Procter & Gamble Co. (NYSE:PG)

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 Procter & Gamble Co. common stock.

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

Rates of Return

Procter & Gamble Co., monthly rates of return

		Procter & Gamble Co. (PG)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_PG,t¹	Dividend_PG,t¹	R_PG,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jul 31, 2019	$118.04			2,980.38
1.	Aug 31, 2019	$120.23		1.86%	2,926.46	-1.81%
2.	Sep 30, 2019	$124.38		3.45%	2,976.74	1.72%
3.	Oct 31, 2019	$124.51	$0.7459	0.70%	3,037.56	2.04%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	May 31, 2025	$169.89		4.50%	5,911.69	6.15%
71.	Jun 30, 2025	$159.32		-6.22%	6,204.95	4.96%
Average (R):				0.74%		1.16%
Standard deviation:				4.99%		4.98%

		Procter & Gamble Co. (PG)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_PG,t¹	Dividend_PG,t¹	R_PG,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jul 31, 2019	$118.04			2,980.38
1.	Aug 31, 2019	$120.23		1.86%	2,926.46	-1.81%
2.	Sep 30, 2019	$124.38		3.45%	2,976.74	1.72%
3.	Oct 31, 2019	$124.51	$0.7459	0.70%	3,037.56	2.04%
4.	Nov 30, 2019	$122.06		-1.97%	3,140.98	3.40%
5.	Dec 31, 2019	$124.90		2.33%	3,230.78	2.86%
6.	Jan 31, 2020	$124.62	$0.7459	0.37%	3,225.52	-0.16%
7.	Feb 29, 2020	$113.23		-9.14%	2,954.22	-8.41%
8.	Mar 31, 2020	$110.00		-2.85%	2,584.59	-12.51%
9.	Apr 30, 2020	$117.87	$0.7907	7.87%	2,912.43	12.68%
10.	May 31, 2020	$115.92		-1.65%	3,044.31	4.53%
11.	Jun 30, 2020	$119.57		3.15%	3,100.29	1.84%
12.	Jul 31, 2020	$131.12	$0.7907	10.32%	3,271.12	5.51%
13.	Aug 31, 2020	$138.33		5.50%	3,500.31	7.01%
14.	Sep 30, 2020	$138.99		0.48%	3,363.00	-3.92%
15.	Oct 31, 2020	$137.10	$0.7907	-0.79%	3,269.96	-2.77%
16.	Nov 30, 2020	$138.87		1.29%	3,621.63	10.75%
17.	Dec 31, 2020	$139.14		0.19%	3,756.07	3.71%
18.	Jan 31, 2021	$128.21	$0.7907	-7.29%	3,714.24	-1.11%
19.	Feb 28, 2021	$123.53		-3.65%	3,811.15	2.61%
20.	Mar 31, 2021	$135.43		9.63%	3,972.89	4.24%
21.	Apr 30, 2021	$133.42	$0.8698	-0.84%	4,181.17	5.24%
22.	May 31, 2021	$134.85		1.07%	4,204.11	0.55%
23.	Jun 30, 2021	$134.93		0.06%	4,297.50	2.22%
24.	Jul 31, 2021	$142.23	$0.8698	6.05%	4,395.26	2.27%
25.	Aug 31, 2021	$142.39		0.11%	4,522.68	2.90%
26.	Sep 30, 2021	$139.80		-1.82%	4,307.54	-4.76%
27.	Oct 31, 2021	$142.99	$0.8698	2.90%	4,605.38	6.91%
28.	Nov 30, 2021	$144.58		1.11%	4,567.00	-0.83%
29.	Dec 31, 2021	$163.58		13.14%	4,766.18	4.36%
30.	Jan 31, 2022	$160.45	$0.8698	-1.38%	4,515.55	-5.26%
31.	Feb 28, 2022	$155.89		-2.84%	4,373.94	-3.14%
32.	Mar 31, 2022	$152.80		-1.98%	4,530.41	3.58%
33.	Apr 30, 2022	$160.55	$0.9133	5.67%	4,131.93	-8.80%
34.	May 31, 2022	$147.88		-7.89%	4,132.15	0.01%
35.	Jun 30, 2022	$143.79		-2.77%	3,785.38	-8.39%
36.	Jul 31, 2022	$138.91	$0.9133	-2.76%	4,130.29	9.11%
37.	Aug 31, 2022	$137.94		-0.70%	3,955.00	-4.24%
38.	Sep 30, 2022	$126.25		-8.47%	3,585.62	-9.34%
39.	Oct 31, 2022	$134.67	$0.9133	7.39%	3,871.98	7.99%
40.	Nov 30, 2022	$149.16		10.76%	4,080.11	5.38%
41.	Dec 31, 2022	$151.56		1.61%	3,839.50	-5.90%
42.	Jan 31, 2023	$142.38	$0.9133	-5.45%	4,076.60	6.18%
43.	Feb 28, 2023	$137.56		-3.39%	3,970.15	-2.61%
44.	Mar 31, 2023	$148.69		8.09%	4,109.31	3.51%
45.	Apr 30, 2023	$156.38	$0.9407	5.80%	4,169.48	1.46%
46.	May 31, 2023	$142.50		-8.88%	4,179.83	0.25%
47.	Jun 30, 2023	$151.74		6.48%	4,376.86	4.71%
48.	Jul 31, 2023	$156.30	$0.9407	3.63%	4,588.96	4.85%
49.	Aug 31, 2023	$154.34		-1.25%	4,507.66	-1.77%
50.	Sep 30, 2023	$145.86		-5.49%	4,288.05	-4.87%
51.	Oct 31, 2023	$150.03	$0.9407	3.50%	4,193.80	-2.20%
52.	Nov 30, 2023	$153.52		2.33%	4,567.80	8.92%
53.	Dec 31, 2023	$146.54		-4.55%	4,769.83	4.42%
54.	Jan 31, 2024	$157.14	$0.9407	7.88%	4,845.65	1.59%
55.	Feb 29, 2024	$158.94		1.15%	5,096.27	5.17%
56.	Mar 31, 2024	$162.25		2.08%	5,254.35	3.10%
57.	Apr 30, 2024	$163.20	$1.0065	1.21%	5,035.69	-4.16%
58.	May 31, 2024	$164.54		0.82%	5,277.51	4.80%
59.	Jun 30, 2024	$164.92		0.23%	5,460.48	3.47%
60.	Jul 31, 2024	$160.76	$1.0065	-1.91%	5,522.30	1.13%
61.	Aug 31, 2024	$171.54		6.71%	5,648.40	2.28%
62.	Sep 30, 2024	$173.20		0.97%	5,762.48	2.02%
63.	Oct 31, 2024	$165.18	$1.0065	-4.05%	5,705.45	-0.99%
64.	Nov 30, 2024	$179.26		8.52%	6,032.38	5.73%
65.	Dec 31, 2024	$167.65		-6.48%	5,881.63	-2.50%
66.	Jan 31, 2025	$165.99	$1.0065	-0.39%	6,040.53	2.70%
67.	Feb 28, 2025	$173.84		4.73%	5,954.50	-1.42%
68.	Mar 31, 2025	$170.42		-1.97%	5,611.85	-5.75%
69.	Apr 30, 2025	$162.57	$1.0568	-3.99%	5,569.06	-0.76%
70.	May 31, 2025	$169.89		4.50%	5,911.69	6.15%
71.	Jun 30, 2025	$159.32		-6.22%	6,204.95	4.96%
Average (R):				0.74%		1.16%
Standard deviation:				4.99%		4.98%

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 PG during period t

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

Variance and Covariance

Procter & Gamble Co., calculation of variance and covariance of returns

t	Date	R_PG,t	R_{S&P 500,t}	(R_PG,t–R_PG)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_PG,t–R_PG)×(R_{S&P 500,t}–R_{S&P 500})
1.	Aug 31, 2019	1.86%	-1.81%	1.23	8.82	-3.30
2.	Sep 30, 2019	3.45%	1.72%	7.33	0.31	1.51
3.	Oct 31, 2019	0.70%	2.04%	0.00	0.78	-0.04
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70.	May 31, 2025	4.50%	6.15%	14.13	24.91	18.76
71.	Jun 30, 2025	-6.22%	4.96%	48.53	14.44	-26.47
Total (Σ):				1,740.05	1,738.13	737.39

t	Date	R_PG,t	R_{S&P 500,t}	(R_PG,t–R_PG)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_PG,t–R_PG)×(R_{S&P 500,t}–R_{S&P 500})
1.	Aug 31, 2019	1.86%	-1.81%	1.23	8.82	-3.30
2.	Sep 30, 2019	3.45%	1.72%	7.33	0.31	1.51
3.	Oct 31, 2019	0.70%	2.04%	0.00	0.78	-0.04
4.	Nov 30, 2019	-1.97%	3.40%	7.36	5.03	-6.08
5.	Dec 31, 2019	2.33%	2.86%	2.50	2.88	2.69
6.	Jan 31, 2020	0.37%	-0.16%	0.14	1.75	0.49
7.	Feb 29, 2020	-9.14%	-8.41%	97.70	91.63	94.61
8.	Mar 31, 2020	-2.85%	-12.51%	12.94	186.95	49.18
9.	Apr 30, 2020	7.87%	12.68%	50.82	132.79	82.15
10.	May 31, 2020	-1.65%	4.53%	5.75	11.34	-8.08
11.	Jun 30, 2020	3.15%	1.84%	5.78	0.46	1.63
12.	Jul 31, 2020	10.32%	5.51%	91.71	18.91	41.65
13.	Aug 31, 2020	5.50%	7.01%	22.60	34.17	27.79
14.	Sep 30, 2020	0.48%	-3.92%	0.07	25.85	1.36
15.	Oct 31, 2020	-0.79%	-2.77%	2.36	15.43	6.03
16.	Nov 30, 2020	1.29%	10.75%	0.30	92.03	5.24
17.	Dec 31, 2020	0.19%	3.71%	0.30	6.51	-1.40
18.	Jan 31, 2021	-7.29%	-1.11%	64.50	5.17	18.27
19.	Feb 28, 2021	-3.65%	2.61%	19.31	2.10	-6.36
20.	Mar 31, 2021	9.63%	4.24%	79.01	9.50	27.40
21.	Apr 30, 2021	-0.84%	5.24%	2.52	16.66	-6.47
22.	May 31, 2021	1.07%	0.55%	0.11	0.38	-0.20
23.	Jun 30, 2021	0.06%	2.22%	0.47	1.12	-0.73
24.	Jul 31, 2021	6.05%	2.27%	28.20	1.24	5.91
25.	Aug 31, 2021	0.11%	2.90%	0.40	3.02	-1.10
26.	Sep 30, 2021	-1.82%	-4.76%	6.57	35.02	15.17
27.	Oct 31, 2021	2.90%	6.91%	4.66	33.10	12.43
28.	Nov 30, 2021	1.11%	-0.83%	0.14	3.98	-0.73
29.	Dec 31, 2021	13.14%	4.36%	153.69	10.24	39.67
30.	Jan 31, 2022	-1.38%	-5.26%	4.52	41.21	13.65
31.	Feb 28, 2022	-2.84%	-3.14%	12.86	18.47	15.41
32.	Mar 31, 2022	-1.98%	3.58%	7.43	5.84	-6.59
33.	Apr 30, 2022	5.67%	-8.80%	24.26	99.14	-49.04
34.	May 31, 2022	-7.89%	0.01%	74.58	1.34	9.98
35.	Jun 30, 2022	-2.77%	-8.39%	12.32	91.26	33.53
36.	Jul 31, 2022	-2.76%	9.11%	12.27	63.21	-27.85
37.	Aug 31, 2022	-0.70%	-4.24%	2.08	29.22	7.80
38.	Sep 30, 2022	-8.47%	-9.34%	84.99	110.27	96.81
39.	Oct 31, 2022	7.39%	7.99%	44.20	46.58	45.38
40.	Nov 30, 2022	10.76%	5.38%	100.31	17.76	42.21
41.	Dec 31, 2022	1.61%	-5.90%	0.75	49.82	-6.10
42.	Jan 31, 2023	-5.45%	6.18%	38.42	25.14	-31.08
43.	Feb 28, 2023	-3.39%	-2.61%	17.05	14.23	15.58
44.	Mar 31, 2023	8.09%	3.51%	53.97	5.49	17.22
45.	Apr 30, 2023	5.80%	1.46%	25.61	0.09	1.53
46.	May 31, 2023	-8.88%	0.25%	92.55	0.83	8.78
47.	Jun 30, 2023	6.48%	4.71%	32.95	12.62	20.39
48.	Jul 31, 2023	3.63%	4.85%	8.30	13.58	10.61
49.	Aug 31, 2023	-1.25%	-1.77%	3.99	8.60	5.86
50.	Sep 30, 2023	-5.49%	-4.87%	38.92	36.40	37.64
51.	Oct 31, 2023	3.50%	-2.20%	7.61	11.28	-9.27
52.	Nov 30, 2023	2.33%	8.92%	2.50	60.17	12.27
53.	Dec 31, 2023	-4.55%	4.42%	27.99	10.64	-17.26
54.	Jan 31, 2024	7.88%	1.59%	50.85	0.18	3.06
55.	Feb 29, 2024	1.15%	5.17%	0.16	16.09	1.61
56.	Mar 31, 2024	2.08%	3.10%	1.79	3.77	2.60
57.	Apr 30, 2024	1.21%	-4.16%	0.21	28.33	-2.46
58.	May 31, 2024	0.82%	4.80%	0.01	13.26	0.28
59.	Jun 30, 2024	0.23%	3.47%	0.26	5.32	-1.18
60.	Jul 31, 2024	-1.91%	1.13%	7.06	0.00	0.08
61.	Aug 31, 2024	6.71%	2.28%	35.54	1.26	6.69
62.	Sep 30, 2024	0.97%	2.02%	0.05	0.74	0.19
63.	Oct 31, 2024	-4.05%	-0.99%	22.98	4.63	10.31
64.	Nov 30, 2024	8.52%	5.73%	60.52	20.88	35.55
65.	Dec 31, 2024	-6.48%	-2.50%	52.14	13.40	26.43
66.	Jan 31, 2025	-0.39%	2.70%	1.29	2.37	-1.75
67.	Feb 28, 2025	4.73%	-1.42%	15.88	6.68	-10.30
68.	Mar 31, 2025	-1.97%	-5.75%	7.35	47.83	18.75
69.	Apr 30, 2025	-3.99%	-0.76%	22.38	3.70	9.10
70.	May 31, 2025	4.50%	6.15%	14.13	24.91	18.76
71.	Jun 30, 2025	-6.22%	4.96%	48.53	14.44	-26.47
Total (Σ):				1,740.05	1,738.13	737.39

Show all

Variance_PG = Σ(R_PG,t–R_PG)² ÷ (71 – 1)
= 1,740.05 ÷ (71 – 1)
= 24.86

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,738.13 ÷ (71 – 1)
= 24.83

Covariance_{PG, S&P 500} = Σ(R_PG,t–R_PG)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 737.39 ÷ (71 – 1)
= 10.53

Systematic Risk (β) Estimation

Variance_PG	24.86
Variance_{S&P 500}	24.83
Covariance_{PG, S&P 500}	10.53
Correlation coefficient_{PG, S&P 500}¹	0.42
β_PG²	0.42
α_PG³	0.25%

Calculations

¹ Correlation coefficient_{PG, S&P 500}
= Covariance_{PG, S&P 500} ÷ (Standard deviation_PG × Standard deviation_{S&P 500})
= 10.53 ÷ (4.99% × 4.98%)
= 0.42

² β_PG
= Covariance_{PG, S&P 500} ÷ Variance_{S&P 500}
= 10.53 ÷ 24.83
= 0.42

³ α_PG
= Average_PG – β_PG × Average_{S&P 500}
= 0.74% – 0.42 × 1.16%
= 0.25%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.76%
Expected rate of return on market portfolio²	E(R_M)	14.65%
Systematic risk (β) of Procter & Gamble Co. common stock	β_PG	0.42

Expected rate of return on Procter & Gamble Co. common stock³	E(R_PG)	8.96%

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_PG) = R_F + β_PG [E(R_M) – R_F]
= 4.76% + 0.42 [14.65% – 4.76%]
= 8.96%