Dollar Tree Inc. (NASDAQ:DLTR)

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 Dollar Tree Inc. common stock.

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

Rates of Return

Dollar Tree Inc., monthly rates of return

		Dollar Tree Inc. (DLTR)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_DLTR,t¹	Dividend_DLTR,t¹	R_DLTR,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Feb 29, 2016	$80.25			1,932.23
1.	Mar 31, 2016	$82.46		2.75%	2,059.74	6.60%
2.	Apr 30, 2016	$79.71		-3.33%	2,065.30	0.27%
3.	May 31, 2016	$90.54		13.59%	2,096.95	1.53%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Dec 31, 2021	$140.52		5.00%	4,766.18	4.36%
71.	Jan 31, 2022	$131.22		-6.62%	4,515.55	-5.26%
Average (R):				1.08%		1.29%
Standard deviation:				8.96%		4.25%

		Dollar Tree Inc. (DLTR)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_DLTR,t¹	Dividend_DLTR,t¹	R_DLTR,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Feb 29, 2016	$80.25			1,932.23
1.	Mar 31, 2016	$82.46		2.75%	2,059.74	6.60%
2.	Apr 30, 2016	$79.71		-3.33%	2,065.30	0.27%
3.	May 31, 2016	$90.54		13.59%	2,096.95	1.53%
4.	Jun 30, 2016	$94.24		4.09%	2,098.86	0.09%
5.	Jul 31, 2016	$96.29		2.18%	2,173.60	3.56%
6.	Aug 31, 2016	$82.70		-14.11%	2,170.95	-0.12%
7.	Sep 30, 2016	$78.93		-4.56%	2,168.27	-0.12%
8.	Oct 31, 2016	$75.55		-4.28%	2,126.15	-1.94%
9.	Nov 30, 2016	$88.16		16.69%	2,198.81	3.42%
10.	Dec 31, 2016	$77.18		-12.45%	2,238.83	1.82%
11.	Jan 31, 2017	$77.19		0.01%	2,278.87	1.79%
12.	Feb 28, 2017	$76.68		-0.66%	2,363.64	3.72%
13.	Mar 31, 2017	$78.46		2.32%	2,362.72	-0.04%
14.	Apr 30, 2017	$82.77		5.49%	2,384.20	0.91%
15.	May 31, 2017	$77.70		-6.13%	2,411.80	1.16%
16.	Jun 30, 2017	$69.92		-10.01%	2,423.41	0.48%
17.	Jul 31, 2017	$72.08		3.09%	2,470.30	1.93%
18.	Aug 31, 2017	$79.64		10.49%	2,471.65	0.05%
19.	Sep 30, 2017	$86.82		9.02%	2,519.36	1.93%
20.	Oct 31, 2017	$91.25		5.10%	2,575.26	2.22%
21.	Nov 30, 2017	$102.76		12.61%	2,647.58	2.81%
22.	Dec 31, 2017	$107.31		4.43%	2,673.61	0.98%
23.	Jan 31, 2018	$115.00		7.17%	2,823.81	5.62%
24.	Feb 28, 2018	$102.64		-10.75%	2,713.83	-3.89%
25.	Mar 31, 2018	$94.90		-7.54%	2,640.87	-2.69%
26.	Apr 30, 2018	$95.89		1.04%	2,648.05	0.27%
27.	May 31, 2018	$82.59		-13.87%	2,705.27	2.16%
28.	Jun 30, 2018	$85.00		2.92%	2,718.37	0.48%
29.	Jul 31, 2018	$91.28		7.39%	2,816.29	3.60%
30.	Aug 31, 2018	$80.51		-11.80%	2,901.52	3.03%
31.	Sep 30, 2018	$81.55		1.29%	2,913.98	0.43%
32.	Oct 31, 2018	$84.30		3.37%	2,711.74	-6.94%
33.	Nov 30, 2018	$86.77		2.93%	2,760.17	1.79%
34.	Dec 31, 2018	$90.32		4.09%	2,506.85	-9.18%
35.	Jan 31, 2019	$96.83		7.21%	2,704.10	7.87%
36.	Feb 28, 2019	$96.33		-0.52%	2,784.49	2.97%
37.	Mar 31, 2019	$105.04		9.04%	2,834.40	1.79%
38.	Apr 30, 2019	$111.28		5.94%	2,945.83	3.93%
39.	May 31, 2019	$101.59		-8.71%	2,752.06	-6.58%
40.	Jun 30, 2019	$107.39		5.71%	2,941.76	6.89%
41.	Jul 31, 2019	$101.75		-5.25%	2,980.38	1.31%
42.	Aug 31, 2019	$101.53		-0.22%	2,926.46	-1.81%
43.	Sep 30, 2019	$114.16		12.44%	2,976.74	1.72%
44.	Oct 31, 2019	$110.40		-3.29%	3,037.56	2.04%
45.	Nov 30, 2019	$91.46		-17.16%	3,140.98	3.40%
46.	Dec 31, 2019	$94.05		2.83%	3,230.78	2.86%
47.	Jan 31, 2020	$87.07		-7.42%	3,225.52	-0.16%
48.	Feb 29, 2020	$83.03		-4.64%	2,954.22	-8.41%
49.	Mar 31, 2020	$73.47		-11.51%	2,584.59	-12.51%
50.	Apr 30, 2020	$79.67		8.44%	2,912.43	12.68%
51.	May 31, 2020	$97.87		22.84%	3,044.31	4.53%
52.	Jun 30, 2020	$92.68		-5.30%	3,100.29	1.84%
53.	Jul 31, 2020	$93.35		0.72%	3,271.12	5.51%
54.	Aug 31, 2020	$96.27		3.13%	3,500.31	7.01%
55.	Sep 30, 2020	$91.34		-5.12%	3,363.00	-3.92%
56.	Oct 31, 2020	$90.32		-1.12%	3,269.96	-2.77%
57.	Nov 30, 2020	$109.24		20.95%	3,621.63	10.75%
58.	Dec 31, 2020	$108.04		-1.10%	3,756.07	3.71%
59.	Jan 31, 2021	$101.66		-5.91%	3,714.24	-1.11%
60.	Feb 28, 2021	$98.20		-3.40%	3,811.15	2.61%
61.	Mar 31, 2021	$114.46		16.56%	3,972.89	4.24%
62.	Apr 30, 2021	$114.90		0.38%	4,181.17	5.24%
63.	May 31, 2021	$97.50		-15.14%	4,204.11	0.55%
64.	Jun 30, 2021	$99.50		2.05%	4,297.50	2.22%
65.	Jul 31, 2021	$99.79		0.29%	4,395.26	2.27%
66.	Aug 31, 2021	$90.54		-9.27%	4,522.68	2.90%
67.	Sep 30, 2021	$95.72		5.72%	4,307.54	-4.76%
68.	Oct 31, 2021	$107.76		12.58%	4,605.38	6.91%
69.	Nov 30, 2021	$133.83		24.19%	4,567.00	-0.83%
70.	Dec 31, 2021	$140.52		5.00%	4,766.18	4.36%
71.	Jan 31, 2022	$131.22		-6.62%	4,515.55	-5.26%
Average (R):				1.08%		1.29%
Standard deviation:				8.96%		4.25%

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 DLTR during period t

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

Variance and Covariance

Dollar Tree Inc., calculation of variance and covariance of returns

t	Date	R_DLTR,t	R_{S&P 500,t}	(R_DLTR,t–R_DLTR)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_DLTR,t–R_DLTR)×(R_{S&P 500,t}–R_{S&P 500})
1.	Mar 31, 2016	2.75%	6.60%	2.79	28.16	8.87
2.	Apr 30, 2016	-3.33%	0.27%	19.52	1.05	4.52
3.	May 31, 2016	13.59%	1.53%	156.34	0.06	3.00
.	.	.	.	.	.	.
.	.	.	.	.	.	.
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70.	Dec 31, 2021	5.00%	4.36%	15.33	9.42	12.02
71.	Jan 31, 2022	-6.62%	-5.26%	59.31	42.91	50.45
Total (Σ):				5,617.47	1,262.70	1,008.02

t	Date	R_DLTR,t	R_{S&P 500,t}	(R_DLTR,t–R_DLTR)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_DLTR,t–R_DLTR)×(R_{S&P 500,t}–R_{S&P 500})
1.	Mar 31, 2016	2.75%	6.60%	2.79	28.16	8.87
2.	Apr 30, 2016	-3.33%	0.27%	19.52	1.05	4.52
3.	May 31, 2016	13.59%	1.53%	156.34	0.06	3.00
4.	Jun 30, 2016	4.09%	0.09%	9.02	1.44	-3.61
5.	Jul 31, 2016	2.18%	3.56%	1.19	5.15	2.48
6.	Aug 31, 2016	-14.11%	-0.12%	230.94	2.00	21.49
7.	Sep 30, 2016	-4.56%	-0.12%	31.83	2.00	7.99
8.	Oct 31, 2016	-4.28%	-1.94%	28.79	10.46	17.36
9.	Nov 30, 2016	16.69%	3.42%	243.61	4.52	33.17
10.	Dec 31, 2016	-12.45%	1.82%	183.27	0.28	-7.15
11.	Jan 31, 2017	0.01%	1.79%	1.14	0.25	-0.53
12.	Feb 28, 2017	-0.66%	3.72%	3.04	5.89	-4.23
13.	Mar 31, 2017	2.32%	-0.04%	1.53	1.77	-1.65
14.	Apr 30, 2017	5.49%	0.91%	19.45	0.15	-1.69
15.	May 31, 2017	-6.13%	1.16%	51.96	0.02	0.97
16.	Jun 30, 2017	-10.01%	0.48%	123.12	0.66	9.00
17.	Jul 31, 2017	3.09%	1.93%	4.03	0.41	1.29
18.	Aug 31, 2017	10.49%	0.05%	88.46	1.53	-11.64
19.	Sep 30, 2017	9.02%	1.93%	62.93	0.41	5.06
20.	Oct 31, 2017	5.10%	2.22%	16.16	0.86	3.72
21.	Nov 30, 2017	12.61%	2.81%	132.96	2.30	17.48
22.	Dec 31, 2017	4.43%	0.98%	11.19	0.10	-1.03
23.	Jan 31, 2018	7.17%	5.62%	37.01	18.71	26.31
24.	Feb 28, 2018	-10.75%	-3.89%	139.97	26.90	61.37
25.	Mar 31, 2018	-7.54%	-2.69%	74.37	15.85	34.33
26.	Apr 30, 2018	1.04%	0.27%	0.00	1.04	0.04
27.	May 31, 2018	-13.87%	2.16%	223.59	0.75	-12.99
28.	Jun 30, 2018	2.92%	0.48%	3.37	0.65	-1.48
29.	Jul 31, 2018	7.39%	3.60%	39.76	5.34	14.56
30.	Aug 31, 2018	-11.80%	3.03%	165.94	3.01	-22.34
31.	Sep 30, 2018	1.29%	0.43%	0.04	0.74	-0.18
32.	Oct 31, 2018	3.37%	-6.94%	5.24	67.78	-18.85
33.	Nov 30, 2018	2.93%	1.79%	3.41	0.24	0.91
34.	Dec 31, 2018	4.09%	-9.18%	9.05	109.62	-31.50
35.	Jan 31, 2019	7.21%	7.87%	37.51	43.25	40.28
36.	Feb 28, 2019	-0.52%	2.97%	2.56	2.82	-2.69
37.	Mar 31, 2019	9.04%	1.79%	63.34	0.25	3.98
38.	Apr 30, 2019	5.94%	3.93%	23.60	6.96	12.82
39.	May 31, 2019	-8.71%	-6.58%	95.86	61.94	77.05
40.	Jun 30, 2019	5.71%	6.89%	21.40	31.37	25.91
41.	Jul 31, 2019	-5.25%	1.31%	40.13	0.00	-0.13
42.	Aug 31, 2019	-0.22%	-1.81%	1.69	9.62	4.03
43.	Sep 30, 2019	12.44%	1.72%	128.97	0.18	4.84
44.	Oct 31, 2019	-3.29%	2.04%	19.15	0.56	-3.29
45.	Nov 30, 2019	-17.16%	3.40%	332.65	4.46	-38.53
46.	Dec 31, 2019	2.83%	2.86%	3.06	2.45	2.74
47.	Jan 31, 2020	-7.42%	-0.16%	72.33	2.12	12.37
48.	Feb 29, 2020	-4.64%	-8.41%	32.75	94.15	55.53
49.	Mar 31, 2020	-11.51%	-12.51%	158.68	190.56	173.89
50.	Apr 30, 2020	8.44%	12.68%	54.11	129.78	83.80
51.	May 31, 2020	22.84%	4.53%	473.55	10.47	70.42
52.	Jun 30, 2020	-5.30%	1.84%	40.78	0.30	-3.49
53.	Jul 31, 2020	0.72%	5.51%	0.13	17.79	-1.52
54.	Aug 31, 2020	3.13%	7.01%	4.18	32.65	11.69
55.	Sep 30, 2020	-5.12%	-3.92%	38.49	27.20	32.35
56.	Oct 31, 2020	-1.12%	-2.77%	4.84	16.47	8.93
57.	Nov 30, 2020	20.95%	10.75%	394.61	89.54	187.97
58.	Dec 31, 2020	-1.10%	3.71%	4.76	5.86	-5.28
59.	Jan 31, 2021	-5.91%	-1.11%	48.83	5.79	16.81
60.	Feb 28, 2021	-3.40%	2.61%	20.13	1.73	-5.91
61.	Mar 31, 2021	16.56%	4.24%	239.48	8.71	45.68
62.	Apr 30, 2021	0.38%	5.24%	0.49	15.60	-2.76
63.	May 31, 2021	-15.14%	0.55%	263.30	0.55	12.07
64.	Jun 30, 2021	2.05%	2.22%	0.94	0.86	0.90
65.	Jul 31, 2021	0.29%	2.27%	0.63	0.97	-0.78
66.	Aug 31, 2021	-9.27%	2.90%	107.17	2.58	-16.63
67.	Sep 30, 2021	5.72%	-4.76%	21.51	36.59	-28.06
68.	Oct 31, 2021	12.58%	6.91%	132.14	31.61	64.63
69.	Nov 30, 2021	24.19%	-0.83%	534.06	4.52	-49.12
70.	Dec 31, 2021	5.00%	4.36%	15.33	9.42	12.02
71.	Jan 31, 2022	-6.62%	-5.26%	59.31	42.91	50.45
Total (Σ):				5,617.47	1,262.70	1,008.02

Show all

Variance_DLTR = Σ(R_DLTR,t–R_DLTR)² ÷ (71 – 1)
= 5,617.47 ÷ (71 – 1)
= 80.25

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,262.70 ÷ (71 – 1)
= 18.04

Covariance_{DLTR, S&P 500} = Σ(R_DLTR,t–R_DLTR)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 1,008.02 ÷ (71 – 1)
= 14.40

Systematic Risk (β) Estimation

Variance_DLTR	80.25
Variance_{S&P 500}	18.04
Covariance_{DLTR, S&P 500}	14.40
Correlation coefficient_{DLTR, S&P 500}¹	0.38
β_DLTR²	0.80
α_DLTR³	0.05%

Calculations

¹ Correlation coefficient_{DLTR, S&P 500}
= Covariance_{DLTR, S&P 500} ÷ (Standard deviation_DLTR × Standard deviation_{S&P 500})
= 14.40 ÷ (8.96% × 4.25%)
= 0.38

² β_DLTR
= Covariance_{DLTR, S&P 500} ÷ Variance_{S&P 500}
= 14.40 ÷ 18.04
= 0.80

³ α_DLTR
= Average_DLTR – β_DLTR × Average_{S&P 500}
= 1.08% – 0.80 × 1.29%
= 0.05%

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 Dollar Tree Inc. common stock	β_DLTR	0.80

Expected rate of return on Dollar Tree Inc. common stock³	E(R_DLTR)	11.95%

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_DLTR) = R_F + β_DLTR [E(R_M) – R_F]
= 4.68% + 0.80 [13.78% – 4.68%]
= 11.95%