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, 2018	$80.88			2,816.29
1.	Aug 31, 2018	$82.95		2.56%	2,901.52	3.03%
2.	Sep 30, 2018	$83.23		0.34%	2,913.98	0.43%
3.	Oct 31, 2018	$88.68	$0.7172	7.41%	2,711.74	-6.94%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	May 31, 2024	$164.54		0.82%	5,277.51	4.80%
71.	Jun 30, 2024	$164.92		0.23%	5,460.48	3.47%
Average (R):				1.33%		1.07%
Standard deviation:				4.91%		5.24%

		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, 2018	$80.88			2,816.29
1.	Aug 31, 2018	$82.95		2.56%	2,901.52	3.03%
2.	Sep 30, 2018	$83.23		0.34%	2,913.98	0.43%
3.	Oct 31, 2018	$88.68	$0.7172	7.41%	2,711.74	-6.94%
4.	Nov 30, 2018	$94.51		6.57%	2,760.17	1.79%
5.	Dec 31, 2018	$91.92		-2.74%	2,506.85	-9.18%
6.	Jan 31, 2019	$96.47	$0.7172	5.73%	2,704.10	7.87%
7.	Feb 28, 2019	$98.55		2.16%	2,784.49	2.97%
8.	Mar 31, 2019	$104.05		5.58%	2,834.40	1.79%
9.	Apr 30, 2019	$106.48	$0.7459	3.05%	2,945.83	3.93%
10.	May 31, 2019	$102.91		-3.35%	2,752.06	-6.58%
11.	Jun 30, 2019	$109.65		6.55%	2,941.76	6.89%
12.	Jul 31, 2019	$118.04	$0.7459	8.33%	2,980.38	1.31%
13.	Aug 31, 2019	$120.23		1.86%	2,926.46	-1.81%
14.	Sep 30, 2019	$124.38		3.45%	2,976.74	1.72%
15.	Oct 31, 2019	$124.51	$0.7459	0.70%	3,037.56	2.04%
16.	Nov 30, 2019	$122.06		-1.97%	3,140.98	3.40%
17.	Dec 31, 2019	$124.90		2.33%	3,230.78	2.86%
18.	Jan 31, 2020	$124.62	$0.7459	0.37%	3,225.52	-0.16%
19.	Feb 29, 2020	$113.23		-9.14%	2,954.22	-8.41%
20.	Mar 31, 2020	$110.00		-2.85%	2,584.59	-12.51%
21.	Apr 30, 2020	$117.87	$0.7907	7.87%	2,912.43	12.68%
22.	May 31, 2020	$115.92		-1.65%	3,044.31	4.53%
23.	Jun 30, 2020	$119.57		3.15%	3,100.29	1.84%
24.	Jul 31, 2020	$131.12	$0.7907	10.32%	3,271.12	5.51%
25.	Aug 31, 2020	$138.33		5.50%	3,500.31	7.01%
26.	Sep 30, 2020	$138.99		0.48%	3,363.00	-3.92%
27.	Oct 31, 2020	$137.10	$0.7907	-0.79%	3,269.96	-2.77%
28.	Nov 30, 2020	$138.87		1.29%	3,621.63	10.75%
29.	Dec 31, 2020	$139.14		0.19%	3,756.07	3.71%
30.	Jan 31, 2021	$128.21	$0.7907	-7.29%	3,714.24	-1.11%
31.	Feb 28, 2021	$123.53		-3.65%	3,811.15	2.61%
32.	Mar 31, 2021	$135.43		9.63%	3,972.89	4.24%
33.	Apr 30, 2021	$133.42	$0.8698	-0.84%	4,181.17	5.24%
34.	May 31, 2021	$134.85		1.07%	4,204.11	0.55%
35.	Jun 30, 2021	$134.93		0.06%	4,297.50	2.22%
36.	Jul 31, 2021	$142.23	$0.8698	6.05%	4,395.26	2.27%
37.	Aug 31, 2021	$142.39		0.11%	4,522.68	2.90%
38.	Sep 30, 2021	$139.80		-1.82%	4,307.54	-4.76%
39.	Oct 31, 2021	$142.99	$0.8698	2.90%	4,605.38	6.91%
40.	Nov 30, 2021	$144.58		1.11%	4,567.00	-0.83%
41.	Dec 31, 2021	$163.58		13.14%	4,766.18	4.36%
42.	Jan 31, 2022	$160.45	$0.8698	-1.38%	4,515.55	-5.26%
43.	Feb 28, 2022	$155.89		-2.84%	4,373.94	-3.14%
44.	Mar 31, 2022	$152.80		-1.98%	4,530.41	3.58%
45.	Apr 30, 2022	$160.55	$0.9133	5.67%	4,131.93	-8.80%
46.	May 31, 2022	$147.88		-7.89%	4,132.15	0.01%
47.	Jun 30, 2022	$143.79		-2.77%	3,785.38	-8.39%
48.	Jul 31, 2022	$138.91	$0.9133	-2.76%	4,130.29	9.11%
49.	Aug 31, 2022	$137.94		-0.70%	3,955.00	-4.24%
50.	Sep 30, 2022	$126.25		-8.47%	3,585.62	-9.34%
51.	Oct 31, 2022	$134.67	$0.9133	7.39%	3,871.98	7.99%
52.	Nov 30, 2022	$149.16		10.76%	4,080.11	5.38%
53.	Dec 31, 2022	$151.56		1.61%	3,839.50	-5.90%
54.	Jan 31, 2023	$142.38	$0.9133	-5.45%	4,076.60	6.18%
55.	Feb 28, 2023	$137.56		-3.39%	3,970.15	-2.61%
56.	Mar 31, 2023	$148.69		8.09%	4,109.31	3.51%
57.	Apr 30, 2023	$156.38	$0.9407	5.80%	4,169.48	1.46%
58.	May 31, 2023	$142.50		-8.88%	4,179.83	0.25%
59.	Jun 30, 2023	$151.74		6.48%	4,376.86	4.71%
60.	Jul 31, 2023	$156.30	$0.9407	3.63%	4,588.96	4.85%
61.	Aug 31, 2023	$154.34		-1.25%	4,507.66	-1.77%
62.	Sep 30, 2023	$145.86		-5.49%	4,288.05	-4.87%
63.	Oct 31, 2023	$150.03	$0.9407	3.50%	4,193.80	-2.20%
64.	Nov 30, 2023	$153.52		2.33%	4,567.80	8.92%
65.	Dec 31, 2023	$146.54		-4.55%	4,769.83	4.42%
66.	Jan 31, 2024	$157.14	$0.9407	7.88%	4,845.65	1.59%
67.	Feb 29, 2024	$158.94		1.15%	5,096.27	5.17%
68.	Mar 31, 2024	$162.25		2.08%	5,254.35	3.10%
69.	Apr 30, 2024	$163.20	$1.0065	1.21%	5,035.69	-4.16%
70.	May 31, 2024	$164.54		0.82%	5,277.51	4.80%
71.	Jun 30, 2024	$164.92		0.23%	5,460.48	3.47%
Average (R):				1.33%		1.07%
Standard deviation:				4.91%		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 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, 2018	2.56%	3.03%	1.51	3.81	2.40
2.	Sep 30, 2018	0.34%	0.43%	0.99	0.41	0.64
3.	Oct 31, 2018	7.41%	-6.94%	36.93	64.22	-48.70
.	.	.	.	.	.	.
.	.	.	.	.	.	.
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70.	May 31, 2024	0.82%	4.80%	0.26	13.90	-1.91
71.	Jun 30, 2024	0.23%	3.47%	1.21	5.73	-2.64
Total (Σ):				1,685.30	1,922.79	754.65

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, 2018	2.56%	3.03%	1.51	3.81	2.40
2.	Sep 30, 2018	0.34%	0.43%	0.99	0.41	0.64
3.	Oct 31, 2018	7.41%	-6.94%	36.93	64.22	-48.70
4.	Nov 30, 2018	6.57%	1.79%	27.47	0.51	3.74
5.	Dec 31, 2018	-2.74%	-9.18%	16.59	105.08	41.75
6.	Jan 31, 2019	5.73%	7.87%	19.34	46.17	29.88
7.	Feb 28, 2019	2.16%	2.97%	0.68	3.61	1.56
8.	Mar 31, 2019	5.58%	1.79%	18.05	0.52	3.05
9.	Apr 30, 2019	3.05%	3.93%	2.96	8.17	4.91
10.	May 31, 2019	-3.35%	-6.58%	21.95	58.54	35.85
11.	Jun 30, 2019	6.55%	6.89%	27.22	33.87	30.36
12.	Jul 31, 2019	8.33%	1.31%	48.99	0.06	1.68
13.	Aug 31, 2019	1.86%	-1.81%	0.27	8.31	-1.51
14.	Sep 30, 2019	3.45%	1.72%	4.49	0.42	1.37
15.	Oct 31, 2019	0.70%	2.04%	0.39	0.94	-0.61
16.	Nov 30, 2019	-1.97%	3.40%	10.89	5.44	-7.69
17.	Dec 31, 2019	2.33%	2.86%	0.99	3.19	1.78
18.	Jan 31, 2020	0.37%	-0.16%	0.92	1.53	1.19
19.	Feb 29, 2020	-9.14%	-8.41%	109.67	89.95	99.32
20.	Mar 31, 2020	-2.85%	-12.51%	17.52	184.56	56.86
21.	Apr 30, 2020	7.87%	12.68%	42.78	134.82	75.95
22.	May 31, 2020	-1.65%	4.53%	8.92	11.94	-10.32
23.	Jun 30, 2020	3.15%	1.84%	3.30	0.59	1.39
24.	Jul 31, 2020	10.32%	5.51%	80.79	19.68	39.88
25.	Aug 31, 2020	5.50%	7.01%	17.36	35.20	24.72
26.	Sep 30, 2020	0.48%	-3.92%	0.73	24.96	4.27
27.	Oct 31, 2020	-0.79%	-2.77%	4.51	14.75	8.15
28.	Nov 30, 2020	1.29%	10.75%	0.00	93.73	-0.40
29.	Dec 31, 2020	0.19%	3.71%	1.30	6.96	-3.00
30.	Jan 31, 2021	-7.29%	-1.11%	74.30	4.78	18.85
31.	Feb 28, 2021	-3.65%	2.61%	24.83	2.36	-7.65
32.	Mar 31, 2021	9.63%	4.24%	68.90	10.05	26.32
33.	Apr 30, 2021	-0.84%	5.24%	4.73	17.38	-9.07
34.	May 31, 2021	1.07%	0.55%	0.07	0.28	0.14
35.	Jun 30, 2021	0.06%	2.22%	1.62	1.32	-1.46
36.	Jul 31, 2021	6.05%	2.27%	22.30	1.44	5.67
37.	Aug 31, 2021	0.11%	2.90%	1.49	3.33	-2.23
38.	Sep 30, 2021	-1.82%	-4.76%	9.93	33.99	18.37
39.	Oct 31, 2021	2.90%	6.91%	2.47	34.12	9.18
40.	Nov 30, 2021	1.11%	-0.83%	0.05	3.64	0.42
41.	Dec 31, 2021	13.14%	4.36%	139.45	10.81	38.83
42.	Jan 31, 2022	-1.38%	-5.26%	7.37	40.09	17.19
43.	Feb 28, 2022	-2.84%	-3.14%	17.43	17.72	17.57
44.	Mar 31, 2022	-1.98%	3.58%	10.99	6.27	-8.30
45.	Apr 30, 2022	5.67%	-8.80%	18.81	97.40	-42.80
46.	May 31, 2022	-7.89%	0.01%	85.09	1.14	9.85
47.	Jun 30, 2022	-2.77%	-8.39%	16.80	89.59	38.79
48.	Jul 31, 2022	-2.76%	9.11%	16.74	64.61	-32.89
49.	Aug 31, 2022	-0.70%	-4.24%	4.12	28.27	10.80
50.	Sep 30, 2022	-8.47%	-9.34%	96.18	108.43	102.12
51.	Oct 31, 2022	7.39%	7.99%	36.73	47.79	41.89
52.	Nov 30, 2022	10.76%	5.38%	88.87	18.51	40.55
53.	Dec 31, 2022	1.61%	-5.90%	0.08	48.59	-1.93
54.	Jan 31, 2023	-5.45%	6.18%	46.06	26.03	-34.63
55.	Feb 28, 2023	-3.39%	-2.61%	22.26	13.58	17.38
56.	Mar 31, 2023	8.09%	3.51%	45.68	5.91	16.44
57.	Apr 30, 2023	5.80%	1.46%	20.00	0.15	1.75
58.	May 31, 2023	-8.88%	0.25%	104.21	0.68	8.42
59.	Jun 30, 2023	6.48%	4.71%	26.54	13.25	18.75
60.	Jul 31, 2023	3.63%	4.85%	5.26	14.23	8.65
61.	Aug 31, 2023	-1.25%	-1.77%	6.69	8.09	7.36
62.	Sep 30, 2023	-5.49%	-4.87%	46.61	35.35	40.59
63.	Oct 31, 2023	3.50%	-2.20%	4.71	10.70	-7.10
64.	Nov 30, 2023	2.33%	8.92%	0.99	61.54	7.79
65.	Dec 31, 2023	-4.55%	4.42%	34.56	11.22	-19.69
66.	Jan 31, 2024	7.88%	1.59%	42.81	0.27	3.38
67.	Feb 29, 2024	1.15%	5.17%	0.03	16.80	-0.77
68.	Mar 31, 2024	2.08%	3.10%	0.56	4.11	1.52
69.	Apr 30, 2024	1.21%	-4.16%	0.02	27.40	0.66
70.	May 31, 2024	0.82%	4.80%	0.26	13.90	-1.91
71.	Jun 30, 2024	0.23%	3.47%	1.21	5.73	-2.64
Total (Σ):				1,685.30	1,922.79	754.65

Show all

Variance_PG = Σ(R_PG,t–R_PG)² ÷ (71 – 1)
= 1,685.30 ÷ (71 – 1)
= 24.08

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_{PG, S&P 500} = Σ(R_PG,t–R_PG)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 754.65 ÷ (71 – 1)
= 10.78

Systematic Risk (β) Estimation

Variance_PG	24.08
Variance_{S&P 500}	27.47
Covariance_{PG, S&P 500}	10.78
Correlation coefficient_{PG, S&P 500}¹	0.42
β_PG²	0.39
α_PG³	0.91%

Calculations

¹ Correlation coefficient_{PG, S&P 500}
= Covariance_{PG, S&P 500} ÷ (Standard deviation_PG × Standard deviation_{S&P 500})
= 10.78 ÷ (4.91% × 5.24%)
= 0.42

² β_PG
= Covariance_{PG, S&P 500} ÷ Variance_{S&P 500}
= 10.78 ÷ 27.47
= 0.39

³ α_PG
= Average_PG – β_PG × Average_{S&P 500}
= 1.33% – 0.39 × 1.07%
= 0.91%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.78%
Expected rate of return on market portfolio²	E(R_M)	14.43%
Systematic risk (β) of Procter & Gamble Co. common stock	β_PG	0.39

Expected rate of return on Procter & Gamble Co. common stock³	E(R_PG)	8.57%

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_PG) = R_F + β_PG [E(R_M) – R_F]
= 4.78% + 0.39 [14.43% – 4.78%]
= 8.57%