Ulta Beauty Inc. (NASDAQ:ULTA)

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 Ulta Beauty Inc. common stock.

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

Rates of Return

Ulta Beauty Inc., monthly rates of return

		Ulta Beauty Inc. (ULTA)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_ULTA,t¹	Dividend_ULTA,t¹	R_ULTA,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Feb 28, 2017	$273.43			2,363.64
1.	Mar 31, 2017	$285.23		4.32%	2,362.72	-0.04%
2.	Apr 30, 2017	$281.44		-1.33%	2,384.20	0.91%
3.	May 31, 2017	$304.84		8.31%	2,411.80	1.16%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Dec 31, 2022	$469.07		0.91%	3,839.50	-5.90%
71.	Jan 31, 2023	$513.96		9.57%	4,076.60	6.18%
Average (R):				1.50%		0.90%
Standard deviation:				10.95%		5.01%

		Ulta Beauty Inc. (ULTA)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_ULTA,t¹	Dividend_ULTA,t¹	R_ULTA,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Feb 28, 2017	$273.43			2,363.64
1.	Mar 31, 2017	$285.23		4.32%	2,362.72	-0.04%
2.	Apr 30, 2017	$281.44		-1.33%	2,384.20	0.91%
3.	May 31, 2017	$304.84		8.31%	2,411.80	1.16%
4.	Jun 30, 2017	$287.34		-5.74%	2,423.41	0.48%
5.	Jul 31, 2017	$251.21		-12.57%	2,470.30	1.93%
6.	Aug 31, 2017	$221.01		-12.02%	2,471.65	0.05%
7.	Sep 30, 2017	$226.06		2.28%	2,519.36	1.93%
8.	Oct 31, 2017	$201.79		-10.74%	2,575.26	2.22%
9.	Nov 30, 2017	$221.71		9.87%	2,647.58	2.81%
10.	Dec 31, 2017	$223.66		0.88%	2,673.61	0.98%
11.	Jan 31, 2018	$222.10		-0.70%	2,823.81	5.62%
12.	Feb 28, 2018	$203.35		-8.44%	2,713.83	-3.89%
13.	Mar 31, 2018	$204.27		0.45%	2,640.87	-2.69%
14.	Apr 30, 2018	$250.91		22.83%	2,648.05	0.27%
15.	May 31, 2018	$246.91		-1.59%	2,705.27	2.16%
16.	Jun 30, 2018	$233.46		-5.45%	2,718.37	0.48%
17.	Jul 31, 2018	$244.39		4.68%	2,816.29	3.60%
18.	Aug 31, 2018	$260.00		6.39%	2,901.52	3.03%
19.	Sep 30, 2018	$282.12		8.51%	2,913.98	0.43%
20.	Oct 31, 2018	$274.52		-2.69%	2,711.74	-6.94%
21.	Nov 30, 2018	$297.79		8.48%	2,760.17	1.79%
22.	Dec 31, 2018	$244.84		-17.78%	2,506.85	-9.18%
23.	Jan 31, 2019	$291.92		19.23%	2,704.10	7.87%
24.	Feb 28, 2019	$312.49		7.05%	2,784.49	2.97%
25.	Mar 31, 2019	$348.73		11.60%	2,834.40	1.79%
26.	Apr 30, 2019	$348.98		0.07%	2,945.83	3.93%
27.	May 31, 2019	$333.38		-4.47%	2,752.06	-6.58%
28.	Jun 30, 2019	$346.89		4.05%	2,941.76	6.89%
29.	Jul 31, 2019	$349.25		0.68%	2,980.38	1.31%
30.	Aug 31, 2019	$237.73		-31.93%	2,926.46	-1.81%
31.	Sep 30, 2019	$250.65		5.43%	2,976.74	1.72%
32.	Oct 31, 2019	$233.15		-6.98%	3,037.56	2.04%
33.	Nov 30, 2019	$233.86		0.30%	3,140.98	3.40%
34.	Dec 31, 2019	$253.14		8.24%	3,230.78	2.86%
35.	Jan 31, 2020	$267.91		5.83%	3,225.52	-0.16%
36.	Feb 29, 2020	$257.09		-4.04%	2,954.22	-8.41%
37.	Mar 31, 2020	$175.70		-31.66%	2,584.59	-12.51%
38.	Apr 30, 2020	$217.92		24.03%	2,912.43	12.68%
39.	May 31, 2020	$244.01		11.97%	3,044.31	4.53%
40.	Jun 30, 2020	$203.42		-16.63%	3,100.29	1.84%
41.	Jul 31, 2020	$192.99		-5.13%	3,271.12	5.51%
42.	Aug 31, 2020	$232.18		20.31%	3,500.31	7.01%
43.	Sep 30, 2020	$223.98		-3.53%	3,363.00	-3.92%
44.	Oct 31, 2020	$206.77		-7.68%	3,269.96	-2.77%
45.	Nov 30, 2020	$275.40		33.19%	3,621.63	10.75%
46.	Dec 31, 2020	$287.16		4.27%	3,756.07	3.71%
47.	Jan 31, 2021	$279.76		-2.58%	3,714.24	-1.11%
48.	Feb 28, 2021	$322.33		15.22%	3,811.15	2.61%
49.	Mar 31, 2021	$309.17		-4.08%	3,972.89	4.24%
50.	Apr 30, 2021	$329.35		6.53%	4,181.17	5.24%
51.	May 31, 2021	$345.36		4.86%	4,204.11	0.55%
52.	Jun 30, 2021	$345.77		0.12%	4,297.50	2.22%
53.	Jul 31, 2021	$335.80		-2.88%	4,395.26	2.27%
54.	Aug 31, 2021	$387.31		15.34%	4,522.68	2.90%
55.	Sep 30, 2021	$360.92		-6.81%	4,307.54	-4.76%
56.	Oct 31, 2021	$367.36		1.78%	4,605.38	6.91%
57.	Nov 30, 2021	$383.95		4.52%	4,567.00	-0.83%
58.	Dec 31, 2021	$412.34		7.39%	4,766.18	4.36%
59.	Jan 31, 2022	$363.74		-11.79%	4,515.55	-5.26%
60.	Feb 28, 2022	$374.50		2.96%	4,373.94	-3.14%
61.	Mar 31, 2022	$398.22		6.33%	4,530.41	3.58%
62.	Apr 30, 2022	$396.80		-0.36%	4,131.93	-8.80%
63.	May 31, 2022	$423.10		6.63%	4,132.15	0.01%
64.	Jun 30, 2022	$385.48		-8.89%	3,785.38	-8.39%
65.	Jul 31, 2022	$388.91		0.89%	4,130.29	9.11%
66.	Aug 31, 2022	$419.87		7.96%	3,955.00	-4.24%
67.	Sep 30, 2022	$401.19		-4.45%	3,585.62	-9.34%
68.	Oct 31, 2022	$419.37		4.53%	3,871.98	7.99%
69.	Nov 30, 2022	$464.84		10.84%	4,080.11	5.38%
70.	Dec 31, 2022	$469.07		0.91%	3,839.50	-5.90%
71.	Jan 31, 2023	$513.96		9.57%	4,076.60	6.18%
Average (R):				1.50%		0.90%
Standard deviation:				10.95%		5.01%

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 ULTA during period t

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

Variance and Covariance

Ulta Beauty Inc., calculation of variance and covariance of returns

t	Date	R_ULTA,t	R_{S&P 500,t}	(R_ULTA,t–R_ULTA)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ULTA,t–R_ULTA)×(R_{S&P 500,t}–R_{S&P 500})
1.	Mar 31, 2017	4.32%	-0.04%	7.91	0.87	-2.63
2.	Apr 30, 2017	-1.33%	0.91%	8.02	0.00	-0.04
3.	May 31, 2017	8.31%	1.16%	46.40	0.07	1.79
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Dec 31, 2022	0.91%	-5.90%	0.35	46.14	4.03
71.	Jan 31, 2023	9.57%	6.18%	65.08	27.88	42.60
Total (Σ):				8,390.96	1,754.14	2,258.16

t	Date	R_ULTA,t	R_{S&P 500,t}	(R_ULTA,t–R_ULTA)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ULTA,t–R_ULTA)×(R_{S&P 500,t}–R_{S&P 500})
1.	Mar 31, 2017	4.32%	-0.04%	7.91	0.87	-2.63
2.	Apr 30, 2017	-1.33%	0.91%	8.02	0.00	-0.04
3.	May 31, 2017	8.31%	1.16%	46.40	0.07	1.79
4.	Jun 30, 2017	-5.74%	0.48%	52.47	0.17	3.00
5.	Jul 31, 2017	-12.57%	1.93%	198.15	1.08	-14.63
6.	Aug 31, 2017	-12.02%	0.05%	182.91	0.71	11.37
7.	Sep 30, 2017	2.28%	1.93%	0.61	1.07	0.81
8.	Oct 31, 2017	-10.74%	2.22%	149.79	1.75	-16.20
9.	Nov 30, 2017	9.87%	2.81%	70.04	3.66	16.01
10.	Dec 31, 2017	0.88%	0.98%	0.39	0.01	-0.05
11.	Jan 31, 2018	-0.70%	5.62%	4.84	22.30	-10.39
12.	Feb 28, 2018	-8.44%	-3.89%	98.90	22.94	47.64
13.	Mar 31, 2018	0.45%	-2.69%	1.10	12.84	3.76
14.	Apr 30, 2018	22.83%	0.27%	454.96	0.39	-13.30
15.	May 31, 2018	-1.59%	2.16%	9.59	1.60	-3.92
16.	Jun 30, 2018	-5.45%	0.48%	48.30	0.17	2.86
17.	Jul 31, 2018	4.68%	3.60%	10.11	7.33	8.61
18.	Aug 31, 2018	6.39%	3.03%	23.86	4.54	10.41
19.	Sep 30, 2018	8.51%	0.43%	49.07	0.22	-3.26
20.	Oct 31, 2018	-2.69%	-6.94%	17.61	61.40	32.88
21.	Nov 30, 2018	8.48%	1.79%	48.63	0.79	6.21
22.	Dec 31, 2018	-17.78%	-9.18%	371.86	101.46	194.24
23.	Jan 31, 2019	19.23%	7.87%	314.22	48.63	123.61
24.	Feb 28, 2019	7.05%	2.97%	30.73	4.32	11.52
25.	Mar 31, 2019	11.60%	1.79%	101.90	0.80	9.06
26.	Apr 30, 2019	0.07%	3.93%	2.05	9.22	-4.34
27.	May 31, 2019	-4.47%	-6.58%	35.68	55.85	44.64
28.	Jun 30, 2019	4.05%	6.89%	6.50	35.97	15.29
29.	Jul 31, 2019	0.68%	1.31%	0.68	0.17	-0.34
30.	Aug 31, 2019	-31.93%	-1.81%	1,117.84	7.31	90.42
31.	Sep 30, 2019	5.43%	1.72%	15.46	0.68	3.24
32.	Oct 31, 2019	-6.98%	2.04%	71.99	1.32	-9.74
33.	Nov 30, 2019	0.30%	3.40%	1.44	6.30	-3.01
34.	Dec 31, 2019	8.24%	2.86%	45.45	3.86	13.24
35.	Jan 31, 2020	5.83%	-0.16%	18.77	1.12	-4.58
36.	Feb 29, 2020	-4.04%	-8.41%	30.71	86.61	51.57
37.	Mar 31, 2020	-31.66%	-12.51%	1,099.65	179.75	444.60
38.	Apr 30, 2020	24.03%	12.68%	507.46	138.98	265.57
39.	May 31, 2020	11.97%	4.53%	109.61	13.20	38.03
40.	Jun 30, 2020	-16.63%	1.84%	328.96	0.89	-17.11
41.	Jul 31, 2020	-5.13%	5.51%	43.96	21.30	-30.60
42.	Aug 31, 2020	20.31%	7.01%	353.59	37.35	114.91
43.	Sep 30, 2020	-3.53%	-3.92%	25.35	23.21	24.26
44.	Oct 31, 2020	-7.68%	-2.77%	84.39	13.41	33.64
45.	Nov 30, 2020	33.19%	10.75%	1,004.17	97.21	312.43
46.	Dec 31, 2020	4.27%	3.71%	7.66	7.93	7.80
47.	Jan 31, 2021	-2.58%	-1.11%	16.64	4.04	8.20
48.	Feb 28, 2021	15.22%	2.61%	188.07	2.94	23.50
49.	Mar 31, 2021	-4.08%	4.24%	31.20	11.21	-18.70
50.	Apr 30, 2021	6.53%	5.24%	25.24	18.90	21.84
51.	May 31, 2021	4.86%	0.55%	11.28	0.12	-1.16
52.	Jun 30, 2021	0.12%	2.22%	1.92	1.76	-1.84
53.	Jul 31, 2021	-2.88%	2.27%	19.24	1.90	-6.05
54.	Aug 31, 2021	15.34%	2.90%	191.45	4.02	27.73
55.	Sep 30, 2021	-6.81%	-4.76%	69.16	31.95	47.01
56.	Oct 31, 2021	1.78%	6.91%	0.08	36.23	1.69
57.	Nov 30, 2021	4.52%	-0.83%	9.08	2.99	-5.21
58.	Dec 31, 2021	7.39%	4.36%	34.71	12.01	20.42
59.	Jan 31, 2022	-11.79%	-5.26%	176.60	37.87	81.78
60.	Feb 28, 2022	2.96%	-3.14%	2.12	16.25	-5.87
61.	Mar 31, 2022	6.33%	3.58%	23.34	7.19	12.96
62.	Apr 30, 2022	-0.36%	-8.80%	3.46	93.91	18.02
63.	May 31, 2022	6.63%	0.01%	26.27	0.79	-4.56
64.	Jun 30, 2022	-8.89%	-8.39%	108.04	86.25	96.53
65.	Jul 31, 2022	0.89%	9.11%	0.38	67.51	-5.04
66.	Aug 31, 2022	7.96%	-4.24%	41.70	26.41	-33.19
67.	Sep 30, 2022	-4.45%	-9.34%	35.42	104.75	60.92
68.	Oct 31, 2022	4.53%	7.99%	9.17	50.28	21.48
69.	Nov 30, 2022	10.84%	5.38%	87.23	20.07	41.84
70.	Dec 31, 2022	0.91%	-5.90%	0.35	46.14	4.03
71.	Jan 31, 2023	9.57%	6.18%	65.08	27.88	42.60
Total (Σ):				8,390.96	1,754.14	2,258.16

Show all

Variance_ULTA = Σ(R_ULTA,t–R_ULTA)² ÷ (71 – 1)
= 8,390.96 ÷ (71 – 1)
= 119.87

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,754.14 ÷ (71 – 1)
= 25.06

Covariance_{ULTA, S&P 500} = Σ(R_ULTA,t–R_ULTA)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 2,258.16 ÷ (71 – 1)
= 32.26

Systematic Risk (β) Estimation

Variance_ULTA	119.87
Variance_{S&P 500}	25.06
Covariance_{ULTA, S&P 500}	32.26
Correlation coefficient_{ULTA, S&P 500}¹	0.59
β_ULTA²	1.29
α_ULTA³	0.35%

Calculations

¹ Correlation coefficient_{ULTA, S&P 500}
= Covariance_{ULTA, S&P 500} ÷ (Standard deviation_ULTA × Standard deviation_{S&P 500})
= 32.26 ÷ (10.95% × 5.01%)
= 0.59

² β_ULTA
= Covariance_{ULTA, S&P 500} ÷ Variance_{S&P 500}
= 32.26 ÷ 25.06
= 1.29

³ α_ULTA
= Average_ULTA – β_ULTA × Average_{S&P 500}
= 1.50% – 1.29 × 0.90%
= 0.35%

Expected Rate of Return

Assumptions
Rate of return on LT Treasury Composite¹	R_F	4.86%
Expected rate of return on market portfolio²	E(R_M)	13.54%
Systematic risk (β) of Ulta Beauty Inc. common stock	β_ULTA	1.29

Expected rate of return on Ulta Beauty Inc. common stock³	E(R_ULTA)	16.03%

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_ULTA) = R_F + β_ULTA [E(R_M) – R_F]
= 4.86% + 1.29 [13.54% – 4.86%]
= 16.03%