Bed Bath & Beyond Inc. (NASDAQ:BBBY)

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 Bed Bath & Beyond Inc. common stock.

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

Rates of Return

Bed Bath & Beyond Inc., monthly rates of return

		Bed Bath & Beyond Inc. (BBBY)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_BBBY,t¹	Dividend_BBBY,t¹	R_BBBY,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Mar 31, 2016	$49.64			2,059.74
1.	Apr 30, 2016	$47.22		-4.88%	2,065.30	0.27%
2.	May 31, 2016	$44.75		-5.23%	2,096.95	1.53%
3.	Jun 30, 2016	$43.22	$0.125	-3.14%	2,098.86	0.09%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	Jan 31, 2022	$16.24		11.39%	4,515.55	-5.26%
71.	Feb 28, 2022	$16.89		4.00%	4,373.94	-3.14%
Average (R):				0.79%		1.16%
Standard deviation:				21.17%		4.23%

		Bed Bath & Beyond Inc. (BBBY)			Standard & Poor’s 500 (S&P 500)
t	Date	Price_BBBY,t¹	Dividend_BBBY,t¹	R_BBBY,t²	Price_{S&P 500,t}	R_{S&P 500,t}³
	Mar 31, 2016	$49.64			2,059.74
1.	Apr 30, 2016	$47.22		-4.88%	2,065.30	0.27%
2.	May 31, 2016	$44.75		-5.23%	2,096.95	1.53%
3.	Jun 30, 2016	$43.22	$0.125	-3.14%	2,098.86	0.09%
4.	Jul 31, 2016	$44.95		4.00%	2,173.60	3.56%
5.	Aug 31, 2016	$46.37		3.16%	2,170.95	-0.12%
6.	Sep 30, 2016	$43.11	$0.125	-6.76%	2,168.27	-0.12%
7.	Oct 31, 2016	$40.42		-6.24%	2,126.15	-1.94%
8.	Nov 30, 2016	$44.81		10.86%	2,198.81	3.42%
9.	Dec 31, 2016	$40.64	$0.125	-9.03%	2,238.83	1.82%
10.	Jan 31, 2017	$40.35		-0.71%	2,278.87	1.79%
11.	Feb 28, 2017	$40.40		0.12%	2,363.64	3.72%
12.	Mar 31, 2017	$39.46	$0.125	-2.02%	2,362.72	-0.04%
13.	Apr 30, 2017	$38.75		-1.80%	2,384.20	0.91%
14.	May 31, 2017	$34.41		-11.20%	2,411.80	1.16%
15.	Jun 30, 2017	$30.40	$0.15	-11.22%	2,423.41	0.48%
16.	Jul 31, 2017	$29.90		-1.64%	2,470.30	1.93%
17.	Aug 31, 2017	$27.59		-7.73%	2,471.65	0.05%
18.	Sep 30, 2017	$23.47	$0.15	-14.39%	2,519.36	1.93%
19.	Oct 31, 2017	$19.90		-15.21%	2,575.26	2.22%
20.	Nov 30, 2017	$22.39		12.51%	2,647.58	2.81%
21.	Dec 31, 2017	$21.99	$0.15	-1.12%	2,673.61	0.98%
22.	Jan 31, 2018	$23.08		4.96%	2,823.81	5.62%
23.	Feb 28, 2018	$21.44		-7.11%	2,713.83	-3.89%
24.	Mar 31, 2018	$20.99	$0.15	-1.40%	2,640.87	-2.69%
25.	Apr 30, 2018	$17.46		-16.82%	2,648.05	0.27%
26.	May 31, 2018	$18.16		4.01%	2,705.27	2.16%
27.	Jun 30, 2018	$19.93	$0.16	10.63%	2,718.37	0.48%
28.	Jul 31, 2018	$18.73		-6.02%	2,816.29	3.60%
29.	Aug 31, 2018	$17.94		-4.22%	2,901.52	3.03%
30.	Sep 30, 2018	$15.00	$0.16	-15.50%	2,913.98	0.43%
31.	Oct 31, 2018	$13.74		-8.40%	2,711.74	-6.94%
32.	Nov 30, 2018	$12.88		-6.26%	2,760.17	1.79%
33.	Dec 31, 2018	$11.32	$0.16	-10.87%	2,506.85	-9.18%
34.	Jan 31, 2019	$15.09		33.30%	2,704.10	7.87%
35.	Feb 28, 2019	$16.73		10.87%	2,784.49	2.97%
36.	Mar 31, 2019	$16.99	$0.16	2.51%	2,834.40	1.79%
37.	Apr 30, 2019	$16.71		-1.65%	2,945.83	3.93%
38.	May 31, 2019	$12.69		-24.06%	2,752.06	-6.58%
39.	Jun 30, 2019	$11.62	$0.17	-7.09%	2,941.76	6.89%
40.	Jul 31, 2019	$9.71		-16.44%	2,980.38	1.31%
41.	Aug 31, 2019	$9.67		-0.41%	2,926.46	-1.81%
42.	Sep 30, 2019	$10.64	$0.17	11.79%	2,976.74	1.72%
43.	Oct 31, 2019	$13.70		28.76%	3,037.56	2.04%
44.	Nov 30, 2019	$14.58		6.42%	3,140.98	3.40%
45.	Dec 31, 2019	$17.30	$0.17	19.82%	3,230.78	2.86%
46.	Jan 31, 2020	$14.25		-17.63%	3,225.52	-0.16%
47.	Feb 29, 2020	$10.81		-24.14%	2,954.22	-8.41%
48.	Mar 31, 2020	$4.21	$0.17	-59.48%	2,584.59	-12.51%
49.	Apr 30, 2020	$6.19		47.03%	2,912.43	12.68%
50.	May 31, 2020	$7.27		17.45%	3,044.31	4.53%
51.	Jun 30, 2020	$10.60		45.80%	3,100.29	1.84%
52.	Jul 31, 2020	$10.82		2.08%	3,271.12	5.51%
53.	Aug 31, 2020	$12.18		12.57%	3,500.31	7.01%
54.	Sep 30, 2020	$14.98		22.99%	3,363.00	-3.92%
55.	Oct 31, 2020	$19.80		32.18%	3,269.96	-2.77%
56.	Nov 30, 2020	$20.96		5.86%	3,621.63	10.75%
57.	Dec 31, 2020	$17.76		-15.27%	3,756.07	3.71%
58.	Jan 31, 2021	$35.33		98.93%	3,714.24	-1.11%
59.	Feb 28, 2021	$26.86		-23.97%	3,811.15	2.61%
60.	Mar 31, 2021	$29.15		8.53%	3,972.89	4.24%
61.	Apr 30, 2021	$25.32		-13.14%	4,181.17	5.24%
62.	May 31, 2021	$27.99		10.55%	4,204.11	0.55%
63.	Jun 30, 2021	$33.29		18.94%	4,297.50	2.22%
64.	Jul 31, 2021	$28.54		-14.27%	4,395.26	2.27%
65.	Aug 31, 2021	$27.54		-3.50%	4,522.68	2.90%
66.	Sep 30, 2021	$17.27		-37.29%	4,307.54	-4.76%
67.	Oct 31, 2021	$14.04		-18.70%	4,605.38	6.91%
68.	Nov 30, 2021	$18.33		30.56%	4,567.00	-0.83%
69.	Dec 31, 2021	$14.58		-20.46%	4,766.18	4.36%
70.	Jan 31, 2022	$16.24		11.39%	4,515.55	-5.26%
71.	Feb 28, 2022	$16.89		4.00%	4,373.94	-3.14%
Average (R):				0.79%		1.16%
Standard deviation:				21.17%		4.23%

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 BBBY during period t

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

Variance and Covariance

Bed Bath & Beyond Inc., calculation of variance and covariance of returns

t	Date	R_BBBY,t	R_{S&P 500,t}	(R_BBBY,t–R_BBBY)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_BBBY,t–R_BBBY)×(R_{S&P 500,t}–R_{S&P 500})
1.	Apr 30, 2016	-4.88%	0.27%	32.10	0.78	5.02
2.	May 31, 2016	-5.23%	1.53%	36.26	0.14	-2.27
3.	Jun 30, 2016	-3.14%	0.09%	15.45	1.13	4.18
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.	.	.	.	.	.	.
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70.	Jan 31, 2022	11.39%	-5.26%	112.24	41.13	-67.95
71.	Feb 28, 2022	4.00%	-3.14%	10.31	18.41	-13.78
Total (Σ):				31,361.94	1,252.81	1,931.29

t	Date	R_BBBY,t	R_{S&P 500,t}	(R_BBBY,t–R_BBBY)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_BBBY,t–R_BBBY)×(R_{S&P 500,t}–R_{S&P 500})
1.	Apr 30, 2016	-4.88%	0.27%	32.10	0.78	5.02
2.	May 31, 2016	-5.23%	1.53%	36.26	0.14	-2.27
3.	Jun 30, 2016	-3.14%	0.09%	15.45	1.13	4.18
4.	Jul 31, 2016	4.00%	3.56%	10.32	5.79	7.73
5.	Aug 31, 2016	3.16%	-0.12%	5.61	1.63	-3.02
6.	Sep 30, 2016	-6.76%	-0.12%	57.03	1.63	9.66
7.	Oct 31, 2016	-6.24%	-1.94%	49.43	9.60	21.78
8.	Nov 30, 2016	10.86%	3.42%	101.40	5.12	22.78
9.	Dec 31, 2016	-9.03%	1.82%	96.39	0.44	-6.53
10.	Jan 31, 2017	-0.71%	1.79%	2.26	0.40	-0.95
11.	Feb 28, 2017	0.12%	3.72%	0.45	6.58	-1.71
12.	Mar 31, 2017	-2.02%	-0.04%	7.89	1.43	3.35
13.	Apr 30, 2017	-1.80%	0.91%	6.71	0.06	0.64
14.	May 31, 2017	-11.20%	1.16%	143.78	0.00	-0.03
15.	Jun 30, 2017	-11.22%	0.48%	144.21	0.45	8.09
16.	Jul 31, 2017	-1.64%	1.93%	5.93	0.61	-1.90
17.	Aug 31, 2017	-7.73%	0.05%	72.54	1.21	9.37
18.	Sep 30, 2017	-14.39%	1.93%	230.44	0.60	-11.77
19.	Oct 31, 2017	-15.21%	2.22%	256.06	1.13	-17.02
20.	Nov 30, 2017	12.51%	2.81%	137.39	2.73	19.38
21.	Dec 31, 2017	-1.12%	0.98%	3.64	0.03	0.33
22.	Jan 31, 2018	4.96%	5.62%	17.35	19.92	18.59
23.	Feb 28, 2018	-7.11%	-3.89%	62.36	25.50	39.88
24.	Mar 31, 2018	-1.40%	-2.69%	4.80	14.77	8.42
25.	Apr 30, 2018	-16.82%	0.27%	310.06	0.78	15.55
26.	May 31, 2018	4.01%	2.16%	10.36	1.01	3.24
27.	Jun 30, 2018	10.63%	0.48%	96.76	0.45	-6.60
28.	Jul 31, 2018	-6.02%	3.60%	46.40	5.99	-16.67
29.	Aug 31, 2018	-4.22%	3.03%	25.09	3.50	-9.37
30.	Sep 30, 2018	-15.50%	0.43%	265.27	0.53	11.82
31.	Oct 31, 2018	-8.40%	-6.94%	84.47	65.54	74.41
32.	Nov 30, 2018	-6.26%	1.79%	49.70	0.40	-4.45
33.	Dec 31, 2018	-10.87%	-9.18%	135.97	106.77	120.49
34.	Jan 31, 2019	33.30%	7.87%	1,057.09	45.07	218.27
35.	Feb 28, 2019	10.87%	2.97%	101.55	3.30	18.32
36.	Mar 31, 2019	2.51%	1.79%	2.96	0.41	1.10
37.	Apr 30, 2019	-1.65%	3.93%	5.95	7.71	-6.77
38.	May 31, 2019	-24.06%	-6.58%	617.45	59.80	192.15
39.	Jun 30, 2019	-7.09%	6.89%	62.14	32.92	-45.23
40.	Jul 31, 2019	-16.44%	1.31%	296.81	0.02	-2.72
41.	Aug 31, 2019	-0.41%	-1.81%	1.45	8.79	3.57
42.	Sep 30, 2019	11.79%	1.72%	120.96	0.32	6.19
43.	Oct 31, 2019	28.76%	2.04%	782.23	0.79	24.84
44.	Nov 30, 2019	6.42%	3.40%	31.72	5.06	12.67
45.	Dec 31, 2019	19.82%	2.86%	362.17	2.90	32.43
46.	Jan 31, 2020	-17.63%	-0.16%	339.34	1.74	24.28
47.	Feb 29, 2020	-24.14%	-8.41%	621.57	91.51	238.50
48.	Mar 31, 2020	-59.48%	-12.51%	3,632.83	186.79	823.75
49.	Apr 30, 2020	47.03%	12.68%	2,138.13	132.92	533.11
50.	May 31, 2020	17.45%	4.53%	277.44	11.38	56.18
51.	Jun 30, 2020	45.80%	1.84%	2,026.23	0.47	30.78
52.	Jul 31, 2020	2.08%	5.51%	1.65	18.97	5.59
53.	Aug 31, 2020	12.57%	7.01%	138.73	34.24	68.92
54.	Sep 30, 2020	22.99%	-3.92%	492.73	25.79	-112.72
55.	Oct 31, 2020	32.18%	-2.77%	985.03	15.38	-123.08
56.	Nov 30, 2020	5.86%	10.75%	25.68	92.15	48.65
57.	Dec 31, 2020	-15.27%	3.71%	257.87	6.54	-41.06
58.	Jan 31, 2021	98.93%	-1.11%	9,631.30	5.15	-222.66
59.	Feb 28, 2021	-23.97%	2.61%	613.30	2.11	-36.01
60.	Mar 31, 2021	8.53%	4.24%	59.83	9.54	23.89
61.	Apr 30, 2021	-13.14%	5.24%	194.04	16.71	-56.94
62.	May 31, 2021	10.55%	0.55%	95.14	0.37	-5.92
63.	Jun 30, 2021	18.94%	2.22%	329.22	1.14	19.35
64.	Jul 31, 2021	-14.27%	2.27%	226.79	1.25	-16.86
65.	Aug 31, 2021	-3.50%	2.90%	18.45	3.04	-7.49
66.	Sep 30, 2021	-37.29%	-4.76%	1,450.26	34.95	225.14
67.	Oct 31, 2021	-18.70%	6.91%	380.01	33.17	-112.27
68.	Nov 30, 2021	30.56%	-0.83%	885.93	3.95	-59.19
69.	Dec 31, 2021	-20.46%	4.36%	451.53	10.28	-68.13
70.	Jan 31, 2022	11.39%	-5.26%	112.24	41.13	-67.95
71.	Feb 28, 2022	4.00%	-3.14%	10.31	18.41	-13.78
Total (Σ):				31,361.94	1,252.81	1,931.29

Show all

Variance_BBBY = Σ(R_BBBY,t–R_BBBY)² ÷ (71 – 1)
= 31,361.94 ÷ (71 – 1)
= 448.03

Variance_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,252.81 ÷ (71 – 1)
= 17.90

Covariance_{BBBY, S&P 500} = Σ(R_BBBY,t–R_BBBY)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 1,931.29 ÷ (71 – 1)
= 27.59

Systematic Risk (β) Estimation

Variance_BBBY	448.03
Variance_{S&P 500}	17.90
Covariance_{BBBY, S&P 500}	27.59
Correlation coefficient_{BBBY, S&P 500}¹	0.31
β_BBBY²	1.54
α_BBBY³	-0.99%

Calculations

¹ Correlation coefficient_{BBBY, S&P 500}
= Covariance_{BBBY, S&P 500} ÷ (Standard deviation_BBBY × Standard deviation_{S&P 500})
= 27.59 ÷ (21.17% × 4.23%)
= 0.31

² β_BBBY
= Covariance_{BBBY, S&P 500} ÷ Variance_{S&P 500}
= 27.59 ÷ 17.90
= 1.54

³ α_BBBY
= Average_BBBY – β_BBBY × Average_{S&P 500}
= 0.79% – 1.54 × 1.16%
= -0.99%

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 Bed Bath & Beyond Inc. common stock	β_BBBY	1.54

Expected rate of return on Bed Bath & Beyond Inc. common stock³	E(R_BBBY)	18.23%

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_BBBY) = R_F + β_BBBY [E(R_M) – R_F]
= 4.86% + 1.54 [13.54% – 4.86%]
= 18.23%