Parker-Hannifin Corp. (NYSE:PH)

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 Parker-Hannifin Corp. common stock.

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

Rates of Return

Parker-Hannifin Corp., monthly rates of return

		Parker-Hannifin Corp. (PH)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_PH,t¹	Dividend_PH,t¹	R_PH,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jul 31, 2016	$114.19			2,173.60
1.	Aug 31, 2016	$122.53	$0.63	7.86%	2,170.95	-0.12%
2.	Sep 30, 2016	$125.53		2.45%	2,168.27	-0.12%
3.	Oct 31, 2016	$122.75		-2.21%	2,126.15	-1.94%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	May 31, 2022	$272.17	$1.33	0.99%	4,132.15	0.01%
71.	Jun 30, 2022	$246.05		-9.60%	3,785.38	-8.39%
Average (R):				1.61%		0.89%
Standard deviation:				8.72%		4.53%

		Parker-Hannifin Corp. (PH)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_PH,t¹	Dividend_PH,t¹	R_PH,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jul 31, 2016	$114.19			2,173.60
1.	Aug 31, 2016	$122.53	$0.63	7.86%	2,170.95	-0.12%
2.	Sep 30, 2016	$125.53		2.45%	2,168.27	-0.12%
3.	Oct 31, 2016	$122.75		-2.21%	2,126.15	-1.94%
4.	Nov 30, 2016	$138.93	$0.63	13.69%	2,198.81	3.42%
5.	Dec 31, 2016	$140.00		0.77%	2,238.83	1.82%
6.	Jan 31, 2017	$147.13		5.09%	2,278.87	1.79%
7.	Feb 28, 2017	$154.84	$0.66	5.69%	2,363.64	3.72%
8.	Mar 31, 2017	$160.32		3.54%	2,362.72	-0.04%
9.	Apr 30, 2017	$160.80		0.30%	2,384.20	0.91%
10.	May 31, 2017	$157.47	$0.66	-1.66%	2,411.80	1.16%
11.	Jun 30, 2017	$159.82		1.49%	2,423.41	0.48%
12.	Jul 31, 2017	$165.98		3.85%	2,470.30	1.93%
13.	Aug 31, 2017	$160.89	$0.66	-2.67%	2,471.65	0.05%
14.	Sep 30, 2017	$175.02		8.78%	2,519.36	1.93%
15.	Oct 31, 2017	$182.61		4.34%	2,575.26	2.22%
16.	Nov 30, 2017	$187.49	$0.66	3.03%	2,647.58	2.81%
17.	Dec 31, 2017	$199.58		6.45%	2,673.61	0.98%
18.	Jan 31, 2018	$201.42		0.92%	2,823.81	5.62%
19.	Feb 28, 2018	$178.47	$0.66	-11.07%	2,713.83	-3.89%
20.	Mar 31, 2018	$171.03		-4.17%	2,640.87	-2.69%
21.	Apr 30, 2018	$164.62		-3.75%	2,648.05	0.27%
22.	May 31, 2018	$170.90	$0.76	4.28%	2,705.27	2.16%
23.	Jun 30, 2018	$155.85		-8.81%	2,718.37	0.48%
24.	Jul 31, 2018	$169.05		8.47%	2,816.29	3.60%
25.	Aug 31, 2018	$175.60	$0.76	4.32%	2,901.52	3.03%
26.	Sep 30, 2018	$183.93		4.74%	2,913.98	0.43%
27.	Oct 31, 2018	$151.63		-17.56%	2,711.74	-6.94%
28.	Nov 30, 2018	$172.04	$0.76	13.96%	2,760.17	1.79%
29.	Dec 31, 2018	$149.14		-13.31%	2,506.85	-9.18%
30.	Jan 31, 2019	$164.81		10.51%	2,704.10	7.87%
31.	Feb 28, 2019	$176.16	$0.76	7.35%	2,784.49	2.97%
32.	Mar 31, 2019	$171.62		-2.58%	2,834.40	1.79%
33.	Apr 30, 2019	$181.08		5.51%	2,945.83	3.93%
34.	May 31, 2019	$152.32	$0.88	-15.40%	2,752.06	-6.58%
35.	Jun 30, 2019	$170.01		11.61%	2,941.76	6.89%
36.	Jul 31, 2019	$175.08		2.98%	2,980.38	1.31%
37.	Aug 31, 2019	$165.77	$0.88	-4.81%	2,926.46	-1.81%
38.	Sep 30, 2019	$180.61		8.95%	2,976.74	1.72%
39.	Oct 31, 2019	$183.49		1.59%	3,037.56	2.04%
40.	Nov 30, 2019	$198.79	$0.88	8.82%	3,140.98	3.40%
41.	Dec 31, 2019	$205.82		3.54%	3,230.78	2.86%
42.	Jan 31, 2020	$195.69		-4.92%	3,225.52	-0.16%
43.	Feb 29, 2020	$184.77	$0.88	-5.13%	2,954.22	-8.41%
44.	Mar 31, 2020	$129.73		-29.79%	2,584.59	-12.51%
45.	Apr 30, 2020	$158.12		21.88%	2,912.43	12.68%
46.	May 31, 2020	$179.97	$0.88	14.38%	3,044.31	4.53%
47.	Jun 30, 2020	$183.27		1.83%	3,100.29	1.84%
48.	Jul 31, 2020	$178.92		-2.37%	3,271.12	5.51%
49.	Aug 31, 2020	$206.01	$0.88	15.63%	3,500.31	7.01%
50.	Sep 30, 2020	$202.34		-1.78%	3,363.00	-3.92%
51.	Oct 31, 2020	$208.36		2.98%	3,269.96	-2.77%
52.	Nov 30, 2020	$267.26	$0.88	28.69%	3,621.63	10.75%
53.	Dec 31, 2020	$272.41		1.93%	3,756.07	3.71%
54.	Jan 31, 2021	$264.61		-2.86%	3,714.24	-1.11%
55.	Feb 28, 2021	$286.96	$0.88	8.78%	3,811.15	2.61%
56.	Mar 31, 2021	$315.43		9.92%	3,972.89	4.24%
57.	Apr 30, 2021	$313.81		-0.51%	4,181.17	5.24%
58.	May 31, 2021	$308.15	$1.03	-1.48%	4,204.11	0.55%
59.	Jun 30, 2021	$307.11		-0.34%	4,297.50	2.22%
60.	Jul 31, 2021	$312.03		1.60%	4,395.26	2.27%
61.	Aug 31, 2021	$296.67	$1.03	-4.59%	4,522.68	2.90%
62.	Sep 30, 2021	$279.62		-5.75%	4,307.54	-4.76%
63.	Oct 31, 2021	$296.59		6.07%	4,605.38	6.91%
64.	Nov 30, 2021	$302.06	$1.03	2.19%	4,567.00	-0.83%
65.	Dec 31, 2021	$318.12		5.32%	4,766.18	4.36%
66.	Jan 31, 2022	$310.01		-2.55%	4,515.55	-5.26%
67.	Feb 28, 2022	$296.39	$1.03	-4.06%	4,373.94	-3.14%
68.	Mar 31, 2022	$283.76		-4.26%	4,530.41	3.58%
69.	Apr 30, 2022	$270.82		-4.56%	4,131.93	-8.80%
70.	May 31, 2022	$272.17	$1.33	0.99%	4,132.15	0.01%
71.	Jun 30, 2022	$246.05		-9.60%	3,785.38	-8.39%
Average (R):				1.61%		0.89%
Standard deviation:				8.72%		4.53%

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 PH during period t

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

Variance and Covariance

Parker-Hannifin Corp., calculation of variance and covariance of returns

t	Date	R_PH,t	R_{S&P 500,t}	(R_PH,t–R_PH)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_PH,t–R_PH)×(R_{S&P 500,t}–R_{S&P 500})
1.	Aug 31, 2016	7.86%	-0.12%	38.96	1.02	-6.30
2.	Sep 30, 2016	2.45%	-0.12%	0.70	1.02	-0.84
3.	Oct 31, 2016	-2.21%	-1.94%	14.65	8.00	10.83
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70.	May 31, 2022	0.99%	0.01%	0.39	0.78	0.55
71.	Jun 30, 2022	-9.60%	-8.39%	125.67	86.09	104.02
Total (Σ):				5,326.54	1,437.21	2,230.11

t	Date	R_PH,t	R_{S&P 500,t}	(R_PH,t–R_PH)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_PH,t–R_PH)×(R_{S&P 500,t}–R_{S&P 500})
1.	Aug 31, 2016	7.86%	-0.12%	38.96	1.02	-6.30
2.	Sep 30, 2016	2.45%	-0.12%	0.70	1.02	-0.84
3.	Oct 31, 2016	-2.21%	-1.94%	14.65	8.00	10.83
4.	Nov 30, 2016	13.69%	3.42%	145.96	6.40	30.57
5.	Dec 31, 2016	0.77%	1.82%	0.71	0.87	-0.79
6.	Jan 31, 2017	5.09%	1.79%	12.11	0.81	3.14
7.	Feb 28, 2017	5.69%	3.72%	16.61	8.03	11.55
8.	Mar 31, 2017	3.54%	-0.04%	3.71	0.86	-1.78
9.	Apr 30, 2017	0.30%	0.91%	1.73	0.00	-0.03
10.	May 31, 2017	-1.66%	1.16%	10.72	0.07	-0.89
11.	Jun 30, 2017	1.49%	0.48%	0.01	0.16	0.05
12.	Jul 31, 2017	3.85%	1.93%	5.02	1.10	2.35
13.	Aug 31, 2017	-2.67%	0.05%	18.34	0.69	3.56
14.	Sep 30, 2017	8.78%	1.93%	51.40	1.09	7.48
15.	Oct 31, 2017	4.34%	2.22%	7.42	1.77	3.63
16.	Nov 30, 2017	3.03%	2.81%	2.02	3.69	2.73
17.	Dec 31, 2017	6.45%	0.98%	23.38	0.01	0.47
18.	Jan 31, 2018	0.92%	5.62%	0.48	22.38	-3.27
19.	Feb 28, 2018	-11.07%	-3.89%	160.77	22.86	60.63
20.	Mar 31, 2018	-4.17%	-2.69%	33.43	12.78	20.67
21.	Apr 30, 2018	-3.75%	0.27%	28.74	0.38	3.30
22.	May 31, 2018	4.28%	2.16%	7.09	1.62	3.39
23.	Jun 30, 2018	-8.81%	0.48%	108.57	0.16	4.19
24.	Jul 31, 2018	8.47%	3.60%	47.01	7.37	18.62
25.	Aug 31, 2018	4.32%	3.03%	7.35	4.58	5.80
26.	Sep 30, 2018	4.74%	0.43%	9.80	0.21	-1.43
27.	Oct 31, 2018	-17.56%	-6.94%	367.65	61.26	150.08
28.	Nov 30, 2018	13.96%	1.79%	152.48	0.81	11.10
29.	Dec 31, 2018	-13.31%	-9.18%	222.73	101.29	150.20
30.	Jan 31, 2019	10.51%	7.87%	79.10	48.74	62.09
31.	Feb 28, 2019	7.35%	2.97%	32.89	4.35	11.96
32.	Mar 31, 2019	-2.58%	1.79%	17.56	0.82	-3.80
33.	Apr 30, 2019	5.51%	3.93%	15.20	9.27	11.87
34.	May 31, 2019	-15.40%	-6.58%	289.33	55.72	126.97
35.	Jun 30, 2019	11.61%	6.89%	100.01	36.08	60.07
36.	Jul 31, 2019	2.98%	1.31%	1.87	0.18	0.58
37.	Aug 31, 2019	-4.81%	-1.81%	41.32	7.27	17.33
38.	Sep 30, 2019	8.95%	1.72%	53.86	0.69	6.10
39.	Oct 31, 2019	1.59%	2.04%	0.00	1.34	-0.02
40.	Nov 30, 2019	8.82%	3.40%	51.91	6.34	18.14
41.	Dec 31, 2019	3.54%	2.86%	3.70	3.89	3.79
42.	Jan 31, 2020	-4.92%	-0.16%	42.71	1.10	6.86
43.	Feb 29, 2020	-5.13%	-8.41%	45.48	86.45	62.70
44.	Mar 31, 2020	-29.79%	-12.51%	986.06	179.52	420.74
45.	Apr 30, 2020	21.88%	12.68%	410.90	139.19	239.15
46.	May 31, 2020	14.38%	4.53%	162.87	13.26	46.47
47.	Jun 30, 2020	1.83%	1.84%	0.05	0.91	0.21
48.	Jul 31, 2020	-2.37%	5.51%	15.89	21.38	-18.43
49.	Aug 31, 2020	15.63%	7.01%	196.55	37.45	85.80
50.	Sep 30, 2020	-1.78%	-3.92%	11.52	23.13	16.33
51.	Oct 31, 2020	2.98%	-2.77%	1.86	13.35	-4.98
52.	Nov 30, 2020	28.69%	10.75%	733.19	97.38	267.20
53.	Dec 31, 2020	1.93%	3.71%	0.10	7.98	0.89
54.	Jan 31, 2021	-2.86%	-1.11%	20.04	4.00	8.95
55.	Feb 28, 2021	8.78%	2.61%	51.35	2.97	12.34
56.	Mar 31, 2021	9.92%	4.24%	69.02	11.27	27.89
57.	Apr 30, 2021	-0.51%	5.24%	4.52	18.97	-9.26
58.	May 31, 2021	-1.48%	0.55%	9.54	0.11	1.04
59.	Jun 30, 2021	-0.34%	2.22%	3.81	1.78	-2.60
60.	Jul 31, 2021	1.60%	2.27%	0.00	1.93	-0.02
61.	Aug 31, 2021	-4.59%	2.90%	38.51	4.05	-12.49
62.	Sep 30, 2021	-5.75%	-4.76%	54.17	31.85	41.54
63.	Oct 31, 2021	6.07%	6.91%	19.85	36.33	26.86
64.	Nov 30, 2021	2.19%	-0.83%	0.33	2.96	-0.99
65.	Dec 31, 2021	5.32%	4.36%	13.72	12.07	12.87
66.	Jan 31, 2022	-2.55%	-5.26%	17.33	37.76	25.58
67.	Feb 28, 2022	-4.06%	-3.14%	32.20	16.18	22.83
68.	Mar 31, 2022	-4.26%	3.58%	34.51	7.24	-15.81
69.	Apr 30, 2022	-4.56%	-8.80%	38.11	93.75	59.77
70.	May 31, 2022	0.99%	0.01%	0.39	0.78	0.55
71.	Jun 30, 2022	-9.60%	-8.39%	125.67	86.09	104.02
Total (Σ):				5,326.54	1,437.21	2,230.11

Show all

Variance_PH = Σ(R_PH,t–R_PH)² ÷ (71 – 1)
= 5,326.54 ÷ (71 – 1)
= 76.09

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,437.21 ÷ (71 – 1)
= 20.53

Covariance_{PH, S&P 500} = Σ(R_PH,t–R_PH)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 2,230.11 ÷ (71 – 1)
= 31.86

Systematic Risk (β) Estimation

Variance_PH	76.09
Variance_{S&P 500}	20.53
Covariance_{PH, S&P 500}	31.86
Correlation coefficient_{PH, S&P 500}¹	0.81
β_PH²	1.55
α_PH³	0.24%

Calculations

¹ Correlation coefficient_{PH, S&P 500}
= Covariance_{PH, S&P 500} ÷ (Standard deviation_PH × Standard deviation_{S&P 500})
= 31.86 ÷ (8.72% × 4.53%)
= 0.81

² β_PH
= Covariance_{PH, S&P 500} ÷ Variance_{S&P 500}
= 31.86 ÷ 20.53
= 1.55

³ α_PH
= Average_PH – β_PH × Average_{S&P 500}
= 1.61% – 1.55 × 0.89%
= 0.24%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.68%
Expected rate of return on market portfolio²	E(R_M)	13.78%
Systematic risk (β) of Parker-Hannifin Corp. common stock	β_PH	1.55

Expected rate of return on Parker-Hannifin Corp. common stock³	E(R_PH)	18.81%

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_PH) = R_F + β_PH [E(R_M) – R_F]
= 4.68% + 1.55 [13.78% – 4.68%]
= 18.81%