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 lululemon athletica inc. common stock.
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Rates of Return
lululemon athletica inc., monthly rates of return
| lululemon athletica inc. (LULU) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceLULU,t1 | DividendLULU,t1 | RLULU,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Feb 28, 2018 | ||||||
| 1. | Mar 31, 2018 | |||||
| 2. | Apr 30, 2018 | |||||
| 3. | May 31, 2018 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Dec 31, 2023 | |||||
| 71. | Jan 31, 2024 | |||||
| Average (R): | ||||||
| Standard deviation: | ||||||
| lululemon athletica inc. (LULU) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceLULU,t1 | DividendLULU,t1 | RLULU,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Feb 28, 2018 | ||||||
| 1. | Mar 31, 2018 | |||||
| 2. | Apr 30, 2018 | |||||
| 3. | May 31, 2018 | |||||
| 4. | Jun 30, 2018 | |||||
| 5. | Jul 31, 2018 | |||||
| 6. | Aug 31, 2018 | |||||
| 7. | Sep 30, 2018 | |||||
| 8. | Oct 31, 2018 | |||||
| 9. | Nov 30, 2018 | |||||
| 10. | Dec 31, 2018 | |||||
| 11. | Jan 31, 2019 | |||||
| 12. | Feb 28, 2019 | |||||
| 13. | Mar 31, 2019 | |||||
| 14. | Apr 30, 2019 | |||||
| 15. | May 31, 2019 | |||||
| 16. | Jun 30, 2019 | |||||
| 17. | Jul 31, 2019 | |||||
| 18. | Aug 31, 2019 | |||||
| 19. | Sep 30, 2019 | |||||
| 20. | Oct 31, 2019 | |||||
| 21. | Nov 30, 2019 | |||||
| 22. | Dec 31, 2019 | |||||
| 23. | Jan 31, 2020 | |||||
| 24. | Feb 29, 2020 | |||||
| 25. | Mar 31, 2020 | |||||
| 26. | Apr 30, 2020 | |||||
| 27. | May 31, 2020 | |||||
| 28. | Jun 30, 2020 | |||||
| 29. | Jul 31, 2020 | |||||
| 30. | Aug 31, 2020 | |||||
| 31. | Sep 30, 2020 | |||||
| 32. | Oct 31, 2020 | |||||
| 33. | Nov 30, 2020 | |||||
| 34. | Dec 31, 2020 | |||||
| 35. | Jan 31, 2021 | |||||
| 36. | Feb 28, 2021 | |||||
| 37. | Mar 31, 2021 | |||||
| 38. | Apr 30, 2021 | |||||
| 39. | May 31, 2021 | |||||
| 40. | Jun 30, 2021 | |||||
| 41. | Jul 31, 2021 | |||||
| 42. | Aug 31, 2021 | |||||
| 43. | Sep 30, 2021 | |||||
| 44. | Oct 31, 2021 | |||||
| 45. | Nov 30, 2021 | |||||
| 46. | Dec 31, 2021 | |||||
| 47. | Jan 31, 2022 | |||||
| 48. | Feb 28, 2022 | |||||
| 49. | Mar 31, 2022 | |||||
| 50. | Apr 30, 2022 | |||||
| 51. | May 31, 2022 | |||||
| 52. | Jun 30, 2022 | |||||
| 53. | Jul 31, 2022 | |||||
| 54. | Aug 31, 2022 | |||||
| 55. | Sep 30, 2022 | |||||
| 56. | Oct 31, 2022 | |||||
| 57. | Nov 30, 2022 | |||||
| 58. | Dec 31, 2022 | |||||
| 59. | Jan 31, 2023 | |||||
| 60. | Feb 28, 2023 | |||||
| 61. | Mar 31, 2023 | |||||
| 62. | Apr 30, 2023 | |||||
| 63. | May 31, 2023 | |||||
| 64. | Jun 30, 2023 | |||||
| 65. | Jul 31, 2023 | |||||
| 66. | Aug 31, 2023 | |||||
| 67. | Sep 30, 2023 | |||||
| 68. | Oct 31, 2023 | |||||
| 69. | Nov 30, 2023 | |||||
| 70. | Dec 31, 2023 | |||||
| 71. | Jan 31, 2024 | |||||
| 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 LULU during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
lululemon athletica inc., calculation of variance and covariance of returns
| t | Date | RLULU,t | RS&P 500,t | (RLULU,t–RLULU)2 | (RS&P 500,t–RS&P 500)2 | (RLULU,t–RLULU)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Mar 31, 2018 | |||||
| 2. | Apr 30, 2018 | |||||
| 3. | May 31, 2018 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Dec 31, 2023 | |||||
| 71. | Jan 31, 2024 | |||||
| Total (Σ): | ||||||
| t | Date | RLULU,t | RS&P 500,t | (RLULU,t–RLULU)2 | (RS&P 500,t–RS&P 500)2 | (RLULU,t–RLULU)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Mar 31, 2018 | |||||
| 2. | Apr 30, 2018 | |||||
| 3. | May 31, 2018 | |||||
| 4. | Jun 30, 2018 | |||||
| 5. | Jul 31, 2018 | |||||
| 6. | Aug 31, 2018 | |||||
| 7. | Sep 30, 2018 | |||||
| 8. | Oct 31, 2018 | |||||
| 9. | Nov 30, 2018 | |||||
| 10. | Dec 31, 2018 | |||||
| 11. | Jan 31, 2019 | |||||
| 12. | Feb 28, 2019 | |||||
| 13. | Mar 31, 2019 | |||||
| 14. | Apr 30, 2019 | |||||
| 15. | May 31, 2019 | |||||
| 16. | Jun 30, 2019 | |||||
| 17. | Jul 31, 2019 | |||||
| 18. | Aug 31, 2019 | |||||
| 19. | Sep 30, 2019 | |||||
| 20. | Oct 31, 2019 | |||||
| 21. | Nov 30, 2019 | |||||
| 22. | Dec 31, 2019 | |||||
| 23. | Jan 31, 2020 | |||||
| 24. | Feb 29, 2020 | |||||
| 25. | Mar 31, 2020 | |||||
| 26. | Apr 30, 2020 | |||||
| 27. | May 31, 2020 | |||||
| 28. | Jun 30, 2020 | |||||
| 29. | Jul 31, 2020 | |||||
| 30. | Aug 31, 2020 | |||||
| 31. | Sep 30, 2020 | |||||
| 32. | Oct 31, 2020 | |||||
| 33. | Nov 30, 2020 | |||||
| 34. | Dec 31, 2020 | |||||
| 35. | Jan 31, 2021 | |||||
| 36. | Feb 28, 2021 | |||||
| 37. | Mar 31, 2021 | |||||
| 38. | Apr 30, 2021 | |||||
| 39. | May 31, 2021 | |||||
| 40. | Jun 30, 2021 | |||||
| 41. | Jul 31, 2021 | |||||
| 42. | Aug 31, 2021 | |||||
| 43. | Sep 30, 2021 | |||||
| 44. | Oct 31, 2021 | |||||
| 45. | Nov 30, 2021 | |||||
| 46. | Dec 31, 2021 | |||||
| 47. | Jan 31, 2022 | |||||
| 48. | Feb 28, 2022 | |||||
| 49. | Mar 31, 2022 | |||||
| 50. | Apr 30, 2022 | |||||
| 51. | May 31, 2022 | |||||
| 52. | Jun 30, 2022 | |||||
| 53. | Jul 31, 2022 | |||||
| 54. | Aug 31, 2022 | |||||
| 55. | Sep 30, 2022 | |||||
| 56. | Oct 31, 2022 | |||||
| 57. | Nov 30, 2022 | |||||
| 58. | Dec 31, 2022 | |||||
| 59. | Jan 31, 2023 | |||||
| 60. | Feb 28, 2023 | |||||
| 61. | Mar 31, 2023 | |||||
| 62. | Apr 30, 2023 | |||||
| 63. | May 31, 2023 | |||||
| 64. | Jun 30, 2023 | |||||
| 65. | Jul 31, 2023 | |||||
| 66. | Aug 31, 2023 | |||||
| 67. | Sep 30, 2023 | |||||
| 68. | Oct 31, 2023 | |||||
| 69. | Nov 30, 2023 | |||||
| 70. | Dec 31, 2023 | |||||
| 71. | Jan 31, 2024 | |||||
| Total (Σ): | ||||||
Show all
VarianceLULU = Σ(RLULU,t–RLULU)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
CovarianceLULU, S&P 500 = Σ(RLULU,t–RLULU)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= ÷ (71 – 1)
=
Systematic Risk (β) Estimation
| VarianceLULU | |
| VarianceS&P 500 | |
| CovarianceLULU, S&P 500 | |
| Correlation coefficientLULU, S&P 5001 | |
| βLULU2 | |
| αLULU3 |
Calculations
1 Correlation coefficientLULU, S&P 500
= CovarianceLULU, S&P 500 ÷ (Standard deviationLULU × Standard deviationS&P 500)
= ÷ ( × )
=
2 βLULU
= CovarianceLULU, S&P 500 ÷ VarianceS&P 500
= ÷
=
3 αLULU
= AverageLULU – βLULU × 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 lululemon athletica inc. common stock | βLULU | |
| Expected rate of return on lululemon athletica inc. common stock3 | E(RLULU) | |
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(RLULU) = RF + βLULU [E(RM) – RF]
= + [ – ]
=