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, 2020 | $11.10 | 3,225.52 | ||||
| 1. | Feb 29, 2020 | $9.96 | -10.27% | 2,954.22 | -8.41% | |
| 2. | Mar 31, 2020 | $6.75 | -32.23% | 2,584.59 | -12.51% | |
| 3. | Apr 30, 2020 | $8.83 | 30.81% | 2,912.43 | 12.68% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | $44.20 | -1.82% | 6,032.38 | 5.73% | |
| 59. | Dec 31, 2024 | $38.08 | -13.85% | 5,881.63 | -2.50% | |
| Average (R): | 3.18% | 1.16% | ||||
| Standard deviation: | 14.27% | 5.28% | ||||
| 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, 2020 | $11.10 | 3,225.52 | ||||
| 1. | Feb 29, 2020 | $9.96 | -10.27% | 2,954.22 | -8.41% | |
| 2. | Mar 31, 2020 | $6.75 | -32.23% | 2,584.59 | -12.51% | |
| 3. | Apr 30, 2020 | $8.83 | 30.81% | 2,912.43 | 12.68% | |
| 4. | May 31, 2020 | $9.07 | 2.72% | 3,044.31 | 4.53% | |
| 5. | Jun 30, 2020 | $11.57 | 27.56% | 3,100.29 | 1.84% | |
| 6. | Jul 31, 2020 | $12.92 | 11.67% | 3,271.12 | 5.51% | |
| 7. | Aug 31, 2020 | $15.61 | 20.82% | 3,500.31 | 7.01% | |
| 8. | Sep 30, 2020 | $15.64 | 0.19% | 3,363.00 | -3.92% | |
| 9. | Oct 31, 2020 | $17.34 | 10.87% | 3,269.96 | -2.77% | |
| 10. | Nov 30, 2020 | $23.39 | 34.89% | 3,621.63 | 10.75% | |
| 11. | Dec 31, 2020 | $26.02 | 11.24% | 3,756.07 | 3.71% | |
| 12. | Jan 31, 2021 | $26.91 | 3.42% | 3,714.24 | -1.11% | |
| 13. | Feb 28, 2021 | $33.91 | 26.01% | 3,811.15 | 2.61% | |
| 14. | Mar 31, 2021 | $32.93 | -2.89% | 3,972.89 | 4.24% | |
| 15. | Apr 30, 2021 | $37.71 | $0.075 | 14.74% | 4,181.17 | 5.24% |
| 16. | May 31, 2021 | $42.72 | 13.29% | 4,204.11 | 0.55% | |
| 17. | Jun 30, 2021 | $37.11 | -13.13% | 4,297.50 | 2.22% | |
| 18. | Jul 31, 2021 | $38.10 | $0.075 | 2.87% | 4,395.26 | 2.27% |
| 19. | Aug 31, 2021 | $36.39 | -4.49% | 4,522.68 | 2.90% | |
| 20. | Sep 30, 2021 | $32.53 | -10.61% | 4,307.54 | -4.76% | |
| 21. | Oct 31, 2021 | $37.72 | $0.075 | 16.19% | 4,605.38 | 6.91% |
| 22. | Nov 30, 2021 | $37.08 | -1.70% | 4,567.00 | -0.83% | |
| 23. | Dec 31, 2021 | $41.73 | 12.54% | 4,766.18 | 4.36% | |
| 24. | Jan 31, 2022 | $37.22 | $0.15 | -10.45% | 4,515.55 | -5.26% |
| 25. | Feb 28, 2022 | $46.95 | 26.14% | 4,373.94 | -3.14% | |
| 26. | Mar 31, 2022 | $49.74 | 5.94% | 4,530.41 | 3.58% | |
| 27. | Apr 30, 2022 | $40.55 | $0.15 | -18.17% | 4,131.93 | -8.80% |
| 28. | May 31, 2022 | $39.08 | -3.63% | 4,132.15 | 0.01% | |
| 29. | Jun 30, 2022 | $29.26 | -25.13% | 3,785.38 | -8.39% | |
| 30. | Jul 31, 2022 | $31.55 | $0.15 | 8.34% | 4,130.29 | 9.11% |
| 31. | Aug 31, 2022 | $29.60 | -6.18% | 3,955.00 | -4.24% | |
| 32. | Sep 30, 2022 | $27.33 | -7.67% | 3,585.62 | -9.34% | |
| 33. | Oct 31, 2022 | $31.69 | $0.15 | 16.50% | 3,871.98 | 7.99% |
| 34. | Nov 30, 2022 | $39.80 | 25.59% | 4,080.11 | 5.38% | |
| 35. | Dec 31, 2022 | $38.00 | -4.52% | 3,839.50 | -5.90% | |
| 36. | Jan 31, 2023 | $44.62 | $0.15 | 17.82% | 4,076.60 | 6.18% |
| 37. | Feb 28, 2023 | $40.97 | -8.18% | 3,970.15 | -2.61% | |
| 38. | Mar 31, 2023 | $40.91 | -0.15% | 4,109.31 | 3.51% | |
| 39. | Apr 30, 2023 | $37.91 | $0.15 | -6.97% | 4,169.48 | 1.46% |
| 40. | May 31, 2023 | $34.34 | -9.42% | 4,179.83 | 0.25% | |
| 41. | Jun 30, 2023 | $40.00 | 16.48% | 4,376.86 | 4.71% | |
| 42. | Jul 31, 2023 | $44.65 | $0.15 | 12.00% | 4,588.96 | 4.85% |
| 43. | Aug 31, 2023 | $39.91 | -10.62% | 4,507.66 | -1.77% | |
| 44. | Sep 30, 2023 | $37.29 | -6.56% | 4,288.05 | -4.87% | |
| 45. | Oct 31, 2023 | $33.78 | $0.15 | -9.01% | 4,193.80 | -2.20% |
| 46. | Nov 30, 2023 | $37.32 | 10.48% | 4,567.80 | 8.92% | |
| 47. | Dec 31, 2023 | $42.57 | 14.07% | 4,769.83 | 4.42% | |
| 48. | Jan 31, 2024 | $39.69 | $0.15 | -6.41% | 4,845.65 | 1.59% |
| 49. | Feb 29, 2024 | $37.81 | -4.74% | 5,096.27 | 5.17% | |
| 50. | Mar 31, 2024 | $47.02 | 24.36% | 5,254.35 | 3.10% | |
| 51. | Apr 30, 2024 | $49.94 | $0.15 | 6.53% | 5,035.69 | -4.16% |
| 52. | May 31, 2024 | $52.73 | 5.59% | 5,277.51 | 4.80% | |
| 53. | Jun 30, 2024 | $48.60 | -7.83% | 5,460.48 | 3.47% | |
| 54. | Jul 31, 2024 | $45.41 | $0.15 | -6.26% | 5,522.30 | 1.13% |
| 55. | Aug 31, 2024 | $44.28 | -2.49% | 5,648.40 | 2.28% | |
| 56. | Sep 30, 2024 | $49.92 | 12.74% | 5,762.48 | 2.02% | |
| 57. | Oct 31, 2024 | $45.02 | $0.15 | -9.52% | 5,705.45 | -0.99% |
| 58. | Nov 30, 2024 | $44.20 | -1.82% | 6,032.38 | 5.73% | |
| 59. | Dec 31, 2024 | $38.08 | -13.85% | 5,881.63 | -2.50% | |
| Average (R): | 3.18% | 1.16% | ||||
| Standard deviation: | 14.27% | 5.28% | ||||
Show all
1 Data in US$ 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 29, 2020 | -10.27% | -8.41% | 180.87 | 91.63 | 128.74 |
| 2. | Mar 31, 2020 | -32.23% | -12.51% | 1,253.70 | 186.96 | 484.14 |
| 3. | Apr 30, 2020 | 30.81% | 12.68% | 763.76 | 132.78 | 318.46 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | Nov 30, 2024 | -1.82% | 5.73% | 25.00 | 20.87 | -22.84 |
| 59. | Dec 31, 2024 | -13.85% | -2.50% | 289.84 | 13.40 | 62.32 |
| Total (Σ): | 11,806.48 | 1,618.62 | 3,016.36 | |||
| 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 29, 2020 | -10.27% | -8.41% | 180.87 | 91.63 | 128.74 |
| 2. | Mar 31, 2020 | -32.23% | -12.51% | 1,253.70 | 186.96 | 484.14 |
| 3. | Apr 30, 2020 | 30.81% | 12.68% | 763.76 | 132.78 | 318.46 |
| 4. | May 31, 2020 | 2.72% | 4.53% | 0.21 | 11.34 | -1.55 |
| 5. | Jun 30, 2020 | 27.56% | 1.84% | 594.62 | 0.46 | 16.52 |
| 6. | Jul 31, 2020 | 11.67% | 5.51% | 72.07 | 18.91 | 36.92 |
| 7. | Aug 31, 2020 | 20.82% | 7.01% | 311.23 | 34.17 | 103.12 |
| 8. | Sep 30, 2020 | 0.19% | -3.92% | 8.92 | 25.85 | 15.18 |
| 9. | Oct 31, 2020 | 10.87% | -2.77% | 59.15 | 15.43 | -30.21 |
| 10. | Nov 30, 2020 | 34.89% | 10.75% | 1,005.64 | 92.03 | 304.22 |
| 11. | Dec 31, 2020 | 11.24% | 3.71% | 65.05 | 6.51 | 20.57 |
| 12. | Jan 31, 2021 | 3.42% | -1.11% | 0.06 | 5.18 | -0.55 |
| 13. | Feb 28, 2021 | 26.01% | 2.61% | 521.39 | 2.10 | 33.06 |
| 14. | Mar 31, 2021 | -2.89% | 4.24% | 36.83 | 9.50 | -18.71 |
| 15. | Apr 30, 2021 | 14.74% | 5.24% | 133.74 | 16.66 | 47.20 |
| 16. | May 31, 2021 | 13.29% | 0.55% | 102.15 | 0.38 | -6.19 |
| 17. | Jun 30, 2021 | -13.13% | 2.22% | 266.04 | 1.12 | -17.29 |
| 18. | Jul 31, 2021 | 2.87% | 2.27% | 0.10 | 1.24 | -0.34 |
| 19. | Aug 31, 2021 | -4.49% | 2.90% | 58.78 | 3.02 | -13.32 |
| 20. | Sep 30, 2021 | -10.61% | -4.76% | 190.05 | 35.02 | 81.59 |
| 21. | Oct 31, 2021 | 16.19% | 6.91% | 169.17 | 33.10 | 74.83 |
| 22. | Nov 30, 2021 | -1.70% | -0.83% | 23.77 | 3.98 | 9.72 |
| 23. | Dec 31, 2021 | 12.54% | 4.36% | 87.64 | 10.24 | 29.96 |
| 24. | Jan 31, 2022 | -10.45% | -5.26% | 185.69 | 41.21 | 87.48 |
| 25. | Feb 28, 2022 | 26.14% | -3.14% | 527.31 | 18.47 | -98.68 |
| 26. | Mar 31, 2022 | 5.94% | 3.58% | 7.64 | 5.84 | 6.68 |
| 27. | Apr 30, 2022 | -18.17% | -8.80% | 455.96 | 99.14 | 212.61 |
| 28. | May 31, 2022 | -3.63% | 0.01% | 46.29 | 1.34 | 7.86 |
| 29. | Jun 30, 2022 | -25.13% | -8.39% | 801.26 | 91.26 | 270.42 |
| 30. | Jul 31, 2022 | 8.34% | 9.11% | 26.63 | 63.21 | 41.03 |
| 31. | Aug 31, 2022 | -6.18% | -4.24% | 87.60 | 29.22 | 50.59 |
| 32. | Sep 30, 2022 | -7.67% | -9.34% | 117.67 | 110.27 | 113.91 |
| 33. | Oct 31, 2022 | 16.50% | 7.99% | 177.51 | 46.58 | 90.93 |
| 34. | Nov 30, 2022 | 25.59% | 5.38% | 502.34 | 17.76 | 94.45 |
| 35. | Dec 31, 2022 | -4.52% | -5.90% | 59.31 | 49.82 | 54.36 |
| 36. | Jan 31, 2023 | 17.82% | 6.18% | 214.25 | 25.14 | 73.39 |
| 37. | Feb 28, 2023 | -8.18% | -2.61% | 129.02 | 14.23 | 42.85 |
| 38. | Mar 31, 2023 | -0.15% | 3.51% | 11.06 | 5.49 | -7.79 |
| 39. | Apr 30, 2023 | -6.97% | 1.46% | 102.92 | 0.09 | -3.07 |
| 40. | May 31, 2023 | -9.42% | 0.25% | 158.65 | 0.83 | 11.50 |
| 41. | Jun 30, 2023 | 16.48% | 4.71% | 176.99 | 12.62 | 47.26 |
| 42. | Jul 31, 2023 | 12.00% | 4.85% | 77.82 | 13.58 | 32.50 |
| 43. | Aug 31, 2023 | -10.62% | -1.77% | 190.29 | 8.60 | 40.46 |
| 44. | Sep 30, 2023 | -6.56% | -4.87% | 94.93 | 36.40 | 58.78 |
| 45. | Oct 31, 2023 | -9.01% | -2.20% | 148.57 | 11.28 | 40.95 |
| 46. | Nov 30, 2023 | 10.48% | 8.92% | 53.30 | 60.17 | 56.63 |
| 47. | Dec 31, 2023 | 14.07% | 4.42% | 118.57 | 10.64 | 35.52 |
| 48. | Jan 31, 2024 | -6.41% | 1.59% | 92.00 | 0.18 | -4.11 |
| 49. | Feb 29, 2024 | -4.74% | 5.17% | 62.65 | 16.09 | -31.75 |
| 50. | Mar 31, 2024 | 24.36% | 3.10% | 448.59 | 3.77 | 41.10 |
| 51. | Apr 30, 2024 | 6.53% | -4.16% | 11.23 | 28.33 | -17.83 |
| 52. | May 31, 2024 | 5.59% | 4.80% | 5.80 | 13.26 | 8.77 |
| 53. | Jun 30, 2024 | -7.83% | 3.47% | 121.24 | 5.32 | -25.39 |
| 54. | Jul 31, 2024 | -6.26% | 1.13% | 89.00 | 0.00 | 0.27 |
| 55. | Aug 31, 2024 | -2.49% | 2.28% | 32.12 | 1.26 | -6.36 |
| 56. | Sep 30, 2024 | 12.74% | 2.02% | 91.36 | 0.74 | 8.21 |
| 57. | Oct 31, 2024 | -9.52% | -0.99% | 161.13 | 4.63 | 27.30 |
| 58. | Nov 30, 2024 | -1.82% | 5.73% | 25.00 | 20.87 | -22.84 |
| 59. | Dec 31, 2024 | -13.85% | -2.50% | 289.84 | 13.40 | 62.32 |
| Total (Σ): | 11,806.48 | 1,618.62 | 3,016.36 | |||
Show all
VarianceFCX = Σ(RFCX,t–RFCX)2 ÷ (59 – 1)
= 11,806.48 ÷ (59 – 1)
= 203.56
VarianceS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,618.62 ÷ (59 – 1)
= 27.91
CovarianceFCX, S&P 500 = Σ(RFCX,t–RFCX)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 3,016.36 ÷ (59 – 1)
= 52.01
Systematic Risk (β) Estimation
| VarianceFCX | 203.56 |
| VarianceS&P 500 | 27.91 |
| CovarianceFCX, S&P 500 | 52.01 |
| Correlation coefficientFCX, S&P 5001 | 0.69 |
| βFCX2 | 1.86 |
| αFCX3 | 1.01% |
Calculations
1 Correlation coefficientFCX, S&P 500
= CovarianceFCX, S&P 500 ÷ (Standard deviationFCX × Standard deviationS&P 500)
= 52.01 ÷ (14.27% × 5.28%)
= 0.69
2 βFCX
= CovarianceFCX, S&P 500 ÷ VarianceS&P 500
= 52.01 ÷ 27.91
= 1.86
3 αFCX
= AverageFCX – βFCX × AverageS&P 500
= 3.18% – 1.86 × 1.16%
= 1.01%
Expected Rate of Return
| Assumptions | ||
| Rate of return on LT Treasury Composite1 | RF | 4.90% |
| Expected rate of return on market portfolio2 | E(RM) | 15.01% |
| Systematic risk (β) of Freeport-McMoRan Inc. common stock | βFCX | 1.86 |
| Expected rate of return on Freeport-McMoRan Inc. common stock3 | E(RFCX) | 23.74% |
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]
= 4.90% + 1.86 [15.01% – 4.90%]
= 23.74%