29	1.84%
24.	Jul 31, 2020	$37.72		16.60%	3,271.12	5.51%
25.	Aug 31, 2020	$33.63		-10.84%	3,500.31	7.01%
26.	Sep 30, 2020	$33.18	$0.13	-0.95%	3,363.00	-3.92%
27.	Oct 31, 2020	$34.21		3.10%	3,269.96	-2.77%
28.	Nov 30, 2020	$45.27		32.33%	3,621.63	10.75%
29.	Dec 31, 2020	$47.23	$0.13	4.62%	3,756.07	3.71%
30.	Jan 31, 2021	$48.40		2.48%	3,714.24	-1.11%
31.	Feb 28, 2021	$56.72		17.19%	3,811.15	2.61%
32.	Mar 31, 2021	$59.52	$0.13	5.17%	3,972.89	4.24%
33.	Apr 30, 2021	$62.05		4.25%	4,181.17	5.24%
34.	May 31, 2021	$64.99		4.74%	4,204.11	0.55%
35.	Jun 30, 2021	$65.07	$0.13	0.32%	4,297.50	2.22%
36.	Jul 31, 2021	$63.74		-2.04%	4,395.26	2.27%
37.	Aug 31, 2021	$60.48		-5.11%	4,522.68	2.90%
38.	Sep 30, 2021	$56.92	$0.15	-5.64%	4,307.54	-4.76%
39.	Oct 31, 2021	$56.36		-0.98%	4,605.38	6.91%
40.	Nov 30, 2021	$67.99		20.64%	4,567.00	-0.83%
41.	Dec 31, 2021	$71.92	$0.15	6.00%	4,766.18	4.36%
42.	Jan 31, 2022	$58.99		-17.98%	4,515.55	-5.26%
43.	Feb 28, 2022	$56.14		-4.83%	4,373.94	-3.14%
44.	Mar 31, 2022	$53.76	$0.15	-3.97%	4,530.41	3.58%
45.	Apr 30, 2022	$46.58		-13.36%	4,131.93	-8.80%
46.	May 31, 2022	$52.00		11.64%	4,132.15	0.01%
47.	Jun 30, 2022	$42.62	$0.15	-17.75%	3,785.38	-8.39%
48.	Jul 31, 2022	$50.05		17.43%	4,130.29	9.11%
49.	Aug 31, 2022	$43.79		-12.51%	3,955.00	-4.24%
50.	Sep 30, 2022	$36.60	$0.1725	-16.03%	3,585.62	-9.34%
51.	Oct 31, 2022	$40.48		10.60%	3,871.98	7.99%
52.	Nov 30, 2022	$47.24		16.70%	4,080.11	5.38%
53.	Dec 31, 2022	$42.03	$0.1725	-10.66%	3,839.50	-5.90%
54.	Jan 31, 2023	$50.01		18.99%	4,076.60	6.18%
55.	Feb 28, 2023	$48.60		-2.82%	3,970.15	-2.61%
56.	Mar 31, 2023	$53.01	$0.1725	9.43%	4,109.31	3.51%
57.	Apr 30, 2023	$52.41		-1.13%	4,169.48	1.46%
58.	May 31, 2023	$61.67		17.67%	4,179.83	0.25%
59.	Jun 30, 2023	$64.29	$0.1725	4.53%	4,376.86	4.71%
60.	Jul 31, 2023	$71.85		11.76%	4,588.96	4.85%
61.	Aug 31, 2023	$70.24		-2.24%	4,507.66	-1.77%
62.	Sep 30, 2023	$62.68	$0.20	-10.48%	4,288.05	-4.87%
63.	Oct 31, 2023	$58.82		-6.16%	4,193.80	-2.20%
64.	Nov 30, 2023	$71.59		21.71%	4,567.80	8.92%
65.	Dec 31, 2023	$78.33	$0.20	9.69%	4,769.83	4.42%
66.	Jan 31, 2024	$82.52		5.35%	4,845.65	1.59%
67.	Feb 29, 2024	$93.83		13.71%	5,096.27	5.17%
68.	Mar 31, 2024	$97.16	$0.20	3.76%	5,254.35	3.10%
69.	Apr 30, 2024	$89.44		-7.95%	5,035.69	-4.16%
70.	May 31, 2024	$93.24		4.25%	5,277.51	4.80%
71.	Jun 30, 2024	$106.49	$0.20	14.43%	5,460.48	3.47%
Average (R):				3.21%		1.07%
Standard deviation:				11.42%		5.24%

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 LRCX during period t

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

Variance and Covariance

Lam Research Corp., calculation of variance and covariance of returns

t	Date	R_LRCX,t	R_{S&P 500,t}	(R_LRCX,t–R_LRCX)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_LRCX,t–R_LRCX)×(R_{S&P 500,t}–R_{S&P 500})
1.	Aug 31, 2018	-9.18%	3.03%	153.61	3.81	-24.20
2.	Sep 30, 2018	-11.73%	0.43%	223.19	0.41	9.62
3.	Oct 31, 2018	-6.59%	-6.94%	96.12	64.22	78.57
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70.	May 31, 2024	4.25%	4.80%	1.07	13.90	3.86
71.	Jun 30, 2024	14.43%	3.47%	125.73	5.73	26.84
Total (Σ):				9,135.72	1,922.79	2,980.70

t	Date	R_LRCX,t	R_{S&P 500,t}	(R_LRCX,t–R_LRCX)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_LRCX,t–R_LRCX)×(R_{S&P 500,t}–R_{S&P 500})
1.	Aug 31, 2018	-9.18%	3.03%	153.61	3.81	-24.20
2.	Sep 30, 2018	-11.73%	0.43%	223.19	0.41	9.62
3.	Oct 31, 2018	-6.59%	-6.94%	96.12	64.22	78.57
4.	Nov 30, 2018	10.80%	1.79%	57.53	0.51	5.41
5.	Dec 31, 2018	-12.55%	-9.18%	248.38	105.08	161.56
6.	Jan 31, 2019	24.52%	7.87%	454.13	46.17	144.81
7.	Feb 28, 2019	3.83%	2.97%	0.38	3.61	1.18
8.	Mar 31, 2019	2.27%	1.79%	0.89	0.52	-0.68
9.	Apr 30, 2019	15.87%	3.93%	160.11	8.17	36.16
10.	May 31, 2019	-15.81%	-6.58%	362.03	58.54	145.58
11.	Jun 30, 2019	8.19%	6.89%	24.78	33.87	28.97
12.	Jul 31, 2019	11.08%	1.31%	61.83	0.06	1.88
13.	Aug 31, 2019	0.91%	-1.81%	5.30	8.31	6.63
14.	Sep 30, 2019	10.33%	1.72%	50.70	0.42	4.59
15.	Oct 31, 2019	17.27%	2.04%	197.48	0.94	13.63
16.	Nov 30, 2019	-1.55%	3.40%	22.68	5.44	-11.10
17.	Dec 31, 2019	10.03%	2.86%	46.43	3.19	12.17
18.	Jan 31, 2020	1.98%	-0.16%	1.51	1.53	1.52
19.	Feb 29, 2020	-1.61%	-8.41%	23.25	89.95	45.73
20.	Mar 31, 2020	-17.81%	-12.51%	441.87	184.56	285.57
21.	Apr 30, 2020	6.38%	12.68%	10.00	134.82	36.72
22.	May 31, 2020	7.21%	4.53%	15.96	11.94	13.80
23.	Jun 30, 2020	18.62%	1.84%	237.25	0.59	11.79
24.	Jul 31, 2020	16.60%	5.51%	179.22	19.68	59.40
25.	Aug 31, 2020	-10.84%	7.01%	197.55	35.20	-83.39
26.	Sep 30, 2020	-0.95%	-3.92%	17.34	24.96	20.80
27.	Oct 31, 2020	3.10%	-2.77%	0.01	14.75	0.41
28.	Nov 30, 2020	32.33%	10.75%	847.82	93.73	281.89
29.	Dec 31, 2020	4.62%	3.71%	1.97	6.96	3.71
30.	Jan 31, 2021	2.48%	-1.11%	0.54	4.78	1.61
31.	Feb 28, 2021	17.19%	2.61%	195.38	2.36	21.47
32.	Mar 31, 2021	5.17%	4.24%	3.82	10.05	6.19
33.	Apr 30, 2021	4.25%	5.24%	1.08	17.38	4.33
34.	May 31, 2021	4.74%	0.55%	2.33	0.28	-0.80
35.	Jun 30, 2021	0.32%	2.22%	8.35	1.32	-3.32
36.	Jul 31, 2021	-2.04%	2.27%	27.63	1.44	-6.32
37.	Aug 31, 2021	-5.11%	2.90%	69.34	3.33	-15.20
38.	Sep 30, 2021	-5.64%	-4.76%	78.33	33.99	51.60
39.	Oct 31, 2021	-0.98%	6.91%	17.61	34.12	-24.51
40.	Nov 30, 2021	20.64%	-0.83%	303.56	3.64	-33.22
41.	Dec 31, 2021	6.00%	4.36%	7.78	10.81	9.17
42.	Jan 31, 2022	-17.98%	-5.26%	449.04	40.09	134.18
43.	Feb 28, 2022	-4.83%	-3.14%	64.70	17.72	33.86
44.	Mar 31, 2022	-3.97%	3.58%	51.62	6.27	-17.99
45.	Apr 30, 2022	-13.36%	-8.80%	274.50	97.40	163.51
46.	May 31, 2022	11.64%	0.01%	70.96	1.14	-9.00
47.	Jun 30, 2022	-17.75%	-8.39%	439.42	89.59	198.42
48.	Jul 31, 2022	17.43%	9.11%	202.23	64.61	114.31
49.	Aug 31, 2022	-12.51%	-4.24%	247.11	28.27	83.59
50.	Sep 30, 2022	-16.03%	-9.34%	370.09	108.43	200.32
51.	Oct 31, 2022	10.60%	7.99%	54.59	47.79	51.08
52.	Nov 30, 2022	16.70%	5.38%	181.91	18.51	58.02
53.	Dec 31, 2022	-10.66%	-5.90%	192.54	48.59	96.72
54.	Jan 31, 2023	18.99%	6.18%	248.82	26.03	80.48
55.	Feb 28, 2023	-2.82%	-2.61%	36.38	13.58	22.22
56.	Mar 31, 2023	9.43%	3.51%	38.65	5.91	15.12
57.	Apr 30, 2023	-1.13%	1.46%	18.87	0.15	-1.70
58.	May 31, 2023	17.67%	0.25%	208.98	0.68	-11.93
59.	Jun 30, 2023	4.53%	4.71%	1.73	13.25	4.79
60.	Jul 31, 2023	11.76%	4.85%	73.05	14.23	32.24
61.	Aug 31, 2023	-2.24%	-1.77%	29.74	8.09	15.51
62.	Sep 30, 2023	-10.48%	-4.87%	187.43	35.35	81.39
63.	Oct 31, 2023	-6.16%	-2.20%	87.81	10.70	30.65
64.	Nov 30, 2023	21.71%	8.92%	342.18	61.54	145.11
65.	Dec 31, 2023	9.69%	4.42%	42.01	11.22	21.71
66.	Jan 31, 2024	5.35%	1.59%	4.57	0.27	1.10
67.	Feb 29, 2024	13.71%	5.17%	110.11	16.80	43.01
68.	Mar 31, 2024	3.76%	3.10%	0.30	4.11	1.12
69.	Apr 30, 2024	-7.95%	-4.16%	124.50	27.40	58.41
70.	May 31, 2024	4.25%	4.80%	1.07	13.90	3.86
71.	Jun 30, 2024	14.43%	3.47%	125.73	5.73	26.84
Total (Σ):				9,135.72	1,922.79	2,980.70

Show all

Variance_LRCX = Σ(R_LRCX,t–R_LRCX)² ÷ (71 – 1)
= 9,135.72 ÷ (71 – 1)
= 130.51

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,922.79 ÷ (71 – 1)
= 27.47

Covariance_{LRCX, S&P 500} = Σ(R_LRCX,t–R_LRCX)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 2,980.70 ÷ (71 – 1)
= 42.58

Systematic Risk (β) Estimation

Variance_LRCX	130.51
Variance_{S&P 500}	27.47
Covariance_{LRCX, S&P 500}	42.58
Correlation coefficient_{LRCX, S&P 500}¹	0.71
β_LRCX²	1.55
α_LRCX³	1.55%

Calculations

¹ Correlation coefficient_{LRCX, S&P 500}
= Covariance_{LRCX, S&P 500} ÷ (Standard deviation_LRCX × Standard deviation_{S&P 500})
= 42.58 ÷ (11.42% × 5.24%)
= 0.71

² β_LRCX
= Covariance_{LRCX, S&P 500} ÷ Variance_{S&P 500}
= 42.58 ÷ 27.47
= 1.55

³ α_LRCX
= Average_LRCX – β_LRCX × Average_{S&P 500}
= 3.21% – 1.55 × 1.07%
= 1.55%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.67%
Expected rate of return on market portfolio²	E(R_M)	13.79%
Systematic risk (β) of Lam Research Corp. common stock	β_LRCX	1.55

Expected rate of return on Lam Research Corp. common stock³	E(R_LRCX)	18.80%

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_LRCX) = R_F + β_LRCX [E(R_M) – R_F]
= 4.67% + 1.55 [13.79% – 4.67%]
= 18.80%