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 Carrier Global Corp. common stock.
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Rates of Return
Carrier Global Corp., monthly rates of return
| Carrier Global Corp. (CARR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCARR,t1 | DividendCARR,t1 | RCARR,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Mar 31, 2020 | ||||||
| 1. | Apr 30, 2020 | |||||
| 2. | May 31, 2020 | |||||
| 3. | Jun 30, 2020 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 32. | Nov 30, 2022 | |||||
| 33. | Dec 31, 2022 | |||||
| Average (R): | ||||||
| Standard deviation: | ||||||
| Carrier Global Corp. (CARR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceCARR,t1 | DividendCARR,t1 | RCARR,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Mar 31, 2020 | ||||||
| 1. | Apr 30, 2020 | |||||
| 2. | May 31, 2020 | |||||
| 3. | Jun 30, 2020 | |||||
| 4. | Jul 31, 2020 | |||||
| 5. | Aug 31, 2020 | |||||
| 6. | Sep 30, 2020 | |||||
| 7. | Oct 31, 2020 | |||||
| 8. | Nov 30, 2020 | |||||
| 9. | Dec 31, 2020 | |||||
| 10. | Jan 31, 2021 | |||||
| 11. | Feb 28, 2021 | |||||
| 12. | Mar 31, 2021 | |||||
| 13. | Apr 30, 2021 | |||||
| 14. | May 31, 2021 | |||||
| 15. | Jun 30, 2021 | |||||
| 16. | Jul 31, 2021 | |||||
| 17. | Aug 31, 2021 | |||||
| 18. | Sep 30, 2021 | |||||
| 19. | Oct 31, 2021 | |||||
| 20. | Nov 30, 2021 | |||||
| 21. | Dec 31, 2021 | |||||
| 22. | Jan 31, 2022 | |||||
| 23. | Feb 28, 2022 | |||||
| 24. | Mar 31, 2022 | |||||
| 25. | Apr 30, 2022 | |||||
| 26. | May 31, 2022 | |||||
| 27. | Jun 30, 2022 | |||||
| 28. | Jul 31, 2022 | |||||
| 29. | Aug 31, 2022 | |||||
| 30. | Sep 30, 2022 | |||||
| 31. | Oct 31, 2022 | |||||
| 32. | Nov 30, 2022 | |||||
| 33. | Dec 31, 2022 | |||||
| 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 CARR during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Carrier Global Corp., calculation of variance and covariance of returns
| t | Date | RCARR,t | RS&P 500,t | (RCARR,t–RCARR)2 | (RS&P 500,t–RS&P 500)2 | (RCARR,t–RCARR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Apr 30, 2020 | |||||
| 2. | May 31, 2020 | |||||
| 3. | Jun 30, 2020 | |||||
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 32. | Nov 30, 2022 | |||||
| 33. | Dec 31, 2022 | |||||
| Total (Σ): | ||||||
| t | Date | RCARR,t | RS&P 500,t | (RCARR,t–RCARR)2 | (RS&P 500,t–RS&P 500)2 | (RCARR,t–RCARR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Apr 30, 2020 | |||||
| 2. | May 31, 2020 | |||||
| 3. | Jun 30, 2020 | |||||
| 4. | Jul 31, 2020 | |||||
| 5. | Aug 31, 2020 | |||||
| 6. | Sep 30, 2020 | |||||
| 7. | Oct 31, 2020 | |||||
| 8. | Nov 30, 2020 | |||||
| 9. | Dec 31, 2020 | |||||
| 10. | Jan 31, 2021 | |||||
| 11. | Feb 28, 2021 | |||||
| 12. | Mar 31, 2021 | |||||
| 13. | Apr 30, 2021 | |||||
| 14. | May 31, 2021 | |||||
| 15. | Jun 30, 2021 | |||||
| 16. | Jul 31, 2021 | |||||
| 17. | Aug 31, 2021 | |||||
| 18. | Sep 30, 2021 | |||||
| 19. | Oct 31, 2021 | |||||
| 20. | Nov 30, 2021 | |||||
| 21. | Dec 31, 2021 | |||||
| 22. | Jan 31, 2022 | |||||
| 23. | Feb 28, 2022 | |||||
| 24. | Mar 31, 2022 | |||||
| 25. | Apr 30, 2022 | |||||
| 26. | May 31, 2022 | |||||
| 27. | Jun 30, 2022 | |||||
| 28. | Jul 31, 2022 | |||||
| 29. | Aug 31, 2022 | |||||
| 30. | Sep 30, 2022 | |||||
| 31. | Oct 31, 2022 | |||||
| 32. | Nov 30, 2022 | |||||
| 33. | Dec 31, 2022 | |||||
| Total (Σ): | ||||||
Show all
VarianceCARR = Σ(RCARR,t–RCARR)2 ÷ (33 – 1)
= ÷ (33 – 1)
=
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (33 – 1)
= ÷ (33 – 1)
=
CovarianceCARR, S&P 500 = Σ(RCARR,t–RCARR)×(RS&P 500,t–RS&P 500) ÷ (33 – 1)
= ÷ (33 – 1)
=
Systematic Risk (β) Estimation
| VarianceCARR | |
| VarianceS&P 500 | |
| CovarianceCARR, S&P 500 | |
| Correlation coefficientCARR, S&P 5001 | |
| βCARR2 | |
| αCARR3 |
Calculations
1 Correlation coefficientCARR, S&P 500
= CovarianceCARR, S&P 500 ÷ (Standard deviationCARR × Standard deviationS&P 500)
= ÷ ( × )
=
2 βCARR
= CovarianceCARR, S&P 500 ÷ VarianceS&P 500
= ÷
=
3 αCARR
= AverageCARR – βCARR × 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 Carrier Global Corp. common stock | βCARR | |
| Expected rate of return on Carrier Global Corp. common stock3 | E(RCARR) | |
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(RCARR) = RF + βCARR [E(RM) – RF]
= + [ – ]
=