Synopsys Inc. (NASDAQ:SNPS)

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 Synopsys Inc. common stock.

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

Rates of Return

Synopsys Inc., monthly rates of return

		Synopsys Inc. (SNPS)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_SNPS,t¹	Dividend_SNPS,t¹	R_SNPS,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Nov 30, 2017	$90.38			2,647.58
1.	Dec 31, 2017	$85.24		-5.69%	2,673.61	0.98%
2.	Jan 31, 2018	$92.61		8.65%	2,823.81	5.62%
3.	Feb 28, 2018	$84.67		-8.57%	2,713.83	-3.89%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Sep 30, 2023	$458.97		0.02%	4,288.05	-4.87%
71.	Oct 31, 2023	$469.44		2.28%	4,193.80	-2.20%
Average (R):				2.68%		0.78%
Standard deviation:				8.38%		5.13%

		Synopsys Inc. (SNPS)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_SNPS,t¹	Dividend_SNPS,t¹	R_SNPS,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Nov 30, 2017	$90.38			2,647.58
1.	Dec 31, 2017	$85.24		-5.69%	2,673.61	0.98%
2.	Jan 31, 2018	$92.61		8.65%	2,823.81	5.62%
3.	Feb 28, 2018	$84.67		-8.57%	2,713.83	-3.89%
4.	Mar 31, 2018	$83.24		-1.69%	2,640.87	-2.69%
5.	Apr 30, 2018	$85.51		2.73%	2,648.05	0.27%
6.	May 31, 2018	$88.07		2.99%	2,705.27	2.16%
7.	Jun 30, 2018	$85.57		-2.84%	2,718.37	0.48%
8.	Jul 31, 2018	$89.43		4.51%	2,816.29	3.60%
9.	Aug 31, 2018	$102.14		14.21%	2,901.52	3.03%
10.	Sep 30, 2018	$98.61		-3.46%	2,913.98	0.43%
11.	Oct 31, 2018	$89.53		-9.21%	2,711.74	-6.94%
12.	Nov 30, 2018	$91.94		2.69%	2,760.17	1.79%
13.	Dec 31, 2018	$84.24		-8.38%	2,506.85	-9.18%
14.	Jan 31, 2019	$93.35		10.81%	2,704.10	7.87%
15.	Feb 28, 2019	$101.68		8.92%	2,784.49	2.97%
16.	Mar 31, 2019	$115.15		13.25%	2,834.40	1.79%
17.	Apr 30, 2019	$121.08		5.15%	2,945.83	3.93%
18.	May 31, 2019	$116.44		-3.83%	2,752.06	-6.58%
19.	Jun 30, 2019	$128.69		10.52%	2,941.76	6.89%
20.	Jul 31, 2019	$132.76		3.16%	2,980.38	1.31%
21.	Aug 31, 2019	$141.81		6.82%	2,926.46	-1.81%
22.	Sep 30, 2019	$137.25		-3.22%	2,976.74	1.72%
23.	Oct 31, 2019	$135.75		-1.09%	3,037.56	2.04%
24.	Nov 30, 2019	$141.04		3.90%	3,140.98	3.40%
25.	Dec 31, 2019	$139.20		-1.30%	3,230.78	2.86%
26.	Jan 31, 2020	$147.51		5.97%	3,225.52	-0.16%
27.	Feb 29, 2020	$137.93		-6.49%	2,954.22	-8.41%
28.	Mar 31, 2020	$128.79		-6.63%	2,584.59	-12.51%
29.	Apr 30, 2020	$157.12		22.00%	2,912.43	12.68%
30.	May 31, 2020	$180.91		15.14%	3,044.31	4.53%
31.	Jun 30, 2020	$195.00		7.79%	3,100.29	1.84%
32.	Jul 31, 2020	$199.22		2.16%	3,271.12	5.51%
33.	Aug 31, 2020	$221.30		11.08%	3,500.31	7.01%
34.	Sep 30, 2020	$213.98		-3.31%	3,363.00	-3.92%
35.	Oct 31, 2020	$213.86		-0.06%	3,269.96	-2.77%
36.	Nov 30, 2020	$227.50		6.38%	3,621.63	10.75%
37.	Dec 31, 2020	$259.24		13.95%	3,756.07	3.71%
38.	Jan 31, 2021	$255.45		-1.46%	3,714.24	-1.11%
39.	Feb 28, 2021	$245.21		-4.01%	3,811.15	2.61%
40.	Mar 31, 2021	$247.78		1.05%	3,972.89	4.24%
41.	Apr 30, 2021	$247.06		-0.29%	4,181.17	5.24%
42.	May 31, 2021	$254.34		2.95%	4,204.11	0.55%
43.	Jun 30, 2021	$275.79		8.43%	4,297.50	2.22%
44.	Jul 31, 2021	$287.99		4.42%	4,395.26	2.27%
45.	Aug 31, 2021	$332.24		15.37%	4,522.68	2.90%
46.	Sep 30, 2021	$299.41		-9.88%	4,307.54	-4.76%
47.	Oct 31, 2021	$333.18		11.28%	4,605.38	6.91%
48.	Nov 30, 2021	$341.00		2.35%	4,567.00	-0.83%
49.	Dec 31, 2021	$368.50		8.06%	4,766.18	4.36%
50.	Jan 31, 2022	$310.50		-15.74%	4,515.55	-5.26%
51.	Feb 28, 2022	$312.39		0.61%	4,373.94	-3.14%
52.	Mar 31, 2022	$333.27		6.68%	4,530.41	3.58%
53.	Apr 30, 2022	$286.79		-13.95%	4,131.93	-8.80%
54.	May 31, 2022	$319.20		11.30%	4,132.15	0.01%
55.	Jun 30, 2022	$303.70		-4.86%	3,785.38	-8.39%
56.	Jul 31, 2022	$367.50		21.01%	4,130.29	9.11%
57.	Aug 31, 2022	$346.02		-5.84%	3,955.00	-4.24%
58.	Sep 30, 2022	$305.51		-11.71%	3,585.62	-9.34%
59.	Oct 31, 2022	$292.55		-4.24%	3,871.98	7.99%
60.	Nov 30, 2022	$339.54		16.06%	4,080.11	5.38%
61.	Dec 31, 2022	$319.29		-5.96%	3,839.50	-5.90%
62.	Jan 31, 2023	$353.75		10.79%	4,076.60	6.18%
63.	Feb 28, 2023	$363.76		2.83%	3,970.15	-2.61%
64.	Mar 31, 2023	$386.25		6.18%	4,109.31	3.51%
65.	Apr 30, 2023	$371.32		-3.87%	4,169.48	1.46%
66.	May 31, 2023	$454.96		22.53%	4,179.83	0.25%
67.	Jun 30, 2023	$435.41		-4.30%	4,376.86	4.71%
68.	Jul 31, 2023	$451.80		3.76%	4,588.96	4.85%
69.	Aug 31, 2023	$458.89		1.57%	4,507.66	-1.77%
70.	Sep 30, 2023	$458.97		0.02%	4,288.05	-4.87%
71.	Oct 31, 2023	$469.44		2.28%	4,193.80	-2.20%
Average (R):				2.68%		0.78%
Standard deviation:				8.38%		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 SNPS during period t

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

Variance and Covariance

Synopsys Inc., calculation of variance and covariance of returns

t	Date	R_SNPS,t	R_{S&P 500,t}	(R_SNPS,t–R_SNPS)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_SNPS,t–R_SNPS)×(R_{S&P 500,t}–R_{S&P 500})
1.	Dec 31, 2017	-5.69%	0.98%	70.05	0.04	-1.69
2.	Jan 31, 2018	8.65%	5.62%	35.57	23.40	28.85
3.	Feb 28, 2018	-8.57%	-3.89%	126.70	21.86	52.63
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Sep 30, 2023	0.02%	-4.87%	7.10	31.95	15.06
71.	Oct 31, 2023	2.28%	-2.20%	0.16	8.87	1.20
Total (Σ):				4,909.89	1,843.80	2,089.57

t	Date	R_SNPS,t	R_{S&P 500,t}	(R_SNPS,t–R_SNPS)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_SNPS,t–R_SNPS)×(R_{S&P 500,t}–R_{S&P 500})
1.	Dec 31, 2017	-5.69%	0.98%	70.05	0.04	-1.69
2.	Jan 31, 2018	8.65%	5.62%	35.57	23.40	28.85
3.	Feb 28, 2018	-8.57%	-3.89%	126.70	21.86	52.63
4.	Mar 31, 2018	-1.69%	-2.69%	19.11	12.04	15.17
5.	Apr 30, 2018	2.73%	0.27%	0.00	0.26	-0.02
6.	May 31, 2018	2.99%	2.16%	0.10	1.90	0.43
7.	Jun 30, 2018	-2.84%	0.48%	30.48	0.09	1.64
8.	Jul 31, 2018	4.51%	3.60%	3.34	7.96	5.16
9.	Aug 31, 2018	14.21%	3.03%	132.93	5.04	25.89
10.	Sep 30, 2018	-3.46%	0.43%	37.68	0.12	2.16
11.	Oct 31, 2018	-9.21%	-6.94%	141.38	59.62	91.81
12.	Nov 30, 2018	2.69%	1.79%	0.00	1.01	0.01
13.	Dec 31, 2018	-8.38%	-9.18%	122.27	99.17	110.12
14.	Jan 31, 2019	10.81%	7.87%	66.13	50.24	57.64
15.	Feb 28, 2019	8.92%	2.97%	38.95	4.81	13.68
16.	Mar 31, 2019	13.25%	1.79%	111.62	1.02	10.69
17.	Apr 30, 2019	5.15%	3.93%	6.09	9.93	7.77
18.	May 31, 2019	-3.83%	-6.58%	42.44	54.15	47.94
19.	Jun 30, 2019	10.52%	6.89%	61.43	37.36	47.91
20.	Jul 31, 2019	3.16%	1.31%	0.23	0.28	0.26
21.	Aug 31, 2019	6.82%	-1.81%	17.09	6.71	-10.71
22.	Sep 30, 2019	-3.22%	1.72%	34.79	0.88	-5.53
23.	Oct 31, 2019	-1.09%	2.04%	14.25	1.59	-4.77
24.	Nov 30, 2019	3.90%	3.40%	1.47	6.89	3.19
25.	Dec 31, 2019	-1.30%	2.86%	15.90	4.32	-8.29
26.	Jan 31, 2020	5.97%	-0.16%	10.81	0.89	-3.10
27.	Feb 29, 2020	-6.49%	-8.41%	84.22	84.49	84.35
28.	Mar 31, 2020	-6.63%	-12.51%	86.66	176.70	123.74
29.	Apr 30, 2020	22.00%	12.68%	373.05	141.70	229.91
30.	May 31, 2020	15.14%	4.53%	155.22	14.04	46.69
31.	Jun 30, 2020	7.79%	1.84%	26.07	1.12	5.40
32.	Jul 31, 2020	2.16%	5.51%	0.27	22.37	-2.45
33.	Aug 31, 2020	11.08%	7.01%	70.57	38.76	52.30
34.	Sep 30, 2020	-3.31%	-3.92%	35.88	22.12	28.18
35.	Oct 31, 2020	-0.06%	-2.77%	7.50	12.58	9.71
36.	Nov 30, 2020	6.38%	10.75%	13.66	99.48	36.86
37.	Dec 31, 2020	13.95%	3.71%	126.99	8.59	33.03
38.	Jan 31, 2021	-1.46%	-1.11%	17.18	3.59	7.85
39.	Feb 28, 2021	-4.01%	2.61%	44.77	3.34	-12.23
40.	Mar 31, 2021	1.05%	4.24%	2.67	11.99	-5.66
41.	Apr 30, 2021	-0.29%	5.24%	8.84	19.91	-13.27
42.	May 31, 2021	2.95%	0.55%	0.07	0.05	-0.06
43.	Jun 30, 2021	8.43%	2.22%	33.08	2.08	8.29
44.	Jul 31, 2021	4.42%	2.27%	3.03	2.23	2.60
45.	Aug 31, 2021	15.37%	2.90%	160.85	4.49	26.87
46.	Sep 30, 2021	-9.88%	-4.76%	157.85	30.67	69.57
47.	Oct 31, 2021	11.28%	6.91%	73.90	37.62	52.73
48.	Nov 30, 2021	2.35%	-0.83%	0.11	2.61	0.54
49.	Dec 31, 2021	8.06%	4.36%	28.97	12.82	19.27
50.	Jan 31, 2022	-15.74%	-5.26%	339.37	36.47	111.26
51.	Feb 28, 2022	0.61%	-3.14%	4.30	15.34	8.12
52.	Mar 31, 2022	6.68%	3.58%	16.01	7.82	11.19
53.	Apr 30, 2022	-13.95%	-8.80%	276.53	91.71	159.25
54.	May 31, 2022	11.30%	0.01%	74.28	0.60	-6.68
55.	Jun 30, 2022	-4.86%	-8.39%	56.83	84.14	69.15
56.	Jul 31, 2022	21.01%	9.11%	335.81	69.40	152.66
57.	Aug 31, 2022	-5.84%	-4.24%	72.72	25.25	42.85
58.	Sep 30, 2022	-11.71%	-9.34%	207.07	102.42	145.63
59.	Oct 31, 2022	-4.24%	7.99%	47.95	51.92	-49.90
60.	Nov 30, 2022	16.06%	5.38%	179.02	21.11	61.47
61.	Dec 31, 2022	-5.96%	-5.90%	74.76	44.59	57.74
62.	Jan 31, 2023	10.79%	6.18%	65.78	29.10	43.75
63.	Feb 28, 2023	2.83%	-2.61%	0.02	11.51	-0.50
64.	Mar 31, 2023	6.18%	3.51%	12.25	7.42	9.54
65.	Apr 30, 2023	-3.87%	1.46%	42.87	0.47	-4.48
66.	May 31, 2023	22.53%	0.25%	393.73	0.28	-10.57
67.	Jun 30, 2023	-4.30%	4.71%	48.71	15.47	-27.45
68.	Jul 31, 2023	3.76%	4.85%	1.17	16.53	4.40
69.	Aug 31, 2023	1.57%	-1.77%	1.24	6.51	2.84
70.	Sep 30, 2023	0.02%	-4.87%	7.10	31.95	15.06
71.	Oct 31, 2023	2.28%	-2.20%	0.16	8.87	1.20
Total (Σ):				4,909.89	1,843.80	2,089.57

Show all

Variance_SNPS = Σ(R_SNPS,t–R_SNPS)² ÷ (71 – 1)
= 4,909.89 ÷ (71 – 1)
= 70.14

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_{SNPS, S&P 500} = Σ(R_SNPS,t–R_SNPS)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 2,089.57 ÷ (71 – 1)
= 29.85

Systematic Risk (β) Estimation

Variance_SNPS	70.14
Variance_{S&P 500}	26.34
Covariance_{SNPS, S&P 500}	29.85
Correlation coefficient_{SNPS, S&P 500}¹	0.69
β_SNPS²	1.13
α_SNPS³	1.80%

Calculations

¹ Correlation coefficient_{SNPS, S&P 500}
= Covariance_{SNPS, S&P 500} ÷ (Standard deviation_SNPS × Standard deviation_{S&P 500})
= 29.85 ÷ (8.38% × 5.13%)
= 0.69

² β_SNPS
= Covariance_{SNPS, S&P 500} ÷ Variance_{S&P 500}
= 29.85 ÷ 26.34
= 1.13

³ α_SNPS
= Average_SNPS – β_SNPS × Average_{S&P 500}
= 2.68% – 1.13 × 0.78%
= 1.80%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.65%
Expected rate of return on market portfolio²	E(R_M)	13.79%
Systematic risk (β) of Synopsys Inc. common stock	β_SNPS	1.13

Expected rate of return on Synopsys Inc. common stock³	E(R_SNPS)	15.00%

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_SNPS) = R_F + β_SNPS [E(R_M) – R_F]
= 4.65% + 1.13 [13.79% – 4.65%]
= 15.00%