Keurig Dr Pepper Inc. (NASDAQ:KDP)

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 Keurig Dr Pepper Inc. common stock.

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

Rates of Return

Keurig Dr Pepper Inc., monthly rates of return

		Keurig Dr Pepper Inc. (KDP)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_KDP,t¹	Dividend_KDP,t¹	R_KDP,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2018	$119.35			2,823.81
1.	Feb 28, 2018	$116.25		-2.60%	2,713.83	-3.89%
2.	Mar 31, 2018	$118.38	$0.58	2.33%	2,640.87	-2.69%
3.	Apr 30, 2018	$119.96		1.33%	2,648.05	0.27%
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46.	Nov 30, 2021	$33.99		-5.82%	4,567.00	-0.83%
47.	Dec 31, 2021	$36.86		8.44%	4,766.18	4.36%
Average (R):				1.39%		1.24%
Standard deviation:				5.96%		4.96%

		Keurig Dr Pepper Inc. (KDP)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_KDP,t¹	Dividend_KDP,t¹	R_KDP,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Jan 31, 2018	$119.35			2,823.81
1.	Feb 28, 2018	$116.25		-2.60%	2,713.83	-3.89%
2.	Mar 31, 2018	$118.38	$0.58	2.33%	2,640.87	-2.69%
3.	Apr 30, 2018	$119.96		1.33%	2,648.05	0.27%
4.	May 31, 2018	$119.30		-0.55%	2,705.27	2.16%
5.	Jun 30, 2018	$122.00		2.26%	2,718.37	0.48%
6.	Jul 31, 2018	$24.01	$103.75	4.72%	2,816.29	3.60%
7.	Aug 31, 2018	$22.80		-5.04%	2,901.52	3.03%
8.	Sep 30, 2018	$23.17		1.62%	2,913.98	0.43%
9.	Oct 31, 2018	$26.00	$0.15	12.86%	2,711.74	-6.94%
10.	Nov 30, 2018	$27.00		3.85%	2,760.17	1.79%
11.	Dec 31, 2018	$25.64		-5.04%	2,506.85	-9.18%
12.	Jan 31, 2019	$27.22	$0.15	6.75%	2,704.10	7.87%
13.	Feb 28, 2019	$25.15		-7.60%	2,784.49	2.97%
14.	Mar 31, 2019	$27.97		11.21%	2,834.40	1.79%
15.	Apr 30, 2019	$29.07	$0.15	4.47%	2,945.83	3.93%
16.	May 31, 2019	$28.19		-3.03%	2,752.06	-6.58%
17.	Jun 30, 2019	$28.90		2.52%	2,941.76	6.89%
18.	Jul 31, 2019	$28.14	$0.15	-2.11%	2,980.38	1.31%
19.	Aug 31, 2019	$27.28		-3.06%	2,926.46	-1.81%
20.	Sep 30, 2019	$27.32		0.15%	2,976.74	1.72%
21.	Oct 31, 2019	$28.16	$0.15	3.62%	3,037.56	2.04%
22.	Nov 30, 2019	$30.94		9.87%	3,140.98	3.40%
23.	Dec 31, 2019	$28.95		-6.43%	3,230.78	2.86%
24.	Jan 31, 2020	$28.53	$0.15	-0.93%	3,225.52	-0.16%
25.	Feb 29, 2020	$27.88		-2.28%	2,954.22	-8.41%
26.	Mar 31, 2020	$24.27		-12.95%	2,584.59	-12.51%
27.	Apr 30, 2020	$26.46	$0.15	9.64%	2,912.43	12.68%
28.	May 31, 2020	$27.92		5.52%	3,044.31	4.53%
29.	Jun 30, 2020	$28.40		1.72%	3,100.29	1.84%
30.	Jul 31, 2020	$30.59	$0.15	8.24%	3,271.12	5.51%
31.	Aug 31, 2020	$29.83		-2.48%	3,500.31	7.01%
32.	Sep 30, 2020	$27.60		-7.48%	3,363.00	-3.92%
33.	Oct 31, 2020	$26.90	$0.15	-1.99%	3,269.96	-2.77%
34.	Nov 30, 2020	$30.45		13.20%	3,621.63	10.75%
35.	Dec 31, 2020	$32.00		5.09%	3,756.07	3.71%
36.	Jan 31, 2021	$31.80	$0.15	-0.16%	3,714.24	-1.11%
37.	Feb 28, 2021	$30.52		-4.03%	3,811.15	2.61%
38.	Mar 31, 2021	$34.37	$0.15	13.11%	3,972.89	4.24%
39.	Apr 30, 2021	$35.85		4.31%	4,181.17	5.24%
40.	May 31, 2021	$36.96		3.10%	4,204.11	0.55%
41.	Jun 30, 2021	$35.24	$0.1875	-4.15%	4,297.50	2.22%
42.	Jul 31, 2021	$35.21		-0.09%	4,395.26	2.27%
43.	Aug 31, 2021	$35.67		1.31%	4,522.68	2.90%
44.	Sep 30, 2021	$34.16	$0.1875	-3.71%	4,307.54	-4.76%
45.	Oct 31, 2021	$36.09		5.65%	4,605.38	6.91%
46.	Nov 30, 2021	$33.99		-5.82%	4,567.00	-0.83%
47.	Dec 31, 2021	$36.86		8.44%	4,766.18	4.36%
Average (R):				1.39%		1.24%
Standard deviation:				5.96%		4.96%

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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 KDP during period t

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

Variance and Covariance

Keurig Dr Pepper Inc., calculation of variance and covariance of returns

t	Date	R_KDP,t	R_{S&P 500,t}	(R_KDP,t–R_KDP)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_KDP,t–R_KDP)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2018	-2.60%	-3.89%	15.91	26.38	20.48
2.	Mar 31, 2018	2.33%	-2.69%	0.88	15.44	-3.69
3.	Apr 30, 2018	1.33%	0.27%	0.00	0.94	0.05
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46.	Nov 30, 2021	-5.82%	-0.83%	51.98	4.30	14.96
47.	Dec 31, 2021	8.44%	4.36%	49.74	9.73	22.00
Total (Σ):				1,634.61	1,131.50	738.06

t	Date	R_KDP,t	R_{S&P 500,t}	(R_KDP,t–R_KDP)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_KDP,t–R_KDP)×(R_{S&P 500,t}–R_{S&P 500})
1.	Feb 28, 2018	-2.60%	-3.89%	15.91	26.38	20.48
2.	Mar 31, 2018	2.33%	-2.69%	0.88	15.44	-3.69
3.	Apr 30, 2018	1.33%	0.27%	0.00	0.94	0.05
4.	May 31, 2018	-0.55%	2.16%	3.77	0.85	-1.79
5.	Jun 30, 2018	2.26%	0.48%	0.76	0.57	-0.66
6.	Jul 31, 2018	4.72%	3.60%	11.09	5.57	7.86
7.	Aug 31, 2018	-5.04%	3.03%	41.35	3.19	-11.48
8.	Sep 30, 2018	1.62%	0.43%	0.05	0.66	-0.19
9.	Oct 31, 2018	12.86%	-6.94%	131.57	66.94	-93.85
10.	Nov 30, 2018	3.85%	1.79%	6.03	0.30	1.34
11.	Dec 31, 2018	-5.04%	-9.18%	41.32	108.55	66.97
12.	Jan 31, 2019	6.75%	7.87%	28.69	43.92	35.50
13.	Feb 28, 2019	-7.60%	2.97%	80.92	3.00	-15.58
14.	Mar 31, 2019	11.21%	1.79%	96.47	0.30	5.41
15.	Apr 30, 2019	4.47%	3.93%	9.47	7.24	8.28
16.	May 31, 2019	-3.03%	-6.58%	19.52	61.14	34.55
17.	Jun 30, 2019	2.52%	6.89%	1.27	31.94	6.37
18.	Jul 31, 2019	-2.11%	1.31%	12.26	0.01	-0.25
19.	Aug 31, 2019	-3.06%	-1.81%	19.78	9.31	13.57
20.	Sep 30, 2019	0.15%	1.72%	1.55	0.23	-0.59
21.	Oct 31, 2019	3.62%	2.04%	4.98	0.64	1.79
22.	Nov 30, 2019	9.87%	3.40%	71.93	4.68	18.35
23.	Dec 31, 2019	-6.43%	2.86%	61.20	2.62	-12.66
24.	Jan 31, 2020	-0.93%	-0.16%	5.40	1.97	3.26
25.	Feb 29, 2020	-2.28%	-8.41%	13.46	93.17	35.42
26.	Mar 31, 2020	-12.95%	-12.51%	205.62	189.15	197.21
27.	Apr 30, 2020	9.64%	12.68%	68.07	130.95	94.41
28.	May 31, 2020	5.52%	4.53%	17.03	10.80	13.56
29.	Jun 30, 2020	1.72%	1.84%	0.11	0.36	0.20
30.	Jul 31, 2020	8.24%	5.51%	46.90	18.22	29.23
31.	Aug 31, 2020	-2.48%	7.01%	15.02	33.24	-22.34
32.	Sep 30, 2020	-7.48%	-3.92%	78.62	26.67	45.79
33.	Oct 31, 2020	-1.99%	-2.77%	11.45	16.06	13.56
34.	Nov 30, 2020	13.20%	10.75%	139.38	90.50	112.31
35.	Dec 31, 2020	5.09%	3.71%	13.68	6.11	9.14
36.	Jan 31, 2021	-0.16%	-1.11%	2.39	5.55	3.64
37.	Feb 28, 2021	-4.03%	2.61%	29.34	1.87	-7.41
38.	Mar 31, 2021	13.11%	4.24%	137.24	9.02	35.18
39.	Apr 30, 2021	4.31%	5.24%	8.50	16.01	11.66
40.	May 31, 2021	3.10%	0.55%	2.91	0.48	-1.18
41.	Jun 30, 2021	-4.15%	2.22%	30.66	0.96	-5.43
42.	Jul 31, 2021	-0.09%	2.27%	2.18	1.07	-1.53
43.	Aug 31, 2021	1.31%	2.90%	0.01	2.75	-0.14
44.	Sep 30, 2021	-3.71%	-4.76%	26.00	35.98	30.58
45.	Oct 31, 2021	5.65%	6.91%	18.14	32.18	24.16
46.	Nov 30, 2021	-5.82%	-0.83%	51.98	4.30	14.96
47.	Dec 31, 2021	8.44%	4.36%	49.74	9.73	22.00
Total (Σ):				1,634.61	1,131.50	738.06

Show all

Variance_KDP = Σ(R_KDP,t–R_KDP)² ÷ (47 – 1)
= 1,634.61 ÷ (47 – 1)
= 35.54

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (47 – 1)
= 1,131.50 ÷ (47 – 1)
= 24.60

Covariance_{KDP, S&P 500} = Σ(R_KDP,t–R_KDP)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (47 – 1)
= 738.06 ÷ (47 – 1)
= 16.04

Systematic Risk (β) Estimation

Variance_KDP	35.54
Variance_{S&P 500}	24.60
Covariance_{KDP, S&P 500}	16.04
Correlation coefficient_{KDP, S&P 500}¹	0.54
β_KDP²	0.65
α_KDP³	0.58%

Calculations

¹ Correlation coefficient_{KDP, S&P 500}
= Covariance_{KDP, S&P 500} ÷ (Standard deviation_KDP × Standard deviation_{S&P 500})
= 16.04 ÷ (5.96% × 4.96%)
= 0.54

² β_KDP
= Covariance_{KDP, S&P 500} ÷ Variance_{S&P 500}
= 16.04 ÷ 24.60
= 0.65

³ α_KDP
= Average_KDP – β_KDP × Average_{S&P 500}
= 1.39% – 0.65 × 1.24%
= 0.58%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.69%
Expected rate of return on market portfolio²	E(R_M)	13.79%
Systematic risk (β) of Keurig Dr Pepper Inc. common stock	β_KDP	0.65

Expected rate of return on Keurig Dr Pepper Inc. common stock³	E(R_KDP)	10.62%

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_KDP) = R_F + β_KDP [E(R_M) – R_F]
= 4.69% + 0.65 [13.79% – 4.69%]
= 10.62%