Colgate-Palmolive Co. (NYSE:CL)

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 Colgate-Palmolive Co.’s common stock.

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

Rates of Return

Colgate-Palmolive Co., monthly rates of return

		Colgate-Palmolive Co. (CL)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_CL,t¹	Dividend_CL,t¹	R_CL,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2016	$67.53			1,940.24
1.	Feb 29, 2016	$65.64		-2.80%	1,932.23	-0.41%
2.	Mar 31, 2016	$70.65		7.63%	2,059.74	6.60%
3.	Apr 30, 2016	$70.92	$0.39	0.93%	2,065.30	0.27%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2020	$85.64		8.56%	3,621.63	10.75%
59.	Dec 31, 2020	$85.51		-0.15%	3,756.07	3.71%
Average (R):				0.70%		1.22%
Standard deviation:				4.77%		4.36%

		Colgate-Palmolive Co. (CL)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_CL,t¹	Dividend_CL,t¹	R_CL,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2016	$67.53			1,940.24
1.	Feb 29, 2016	$65.64		-2.80%	1,932.23	-0.41%
2.	Mar 31, 2016	$70.65		7.63%	2,059.74	6.60%
3.	Apr 30, 2016	$70.92	$0.39	0.93%	2,065.30	0.27%
4.	May 31, 2016	$70.41		-0.72%	2,096.95	1.53%
5.	Jun 30, 2016	$73.20		3.96%	2,098.86	0.09%
6.	Jul 31, 2016	$74.43	$0.39	2.21%	2,173.60	3.56%
7.	Aug 31, 2016	$74.34		-0.12%	2,170.95	-0.12%
8.	Sep 30, 2016	$74.14		-0.27%	2,168.27	-0.12%
9.	Oct 31, 2016	$71.36	$0.39	-3.22%	2,126.15	-1.94%
10.	Nov 30, 2016	$65.23		-8.59%	2,198.81	3.42%
11.	Dec 31, 2016	$65.44		0.32%	2,238.83	1.82%
12.	Jan 31, 2017	$64.58	$0.39	-0.72%	2,278.87	1.79%
13.	Feb 28, 2017	$72.98		13.01%	2,363.64	3.72%
14.	Mar 31, 2017	$73.19		0.29%	2,362.72	-0.04%
15.	Apr 30, 2017	$72.04	$0.40	-1.02%	2,384.20	0.91%
16.	May 31, 2017	$76.36		6.00%	2,411.80	1.16%
17.	Jun 30, 2017	$74.13		-2.92%	2,423.41	0.48%
18.	Jul 31, 2017	$72.20	$0.40	-2.06%	2,470.30	1.93%
19.	Aug 31, 2017	$71.64		-0.78%	2,471.65	0.05%
20.	Sep 30, 2017	$72.85		1.69%	2,519.36	1.93%
21.	Oct 31, 2017	$70.45	$0.40	-2.75%	2,575.26	2.22%
22.	Nov 30, 2017	$72.45		2.84%	2,647.58	2.81%
23.	Dec 31, 2017	$75.45		4.14%	2,673.61	0.98%
24.	Jan 31, 2018	$74.24	$0.40	-1.07%	2,823.81	5.62%
25.	Feb 28, 2018	$68.97		-7.10%	2,713.83	-3.89%
26.	Mar 31, 2018	$71.68		3.93%	2,640.87	-2.69%
27.	Apr 30, 2018	$65.23	$0.42	-8.41%	2,648.05	0.27%
28.	May 31, 2018	$63.09		-3.28%	2,705.27	2.16%
29.	Jun 30, 2018	$64.81		2.73%	2,718.37	0.48%
30.	Jul 31, 2018	$67.01	$0.42	4.04%	2,816.29	3.60%
31.	Aug 31, 2018	$66.41		-0.90%	2,901.52	3.03%
32.	Sep 30, 2018	$66.95		0.81%	2,913.98	0.43%
33.	Oct 31, 2018	$59.55	$0.42	-10.43%	2,711.74	-6.94%
34.	Nov 30, 2018	$63.52		6.67%	2,760.17	1.79%
35.	Dec 31, 2018	$59.52		-6.30%	2,506.85	-9.18%
36.	Jan 31, 2019	$64.68	$0.42	9.38%	2,704.10	7.87%
37.	Feb 28, 2019	$65.87		1.84%	2,784.49	2.97%
38.	Mar 31, 2019	$68.54		4.05%	2,834.40	1.79%
39.	Apr 30, 2019	$72.79	$0.43	6.83%	2,945.83	3.93%
40.	May 31, 2019	$69.62		-4.35%	2,752.06	-6.58%
41.	Jun 30, 2019	$71.67		2.94%	2,941.76	6.89%
42.	Jul 31, 2019	$71.74	$0.43	0.70%	2,980.38	1.31%
43.	Aug 31, 2019	$74.15		3.36%	2,926.46	-1.81%
44.	Sep 30, 2019	$73.51		-0.86%	2,976.74	1.72%
45.	Oct 31, 2019	$68.60	$0.43	-6.09%	3,037.56	2.04%
46.	Nov 30, 2019	$67.82		-1.14%	3,140.98	3.40%
47.	Dec 31, 2019	$68.84		1.50%	3,230.78	2.86%
48.	Jan 31, 2020	$73.78	$0.43	7.80%	3,225.52	-0.16%
49.	Feb 29, 2020	$67.57		-8.42%	2,954.22	-8.41%
50.	Mar 31, 2020	$66.36		-1.79%	2,584.59	-12.51%
51.	Apr 30, 2020	$70.27	$0.44	6.56%	2,912.43	12.68%
52.	May 31, 2020	$72.33		2.93%	3,044.31	4.53%
53.	Jun 30, 2020	$73.26		1.29%	3,100.29	1.84%
54.	Jul 31, 2020	$77.20	$0.44	5.98%	3,271.12	5.51%
55.	Aug 31, 2020	$79.26		2.67%	3,500.31	7.01%
56.	Sep 30, 2020	$77.15		-2.66%	3,363.00	-3.92%
57.	Oct 31, 2020	$78.89	$0.44	2.83%	3,269.96	-2.77%
58.	Nov 30, 2020	$85.64		8.56%	3,621.63	10.75%
59.	Dec 31, 2020	$85.51		-0.15%	3,756.07	3.71%
Average (R):				0.70%		1.22%
Standard deviation:				4.77%		4.36%

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 CL during period t

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

Variance and Covariance

Colgate-Palmolive Co., calculation of variance and covariance of returns

t	Date	R_CL,t	R_{S&P 500,t}	(R_CL,t–R_CL)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_CL,t–R_CL)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2016	-2.80%	-0.41%	12.26	2.67	5.72
2.	Mar 31, 2016	7.63%	6.60%	48.02	28.93	37.27
3.	Apr 30, 2016	0.93%	0.27%	0.05	0.90	-0.22
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	Nov 30, 2020	8.56%	10.75%	61.67	90.91	74.88
59.	Dec 31, 2020	-0.15%	3.71%	0.73	6.21	-2.13
Total (Σ):				1,320.08	1,103.45	680.03

t	Date	R_CL,t	R_{S&P 500,t}	(R_CL,t–R_CL)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_CL,t–R_CL)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 29, 2016	-2.80%	-0.41%	12.26	2.67	5.72
2.	Mar 31, 2016	7.63%	6.60%	48.02	28.93	37.27
3.	Apr 30, 2016	0.93%	0.27%	0.05	0.90	-0.22
4.	May 31, 2016	-0.72%	1.53%	2.02	0.10	-0.44
5.	Jun 30, 2016	3.96%	0.09%	10.62	1.27	-3.68
6.	Jul 31, 2016	2.21%	3.56%	2.28	5.48	3.53
7.	Aug 31, 2016	-0.12%	-0.12%	0.68	1.80	1.11
8.	Sep 30, 2016	-0.27%	-0.12%	0.95	1.81	1.31
9.	Oct 31, 2016	-3.22%	-1.94%	15.42	10.00	12.42
10.	Nov 30, 2016	-8.59%	3.42%	86.37	4.83	-20.42
11.	Dec 31, 2016	0.32%	1.82%	0.15	0.36	-0.23
12.	Jan 31, 2017	-0.72%	1.79%	2.02	0.32	-0.81
13.	Feb 28, 2017	13.01%	3.72%	151.39	6.25	30.76
14.	Mar 31, 2017	0.29%	-0.04%	0.17	1.59	0.52
15.	Apr 30, 2017	-1.02%	0.91%	2.99	0.10	0.54
16.	May 31, 2017	6.00%	1.16%	28.02	0.00	-0.33
17.	Jun 30, 2017	-2.92%	0.48%	13.13	0.55	2.68
18.	Jul 31, 2017	-2.06%	1.93%	7.66	0.51	-1.98
19.	Aug 31, 2017	-0.78%	0.05%	2.19	1.36	1.72
20.	Sep 30, 2017	1.69%	1.93%	0.97	0.50	0.70
21.	Oct 31, 2017	-2.75%	2.22%	11.89	1.00	-3.44
22.	Nov 30, 2017	2.84%	2.81%	4.56	2.52	3.39
23.	Dec 31, 2017	4.14%	0.98%	11.82	0.06	-0.81
24.	Jan 31, 2018	-1.07%	5.62%	3.16	19.34	-7.81
25.	Feb 28, 2018	-7.10%	-3.89%	60.87	26.16	39.90
26.	Mar 31, 2018	3.93%	-2.69%	10.41	15.28	-12.61
27.	Apr 30, 2018	-8.41%	0.27%	83.09	0.90	8.64
28.	May 31, 2018	-3.28%	2.16%	15.87	0.89	-3.75
29.	Jun 30, 2018	2.73%	0.48%	4.09	0.54	-1.49
30.	Jul 31, 2018	4.04%	3.60%	11.15	5.67	7.96
31.	Aug 31, 2018	-0.90%	3.03%	2.56	3.26	-2.89
32.	Sep 30, 2018	0.81%	0.43%	0.01	0.63	-0.09
33.	Oct 31, 2018	-10.43%	-6.94%	123.85	66.59	90.82
34.	Nov 30, 2018	6.67%	1.79%	35.56	0.32	3.37
35.	Dec 31, 2018	-6.30%	-9.18%	49.00	108.11	72.79
36.	Jan 31, 2019	9.38%	7.87%	75.20	44.20	57.65
37.	Feb 28, 2019	1.84%	2.97%	1.29	3.07	1.99
38.	Mar 31, 2019	4.05%	1.79%	11.22	0.33	1.92
39.	Apr 30, 2019	6.83%	3.93%	37.52	7.35	16.61
40.	May 31, 2019	-4.35%	-6.58%	25.58	60.81	39.44
41.	Jun 30, 2019	2.94%	6.89%	5.02	32.18	12.72
42.	Jul 31, 2019	0.70%	1.31%	0.00	0.01	0.00
43.	Aug 31, 2019	3.36%	-1.81%	7.06	9.18	-8.05
44.	Sep 30, 2019	-0.86%	1.72%	2.45	0.25	-0.78
45.	Oct 31, 2019	-6.09%	2.04%	46.21	0.68	-5.60
46.	Nov 30, 2019	-1.14%	3.40%	3.39	4.77	-4.02
47.	Dec 31, 2019	1.50%	2.86%	0.64	2.69	1.31
48.	Jan 31, 2020	7.80%	-0.16%	50.38	1.91	-9.82
49.	Feb 29, 2020	-8.42%	-8.41%	83.17	92.76	87.84
50.	Mar 31, 2020	-1.79%	-12.51%	6.22	188.57	34.25
51.	Apr 30, 2020	6.56%	12.68%	34.25	131.43	67.09
52.	May 31, 2020	2.93%	4.53%	4.97	10.94	7.37
53.	Jun 30, 2020	1.29%	1.84%	0.34	0.38	0.36
54.	Jul 31, 2020	5.98%	5.51%	27.83	18.40	22.63
55.	Aug 31, 2020	2.67%	7.01%	3.86	33.48	11.37
56.	Sep 30, 2020	-2.66%	-3.92%	11.32	26.45	17.31
57.	Oct 31, 2020	2.83%	-2.77%	4.51	15.89	-8.46
58.	Nov 30, 2020	8.56%	10.75%	61.67	90.91	74.88
59.	Dec 31, 2020	-0.15%	3.71%	0.73	6.21	-2.13
Total (Σ):				1,320.08	1,103.45	680.03

Show all

Variance_CL = Σ(R_CL,t–R_CL)² ÷ (59 – 1)
= 1,320.08 ÷ (59 – 1)
= 22.76

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (59 – 1)
= 1,103.45 ÷ (59 – 1)
= 19.02

Covariance_{CL, S&P 500} = Σ(R_CL,t–R_CL)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 680.03 ÷ (59 – 1)
= 11.72

Systematic Risk (β) Estimation

Variance_CL	22.76
Variance_{S&P 500}	19.02
Covariance_{CL, S&P 500}	11.72
Correlation coefficient_{CL, S&P 500}¹	0.56
β_CL²	0.62
α_CL³	-0.05%

Calculations

¹ Correlation coefficient_{CL, S&P 500}
= Covariance_{CL, S&P 500} ÷ (Standard deviation_CL × Standard deviation_{S&P 500})
= 11.72 ÷ (4.77% × 4.36%)
= 0.56

² β_CL
= Covariance_{CL, S&P 500} ÷ Variance_{S&P 500}
= 11.72 ÷ 19.02
= 0.62

³ α_CL
= Average_CL – β_CL × Average_{S&P 500}
= 0.70% – 0.62 × 1.22%
= -0.05%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	2.02%
Expected rate of return on market portfolio²	E(R_M)	11.66%
Systematic risk (β) of Colgate-Palmolive Co.’s common stock	β_CL	0.62

Expected rate of return on Colgate-Palmolive Co.’s common stock³	E(R_CL)	7.96%

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_CL) = R_F + β_CL [E(R_M) – R_F]
= 2.02% + 0.62 [11.66% – 2.02%]
= 7.96%