Modelo de fijación de precios de activos de capital (CAPM)
El modelo de valoración de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida en activos de riesgo como las acciones ordinarias de TPL.
Tasas de retorno
Texas Pacific Land Corp., tasas mensuales de retorno
| Texas Pacific Land Corp. (TPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioTPL,t1 | DividendoTPL,t1 | RTPL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $231.80 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $247.87 | 6.93% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $257.88 | $2.00 | 4.85% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $267.45 | 3.71% | 2,945.83 | 3.93% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | $557.32 | $1.0833 | -9.25% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $524.15 | -5.95% | 4,769.83 | 4.42% | |
| Promedio (R): | 2.78% | 1.11% | ||||
| Desviación estándar: | 16.07% | 5.31% | ||||
| Texas Pacific Land Corp. (TPL) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioTPL,t1 | DividendoTPL,t1 | RTPL,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2019 | $231.80 | 2,704.10 | ||||
| 1. | 28 feb. 2019 | $247.87 | 6.93% | 2,784.49 | 2.97% | |
| 2. | 31 mar. 2019 | $257.88 | $2.00 | 4.85% | 2,834.40 | 1.79% |
| 3. | 30 abr. 2019 | $267.45 | 3.71% | 2,945.83 | 3.93% | |
| 4. | 31 may. 2019 | $245.67 | -8.14% | 2,752.06 | -6.58% | |
| 5. | 30 jun. 2019 | $262.33 | 6.78% | 2,941.76 | 6.89% | |
| 6. | 31 jul. 2019 | $265.73 | 1.30% | 2,980.38 | 1.31% | |
| 7. | 31 ago. 2019 | $218.40 | -17.81% | 2,926.46 | -1.81% | |
| 8. | 30 sept. 2019 | $216.52 | -0.86% | 2,976.74 | 1.72% | |
| 9. | 31 oct. 2019 | $189.68 | -12.40% | 3,037.56 | 2.04% | |
| 10. | 30 nov. 2019 | $224.99 | 18.62% | 3,140.98 | 3.40% | |
| 11. | 31 dic. 2019 | $260.41 | 15.74% | 3,230.78 | 2.86% | |
| 12. | 31 ene. 2020 | $251.90 | -3.27% | 3,225.52 | -0.16% | |
| 13. | 29 feb. 2020 | $231.93 | -7.93% | 2,954.22 | -8.41% | |
| 14. | 31 mar. 2020 | $126.67 | $5.3333 | -43.08% | 2,584.59 | -12.51% |
| 15. | 30 abr. 2020 | $189.88 | 49.90% | 2,912.43 | 12.68% | |
| 16. | 31 may. 2020 | $195.46 | 2.94% | 3,044.31 | 4.53% | |
| 17. | 30 jun. 2020 | $198.23 | 1.42% | 3,100.29 | 1.84% | |
| 18. | 31 jul. 2020 | $177.66 | -10.38% | 3,271.12 | 5.51% | |
| 19. | 31 ago. 2020 | $175.57 | -1.18% | 3,500.31 | 7.01% | |
| 20. | 30 sept. 2020 | $150.52 | -14.27% | 3,363.00 | -3.92% | |
| 21. | 31 oct. 2020 | $150.14 | -0.25% | 3,269.96 | -2.77% | |
| 22. | 30 nov. 2020 | $203.31 | 35.41% | 3,621.63 | 10.75% | |
| 23. | 31 dic. 2020 | $242.33 | $3.3333 | 20.83% | 3,756.07 | 3.71% |
| 24. | 31 ene. 2021 | $277.41 | 14.48% | 3,714.24 | -1.11% | |
| 25. | 28 feb. 2021 | $368.01 | 32.66% | 3,811.15 | 2.61% | |
| 26. | 31 mar. 2021 | $529.81 | $0.9167 | 44.22% | 3,972.89 | 4.24% |
| 27. | 30 abr. 2021 | $513.38 | -3.10% | 4,181.17 | 5.24% | |
| 28. | 31 may. 2021 | $484.37 | -5.65% | 4,204.11 | 0.55% | |
| 29. | 30 jun. 2021 | $533.25 | $0.9167 | 10.28% | 4,297.50 | 2.22% |
| 30. | 31 jul. 2021 | $497.52 | -6.70% | 4,395.26 | 2.27% | |
| 31. | 31 ago. 2021 | $453.25 | -8.90% | 4,522.68 | 2.90% | |
| 32. | 30 sept. 2021 | $403.12 | $0.9167 | -10.86% | 4,307.54 | -4.76% |
| 33. | 31 oct. 2021 | $424.56 | 5.32% | 4,605.38 | 6.91% | |
| 34. | 30 nov. 2021 | $402.92 | -5.10% | 4,567.00 | -0.83% | |
| 35. | 31 dic. 2021 | $416.29 | $0.9167 | 3.55% | 4,766.18 | 4.36% |
| 36. | 31 ene. 2022 | $358.33 | -13.92% | 4,515.55 | -5.26% | |
| 37. | 28 feb. 2022 | $396.24 | 10.58% | 4,373.94 | -3.14% | |
| 38. | 31 mar. 2022 | $450.70 | $1.00 | 14.00% | 4,530.41 | 3.58% |
| 39. | 30 abr. 2022 | $455.53 | 1.07% | 4,131.93 | -8.80% | |
| 40. | 31 may. 2022 | $522.00 | 14.59% | 4,132.15 | 0.01% | |
| 41. | 30 jun. 2022 | $496.01 | $7.6667 | -3.51% | 3,785.38 | -8.39% |
| 42. | 31 jul. 2022 | $611.28 | 23.24% | 4,130.29 | 9.11% | |
| 43. | 31 ago. 2022 | $613.49 | 0.36% | 3,955.00 | -4.24% | |
| 44. | 30 sept. 2022 | $592.41 | $1.00 | -3.27% | 3,585.62 | -9.34% |
| 45. | 31 oct. 2022 | $767.96 | 29.63% | 3,871.98 | 7.99% | |
| 46. | 30 nov. 2022 | $864.18 | 12.53% | 4,080.11 | 5.38% | |
| 47. | 31 dic. 2022 | $781.41 | $1.00 | -9.46% | 3,839.50 | -5.90% |
| 48. | 31 ene. 2023 | $665.28 | -14.86% | 4,076.60 | 6.18% | |
| 49. | 28 feb. 2023 | $593.40 | -10.80% | 3,970.15 | -2.61% | |
| 50. | 31 mar. 2023 | $567.01 | $1.0833 | -4.26% | 4,109.31 | 3.51% |
| 51. | 30 abr. 2023 | $492.55 | -13.13% | 4,169.48 | 1.46% | |
| 52. | 31 may. 2023 | $434.57 | -11.77% | 4,179.83 | 0.25% | |
| 53. | 30 jun. 2023 | $438.83 | $1.0833 | 1.23% | 4,376.86 | 4.71% |
| 54. | 31 jul. 2023 | $502.10 | 14.42% | 4,588.96 | 4.85% | |
| 55. | 31 ago. 2023 | $628.25 | $1.0833 | 25.34% | 4,507.66 | -1.77% |
| 56. | 30 sept. 2023 | $607.85 | -3.25% | 4,288.05 | -4.87% | |
| 57. | 31 oct. 2023 | $615.32 | 1.23% | 4,193.80 | -2.20% | |
| 58. | 30 nov. 2023 | $557.32 | $1.0833 | -9.25% | 4,567.80 | 8.92% |
| 59. | 31 dic. 2023 | $524.15 | -5.95% | 4,769.83 | 4.42% | |
| Promedio (R): | 2.78% | 1.11% | ||||
| Desviación estándar: | 16.07% | 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 TPL 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
Texas Pacific Land Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RTPL,t | RS&P 500,t | (RTPL,t–RTPL)2 | (RS&P 500,t–RS&P 500)2 | (RTPL,t–RTPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 6.93% | 2.97% | 17.27 | 3.49 | 7.76 |
| 2. | 31 mar. 2019 | 4.85% | 1.79% | 4.28 | 0.47 | 1.42 |
| 3. | 30 abr. 2019 | 3.71% | 3.93% | 0.87 | 7.98 | 2.64 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2023 | -9.25% | 8.92% | 144.64 | 61.03 | -93.95 |
| 59. | 31 dic. 2023 | -5.95% | 4.42% | 76.18 | 11.00 | -28.95 |
| Total (Σ): | 14,984.07 | 1,634.30 | 2,655.68 | |||
| t | Fecha | RTPL,t | RS&P 500,t | (RTPL,t–RTPL)2 | (RS&P 500,t–RS&P 500)2 | (RTPL,t–RTPL)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2019 | 6.93% | 2.97% | 17.27 | 3.49 | 7.76 |
| 2. | 31 mar. 2019 | 4.85% | 1.79% | 4.28 | 0.47 | 1.42 |
| 3. | 30 abr. 2019 | 3.71% | 3.93% | 0.87 | 7.98 | 2.64 |
| 4. | 31 may. 2019 | -8.14% | -6.58% | 119.25 | 59.04 | 83.91 |
| 5. | 30 jun. 2019 | 6.78% | 6.89% | 16.04 | 33.49 | 23.18 |
| 6. | 31 jul. 2019 | 1.30% | 1.31% | 2.19 | 0.04 | -0.31 |
| 7. | 31 ago. 2019 | -17.81% | -1.81% | 423.86 | 8.50 | 60.01 |
| 8. | 30 sept. 2019 | -0.86% | 1.72% | 13.23 | 0.37 | -2.23 |
| 9. | 31 oct. 2019 | -12.40% | 2.04% | 230.21 | 0.88 | -14.22 |
| 10. | 30 nov. 2019 | 18.62% | 3.40% | 250.87 | 5.28 | 36.41 |
| 11. | 31 dic. 2019 | 15.74% | 2.86% | 168.12 | 3.07 | 22.73 |
| 12. | 31 ene. 2020 | -3.27% | -0.16% | 36.54 | 1.61 | 7.67 |
| 13. | 29 feb. 2020 | -7.93% | -8.41% | 114.58 | 90.57 | 101.87 |
| 14. | 31 mar. 2020 | -43.08% | -12.51% | 2,103.27 | 185.44 | 624.53 |
| 15. | 30 abr. 2020 | 49.90% | 12.68% | 2,220.74 | 134.06 | 545.64 |
| 16. | 31 may. 2020 | 2.94% | 4.53% | 0.03 | 11.71 | 0.55 |
| 17. | 30 jun. 2020 | 1.42% | 1.84% | 1.85 | 0.54 | -1.00 |
| 18. | 31 jul. 2020 | -10.38% | 5.51% | 173.01 | 19.40 | -57.93 |
| 19. | 31 ago. 2020 | -1.18% | 7.01% | 15.63 | 34.82 | -23.33 |
| 20. | 30 sept. 2020 | -14.27% | -3.92% | 290.51 | 25.29 | 85.71 |
| 21. | 31 oct. 2020 | -0.25% | -2.77% | 9.18 | 15.00 | 11.73 |
| 22. | 30 nov. 2020 | 35.41% | 10.75% | 1,065.17 | 93.10 | 314.91 |
| 23. | 31 dic. 2020 | 20.83% | 3.71% | 325.99 | 6.79 | 47.06 |
| 24. | 31 ene. 2021 | 14.48% | -1.11% | 136.88 | 4.93 | -25.97 |
| 25. | 28 feb. 2021 | 32.66% | 2.61% | 892.97 | 2.26 | 44.92 |
| 26. | 31 mar. 2021 | 44.22% | 4.24% | 1,717.16 | 9.85 | 130.04 |
| 27. | 30 abr. 2021 | -3.10% | 5.24% | 34.55 | 17.11 | -24.31 |
| 28. | 31 may. 2021 | -5.65% | 0.55% | 71.02 | 0.31 | 4.70 |
| 29. | 30 jun. 2021 | 10.28% | 2.22% | 56.31 | 1.24 | 8.37 |
| 30. | 31 jul. 2021 | -6.70% | 2.27% | 89.81 | 1.37 | -11.08 |
| 31. | 31 ago. 2021 | -8.90% | 2.90% | 136.30 | 3.22 | -20.93 |
| 32. | 30 sept. 2021 | -10.86% | -4.76% | 185.90 | 34.37 | 79.94 |
| 33. | 31 oct. 2021 | 5.32% | 6.91% | 6.46 | 33.74 | 14.76 |
| 34. | 30 nov. 2021 | -5.10% | -0.83% | 61.99 | 3.76 | 15.27 |
| 35. | 31 dic. 2021 | 3.55% | 4.36% | 0.59 | 10.60 | 2.50 |
| 36. | 31 ene. 2022 | -13.92% | -5.26% | 278.88 | 40.51 | 106.28 |
| 37. | 28 feb. 2022 | 10.58% | -3.14% | 60.89 | 17.99 | -33.10 |
| 38. | 31 mar. 2022 | 14.00% | 3.58% | 125.89 | 6.11 | 27.73 |
| 39. | 30 abr. 2022 | 1.07% | -8.80% | 2.91 | 98.04 | 16.88 |
| 40. | 31 may. 2022 | 14.59% | 0.01% | 139.60 | 1.21 | -13.00 |
| 41. | 30 jun. 2022 | -3.51% | -8.39% | 39.52 | 90.21 | 59.71 |
| 42. | 31 jul. 2022 | 23.24% | 9.11% | 418.73 | 64.09 | 163.82 |
| 43. | 31 ago. 2022 | 0.36% | -4.24% | 5.83 | 28.62 | 12.92 |
| 44. | 30 sept. 2022 | -3.27% | -9.34% | 36.60 | 109.11 | 63.19 |
| 45. | 31 oct. 2022 | 29.63% | 7.99% | 721.28 | 47.34 | 184.79 |
| 46. | 30 nov. 2022 | 12.53% | 5.38% | 95.11 | 18.23 | 41.64 |
| 47. | 31 dic. 2022 | -9.46% | -5.90% | 149.79 | 49.04 | 85.71 |
| 48. | 31 ene. 2023 | -14.86% | 6.18% | 311.11 | 25.70 | -89.42 |
| 49. | 28 feb. 2023 | -10.80% | -2.61% | 184.45 | 13.82 | 50.48 |
| 50. | 31 mar. 2023 | -4.26% | 3.51% | 49.58 | 5.76 | -16.89 |
| 51. | 30 abr. 2023 | -13.13% | 1.46% | 253.09 | 0.13 | -5.70 |
| 52. | 31 may. 2023 | -11.77% | 0.25% | 211.64 | 0.74 | 12.48 |
| 53. | 30 jun. 2023 | 1.23% | 4.71% | 2.39 | 13.02 | -5.58 |
| 54. | 31 jul. 2023 | 14.42% | 4.85% | 135.52 | 13.99 | 43.54 |
| 55. | 31 ago. 2023 | 25.34% | -1.77% | 509.12 | 8.28 | -64.93 |
| 56. | 30 sept. 2023 | -3.25% | -4.87% | 36.29 | 35.73 | 36.01 |
| 57. | 31 oct. 2023 | 1.23% | -2.20% | 2.40 | 10.92 | 5.11 |
| 58. | 30 nov. 2023 | -9.25% | 8.92% | 144.64 | 61.03 | -93.95 |
| 59. | 31 dic. 2023 | -5.95% | 4.42% | 76.18 | 11.00 | -28.95 |
| Total (Σ): | 14,984.07 | 1,634.30 | 2,655.68 | |||
Mostrar todo
VarianzaTPL = Σ(RTPL,t–RTPL)2 ÷ (59 – 1)
= 14,984.07 ÷ (59 – 1)
= 258.35
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaTPL, S&P 500 = Σ(RTPL,t–RTPL)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,655.68 ÷ (59 – 1)
= 45.79
Estimación sistemática del riesgo (β)
| VarianzaTPL | 258.35 |
| VarianzaS&P 500 | 28.18 |
| CovarianzaTPL, S&P 500 | 45.79 |
| Coeficiente de correlaciónTPL, S&P 5001 | 0.54 |
| βTPL2 | 1.62 |
| αTPL3 | 0.98% |
Cálculos
1 Coeficiente de correlaciónTPL, S&P 500
= CovarianzaTPL, S&P 500 ÷ (Desviación estándarTPL × Desviación estándarS&P 500)
= 45.79 ÷ (16.07% × 5.31%)
= 0.54
2 βTPL
= CovarianzaTPL, S&P 500 ÷ VarianzaS&P 500
= 45.79 ÷ 28.18
= 1.62
3 αTPL
= PromedioTPL – βTPL × PromedioS&P 500
= 2.78% – 1.62 × 1.11%
= 0.98%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.67% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.77% |
| Riesgo sistemático de TPL acciones ordinarias | βTPL | 1.62 |
| Tasa de rendimiento esperada sobre las acciones ordinarias de TPL3 | E(RTPL) | 19.46% |
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(RTPL) = RF + βTPL [E(RM) – RF]
= 4.67% + 1.62 [13.77% – 4.67%]
= 19.46%