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 Caterpillar Inc. common stock.
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Rates of Return
Caterpillar Inc., monthly rates of return
| Caterpillar Inc. (CAT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCAT,t1 | DividendCAT,t1 | RCAT,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2020 | ||||||
| 1. | Feb 29, 2020 | |||||
| 2. | Mar 31, 2020 | |||||
| 3. | Apr 30, 2020 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | |||||
| 59. | Dec 31, 2024 | |||||
| Average (R): | ||||||
| Standard deviation: | ||||||
| Caterpillar Inc. (CAT) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCAT,t1 | DividendCAT,t1 | RCAT,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2020 | ||||||
| 1. | Feb 29, 2020 | |||||
| 2. | Mar 31, 2020 | |||||
| 3. | Apr 30, 2020 | |||||
| 4. | May 31, 2020 | |||||
| 5. | Jun 30, 2020 | |||||
| 6. | Jul 31, 2020 | |||||
| 7. | Aug 31, 2020 | |||||
| 8. | Sep 30, 2020 | |||||
| 9. | Oct 31, 2020 | |||||
| 10. | Nov 30, 2020 | |||||
| 11. | Dec 31, 2020 | |||||
| 12. | Jan 31, 2021 | |||||
| 13. | Feb 28, 2021 | |||||
| 14. | Mar 31, 2021 | |||||
| 15. | Apr 30, 2021 | |||||
| 16. | May 31, 2021 | |||||
| 17. | Jun 30, 2021 | |||||
| 18. | Jul 31, 2021 | |||||
| 19. | Aug 31, 2021 | |||||
| 20. | Sep 30, 2021 | |||||
| 21. | Oct 31, 2021 | |||||
| 22. | Nov 30, 2021 | |||||
| 23. | Dec 31, 2021 | |||||
| 24. | Jan 31, 2022 | |||||
| 25. | Feb 28, 2022 | |||||
| 26. | Mar 31, 2022 | |||||
| 27. | Apr 30, 2022 | |||||
| 28. | May 31, 2022 | |||||
| 29. | Jun 30, 2022 | |||||
| 30. | Jul 31, 2022 | |||||
| 31. | Aug 31, 2022 | |||||
| 32. | Sep 30, 2022 | |||||
| 33. | Oct 31, 2022 | |||||
| 34. | Nov 30, 2022 | |||||
| 35. | Dec 31, 2022 | |||||
| 36. | Jan 31, 2023 | |||||
| 37. | Feb 28, 2023 | |||||
| 38. | Mar 31, 2023 | |||||
| 39. | Apr 30, 2023 | |||||
| 40. | May 31, 2023 | |||||
| 41. | Jun 30, 2023 | |||||
| 42. | Jul 31, 2023 | |||||
| 43. | Aug 31, 2023 | |||||
| 44. | Sep 30, 2023 | |||||
| 45. | Oct 31, 2023 | |||||
| 46. | Nov 30, 2023 | |||||
| 47. | Dec 31, 2023 | |||||
| 48. | Jan 31, 2024 | |||||
| 49. | Feb 29, 2024 | |||||
| 50. | Mar 31, 2024 | |||||
| 51. | Apr 30, 2024 | |||||
| 52. | May 31, 2024 | |||||
| 53. | Jun 30, 2024 | |||||
| 54. | Jul 31, 2024 | |||||
| 55. | Aug 31, 2024 | |||||
| 56. | Sep 30, 2024 | |||||
| 57. | Oct 31, 2024 | |||||
| 58. | Nov 30, 2024 | |||||
| 59. | Dec 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 CAT during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Caterpillar Inc., calculation of variance and covariance of returns
| t | Date | RCAT,t | RS&P 500,t | (RCAT,t–RCAT)2 | (RS&P 500,t–RS&P 500)2 | (RCAT,t–RCAT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 29, 2020 | |||||
| 2. | Mar 31, 2020 | |||||
| 3. | Apr 30, 2020 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | |||||
| 59. | Dec 31, 2024 | |||||
| Total (Σ): | ||||||
| t | Date | RCAT,t | RS&P 500,t | (RCAT,t–RCAT)2 | (RS&P 500,t–RS&P 500)2 | (RCAT,t–RCAT)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 29, 2020 | |||||
| 2. | Mar 31, 2020 | |||||
| 3. | Apr 30, 2020 | |||||
| 4. | May 31, 2020 | |||||
| 5. | Jun 30, 2020 | |||||
| 6. | Jul 31, 2020 | |||||
| 7. | Aug 31, 2020 | |||||
| 8. | Sep 30, 2020 | |||||
| 9. | Oct 31, 2020 | |||||
| 10. | Nov 30, 2020 | |||||
| 11. | Dec 31, 2020 | |||||
| 12. | Jan 31, 2021 | |||||
| 13. | Feb 28, 2021 | |||||
| 14. | Mar 31, 2021 | |||||
| 15. | Apr 30, 2021 | |||||
| 16. | May 31, 2021 | |||||
| 17. | Jun 30, 2021 | |||||
| 18. | Jul 31, 2021 | |||||
| 19. | Aug 31, 2021 | |||||
| 20. | Sep 30, 2021 | |||||
| 21. | Oct 31, 2021 | |||||
| 22. | Nov 30, 2021 | |||||
| 23. | Dec 31, 2021 | |||||
| 24. | Jan 31, 2022 | |||||
| 25. | Feb 28, 2022 | |||||
| 26. | Mar 31, 2022 | |||||
| 27. | Apr 30, 2022 | |||||
| 28. | May 31, 2022 | |||||
| 29. | Jun 30, 2022 | |||||
| 30. | Jul 31, 2022 | |||||
| 31. | Aug 31, 2022 | |||||
| 32. | Sep 30, 2022 | |||||
| 33. | Oct 31, 2022 | |||||
| 34. | Nov 30, 2022 | |||||
| 35. | Dec 31, 2022 | |||||
| 36. | Jan 31, 2023 | |||||
| 37. | Feb 28, 2023 | |||||
| 38. | Mar 31, 2023 | |||||
| 39. | Apr 30, 2023 | |||||
| 40. | May 31, 2023 | |||||
| 41. | Jun 30, 2023 | |||||
| 42. | Jul 31, 2023 | |||||
| 43. | Aug 31, 2023 | |||||
| 44. | Sep 30, 2023 | |||||
| 45. | Oct 31, 2023 | |||||
| 46. | Nov 30, 2023 | |||||
| 47. | Dec 31, 2023 | |||||
| 48. | Jan 31, 2024 | |||||
| 49. | Feb 29, 2024 | |||||
| 50. | Mar 31, 2024 | |||||
| 51. | Apr 30, 2024 | |||||
| 52. | May 31, 2024 | |||||
| 53. | Jun 30, 2024 | |||||
| 54. | Jul 31, 2024 | |||||
| 55. | Aug 31, 2024 | |||||
| 56. | Sep 30, 2024 | |||||
| 57. | Oct 31, 2024 | |||||
| 58. | Nov 30, 2024 | |||||
| 59. | Dec 31, 2024 | |||||
| Total (Σ): | ||||||
Show all
VarianceCAT = Σ(RCAT,t–RCAT)2 ÷ (59 – 1)
= ÷ (59 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= ÷ (59 – 1)
=
CovarianceCAT, S&P 500 = Σ(RCAT,t–RCAT)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= ÷ (59 – 1)
=
Systematic Risk (β) Estimation
| VarianceCAT | |
| VarianceS&P 500 | |
| CovarianceCAT, S&P 500 | |
| Correlation coefficientCAT, S&P 5001 | |
| βCAT2 | |
| αCAT3 |
Calculations
1 Correlation coefficientCAT, S&P 500
= CovarianceCAT, S&P 500 ÷ (Standard deviationCAT × Standard deviationS&P 500)
= ÷ ( × )
=
2 βCAT
= CovarianceCAT, S&P 500 ÷ VarianceS&P 500
= ÷
=
3 αCAT
= AverageCAT – βCAT × 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 Caterpillar Inc. common stock | βCAT | |
| Expected rate of return on Caterpillar Inc. common stock3 | E(RCAT) | |
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(RCAT) = RF + βCAT [E(RM) – RF]
= + [ – ]
=