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 LVSC.
Tasas de retorno
Las Vegas Sands Corp., tasas mensuales de retorno
| Las Vegas Sands Corp. (LVS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioLVS,t1 | DividendoLVS,t1 | RLVS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $77.52 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $72.81 | -6.08% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $71.90 | $0.75 | -0.22% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $73.33 | 1.99% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $46.84 | 23.23% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $48.07 | 2.63% | 3,839.50 | -5.90% | |
| Promedio (R): | -0.05% | 0.67% | ||||
| Desviación estándar: | 10.72% | 5.40% | ||||
| Las Vegas Sands Corp. (LVS) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioLVS,t1 | DividendoLVS,t1 | RLVS,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $77.52 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $72.81 | -6.08% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $71.90 | $0.75 | -0.22% | 2,640.87 | -2.69% |
| 3. | 30 abr. 2018 | $73.33 | 1.99% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $80.61 | 9.93% | 2,705.27 | 2.16% | |
| 5. | 30 jun. 2018 | $76.36 | $0.75 | -4.34% | 2,718.37 | 0.48% |
| 6. | 31 jul. 2018 | $71.90 | -5.84% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $65.42 | -9.01% | 2,901.52 | 3.03% | |
| 8. | 30 sept. 2018 | $59.33 | $0.75 | -8.16% | 2,913.98 | 0.43% |
| 9. | 31 oct. 2018 | $51.03 | -13.99% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $54.94 | 7.66% | 2,760.17 | 1.79% | |
| 11. | 31 dic. 2018 | $52.05 | $0.75 | -3.90% | 2,506.85 | -9.18% |
| 12. | 31 ene. 2019 | $58.36 | 12.12% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $61.43 | 5.26% | 2,784.49 | 2.97% | |
| 14. | 31 mar. 2019 | $60.96 | $0.77 | 0.49% | 2,834.40 | 1.79% |
| 15. | 30 abr. 2019 | $67.05 | 9.99% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $55.00 | -17.97% | 2,752.06 | -6.58% | |
| 17. | 30 jun. 2019 | $59.09 | $0.77 | 8.84% | 2,941.76 | 6.89% |
| 18. | 31 jul. 2019 | $60.44 | 2.28% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $55.47 | -8.22% | 2,926.46 | -1.81% | |
| 20. | 30 sept. 2019 | $57.76 | $0.77 | 5.52% | 2,976.74 | 1.72% |
| 21. | 31 oct. 2019 | $61.84 | 7.06% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $62.75 | 1.47% | 3,140.98 | 3.40% | |
| 23. | 31 dic. 2019 | $69.04 | $0.77 | 11.25% | 3,230.78 | 2.86% |
| 24. | 31 ene. 2020 | $65.31 | -5.40% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $58.31 | -10.72% | 2,954.22 | -8.41% | |
| 26. | 31 mar. 2020 | $42.47 | $0.79 | -25.81% | 2,584.59 | -12.51% |
| 27. | 30 abr. 2020 | $48.02 | 13.07% | 2,912.43 | 12.68% | |
| 28. | 31 may. 2020 | $47.94 | -0.17% | 3,044.31 | 4.53% | |
| 29. | 30 jun. 2020 | $45.54 | -5.01% | 3,100.29 | 1.84% | |
| 30. | 31 jul. 2020 | $43.64 | -4.17% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $50.71 | 16.20% | 3,500.31 | 7.01% | |
| 32. | 30 sept. 2020 | $46.66 | -7.99% | 3,363.00 | -3.92% | |
| 33. | 31 oct. 2020 | $48.06 | 3.00% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $55.71 | 15.92% | 3,621.63 | 10.75% | |
| 35. | 31 dic. 2020 | $59.60 | 6.98% | 3,756.07 | 3.71% | |
| 36. | 31 ene. 2021 | $48.09 | -19.31% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $62.60 | 30.17% | 3,811.15 | 2.61% | |
| 38. | 31 mar. 2021 | $60.76 | -2.94% | 3,972.89 | 4.24% | |
| 39. | 30 abr. 2021 | $61.26 | 0.82% | 4,181.17 | 5.24% | |
| 40. | 31 may. 2021 | $57.75 | -5.73% | 4,204.11 | 0.55% | |
| 41. | 30 jun. 2021 | $52.69 | -8.76% | 4,297.50 | 2.22% | |
| 42. | 31 jul. 2021 | $42.35 | -19.62% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $44.61 | 5.34% | 4,522.68 | 2.90% | |
| 44. | 30 sept. 2021 | $36.60 | -17.96% | 4,307.54 | -4.76% | |
| 45. | 31 oct. 2021 | $38.81 | 6.04% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $35.62 | -8.22% | 4,567.00 | -0.83% | |
| 47. | 31 dic. 2021 | $37.64 | 5.67% | 4,766.18 | 4.36% | |
| 48. | 31 ene. 2022 | $43.80 | 16.37% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $42.86 | -2.15% | 4,373.94 | -3.14% | |
| 50. | 31 mar. 2022 | $38.87 | -9.31% | 4,530.41 | 3.58% | |
| 51. | 30 abr. 2022 | $35.43 | -8.85% | 4,131.93 | -8.80% | |
| 52. | 31 may. 2022 | $35.46 | 0.08% | 4,132.15 | 0.01% | |
| 53. | 30 jun. 2022 | $33.59 | -5.27% | 3,785.38 | -8.39% | |
| 54. | 31 jul. 2022 | $37.69 | 12.21% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $37.63 | -0.16% | 3,955.00 | -4.24% | |
| 56. | 30 sept. 2022 | $37.52 | -0.29% | 3,585.62 | -9.34% | |
| 57. | 31 oct. 2022 | $38.01 | 1.31% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $46.84 | 23.23% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $48.07 | 2.63% | 3,839.50 | -5.90% | |
| Promedio (R): | -0.05% | 0.67% | ||||
| Desviación estándar: | 10.72% | 5.40% | ||||
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 LVS 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
Las Vegas Sands Corp., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RLVS,t | RS&P 500,t | (RLVS,t–RLVS)2 | (RS&P 500,t–RS&P 500)2 | (RLVS,t–RLVS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -6.08% | -3.89% | 36.37 | 20.81 | 27.51 |
| 2. | 31 mar. 2018 | -0.22% | -2.69% | 0.03 | 11.26 | 0.59 |
| 3. | 30 abr. 2018 | 1.99% | 0.27% | 4.14 | 0.16 | -0.80 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | 23.23% | 5.38% | 541.77 | 22.17 | 109.60 |
| 59. | 31 dic. 2022 | 2.63% | -5.90% | 7.14 | 43.08 | -17.53 |
| Total (Σ): | 6,665.35 | 1,691.48 | 1,873.27 | |||
| t | Fecha | RLVS,t | RS&P 500,t | (RLVS,t–RLVS)2 | (RS&P 500,t–RS&P 500)2 | (RLVS,t–RLVS)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -6.08% | -3.89% | 36.37 | 20.81 | 27.51 |
| 2. | 31 mar. 2018 | -0.22% | -2.69% | 0.03 | 11.26 | 0.59 |
| 3. | 30 abr. 2018 | 1.99% | 0.27% | 4.14 | 0.16 | -0.80 |
| 4. | 31 may. 2018 | 9.93% | 2.16% | 99.46 | 2.23 | 14.90 |
| 5. | 30 jun. 2018 | -4.34% | 0.48% | 18.46 | 0.03 | 0.78 |
| 6. | 31 jul. 2018 | -5.84% | 3.60% | 33.59 | 8.62 | -17.01 |
| 7. | 31 ago. 2018 | -9.01% | 3.03% | 80.41 | 5.57 | -21.16 |
| 8. | 30 sept. 2018 | -8.16% | 0.43% | 65.89 | 0.06 | 1.93 |
| 9. | 31 oct. 2018 | -13.99% | -6.94% | 194.44 | 57.87 | 106.07 |
| 10. | 30 nov. 2018 | 7.66% | 1.79% | 59.41 | 1.25 | 8.63 |
| 11. | 31 dic. 2018 | -3.90% | -9.18% | 14.82 | 96.91 | 37.90 |
| 12. | 31 ene. 2019 | 12.12% | 7.87% | 148.07 | 51.87 | 87.63 |
| 13. | 28 feb. 2019 | 5.26% | 2.97% | 28.15 | 5.32 | 12.24 |
| 14. | 31 mar. 2019 | 0.49% | 1.79% | 0.28 | 1.27 | 0.60 |
| 15. | 30 abr. 2019 | 9.99% | 3.93% | 100.71 | 10.66 | 32.76 |
| 16. | 31 may. 2019 | -17.97% | -6.58% | 321.35 | 52.48 | 129.87 |
| 17. | 30 jun. 2019 | 8.84% | 6.89% | 78.88 | 38.77 | 55.30 |
| 18. | 31 jul. 2019 | 2.28% | 1.31% | 5.43 | 0.42 | 1.51 |
| 19. | 31 ago. 2019 | -8.22% | -1.81% | 66.87 | 6.13 | 20.25 |
| 20. | 30 sept. 2019 | 5.52% | 1.72% | 30.93 | 1.11 | 5.85 |
| 21. | 31 oct. 2019 | 7.06% | 2.04% | 50.54 | 1.89 | 9.79 |
| 22. | 30 nov. 2019 | 1.47% | 3.40% | 2.30 | 7.50 | 4.15 |
| 23. | 31 dic. 2019 | 11.25% | 2.86% | 127.61 | 4.81 | 24.77 |
| 24. | 31 ene. 2020 | -5.40% | -0.16% | 28.70 | 0.69 | 4.44 |
| 25. | 29 feb. 2020 | -10.72% | -8.41% | 113.91 | 82.40 | 96.88 |
| 26. | 31 mar. 2020 | -25.81% | -12.51% | 663.83 | 173.67 | 339.55 |
| 27. | 30 abr. 2020 | 13.07% | 12.68% | 171.96 | 144.43 | 157.59 |
| 28. | 31 may. 2020 | -0.17% | 4.53% | 0.01 | 14.91 | -0.47 |
| 29. | 30 jun. 2020 | -5.01% | 1.84% | 24.61 | 1.37 | -5.82 |
| 30. | 31 jul. 2020 | -4.17% | 5.51% | 17.03 | 23.46 | -19.99 |
| 31. | 31 ago. 2020 | 16.20% | 7.01% | 263.93 | 40.19 | 103.00 |
| 32. | 30 sept. 2020 | -7.99% | -3.92% | 63.06 | 21.06 | 36.45 |
| 33. | 31 oct. 2020 | 3.00% | -2.77% | 9.28 | 11.79 | -10.46 |
| 34. | 30 nov. 2020 | 15.92% | 10.75% | 254.82 | 101.77 | 161.03 |
| 35. | 31 dic. 2020 | 6.98% | 3.71% | 49.39 | 9.28 | 21.40 |
| 36. | 31 ene. 2021 | -19.31% | -1.11% | 371.21 | 3.17 | 34.30 |
| 37. | 28 feb. 2021 | 30.17% | 2.61% | 913.12 | 3.77 | 58.70 |
| 38. | 31 mar. 2021 | -2.94% | 4.24% | 8.38 | 12.80 | -10.35 |
| 39. | 30 abr. 2021 | 0.82% | 5.24% | 0.75 | 20.94 | 3.97 |
| 40. | 31 may. 2021 | -5.73% | 0.55% | 32.31 | 0.01 | 0.67 |
| 41. | 30 jun. 2021 | -8.76% | 2.22% | 75.98 | 2.42 | -13.55 |
| 42. | 31 jul. 2021 | -19.62% | 2.27% | 383.33 | 2.59 | -31.49 |
| 43. | 31 ago. 2021 | 5.34% | 2.90% | 28.96 | 4.98 | 12.01 |
| 44. | 30 sept. 2021 | -17.96% | -4.76% | 320.78 | 29.42 | 97.14 |
| 45. | 31 oct. 2021 | 6.04% | 6.91% | 37.01 | 39.03 | 38.01 |
| 46. | 30 nov. 2021 | -8.22% | -0.83% | 66.82 | 2.25 | 12.26 |
| 47. | 31 dic. 2021 | 5.67% | 4.36% | 32.68 | 13.65 | 21.12 |
| 48. | 31 ene. 2022 | 16.37% | -5.26% | 269.32 | 35.11 | -97.24 |
| 49. | 28 feb. 2022 | -2.15% | -3.14% | 4.41 | 14.46 | 7.99 |
| 50. | 31 mar. 2022 | -9.31% | 3.58% | 85.82 | 8.47 | -26.96 |
| 51. | 30 abr. 2022 | -8.85% | -8.80% | 77.52 | 89.54 | 83.31 |
| 52. | 31 may. 2022 | 0.08% | 0.01% | 0.02 | 0.44 | -0.09 |
| 53. | 30 jun. 2022 | -5.27% | -8.39% | 27.33 | 82.06 | 47.36 |
| 54. | 31 jul. 2022 | 12.21% | 9.11% | 150.10 | 71.32 | 103.46 |
| 55. | 31 ago. 2022 | -0.16% | -4.24% | 0.01 | 24.11 | 0.56 |
| 56. | 30 sept. 2022 | -0.29% | -9.34% | 0.06 | 100.12 | 2.47 |
| 57. | 31 oct. 2022 | 1.31% | 7.99% | 1.83 | 53.58 | 9.89 |
| 58. | 30 nov. 2022 | 23.23% | 5.38% | 541.77 | 22.17 | 109.60 |
| 59. | 31 dic. 2022 | 2.63% | -5.90% | 7.14 | 43.08 | -17.53 |
| Total (Σ): | 6,665.35 | 1,691.48 | 1,873.27 | |||
Mostrar todo
VarianzaLVS = Σ(RLVS,t–RLVS)2 ÷ (59 – 1)
= 6,665.35 ÷ (59 – 1)
= 114.92
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaLVS, S&P 500 = Σ(RLVS,t–RLVS)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,873.27 ÷ (59 – 1)
= 32.30
Estimación sistemática del riesgo (β)
| VarianzaLVS | 114.92 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaLVS, S&P 500 | 32.30 |
| Coeficiente de correlaciónLVS, S&P 5001 | 0.56 |
| βLVS2 | 1.11 |
| αLVS3 | -0.78% |
Cálculos
1 Coeficiente de correlaciónLVS, S&P 500
= CovarianzaLVS, S&P 500 ÷ (Desviación estándarLVS × Desviación estándarS&P 500)
= 32.30 ÷ (10.72% × 5.40%)
= 0.56
2 βLVS
= CovarianzaLVS, S&P 500 ÷ VarianzaS&P 500
= 32.30 ÷ 29.16
= 1.11
3 αLVS
= PromedioLVS – βLVS × PromedioS&P 500
= -0.05% – 1.11 × 0.67%
= -0.78%
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) | 13.79% |
| Riesgo sistemático de LVSC acciones ordinarias | βLVS | 1.11 |
| Tasa de rendimiento esperada de las acciones ordinarias de LVSC3 | E(RLVS) | 14.77% |
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(RLVS) = RF + βLVS [E(RM) – RF]
= 4.67% + 1.11 [13.79% – 4.67%]
= 14.77%