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
Bed Bath & Beyond Inc. (BBBY) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceBBBY,t1 | DividendBBBY,t1 | RBBBY,t2 | PriceS&P 500,t | RS&P 500,t3 |
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 | PriceBBBY,t1 | DividendBBBY,t1 | RBBBY,t2 | PriceS&P 500,t | RS&P 500,t3 |
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
t | Date | RBBBY,t | RS&P 500,t | (RBBBY,t–RBBBY)2 | (RS&P 500,t–RS&P 500)2 | (RBBBY,t–RBBBY)×(RS&P 500,t–RS&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 |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
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 | RBBBY,t | RS&P 500,t | (RBBBY,t–RBBBY)2 | (RS&P 500,t–RS&P 500)2 | (RBBBY,t–RBBBY)×(RS&P 500,t–RS&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
VarianceBBBY = Σ(RBBBY,t–RBBBY)2 ÷ (71 – 1)
= 31,361.94 ÷ (71 – 1)
= 448.03
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,252.81 ÷ (71 – 1)
= 17.90
CovarianceBBBY, S&P 500 = Σ(RBBBY,t–RBBBY)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 1,931.29 ÷ (71 – 1)
= 27.59
Systematic Risk (β) Estimation
VarianceBBBY | 448.03 |
VarianceS&P 500 | 17.90 |
CovarianceBBBY, S&P 500 | 27.59 |
Correlation coefficientBBBY, S&P 5001 | 0.31 |
βBBBY2 | 1.54 |
αBBBY3 | -0.99% |
Calculations
1 Correlation coefficientBBBY, S&P 500
= CovarianceBBBY, S&P 500 ÷ (Standard deviationBBBY × Standard deviationS&P 500)
= 27.59 ÷ (21.17% × 4.23%)
= 0.31
2 βBBBY
= CovarianceBBBY, S&P 500 ÷ VarianceS&P 500
= 27.59 ÷ 17.90
= 1.54
3 αBBBY
= AverageBBBY – βBBBY × AverageS&P 500
= 0.79% – 1.54 × 1.16%
= -0.99%
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | 4.56% |
Expected rate of return on market portfolio2 | E(RM) | 13.77% |
Systematic risk (β) of Bed Bath & Beyond Inc. common stock | βBBBY | 1.54 |
Expected rate of return on Bed Bath & Beyond Inc. common stock3 | E(RBBBY) | 18.76% |
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).
3 E(RBBBY) = RF + βBBBY [E(RM) – RF]
= 4.56% + 1.54 [13.77% – 4.56%]
= 18.76%