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 Freeport-McMoRan Inc. common stock.
Rates of Return
Freeport-McMoRan Inc., monthly rates of return
| Freeport-McMoRan Inc. (FCX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceFCX,t1 | DividendFCX,t1 | RFCX,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2019 | $11.64 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $12.90 | 10.82% | 2,784.49 | 2.97% | |
| 2. | Mar 31, 2019 | $12.89 | -0.08% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $12.31 | $0.05 | -4.11% | 2,945.83 | 3.93% |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | $37.32 | 10.48% | 4,567.80 | 8.92% | |
| 59. | Dec 31, 2023 | $42.57 | 14.07% | 4,769.83 | 4.42% | |
| Average (R): | 3.37% | 1.11% | ||||
| Standard deviation: | 14.65% | 5.31% | ||||
| Freeport-McMoRan Inc. (FCX) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Date | PriceFCX,t1 | DividendFCX,t1 | RFCX,t2 | PriceS&P 500,t | RS&P 500,t3 |
| Jan 31, 2019 | $11.64 | 2,704.10 | ||||
| 1. | Feb 28, 2019 | $12.90 | 10.82% | 2,784.49 | 2.97% | |
| 2. | Mar 31, 2019 | $12.89 | -0.08% | 2,834.40 | 1.79% | |
| 3. | Apr 30, 2019 | $12.31 | $0.05 | -4.11% | 2,945.83 | 3.93% |
| 4. | May 31, 2019 | $9.71 | -21.12% | 2,752.06 | -6.58% | |
| 5. | Jun 30, 2019 | $11.61 | 19.57% | 2,941.76 | 6.89% | |
| 6. | Jul 31, 2019 | $11.06 | $0.05 | -4.31% | 2,980.38 | 1.31% |
| 7. | Aug 31, 2019 | $9.19 | -16.91% | 2,926.46 | -1.81% | |
| 8. | Sep 30, 2019 | $9.57 | 4.13% | 2,976.74 | 1.72% | |
| 9. | Oct 31, 2019 | $9.82 | $0.05 | 3.13% | 3,037.56 | 2.04% |
| 10. | Nov 30, 2019 | $11.38 | 15.89% | 3,140.98 | 3.40% | |
| 11. | Dec 31, 2019 | $13.12 | 15.29% | 3,230.78 | 2.86% | |
| 12. | Jan 31, 2020 | $11.10 | $0.05 | -15.02% | 3,225.52 | -0.16% |
| 13. | Feb 29, 2020 | $9.96 | -10.27% | 2,954.22 | -8.41% | |
| 14. | Mar 31, 2020 | $6.75 | -32.23% | 2,584.59 | -12.51% | |
| 15. | Apr 30, 2020 | $8.83 | 30.81% | 2,912.43 | 12.68% | |
| 16. | May 31, 2020 | $9.07 | 2.72% | 3,044.31 | 4.53% | |
| 17. | Jun 30, 2020 | $11.57 | 27.56% | 3,100.29 | 1.84% | |
| 18. | Jul 31, 2020 | $12.92 | 11.67% | 3,271.12 | 5.51% | |
| 19. | Aug 31, 2020 | $15.61 | 20.82% | 3,500.31 | 7.01% | |
| 20. | Sep 30, 2020 | $15.64 | 0.19% | 3,363.00 | -3.92% | |
| 21. | Oct 31, 2020 | $17.34 | 10.87% | 3,269.96 | -2.77% | |
| 22. | Nov 30, 2020 | $23.39 | 34.89% | 3,621.63 | 10.75% | |
| 23. | Dec 31, 2020 | $26.02 | 11.24% | 3,756.07 | 3.71% | |
| 24. | Jan 31, 2021 | $26.91 | 3.42% | 3,714.24 | -1.11% | |
| 25. | Feb 28, 2021 | $33.91 | 26.01% | 3,811.15 | 2.61% | |
| 26. | Mar 31, 2021 | $32.93 | -2.89% | 3,972.89 | 4.24% | |
| 27. | Apr 30, 2021 | $37.71 | $0.075 | 14.74% | 4,181.17 | 5.24% |
| 28. | May 31, 2021 | $42.72 | 13.29% | 4,204.11 | 0.55% | |
| 29. | Jun 30, 2021 | $37.11 | -13.13% | 4,297.50 | 2.22% | |
| 30. | Jul 31, 2021 | $38.10 | $0.075 | 2.87% | 4,395.26 | 2.27% |
| 31. | Aug 31, 2021 | $36.39 | -4.49% | 4,522.68 | 2.90% | |
| 32. | Sep 30, 2021 | $32.53 | -10.61% | 4,307.54 | -4.76% | |
| 33. | Oct 31, 2021 | $37.72 | $0.075 | 16.19% | 4,605.38 | 6.91% |
| 34. | Nov 30, 2021 | $37.08 | -1.70% | 4,567.00 | -0.83% | |
| 35. | Dec 31, 2021 | $41.73 | 12.54% | 4,766.18 | 4.36% | |
| 36. | Jan 31, 2022 | $37.22 | $0.15 | -10.45% | 4,515.55 | -5.26% |
| 37. | Feb 28, 2022 | $46.95 | 26.14% | 4,373.94 | -3.14% | |
| 38. | Mar 31, 2022 | $49.74 | 5.94% | 4,530.41 | 3.58% | |
| 39. | Apr 30, 2022 | $40.55 | $0.15 | -18.17% | 4,131.93 | -8.80% |
| 40. | May 31, 2022 | $39.08 | -3.63% | 4,132.15 | 0.01% | |
| 41. | Jun 30, 2022 | $29.26 | -25.13% | 3,785.38 | -8.39% | |
| 42. | Jul 31, 2022 | $31.55 | $0.15 | 8.34% | 4,130.29 | 9.11% |
| 43. | Aug 31, 2022 | $29.60 | -6.18% | 3,955.00 | -4.24% | |
| 44. | Sep 30, 2022 | $27.33 | -7.67% | 3,585.62 | -9.34% | |
| 45. | Oct 31, 2022 | $31.69 | $0.15 | 16.50% | 3,871.98 | 7.99% |
| 46. | Nov 30, 2022 | $39.80 | 25.59% | 4,080.11 | 5.38% | |
| 47. | Dec 31, 2022 | $38.00 | -4.52% | 3,839.50 | -5.90% | |
| 48. | Jan 31, 2023 | $44.62 | $0.15 | 17.82% | 4,076.60 | 6.18% |
| 49. | Feb 28, 2023 | $40.97 | -8.18% | 3,970.15 | -2.61% | |
| 50. | Mar 31, 2023 | $40.91 | -0.15% | 4,109.31 | 3.51% | |
| 51. | Apr 30, 2023 | $37.91 | $0.15 | -6.97% | 4,169.48 | 1.46% |
| 52. | May 31, 2023 | $34.34 | -9.42% | 4,179.83 | 0.25% | |
| 53. | Jun 30, 2023 | $40.00 | 16.48% | 4,376.86 | 4.71% | |
| 54. | Jul 31, 2023 | $44.65 | $0.15 | 12.00% | 4,588.96 | 4.85% |
| 55. | Aug 31, 2023 | $39.91 | -10.62% | 4,507.66 | -1.77% | |
| 56. | Sep 30, 2023 | $37.29 | -6.56% | 4,288.05 | -4.87% | |
| 57. | Oct 31, 2023 | $33.78 | $0.15 | -9.01% | 4,193.80 | -2.20% |
| 58. | Nov 30, 2023 | $37.32 | 10.48% | 4,567.80 | 8.92% | |
| 59. | Dec 31, 2023 | $42.57 | 14.07% | 4,769.83 | 4.42% | |
| Average (R): | 3.37% | 1.11% | ||||
| Standard deviation: | 14.65% | 5.31% | ||||
Show all
1 Data in US$ per share of common stock, adjusted for splits and stock dividends.
2 Rate of return on common stock of FCX during period t
3 Rate of return on S&P 500 (the market portfolio proxy) during period t
Variance and Covariance
Freeport-McMoRan Inc., calculation of variance and covariance of returns
| t | Date | RFCX,t | RS&P 500,t | (RFCX,t–RFCX)2 | (RS&P 500,t–RS&P 500)2 | (RFCX,t–RFCX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2019 | 10.82% | 2.97% | 55.65 | 3.49 | 13.93 |
| 2. | Mar 31, 2019 | -0.08% | 1.79% | 11.85 | 0.47 | -2.36 |
| 3. | Apr 30, 2019 | -4.11% | 3.93% | 55.90 | 7.98 | -21.13 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2023 | 10.48% | 8.92% | 50.62 | 61.03 | 55.58 |
| 59. | Dec 31, 2023 | 14.07% | 4.42% | 114.54 | 11.00 | 35.50 |
| Total (Σ): | 12,455.34 | 1,634.30 | 3,383.06 | |||
| t | Date | RFCX,t | RS&P 500,t | (RFCX,t–RFCX)2 | (RS&P 500,t–RS&P 500)2 | (RFCX,t–RFCX)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | Feb 28, 2019 | 10.82% | 2.97% | 55.65 | 3.49 | 13.93 |
| 2. | Mar 31, 2019 | -0.08% | 1.79% | 11.85 | 0.47 | -2.36 |
| 3. | Apr 30, 2019 | -4.11% | 3.93% | 55.90 | 7.98 | -21.13 |
| 4. | May 31, 2019 | -21.12% | -6.58% | 599.57 | 59.04 | 188.14 |
| 5. | Jun 30, 2019 | 19.57% | 6.89% | 262.52 | 33.49 | 93.77 |
| 6. | Jul 31, 2019 | -4.31% | 1.31% | 58.85 | 0.04 | -1.59 |
| 7. | Aug 31, 2019 | -16.91% | -1.81% | 410.99 | 8.50 | 59.10 |
| 8. | Sep 30, 2019 | 4.13% | 1.72% | 0.59 | 0.37 | 0.47 |
| 9. | Oct 31, 2019 | 3.13% | 2.04% | 0.05 | 0.88 | -0.22 |
| 10. | Nov 30, 2019 | 15.89% | 3.40% | 156.77 | 5.28 | 28.78 |
| 11. | Dec 31, 2019 | 15.29% | 2.86% | 142.20 | 3.07 | 20.91 |
| 12. | Jan 31, 2020 | -15.02% | -0.16% | 337.83 | 1.61 | 23.32 |
| 13. | Feb 29, 2020 | -10.27% | -8.41% | 185.92 | 90.57 | 129.77 |
| 14. | Mar 31, 2020 | -32.23% | -12.51% | 1,266.93 | 185.44 | 484.71 |
| 15. | Apr 30, 2020 | 30.81% | 12.68% | 753.49 | 134.06 | 317.83 |
| 16. | May 31, 2020 | 2.72% | 4.53% | 0.42 | 11.71 | -2.21 |
| 17. | Jun 30, 2020 | 27.56% | 1.84% | 585.56 | 0.54 | 17.74 |
| 18. | Jul 31, 2020 | 11.67% | 5.51% | 68.94 | 19.40 | 36.57 |
| 19. | Aug 31, 2020 | 20.82% | 7.01% | 304.69 | 34.82 | 103.00 |
| 20. | Sep 30, 2020 | 0.19% | -3.92% | 10.07 | 25.29 | 15.96 |
| 21. | Oct 31, 2020 | 10.87% | -2.77% | 56.32 | 15.00 | -29.06 |
| 22. | Nov 30, 2020 | 34.89% | 10.75% | 993.85 | 93.10 | 304.18 |
| 23. | Dec 31, 2020 | 11.24% | 3.71% | 62.08 | 6.79 | 20.54 |
| 24. | Jan 31, 2021 | 3.42% | -1.11% | 0.00 | 4.93 | -0.12 |
| 25. | Feb 28, 2021 | 26.01% | 2.61% | 512.91 | 2.26 | 34.05 |
| 26. | Mar 31, 2021 | -2.89% | 4.24% | 39.13 | 9.85 | -19.63 |
| 27. | Apr 30, 2021 | 14.74% | 5.24% | 129.47 | 17.11 | 47.07 |
| 28. | May 31, 2021 | 13.29% | 0.55% | 98.42 | 0.31 | -5.53 |
| 29. | Jun 30, 2021 | -13.13% | 2.22% | 272.15 | 1.24 | -18.40 |
| 30. | Jul 31, 2021 | 2.87% | 2.27% | 0.25 | 1.37 | -0.58 |
| 31. | Aug 31, 2021 | -4.49% | 2.90% | 61.67 | 3.22 | -14.08 |
| 32. | Sep 30, 2021 | -10.61% | -4.76% | 195.23 | 34.37 | 81.92 |
| 33. | Oct 31, 2021 | 16.19% | 6.91% | 164.35 | 33.74 | 74.47 |
| 34. | Nov 30, 2021 | -1.70% | -0.83% | 25.62 | 3.76 | 9.82 |
| 35. | Dec 31, 2021 | 12.54% | 4.36% | 84.19 | 10.60 | 29.87 |
| 36. | Jan 31, 2022 | -10.45% | -5.26% | 190.80 | 40.51 | 87.91 |
| 37. | Feb 28, 2022 | 26.14% | -3.14% | 518.78 | 17.99 | -96.62 |
| 38. | Mar 31, 2022 | 5.94% | 3.58% | 6.64 | 6.11 | 6.37 |
| 39. | Apr 30, 2022 | -18.17% | -8.80% | 463.95 | 98.04 | 213.27 |
| 40. | May 31, 2022 | -3.63% | 0.01% | 48.86 | 1.21 | 7.69 |
| 41. | Jun 30, 2022 | -25.13% | -8.39% | 811.85 | 90.21 | 270.62 |
| 42. | Jul 31, 2022 | 8.34% | 9.11% | 24.74 | 64.09 | 39.82 |
| 43. | Aug 31, 2022 | -6.18% | -4.24% | 91.12 | 28.62 | 51.07 |
| 44. | Sep 30, 2022 | -7.67% | -9.34% | 121.75 | 109.11 | 115.25 |
| 45. | Oct 31, 2022 | 16.50% | 7.99% | 172.58 | 47.34 | 90.39 |
| 46. | Nov 30, 2022 | 25.59% | 5.38% | 494.02 | 18.23 | 94.90 |
| 47. | Dec 31, 2022 | -4.52% | -5.90% | 62.21 | 49.04 | 55.24 |
| 48. | Jan 31, 2023 | 17.82% | 6.18% | 208.82 | 25.70 | 73.26 |
| 49. | Feb 28, 2023 | -8.18% | -2.61% | 133.29 | 13.82 | 42.91 |
| 50. | Mar 31, 2023 | -0.15% | 3.51% | 12.33 | 5.76 | -8.43 |
| 51. | Apr 30, 2023 | -6.97% | 1.46% | 106.74 | 0.13 | -3.70 |
| 52. | May 31, 2023 | -9.42% | 0.25% | 163.38 | 0.74 | 10.96 |
| 53. | Jun 30, 2023 | 16.48% | 4.71% | 172.06 | 13.02 | 47.33 |
| 54. | Jul 31, 2023 | 12.00% | 4.85% | 74.56 | 13.99 | 32.30 |
| 55. | Aug 31, 2023 | -10.62% | -1.77% | 195.47 | 8.28 | 40.23 |
| 56. | Sep 30, 2023 | -6.56% | -4.87% | 98.60 | 35.73 | 59.36 |
| 57. | Oct 31, 2023 | -9.01% | -2.20% | 153.15 | 10.92 | 40.89 |
| 58. | Nov 30, 2023 | 10.48% | 8.92% | 50.62 | 61.03 | 55.58 |
| 59. | Dec 31, 2023 | 14.07% | 4.42% | 114.54 | 11.00 | 35.50 |
| Total (Σ): | 12,455.34 | 1,634.30 | 3,383.06 | |||
Show all
VarianceFCX = Σ(RFCX,t–RFCX)2 ÷ (59 – 1)
= 12,455.34 ÷ (59 – 1)
= 214.75
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianceFCX, S&P 500 = Σ(RFCX,t–RFCX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,383.06 ÷ (59 – 1)
= 58.33
Systematic Risk (β) Estimation
| VarianceFCX | 214.75 |
| VarianceS&P 500 | 28.18 |
| CovarianceFCX, S&P 500 | 58.33 |
| Correlation coefficientFCX, S&P 5001 | 0.75 |
| βFCX2 | 2.07 |
| αFCX3 | 1.08% |
Calculations
1 Correlation coefficientFCX, S&P 500
= CovarianceFCX, S&P 500 ÷ (Standard deviationFCX × Standard deviationS&P 500)
= 58.33 ÷ (14.65% × 5.31%)
= 0.75
2 βFCX
= CovarianceFCX, S&P 500 ÷ VarianceS&P 500
= 58.33 ÷ 28.18
= 2.07
3 αFCX
= AverageFCX – βFCX × AverageS&P 500
= 3.37% – 2.07 × 1.11%
= 1.08%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.79% |
| Expected rate of return on market portfolio2 | E(RM) | 13.79% |
| Systematic risk (β) of Freeport-McMoRan Inc. common stock | βFCX | 2.07 |
| Expected rate of return on Freeport-McMoRan Inc. common stock3 | E(RFCX) | 23.43% |
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(RFCX) = RF + βFCX [E(RM) – RF]
= 4.79% + 2.07 [13.79% – 4.79%]
= 23.43%