Palo Alto Networks Inc. (NASDAQ:PANW)

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 Palo Alto Networks Inc. common stock.

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

Rates of Return

Palo Alto Networks Inc., monthly rates of return

		Palo Alto Networks Inc. (PANW)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_PANW,t¹	Dividend_PANW,t¹	R_PANW,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Aug 31, 2017	$44.23			2,471.65
1.	Sep 30, 2017	$48.03		8.59%	2,519.36	1.93%
2.	Oct 31, 2017	$49.07		2.17%	2,575.26	2.22%
3.	Nov 30, 2017	$48.58		-1.00%	2,647.58	2.81%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Jun 30, 2023	$255.51		19.74%	4,376.86	4.71%
71.	Jul 31, 2023	$249.96		-2.17%	4,588.96	4.85%
Average (R):				3.02%		1.00%
Standard deviation:				10.61%		5.07%

		Palo Alto Networks Inc. (PANW)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_PANW,t¹	Dividend_PANW,t¹	R_PANW,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Aug 31, 2017	$44.23			2,471.65
1.	Sep 30, 2017	$48.03		8.59%	2,519.36	1.93%
2.	Oct 31, 2017	$49.07		2.17%	2,575.26	2.22%
3.	Nov 30, 2017	$48.58		-1.00%	2,647.58	2.81%
4.	Dec 31, 2017	$48.31		-0.56%	2,673.61	0.98%
5.	Jan 31, 2018	$52.62		8.92%	2,823.81	5.62%
6.	Feb 28, 2018	$57.79		9.83%	2,713.83	-3.89%
7.	Mar 31, 2018	$60.51		4.71%	2,640.87	-2.69%
8.	Apr 30, 2018	$64.17		6.05%	2,648.05	0.27%
9.	May 31, 2018	$69.36		8.09%	2,705.27	2.16%
10.	Jun 30, 2018	$68.49		-1.25%	2,718.37	0.48%
11.	Jul 31, 2018	$66.09		-3.50%	2,816.29	3.60%
12.	Aug 31, 2018	$77.05		16.58%	2,901.52	3.03%
13.	Sep 30, 2018	$75.09		-2.54%	2,913.98	0.43%
14.	Oct 31, 2018	$61.01		-18.75%	2,711.74	-6.94%
15.	Nov 30, 2018	$57.65		-5.51%	2,760.17	1.79%
16.	Dec 31, 2018	$62.78		8.90%	2,506.85	-9.18%
17.	Jan 31, 2019	$71.61		14.06%	2,704.10	7.87%
18.	Feb 28, 2019	$82.09		14.63%	2,784.49	2.97%
19.	Mar 31, 2019	$80.96		-1.38%	2,834.40	1.79%
20.	Apr 30, 2019	$82.94		2.45%	2,945.83	3.93%
21.	May 31, 2019	$66.71		-19.57%	2,752.06	-6.58%
22.	Jun 30, 2019	$67.92		1.81%	2,941.76	6.89%
23.	Jul 31, 2019	$75.51		11.17%	2,980.38	1.31%
24.	Aug 31, 2019	$67.87		-10.12%	2,926.46	-1.81%
25.	Sep 30, 2019	$67.94		0.10%	2,976.74	1.72%
26.	Oct 31, 2019	$75.80		11.57%	3,037.56	2.04%
27.	Nov 30, 2019	$75.74		-0.08%	3,140.98	3.40%
28.	Dec 31, 2019	$77.08		1.77%	3,230.78	2.86%
29.	Jan 31, 2020	$78.26		1.53%	3,225.52	-0.16%
30.	Feb 29, 2020	$61.54		-21.36%	2,954.22	-8.41%
31.	Mar 31, 2020	$54.65		-11.20%	2,584.59	-12.51%
32.	Apr 30, 2020	$65.50		19.85%	2,912.43	12.68%
33.	May 31, 2020	$78.42		19.73%	3,044.31	4.53%
34.	Jun 30, 2020	$76.56		-2.37%	3,100.29	1.84%
35.	Jul 31, 2020	$85.31		11.43%	3,271.12	5.51%
36.	Aug 31, 2020	$85.80		0.57%	3,500.31	7.01%
37.	Sep 30, 2020	$81.58		-4.92%	3,363.00	-3.92%
38.	Oct 31, 2020	$73.73		-9.62%	3,269.96	-2.77%
39.	Nov 30, 2020	$97.97		32.88%	3,621.63	10.75%
40.	Dec 31, 2020	$118.46		20.91%	3,756.07	3.71%
41.	Jan 31, 2021	$116.92		-1.30%	3,714.24	-1.11%
42.	Feb 28, 2021	$119.44		2.16%	3,811.15	2.61%
43.	Mar 31, 2021	$107.35		-10.12%	3,972.89	4.24%
44.	Apr 30, 2021	$117.80		9.73%	4,181.17	5.24%
45.	May 31, 2021	$121.08		2.78%	4,204.11	0.55%
46.	Jun 30, 2021	$123.68		2.15%	4,297.50	2.22%
47.	Jul 31, 2021	$133.02		7.55%	4,395.26	2.27%
48.	Aug 31, 2021	$153.68		15.53%	4,522.68	2.90%
49.	Sep 30, 2021	$159.67		3.90%	4,307.54	-4.76%
50.	Oct 31, 2021	$169.70		6.28%	4,605.38	6.91%
51.	Nov 30, 2021	$182.31		7.43%	4,567.00	-0.83%
52.	Dec 31, 2021	$185.59		1.80%	4,766.18	4.36%
53.	Jan 31, 2022	$172.47		-7.07%	4,515.55	-5.26%
54.	Feb 28, 2022	$198.08		14.85%	4,373.94	-3.14%
55.	Mar 31, 2022	$207.50		4.76%	4,530.41	3.58%
56.	Apr 30, 2022	$187.09		-9.84%	4,131.93	-8.80%
57.	May 31, 2022	$167.59		-10.42%	4,132.15	0.01%
58.	Jun 30, 2022	$164.65		-1.75%	3,785.38	-8.39%
59.	Jul 31, 2022	$166.37		1.04%	4,130.29	9.11%
60.	Aug 31, 2022	$185.60		11.56%	3,955.00	-4.24%
61.	Sep 30, 2022	$163.79		-11.75%	3,585.62	-9.34%
62.	Oct 31, 2022	$171.59		4.76%	3,871.98	7.99%
63.	Nov 30, 2022	$169.90		-0.98%	4,080.11	5.38%
64.	Dec 31, 2022	$139.54		-17.87%	3,839.50	-5.90%
65.	Jan 31, 2023	$158.64		13.69%	4,076.60	6.18%
66.	Feb 28, 2023	$188.37		18.74%	3,970.15	-2.61%
67.	Mar 31, 2023	$199.74		6.04%	4,109.31	3.51%
68.	Apr 30, 2023	$182.46		-8.65%	4,169.48	1.46%
69.	May 31, 2023	$213.39		16.95%	4,179.83	0.25%
70.	Jun 30, 2023	$255.51		19.74%	4,376.86	4.71%
71.	Jul 31, 2023	$249.96		-2.17%	4,588.96	4.85%
Average (R):				3.02%		1.00%
Standard deviation:				10.61%		5.07%

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¹ Data in US$ per share of common stock, adjusted for splits and stock dividends.

² Rate of return on common stock of PANW during period t

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

Variance and Covariance

Palo Alto Networks Inc., calculation of variance and covariance of returns

t	Date	R_PANW,t	R_{S&P 500,t}	(R_PANW,t–R_PANW)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_PANW,t–R_PANW)×(R_{S&P 500,t}–R_{S&P 500})
1.	Sep 30, 2017	8.59%	1.93%	31.09	0.86	5.17
2.	Oct 31, 2017	2.17%	2.22%	0.72	1.48	-1.03
3.	Nov 30, 2017	-1.00%	2.81%	16.11	3.26	-7.24
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70.	Jun 30, 2023	19.74%	4.71%	279.67	13.77	62.05
71.	Jul 31, 2023	-2.17%	4.85%	26.91	14.77	-19.93
Total (Σ):				7,876.48	1,800.45	2,018.78

t	Date	R_PANW,t	R_{S&P 500,t}	(R_PANW,t–R_PANW)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_PANW,t–R_PANW)×(R_{S&P 500,t}–R_{S&P 500})
1.	Sep 30, 2017	8.59%	1.93%	31.09	0.86	5.17
2.	Oct 31, 2017	2.17%	2.22%	0.72	1.48	-1.03
3.	Nov 30, 2017	-1.00%	2.81%	16.11	3.26	-7.24
4.	Dec 31, 2017	-0.56%	0.98%	12.75	0.00	0.07
5.	Jan 31, 2018	8.92%	5.62%	34.88	21.29	27.26
6.	Feb 28, 2018	9.83%	-3.89%	46.37	23.99	-33.35
7.	Mar 31, 2018	4.71%	-2.69%	2.86	13.63	-6.24
8.	Apr 30, 2018	6.05%	0.27%	9.20	0.53	-2.22
9.	May 31, 2018	8.09%	2.16%	25.73	1.34	5.87
10.	Jun 30, 2018	-1.25%	0.48%	18.23	0.27	2.22
11.	Jul 31, 2018	-3.50%	3.60%	42.50	6.75	-16.94
12.	Aug 31, 2018	16.58%	3.03%	184.10	4.09	27.45
13.	Sep 30, 2018	-2.54%	0.43%	30.90	0.33	3.19
14.	Oct 31, 2018	-18.75%	-6.94%	473.76	63.10	172.90
15.	Nov 30, 2018	-5.51%	1.79%	72.63	0.61	-6.67
16.	Dec 31, 2018	8.90%	-9.18%	34.61	103.65	-59.90
17.	Jan 31, 2019	14.06%	7.87%	122.10	47.13	75.86
18.	Feb 28, 2019	14.63%	2.97%	135.01	3.88	22.89
19.	Mar 31, 2019	-1.38%	1.79%	19.29	0.62	-3.47
20.	Apr 30, 2019	2.45%	3.93%	0.32	8.57	-1.67
21.	May 31, 2019	-19.57%	-6.58%	510.02	57.47	171.21
22.	Jun 30, 2019	1.81%	6.89%	1.44	34.69	-7.08
23.	Jul 31, 2019	11.17%	1.31%	66.58	0.10	2.53
24.	Aug 31, 2019	-10.12%	-1.81%	172.48	7.91	36.94
25.	Sep 30, 2019	0.10%	1.72%	8.48	0.51	-2.08
26.	Oct 31, 2019	11.57%	2.04%	73.17	1.08	8.90
27.	Nov 30, 2019	-0.08%	3.40%	9.58	5.77	-7.43
28.	Dec 31, 2019	1.77%	2.86%	1.55	3.44	-2.31
29.	Jan 31, 2020	1.53%	-0.16%	2.20	1.36	1.73
30.	Feb 29, 2020	-21.36%	-8.41%	594.38	88.63	229.52
31.	Mar 31, 2020	-11.20%	-12.51%	201.96	182.66	192.07
32.	Apr 30, 2020	19.85%	12.68%	283.53	136.45	196.69
33.	May 31, 2020	19.73%	4.53%	279.22	12.42	58.90
34.	Jun 30, 2020	-2.37%	1.84%	29.02	0.70	-4.50
35.	Jul 31, 2020	11.43%	5.51%	70.79	20.31	37.92
36.	Aug 31, 2020	0.57%	7.01%	5.96	36.04	-14.65
37.	Sep 30, 2020	-4.92%	-3.92%	62.94	24.27	39.08
38.	Oct 31, 2020	-9.62%	-2.77%	159.71	14.21	47.64
39.	Nov 30, 2020	32.88%	10.75%	891.71	95.09	291.19
40.	Dec 31, 2020	20.91%	3.71%	320.39	7.34	48.49
41.	Jan 31, 2021	-1.30%	-1.11%	18.62	4.48	9.14
42.	Feb 28, 2021	2.16%	2.61%	0.74	2.58	-1.38
43.	Mar 31, 2021	-10.12%	4.24%	172.59	10.50	-42.57
44.	Apr 30, 2021	9.73%	5.24%	45.15	17.97	28.48
45.	May 31, 2021	2.78%	0.55%	0.05	0.21	0.10
46.	Jun 30, 2021	2.15%	2.22%	0.75	1.48	-1.06
47.	Jul 31, 2021	7.55%	2.27%	20.58	1.62	5.77
48.	Aug 31, 2021	15.53%	2.90%	156.66	3.59	23.73
49.	Sep 30, 2021	3.90%	-4.76%	0.78	33.18	-5.08
50.	Oct 31, 2021	6.28%	6.91%	10.67	34.94	19.31
51.	Nov 30, 2021	7.43%	-0.83%	19.50	3.37	-8.11
52.	Dec 31, 2021	1.80%	4.36%	1.48	11.28	-4.08
53.	Jan 31, 2022	-7.07%	-5.26%	101.70	39.21	63.15
54.	Feb 28, 2022	14.85%	-3.14%	140.04	17.13	-48.98
55.	Mar 31, 2022	4.76%	3.58%	3.03	6.63	4.48
56.	Apr 30, 2022	-9.84%	-8.80%	165.16	96.02	125.93
57.	May 31, 2022	-10.42%	0.01%	180.58	1.00	13.41
58.	Jun 30, 2022	-1.75%	-8.39%	22.75	88.27	44.81
59.	Jul 31, 2022	1.04%	9.11%	3.88	65.75	-15.98
60.	Aug 31, 2022	11.56%	-4.24%	72.99	27.53	-44.83
61.	Sep 30, 2022	-11.75%	-9.34%	218.04	106.97	152.73
62.	Oct 31, 2022	4.76%	7.99%	3.05	48.76	12.20
63.	Nov 30, 2022	-0.98%	5.38%	16.00	19.11	-17.49
64.	Dec 31, 2022	-17.87%	-5.90%	436.17	47.62	144.11
65.	Jan 31, 2023	13.69%	6.18%	113.90	26.75	55.20
66.	Feb 28, 2023	18.74%	-2.61%	247.28	13.06	-56.84
67.	Mar 31, 2023	6.04%	3.51%	9.12	6.26	7.56
68.	Apr 30, 2023	-8.65%	1.46%	136.11	0.21	-5.38
69.	May 31, 2023	16.95%	0.25%	194.22	0.57	-10.52
70.	Jun 30, 2023	19.74%	4.71%	279.67	13.77	62.05
71.	Jul 31, 2023	-2.17%	4.85%	26.91	14.77	-19.93
Total (Σ):				7,876.48	1,800.45	2,018.78

Show all

Variance_PANW = Σ(R_PANW,t–R_PANW)² ÷ (71 – 1)
= 7,876.48 ÷ (71 – 1)
= 112.52

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,800.45 ÷ (71 – 1)
= 25.72

Covariance_{PANW, S&P 500} = Σ(R_PANW,t–R_PANW)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 2,018.78 ÷ (71 – 1)
= 28.84

Systematic Risk (β) Estimation

Variance_PANW	112.52
Variance_{S&P 500}	25.72
Covariance_{PANW, S&P 500}	28.84
Correlation coefficient_{PANW, S&P 500}¹	0.54
β_PANW²	1.12
α_PANW³	1.89%

Calculations

¹ Correlation coefficient_{PANW, S&P 500}
= Covariance_{PANW, S&P 500} ÷ (Standard deviation_PANW × Standard deviation_{S&P 500})
= 28.84 ÷ (10.61% × 5.07%)
= 0.54

² β_PANW
= Covariance_{PANW, S&P 500} ÷ Variance_{S&P 500}
= 28.84 ÷ 25.72
= 1.12

³ α_PANW
= Average_PANW – β_PANW × Average_{S&P 500}
= 3.02% – 1.12 × 1.00%
= 1.89%

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 Palo Alto Networks Inc. common stock	β_PANW	1.12

Expected rate of return on Palo Alto Networks Inc. common stock³	E(R_PANW)	14.57%

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_PANW) = R_F + β_PANW [E(R_M) – R_F]
= 4.86% + 1.12 [13.52% – 4.86%]
= 14.57%