Capital asset pricing model (CAPM) indicates what should be the expected or required rate of return on risky assets like RH common stock.
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Rates of Return
RH (RH) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceRH,t1 | DividendRH,t1 | RRH,t2 | PriceS&P 500,t | RS&P 500,t3 |
Feb 28, 2017 | ||||||
1. | Mar 31, 2017 | |||||
2. | Apr 30, 2017 | |||||
3. | May 31, 2017 | |||||
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Dec 31, 2022 | |||||
71. | Jan 31, 2023 | |||||
Average (R): | ||||||
Standard deviation: |
RH (RH) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Date | PriceRH,t1 | DividendRH,t1 | RRH,t2 | PriceS&P 500,t | RS&P 500,t3 |
Feb 28, 2017 | ||||||
1. | Mar 31, 2017 | |||||
2. | Apr 30, 2017 | |||||
3. | May 31, 2017 | |||||
4. | Jun 30, 2017 | |||||
5. | Jul 31, 2017 | |||||
6. | Aug 31, 2017 | |||||
7. | Sep 30, 2017 | |||||
8. | Oct 31, 2017 | |||||
9. | Nov 30, 2017 | |||||
10. | Dec 31, 2017 | |||||
11. | Jan 31, 2018 | |||||
12. | Feb 28, 2018 | |||||
13. | Mar 31, 2018 | |||||
14. | Apr 30, 2018 | |||||
15. | May 31, 2018 | |||||
16. | Jun 30, 2018 | |||||
17. | Jul 31, 2018 | |||||
18. | Aug 31, 2018 | |||||
19. | Sep 30, 2018 | |||||
20. | Oct 31, 2018 | |||||
21. | Nov 30, 2018 | |||||
22. | Dec 31, 2018 | |||||
23. | Jan 31, 2019 | |||||
24. | Feb 28, 2019 | |||||
25. | Mar 31, 2019 | |||||
26. | Apr 30, 2019 | |||||
27. | May 31, 2019 | |||||
28. | Jun 30, 2019 | |||||
29. | Jul 31, 2019 | |||||
30. | Aug 31, 2019 | |||||
31. | Sep 30, 2019 | |||||
32. | Oct 31, 2019 | |||||
33. | Nov 30, 2019 | |||||
34. | Dec 31, 2019 | |||||
35. | Jan 31, 2020 | |||||
36. | Feb 29, 2020 | |||||
37. | Mar 31, 2020 | |||||
38. | Apr 30, 2020 | |||||
39. | May 31, 2020 | |||||
40. | Jun 30, 2020 | |||||
41. | Jul 31, 2020 | |||||
42. | Aug 31, 2020 | |||||
43. | Sep 30, 2020 | |||||
44. | Oct 31, 2020 | |||||
45. | Nov 30, 2020 | |||||
46. | Dec 31, 2020 | |||||
47. | Jan 31, 2021 | |||||
48. | Feb 28, 2021 | |||||
49. | Mar 31, 2021 | |||||
50. | Apr 30, 2021 | |||||
51. | May 31, 2021 | |||||
52. | Jun 30, 2021 | |||||
53. | Jul 31, 2021 | |||||
54. | Aug 31, 2021 | |||||
55. | Sep 30, 2021 | |||||
56. | Oct 31, 2021 | |||||
57. | Nov 30, 2021 | |||||
58. | Dec 31, 2021 | |||||
59. | Jan 31, 2022 | |||||
60. | Feb 28, 2022 | |||||
61. | Mar 31, 2022 | |||||
62. | Apr 30, 2022 | |||||
63. | May 31, 2022 | |||||
64. | Jun 30, 2022 | |||||
65. | Jul 31, 2022 | |||||
66. | Aug 31, 2022 | |||||
67. | Sep 30, 2022 | |||||
68. | Oct 31, 2022 | |||||
69. | Nov 30, 2022 | |||||
70. | Dec 31, 2022 | |||||
71. | Jan 31, 2023 | |||||
Average (R): | ||||||
Standard deviation: |
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 RH during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
t | Date | RRH,t | RS&P 500,t | (RRH,t–RRH)2 | (RS&P 500,t–RS&P 500)2 | (RRH,t–RRH)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Mar 31, 2017 | |||||
2. | Apr 30, 2017 | |||||
3. | May 31, 2017 | |||||
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
. | . | . | . | . | . | . |
70. | Dec 31, 2022 | |||||
71. | Jan 31, 2023 | |||||
Total (Σ): |
t | Date | RRH,t | RS&P 500,t | (RRH,t–RRH)2 | (RS&P 500,t–RS&P 500)2 | (RRH,t–RRH)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | Mar 31, 2017 | |||||
2. | Apr 30, 2017 | |||||
3. | May 31, 2017 | |||||
4. | Jun 30, 2017 | |||||
5. | Jul 31, 2017 | |||||
6. | Aug 31, 2017 | |||||
7. | Sep 30, 2017 | |||||
8. | Oct 31, 2017 | |||||
9. | Nov 30, 2017 | |||||
10. | Dec 31, 2017 | |||||
11. | Jan 31, 2018 | |||||
12. | Feb 28, 2018 | |||||
13. | Mar 31, 2018 | |||||
14. | Apr 30, 2018 | |||||
15. | May 31, 2018 | |||||
16. | Jun 30, 2018 | |||||
17. | Jul 31, 2018 | |||||
18. | Aug 31, 2018 | |||||
19. | Sep 30, 2018 | |||||
20. | Oct 31, 2018 | |||||
21. | Nov 30, 2018 | |||||
22. | Dec 31, 2018 | |||||
23. | Jan 31, 2019 | |||||
24. | Feb 28, 2019 | |||||
25. | Mar 31, 2019 | |||||
26. | Apr 30, 2019 | |||||
27. | May 31, 2019 | |||||
28. | Jun 30, 2019 | |||||
29. | Jul 31, 2019 | |||||
30. | Aug 31, 2019 | |||||
31. | Sep 30, 2019 | |||||
32. | Oct 31, 2019 | |||||
33. | Nov 30, 2019 | |||||
34. | Dec 31, 2019 | |||||
35. | Jan 31, 2020 | |||||
36. | Feb 29, 2020 | |||||
37. | Mar 31, 2020 | |||||
38. | Apr 30, 2020 | |||||
39. | May 31, 2020 | |||||
40. | Jun 30, 2020 | |||||
41. | Jul 31, 2020 | |||||
42. | Aug 31, 2020 | |||||
43. | Sep 30, 2020 | |||||
44. | Oct 31, 2020 | |||||
45. | Nov 30, 2020 | |||||
46. | Dec 31, 2020 | |||||
47. | Jan 31, 2021 | |||||
48. | Feb 28, 2021 | |||||
49. | Mar 31, 2021 | |||||
50. | Apr 30, 2021 | |||||
51. | May 31, 2021 | |||||
52. | Jun 30, 2021 | |||||
53. | Jul 31, 2021 | |||||
54. | Aug 31, 2021 | |||||
55. | Sep 30, 2021 | |||||
56. | Oct 31, 2021 | |||||
57. | Nov 30, 2021 | |||||
58. | Dec 31, 2021 | |||||
59. | Jan 31, 2022 | |||||
60. | Feb 28, 2022 | |||||
61. | Mar 31, 2022 | |||||
62. | Apr 30, 2022 | |||||
63. | May 31, 2022 | |||||
64. | Jun 30, 2022 | |||||
65. | Jul 31, 2022 | |||||
66. | Aug 31, 2022 | |||||
67. | Sep 30, 2022 | |||||
68. | Oct 31, 2022 | |||||
69. | Nov 30, 2022 | |||||
70. | Dec 31, 2022 | |||||
71. | Jan 31, 2023 | |||||
Total (Σ): |
Show all
VarianceRH = Σ(RRH,t–RRH)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
CovarianceRH, S&P 500 = Σ(RRH,t–RRH)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= ÷ (71 – 1)
=
Systematic Risk (β) Estimation
VarianceRH | |
VarianceS&P 500 | |
CovarianceRH, S&P 500 | |
Correlation coefficientRH, S&P 5001 | |
βRH2 | |
αRH3 |
Calculations
1 Correlation coefficientRH, S&P 500
= CovarianceRH, S&P 500 ÷ (Standard deviationRH × Standard deviationS&P 500)
= ÷ ( × )
=
2 βRH
= CovarianceRH, S&P 500 ÷ VarianceS&P 500
= ÷
=
3 αRH
= AverageRH – βRH × AverageS&P 500
= – ×
=
Expected Rate of Return
Assumptions | ||
Rate of return on LT Treasury Composite1 | RF | |
Expected rate of return on market portfolio2 | E(RM) | |
Systematic risk (β) of RH common stock | βRH | |
Expected rate of return on RH common stock3 | E(RRH) |
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(RRH) = RF + βRH [E(RM) – RF]
= + [ – ]
=