Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios de activos de capital (CAPM, por sus siglas en inglés) indica cuál debería ser la tasa de rendimiento esperada o requerida en activos de riesgo como las acciones ordinarias de Occidental.
Tasas de retorno
Occidental Petroleum Corp., tasas mensuales de retorno
| Occidental Petroleum Corp. (OXY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioOXY,t1 | DividendoOXY,t1 | ROXY,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $66.78 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $66.15 | -0.94% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $66.20 | $0.78 | 1.25% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $58.88 | -11.06% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $59.15 | -4.30% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $59.71 | $0.18 | 1.25% | 4,769.83 | 4.42% |
| Promedio (R): | 1.99% | 1.11% | ||||
| Desviación estándar: | 19.46% | 5.31% | ||||
| Occidental Petroleum Corp. (OXY) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioOXY,t1 | DividendoOXY,t1 | ROXY,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $66.78 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $66.15 | -0.94% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $66.20 | $0.78 | 1.25% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $58.88 | -11.06% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $49.77 | -15.47% | 2,752.06 | -6.58% | |
| 5. | 30 jun. 2019 | $50.28 | $0.78 | 2.59% | 2,941.76 | 6.89% |
| 6. | 31 jul. 2019 | $51.36 | 2.15% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $43.48 | -15.34% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $44.47 | $0.79 | 4.09% | 2,976.74 | 1.72% |
| 9. | 31 oct. 2019 | $40.50 | -8.93% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $38.57 | -4.77% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $41.21 | $0.79 | 8.89% | 3,230.78 | 2.86% |
| 12. | 31 ene. 2020 | $39.72 | -3.62% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $32.74 | -17.57% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $11.58 | $0.79 | -62.22% | 2,584.59 | -12.51% |
| 15. | 30 abr. 2020 | $16.60 | 43.35% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $12.95 | -21.99% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $18.30 | $0.01 | 41.39% | 3,100.29 | 1.84% |
| 18. | 31 jul. 2020 | $15.74 | -13.99% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $12.74 | -19.06% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $10.01 | $0.01 | -21.35% | 3,363.00 | -3.92% |
| 21. | 31 oct. 2020 | $9.13 | -8.79% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $15.76 | 72.62% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $17.31 | $0.01 | 9.90% | 3,756.07 | 3.71% |
| 24. | 31 ene. 2021 | $20.06 | 15.89% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $26.61 | 32.65% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $26.62 | $0.01 | 0.08% | 3,972.89 | 4.24% |
| 27. | 30 abr. 2021 | $25.36 | -4.73% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $25.96 | 2.37% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $31.27 | $0.01 | 20.49% | 4,297.50 | 2.22% |
| 30. | 31 jul. 2021 | $26.10 | -16.53% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $25.69 | -1.57% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $29.58 | $0.01 | 15.18% | 4,307.54 | -4.76% |
| 33. | 31 oct. 2021 | $33.53 | 13.35% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $29.65 | -11.57% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $28.99 | $0.01 | -2.19% | 4,766.18 | 4.36% |
| 36. | 31 ene. 2022 | $37.67 | 29.94% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $43.73 | 16.09% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $56.74 | $0.13 | 30.05% | 4,530.41 | 3.58% |
| 39. | 30 abr. 2022 | $55.09 | -2.91% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $69.31 | 25.81% | 4,132.15 | 0.01% | |
| 41. | 30 jun. 2022 | $58.88 | $0.13 | -14.86% | 3,785.38 | -8.39% |
| 42. | 31 jul. 2022 | $65.75 | 11.67% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $71.00 | 7.98% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $61.45 | $0.13 | -13.27% | 3,585.62 | -9.34% |
| 45. | 31 oct. 2022 | $72.60 | 18.14% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $69.49 | -4.28% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $62.99 | $0.13 | -9.17% | 3,839.50 | -5.90% |
| 48. | 31 ene. 2023 | $64.79 | 2.86% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $58.56 | -9.62% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $62.43 | $0.18 | 6.92% | 4,109.31 | 3.51% |
| 51. | 30 abr. 2023 | $61.53 | -1.44% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $57.66 | -6.29% | 4,179.83 | 0.25% | |
| 53. | 30 jun. 2023 | $58.80 | $0.18 | 2.29% | 4,376.86 | 4.71% |
| 54. | 31 jul. 2023 | $63.13 | 7.36% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $62.79 | -0.54% | 4,507.66 | -1.77% | |
| 56. | 30 sept. 2023 | $64.88 | $0.18 | 3.62% | 4,288.05 | -4.87% |
| 57. | 31 oct. 2023 | $61.81 | -4.73% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $59.15 | -4.30% | 4,567.80 | 8.92% | |
| 59. | 31 dic. 2023 | $59.71 | $0.18 | 1.25% | 4,769.83 | 4.42% |
| Promedio (R): | 1.99% | 1.11% | ||||
| Desviación estándar: | 19.46% | 5.31% | ||||
Mostrar todo
1 Datos en dólares estadounidenses por acción ordinaria, ajustados por divisiones y dividendos de acciones.
2 Tasa de rendimiento de las acciones ordinarias de OXY durante el período t.
3 Tasa de rendimiento del S&P 500 (el proxy de la cartera de mercado) durante el período t.
Varianza y covarianza
Occidental Petroleum Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | ROXY,t | RS&P 500,t | (ROXY,t–ROXY)2 | (RS&P 500,t–RS&P 500)2 | (ROXY,t–ROXY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | -0.94% | 2.97% | 8.58 | 3.49 | -5.47 |
| 2. | 31 mar. 2019 | 1.25% | 1.79% | 0.53 | 0.47 | -0.50 |
| 3. | 30 abr. 2019 | -11.06% | 3.93% | 170.11 | 7.98 | -36.85 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | -4.30% | 8.92% | 39.55 | 61.03 | -49.13 |
| 59. | 31 dic. 2023 | 1.25% | 4.42% | 0.54 | 11.00 | -2.44 |
| Total (Σ): | 21,965.27 | 1,634.30 | 2,703.97 | |||
| t | Fecha | ROXY,t | RS&P 500,t | (ROXY,t–ROXY)2 | (RS&P 500,t–RS&P 500)2 | (ROXY,t–ROXY)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | -0.94% | 2.97% | 8.58 | 3.49 | -5.47 |
| 2. | 31 mar. 2019 | 1.25% | 1.79% | 0.53 | 0.47 | -0.50 |
| 3. | 30 abr. 2019 | -11.06% | 3.93% | 170.11 | 7.98 | -36.85 |
| 4. | 31 may. 2019 | -15.47% | -6.58% | 304.76 | 59.04 | 134.14 |
| 5. | 30 jun. 2019 | 2.59% | 6.89% | 0.37 | 33.49 | 3.51 |
| 6. | 31 jul. 2019 | 2.15% | 1.31% | 0.03 | 0.04 | 0.03 |
| 7. | 31 ago. 2019 | -15.34% | -1.81% | 300.25 | 8.50 | 50.51 |
| 8. | 30 sept. 2019 | 4.09% | 1.72% | 4.45 | 0.37 | 1.29 |
| 9. | 31 oct. 2019 | -8.93% | 2.04% | 119.08 | 0.88 | -10.23 |
| 10. | 30 nov. 2019 | -4.77% | 3.40% | 45.57 | 5.28 | -15.52 |
| 11. | 31 dic. 2019 | 8.89% | 2.86% | 47.72 | 3.07 | 12.11 |
| 12. | 31 ene. 2020 | -3.62% | -0.16% | 31.37 | 1.61 | 7.11 |
| 13. | 29 feb. 2020 | -17.57% | -8.41% | 382.52 | 90.57 | 186.13 |
| 14. | 31 mar. 2020 | -62.22% | -12.51% | 4,121.98 | 185.44 | 874.30 |
| 15. | 30 abr. 2020 | 43.35% | 12.68% | 1,711.10 | 134.06 | 478.95 |
| 16. | 31 may. 2020 | -21.99% | 4.53% | 574.71 | 11.71 | -82.04 |
| 17. | 30 jun. 2020 | 41.39% | 1.84% | 1,552.74 | 0.54 | 28.88 |
| 18. | 31 jul. 2020 | -13.99% | 5.51% | 255.18 | 19.40 | -70.35 |
| 19. | 31 ago. 2020 | -19.06% | 7.01% | 442.89 | 34.82 | -124.18 |
| 20. | 30 sept. 2020 | -21.35% | -3.92% | 544.53 | 25.29 | 117.34 |
| 21. | 31 oct. 2020 | -8.79% | -2.77% | 116.13 | 15.00 | 41.73 |
| 22. | 30 nov. 2020 | 72.62% | 10.75% | 4,988.96 | 93.10 | 681.51 |
| 23. | 31 dic. 2020 | 9.90% | 3.71% | 62.62 | 6.79 | 20.62 |
| 24. | 31 ene. 2021 | 15.89% | -1.11% | 193.26 | 4.93 | -30.85 |
| 25. | 28 feb. 2021 | 32.65% | 2.61% | 940.46 | 2.26 | 46.10 |
| 26. | 31 mar. 2021 | 0.08% | 4.24% | 3.65 | 9.85 | -5.99 |
| 27. | 30 abr. 2021 | -4.73% | 5.24% | 45.14 | 17.11 | -27.79 |
| 28. | 31 may. 2021 | 2.37% | 0.55% | 0.15 | 0.31 | -0.21 |
| 29. | 30 jun. 2021 | 20.49% | 2.22% | 342.54 | 1.24 | 20.65 |
| 30. | 31 jul. 2021 | -16.53% | 2.27% | 342.94 | 1.37 | -21.65 |
| 31. | 31 ago. 2021 | -1.57% | 2.90% | 12.65 | 3.22 | -6.38 |
| 32. | 30 sept. 2021 | 15.18% | -4.76% | 174.13 | 34.37 | -77.36 |
| 33. | 31 oct. 2021 | 13.35% | 6.91% | 129.24 | 33.74 | 66.03 |
| 34. | 30 nov. 2021 | -11.57% | -0.83% | 183.79 | 3.76 | 26.29 |
| 35. | 31 dic. 2021 | -2.19% | 4.36% | 17.45 | 10.60 | -13.60 |
| 36. | 31 ene. 2022 | 29.94% | -5.26% | 781.55 | 40.51 | -177.92 |
| 37. | 28 feb. 2022 | 16.09% | -3.14% | 198.86 | 17.99 | -59.82 |
| 38. | 31 mar. 2022 | 30.05% | 3.58% | 787.53 | 6.11 | 69.36 |
| 39. | 30 abr. 2022 | -2.91% | -8.80% | 23.94 | 98.04 | 48.45 |
| 40. | 31 may. 2022 | 25.81% | 0.01% | 567.73 | 1.21 | -26.22 |
| 41. | 30 jun. 2022 | -14.86% | -8.39% | 283.78 | 90.21 | 160.00 |
| 42. | 31 jul. 2022 | 11.67% | 9.11% | 93.75 | 64.09 | 77.52 |
| 43. | 31 ago. 2022 | 7.98% | -4.24% | 36.00 | 28.62 | -32.10 |
| 44. | 30 sept. 2022 | -13.27% | -9.34% | 232.65 | 109.11 | 159.32 |
| 45. | 31 oct. 2022 | 18.14% | 7.99% | 261.14 | 47.34 | 111.19 |
| 46. | 30 nov. 2022 | -4.28% | 5.38% | 39.30 | 18.23 | -26.76 |
| 47. | 31 dic. 2022 | -9.17% | -5.90% | 124.37 | 49.04 | 78.10 |
| 48. | 31 ene. 2023 | 2.86% | 6.18% | 0.76 | 25.70 | 4.42 |
| 49. | 28 feb. 2023 | -9.62% | -2.61% | 134.58 | 13.82 | 43.12 |
| 50. | 31 mar. 2023 | 6.92% | 3.51% | 24.31 | 5.76 | 11.83 |
| 51. | 30 abr. 2023 | -1.44% | 1.46% | 11.74 | 0.13 | -1.23 |
| 52. | 31 may. 2023 | -6.29% | 0.25% | 68.47 | 0.74 | 7.10 |
| 53. | 30 jun. 2023 | 2.29% | 4.71% | 0.09 | 13.02 | 1.10 |
| 54. | 31 jul. 2023 | 7.36% | 4.85% | 28.93 | 13.99 | 20.12 |
| 55. | 31 ago. 2023 | -0.54% | -1.77% | 6.37 | 8.28 | 7.26 |
| 56. | 30 sept. 2023 | 3.62% | -4.87% | 2.66 | 35.73 | -9.74 |
| 57. | 31 oct. 2023 | -4.73% | -2.20% | 45.12 | 10.92 | 22.19 |
| 58. | 30 nov. 2023 | -4.30% | 8.92% | 39.55 | 61.03 | -49.13 |
| 59. | 31 dic. 2023 | 1.25% | 4.42% | 0.54 | 11.00 | -2.44 |
| Total (Σ): | 21,965.27 | 1,634.30 | 2,703.97 | |||
Mostrar todo
VarianzaOXY = Σ(ROXY,t–ROXY)2 ÷ (59 – 1)
= 21,965.27 ÷ (59 – 1)
= 378.71
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaOXY, S&P 500 = Σ(ROXY,t–ROXY)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,703.97 ÷ (59 – 1)
= 46.62
Estimación sistemática del riesgo (β)
| VarianzaOXY | 378.71 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaOXY, S&P 500 | 46.62 |
| Coeficiente de correlaciónOXY, S&P 5001 | 0.45 |
| βOXY2 | 1.65 |
| αOXY3 | 0.16% |
Cálculos
1 Coeficiente de correlaciónOXY, S&P 500
= CovarianzaOXY, S&P 500 ÷ (Desviación estándarOXY × Desviación estándarS&P 500)
= 46.62 ÷ (19.46% × 5.31%)
= 0.45
2 βOXY
= CovarianzaOXY, S&P 500 ÷ VarianzaS&P 500
= 46.62 ÷ 28.18
= 1.65
3 αOXY
= PromedioOXY – βOXY × PromedioS&P 500
= 1.99% – 1.65 × 1.11%
= 0.16%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.90% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.54% |
| Riesgo sistemático de Occidental acciones ordinarias | βOXY | 1.65 |
| Tasa de rendimiento esperada de las acciones ordinarias de Occidental3 | E(ROXY) | 19.20% |
1 Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de EE. UU. con cupón fijo en circulación que no vencen ni son rescatables en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).
3 E(ROXY) = RF + βOXY [E(RM) – RF]
= 4.90% + 1.65 [13.54% – 4.90%]
= 19.20%