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 Air Products & Chemicals Inc. common stock.
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Rates of Return
Air Products & Chemicals Inc., monthly rates of return
| Air Products & Chemicals Inc. (APD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceAPD,t1 | DividendAPD,t1 | RAPD,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Oct 31, 2014 | ||||||
| 1. | Nov 30, 2014 | |||||
| 2. | Dec 31, 2014 | |||||
| 3. | Jan 31, 2015 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Aug 31, 2020 | |||||
| 71. | Sep 30, 2020 | |||||
| Average (R): | ||||||
| Standard deviation: | ||||||
| Air Products & Chemicals Inc. (APD) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceAPD,t1 | DividendAPD,t1 | RAPD,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Oct 31, 2014 | ||||||
| 1. | Nov 30, 2014 | |||||
| 2. | Dec 31, 2014 | |||||
| 3. | Jan 31, 2015 | |||||
| 4. | Feb 28, 2015 | |||||
| 5. | Mar 31, 2015 | |||||
| 6. | Apr 30, 2015 | |||||
| 7. | May 31, 2015 | |||||
| 8. | Jun 30, 2015 | |||||
| 9. | Jul 31, 2015 | |||||
| 10. | Aug 31, 2015 | |||||
| 11. | Sep 30, 2015 | |||||
| 12. | Oct 31, 2015 | |||||
| 13. | Nov 30, 2015 | |||||
| 14. | Dec 31, 2015 | |||||
| 15. | Jan 31, 2016 | |||||
| 16. | Feb 29, 2016 | |||||
| 17. | Mar 31, 2016 | |||||
| 18. | Apr 30, 2016 | |||||
| 19. | May 31, 2016 | |||||
| 20. | Jun 30, 2016 | |||||
| 21. | Jul 31, 2016 | |||||
| 22. | Aug 31, 2016 | |||||
| 23. | Sep 30, 2016 | |||||
| 24. | Oct 31, 2016 | |||||
| 25. | Nov 30, 2016 | |||||
| 26. | Dec 31, 2016 | |||||
| 27. | Jan 31, 2017 | |||||
| 28. | Feb 28, 2017 | |||||
| 29. | Mar 31, 2017 | |||||
| 30. | Apr 30, 2017 | |||||
| 31. | May 31, 2017 | |||||
| 32. | Jun 30, 2017 | |||||
| 33. | Jul 31, 2017 | |||||
| 34. | Aug 31, 2017 | |||||
| 35. | Sep 30, 2017 | |||||
| 36. | Oct 31, 2017 | |||||
| 37. | Nov 30, 2017 | |||||
| 38. | Dec 31, 2017 | |||||
| 39. | Jan 31, 2018 | |||||
| 40. | Feb 28, 2018 | |||||
| 41. | Mar 31, 2018 | |||||
| 42. | Apr 30, 2018 | |||||
| 43. | May 31, 2018 | |||||
| 44. | Jun 30, 2018 | |||||
| 45. | Jul 31, 2018 | |||||
| 46. | Aug 31, 2018 | |||||
| 47. | Sep 30, 2018 | |||||
| 48. | Oct 31, 2018 | |||||
| 49. | Nov 30, 2018 | |||||
| 50. | Dec 31, 2018 | |||||
| 51. | Jan 31, 2019 | |||||
| 52. | Feb 28, 2019 | |||||
| 53. | Mar 31, 2019 | |||||
| 54. | Apr 30, 2019 | |||||
| 55. | May 31, 2019 | |||||
| 56. | Jun 30, 2019 | |||||
| 57. | Jul 31, 2019 | |||||
| 58. | Aug 31, 2019 | |||||
| 59. | Sep 30, 2019 | |||||
| 60. | Oct 31, 2019 | |||||
| 61. | Nov 30, 2019 | |||||
| 62. | Dec 31, 2019 | |||||
| 63. | Jan 31, 2020 | |||||
| 64. | Feb 29, 2020 | |||||
| 65. | Mar 31, 2020 | |||||
| 66. | Apr 30, 2020 | |||||
| 67. | May 31, 2020 | |||||
| 68. | Jun 30, 2020 | |||||
| 69. | Jul 31, 2020 | |||||
| 70. | Aug 31, 2020 | |||||
| 71. | Sep 30, 2020 | |||||
| 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 APD during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Air Products & Chemicals Inc., calculation of variance and covariance of returns
| t | Date | RAPD,t | RS&P 500,t | (RAPD,t–RAPD)2 | (RS&P 500,t–RS&P 500)2 | (RAPD,t–RAPD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Nov 30, 2014 | |||||
| 2. | Dec 31, 2014 | |||||
| 3. | Jan 31, 2015 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | Aug 31, 2020 | |||||
| 71. | Sep 30, 2020 | |||||
| Total (Σ): | ||||||
| t | Date | RAPD,t | RS&P 500,t | (RAPD,t–RAPD)2 | (RS&P 500,t–RS&P 500)2 | (RAPD,t–RAPD)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Nov 30, 2014 | |||||
| 2. | Dec 31, 2014 | |||||
| 3. | Jan 31, 2015 | |||||
| 4. | Feb 28, 2015 | |||||
| 5. | Mar 31, 2015 | |||||
| 6. | Apr 30, 2015 | |||||
| 7. | May 31, 2015 | |||||
| 8. | Jun 30, 2015 | |||||
| 9. | Jul 31, 2015 | |||||
| 10. | Aug 31, 2015 | |||||
| 11. | Sep 30, 2015 | |||||
| 12. | Oct 31, 2015 | |||||
| 13. | Nov 30, 2015 | |||||
| 14. | Dec 31, 2015 | |||||
| 15. | Jan 31, 2016 | |||||
| 16. | Feb 29, 2016 | |||||
| 17. | Mar 31, 2016 | |||||
| 18. | Apr 30, 2016 | |||||
| 19. | May 31, 2016 | |||||
| 20. | Jun 30, 2016 | |||||
| 21. | Jul 31, 2016 | |||||
| 22. | Aug 31, 2016 | |||||
| 23. | Sep 30, 2016 | |||||
| 24. | Oct 31, 2016 | |||||
| 25. | Nov 30, 2016 | |||||
| 26. | Dec 31, 2016 | |||||
| 27. | Jan 31, 2017 | |||||
| 28. | Feb 28, 2017 | |||||
| 29. | Mar 31, 2017 | |||||
| 30. | Apr 30, 2017 | |||||
| 31. | May 31, 2017 | |||||
| 32. | Jun 30, 2017 | |||||
| 33. | Jul 31, 2017 | |||||
| 34. | Aug 31, 2017 | |||||
| 35. | Sep 30, 2017 | |||||
| 36. | Oct 31, 2017 | |||||
| 37. | Nov 30, 2017 | |||||
| 38. | Dec 31, 2017 | |||||
| 39. | Jan 31, 2018 | |||||
| 40. | Feb 28, 2018 | |||||
| 41. | Mar 31, 2018 | |||||
| 42. | Apr 30, 2018 | |||||
| 43. | May 31, 2018 | |||||
| 44. | Jun 30, 2018 | |||||
| 45. | Jul 31, 2018 | |||||
| 46. | Aug 31, 2018 | |||||
| 47. | Sep 30, 2018 | |||||
| 48. | Oct 31, 2018 | |||||
| 49. | Nov 30, 2018 | |||||
| 50. | Dec 31, 2018 | |||||
| 51. | Jan 31, 2019 | |||||
| 52. | Feb 28, 2019 | |||||
| 53. | Mar 31, 2019 | |||||
| 54. | Apr 30, 2019 | |||||
| 55. | May 31, 2019 | |||||
| 56. | Jun 30, 2019 | |||||
| 57. | Jul 31, 2019 | |||||
| 58. | Aug 31, 2019 | |||||
| 59. | Sep 30, 2019 | |||||
| 60. | Oct 31, 2019 | |||||
| 61. | Nov 30, 2019 | |||||
| 62. | Dec 31, 2019 | |||||
| 63. | Jan 31, 2020 | |||||
| 64. | Feb 29, 2020 | |||||
| 65. | Mar 31, 2020 | |||||
| 66. | Apr 30, 2020 | |||||
| 67. | May 31, 2020 | |||||
| 68. | Jun 30, 2020 | |||||
| 69. | Jul 31, 2020 | |||||
| 70. | Aug 31, 2020 | |||||
| 71. | Sep 30, 2020 | |||||
| Total (Σ): | ||||||
Show all
VarianceAPD = Σ(RAPD,t–RAPD)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= ÷ (71 – 1)
=
CovarianceAPD, S&P 500 = Σ(RAPD,t–RAPD)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= ÷ (71 – 1)
=
Systematic Risk (β) Estimation
| VarianceAPD | |
| VarianceS&P 500 | |
| CovarianceAPD, S&P 500 | |
| Correlation coefficientAPD, S&P 5001 | |
| βAPD2 | |
| αAPD3 |
Calculations
1 Correlation coefficientAPD, S&P 500
= CovarianceAPD, S&P 500 ÷ (Standard deviationAPD × Standard deviationS&P 500)
= ÷ ( × )
=
2 βAPD
= CovarianceAPD, S&P 500 ÷ VarianceS&P 500
= ÷
=
3 αAPD
= AverageAPD – βAPD × 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 Air Products & Chemicals Inc. common stock | βAPD | |
| Expected rate of return on Air Products & Chemicals Inc. common stock3 | E(RAPD) | |
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(RAPD) = RF + βAPD [E(RM) – RF]
= + [ – ]
=