Modelo de fijación de precios de activos de capital (CAPM)
El modelo de fijación de precios 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 CoStar Group.
Tasas de retorno
CoStar Group Inc., tasas mensuales de retorno
| CoStar Group Inc. (CSGP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCSGP,t1 | DividendoCSGP,t1 | RCSGP,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $34.61 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $34.21 | -1.16% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $36.27 | 6.02% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $36.67 | 1.10% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $81.04 | -2.03% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $77.28 | -4.64% | 3,839.50 | -5.90% | |
| Promedio (R): | 1.68% | 0.67% | ||||
| Desviación estándar: | 8.00% | 5.40% | ||||
| CoStar Group Inc. (CSGP) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioCSGP,t1 | DividendoCSGP,t1 | RCSGP,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $34.61 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $34.21 | -1.16% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $36.27 | 6.02% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $36.67 | 1.10% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $38.12 | 3.95% | 2,705.27 | 2.16% | |
| 5. | 30 jun. 2018 | $41.26 | 8.24% | 2,718.37 | 0.48% | |
| 6. | 31 jul. 2018 | $41.58 | 0.78% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $44.22 | 6.35% | 2,901.52 | 3.03% | |
| 8. | 30 sept. 2018 | $42.08 | -4.84% | 2,913.98 | 0.43% | |
| 9. | 31 oct. 2018 | $36.14 | -14.12% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $36.94 | 2.21% | 2,760.17 | 1.79% | |
| 11. | 31 dic. 2018 | $33.73 | -8.69% | 2,506.85 | -9.18% | |
| 12. | 31 ene. 2019 | $39.07 | 15.83% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $45.75 | 17.10% | 2,784.49 | 2.97% | |
| 14. | 31 mar. 2019 | $46.64 | 1.95% | 2,834.40 | 1.79% | |
| 15. | 30 abr. 2019 | $49.63 | 6.41% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $50.96 | 2.68% | 2,752.06 | -6.58% | |
| 17. | 30 jun. 2019 | $55.41 | 8.73% | 2,941.76 | 6.89% | |
| 18. | 31 jul. 2019 | $61.54 | 11.06% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $61.49 | -0.08% | 2,926.46 | -1.81% | |
| 20. | 30 sept. 2019 | $59.32 | -3.53% | 2,976.74 | 1.72% | |
| 21. | 31 oct. 2019 | $54.95 | -7.37% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $61.29 | 11.54% | 3,140.98 | 3.40% | |
| 23. | 31 dic. 2019 | $59.83 | -2.38% | 3,230.78 | 2.86% | |
| 24. | 31 ene. 2020 | $65.30 | 9.14% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $66.76 | 2.24% | 2,954.22 | -8.41% | |
| 26. | 31 mar. 2020 | $58.72 | -12.04% | 2,584.59 | -12.51% | |
| 27. | 30 abr. 2020 | $64.83 | 10.41% | 2,912.43 | 12.68% | |
| 28. | 31 may. 2020 | $65.68 | 1.31% | 3,044.31 | 4.53% | |
| 29. | 30 jun. 2020 | $71.07 | 8.21% | 3,100.29 | 1.84% | |
| 30. | 31 jul. 2020 | $84.98 | 19.57% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $84.86 | -0.14% | 3,500.31 | 7.01% | |
| 32. | 30 sept. 2020 | $84.85 | -0.01% | 3,363.00 | -3.92% | |
| 33. | 31 oct. 2020 | $82.36 | -2.93% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $91.06 | 10.56% | 3,621.63 | 10.75% | |
| 35. | 31 dic. 2020 | $92.43 | 1.50% | 3,756.07 | 3.71% | |
| 36. | 31 ene. 2021 | $89.97 | -2.66% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $82.38 | -8.44% | 3,811.15 | 2.61% | |
| 38. | 31 mar. 2021 | $82.19 | -0.23% | 3,972.89 | 4.24% | |
| 39. | 30 abr. 2021 | $85.44 | 3.95% | 4,181.17 | 5.24% | |
| 40. | 31 may. 2021 | $85.40 | -0.05% | 4,204.11 | 0.55% | |
| 41. | 30 jun. 2021 | $82.82 | -3.02% | 4,297.50 | 2.22% | |
| 42. | 31 jul. 2021 | $88.85 | 7.28% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $84.74 | -4.63% | 4,522.68 | 2.90% | |
| 44. | 30 sept. 2021 | $86.06 | 1.56% | 4,307.54 | -4.76% | |
| 45. | 31 oct. 2021 | $86.05 | -0.01% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $77.76 | -9.63% | 4,567.00 | -0.83% | |
| 47. | 31 dic. 2021 | $79.03 | 1.63% | 4,766.18 | 4.36% | |
| 48. | 31 ene. 2022 | $70.16 | -11.22% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $61.01 | -13.04% | 4,373.94 | -3.14% | |
| 50. | 31 mar. 2022 | $66.61 | 9.18% | 4,530.41 | 3.58% | |
| 51. | 30 abr. 2022 | $63.62 | -4.49% | 4,131.93 | -8.80% | |
| 52. | 31 may. 2022 | $60.94 | -4.21% | 4,132.15 | 0.01% | |
| 53. | 30 jun. 2022 | $60.41 | -0.87% | 3,785.38 | -8.39% | |
| 54. | 31 jul. 2022 | $72.59 | 20.16% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $69.64 | -4.06% | 3,955.00 | -4.24% | |
| 56. | 30 sept. 2022 | $69.65 | 0.01% | 3,585.62 | -9.34% | |
| 57. | 31 oct. 2022 | $82.72 | 18.77% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $81.04 | -2.03% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $77.28 | -4.64% | 3,839.50 | -5.90% | |
| Promedio (R): | 1.68% | 0.67% | ||||
| Desviación estándar: | 8.00% | 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 CSGP 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
CoStar Group Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RCSGP,t | RS&P 500,t | (RCSGP,t–RCSGP)2 | (RS&P 500,t–RS&P 500)2 | (RCSGP,t–RCSGP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -1.16% | -3.89% | 8.02 | 20.81 | 12.92 |
| 2. | 31 mar. 2018 | 6.02% | -2.69% | 18.88 | 11.26 | -14.58 |
| 3. | 30 abr. 2018 | 1.10% | 0.27% | 0.33 | 0.16 | 0.23 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | -2.03% | 5.38% | 13.74 | 22.17 | -17.46 |
| 59. | 31 dic. 2022 | -4.64% | -5.90% | 39.89 | 43.08 | 41.46 |
| Total (Σ): | 3,711.35 | 1,691.48 | 1,478.53 | |||
| t | Fecha | RCSGP,t | RS&P 500,t | (RCSGP,t–RCSGP)2 | (RS&P 500,t–RS&P 500)2 | (RCSGP,t–RCSGP)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | -1.16% | -3.89% | 8.02 | 20.81 | 12.92 |
| 2. | 31 mar. 2018 | 6.02% | -2.69% | 18.88 | 11.26 | -14.58 |
| 3. | 30 abr. 2018 | 1.10% | 0.27% | 0.33 | 0.16 | 0.23 |
| 4. | 31 may. 2018 | 3.95% | 2.16% | 5.19 | 2.23 | 3.40 |
| 5. | 30 jun. 2018 | 8.24% | 0.48% | 43.04 | 0.03 | -1.20 |
| 6. | 31 jul. 2018 | 0.78% | 3.60% | 0.81 | 8.62 | -2.64 |
| 7. | 31 ago. 2018 | 6.35% | 3.03% | 21.83 | 5.57 | 11.03 |
| 8. | 30 sept. 2018 | -4.84% | 0.43% | 42.46 | 0.06 | 1.55 |
| 9. | 31 oct. 2018 | -14.12% | -6.94% | 249.40 | 57.87 | 120.13 |
| 10. | 30 nov. 2018 | 2.21% | 1.79% | 0.29 | 1.25 | 0.60 |
| 11. | 31 dic. 2018 | -8.69% | -9.18% | 107.46 | 96.91 | 102.05 |
| 12. | 31 ene. 2019 | 15.83% | 7.87% | 200.37 | 51.87 | 101.94 |
| 13. | 28 feb. 2019 | 17.10% | 2.97% | 237.81 | 5.32 | 35.56 |
| 14. | 31 mar. 2019 | 1.95% | 1.79% | 0.07 | 1.27 | 0.30 |
| 15. | 30 abr. 2019 | 6.41% | 3.93% | 22.41 | 10.66 | 15.46 |
| 16. | 31 may. 2019 | 2.68% | -6.58% | 1.01 | 52.48 | -7.27 |
| 17. | 30 jun. 2019 | 8.73% | 6.89% | 49.79 | 38.77 | 43.93 |
| 18. | 31 jul. 2019 | 11.06% | 1.31% | 88.11 | 0.42 | 6.07 |
| 19. | 31 ago. 2019 | -0.08% | -1.81% | 3.09 | 6.13 | 4.35 |
| 20. | 30 sept. 2019 | -3.53% | 1.72% | 27.10 | 1.11 | -5.47 |
| 21. | 31 oct. 2019 | -7.37% | 2.04% | 81.78 | 1.89 | -12.45 |
| 22. | 30 nov. 2019 | 11.54% | 3.40% | 97.25 | 7.50 | 27.00 |
| 23. | 31 dic. 2019 | -2.38% | 2.86% | 16.47 | 4.81 | -8.90 |
| 24. | 31 ene. 2020 | 9.14% | -0.16% | 55.74 | 0.69 | -6.19 |
| 25. | 29 feb. 2020 | 2.24% | -8.41% | 0.31 | 82.40 | -5.08 |
| 26. | 31 mar. 2020 | -12.04% | -12.51% | 188.23 | 173.67 | 180.80 |
| 27. | 30 abr. 2020 | 10.41% | 12.68% | 76.19 | 144.43 | 104.90 |
| 28. | 31 may. 2020 | 1.31% | 4.53% | 0.13 | 14.91 | -1.41 |
| 29. | 30 jun. 2020 | 8.21% | 1.84% | 42.64 | 1.37 | 7.65 |
| 30. | 31 jul. 2020 | 19.57% | 5.51% | 320.26 | 23.46 | 86.68 |
| 31. | 31 ago. 2020 | -0.14% | 7.01% | 3.30 | 40.19 | -11.52 |
| 32. | 30 sept. 2020 | -0.01% | -3.92% | 2.85 | 21.06 | 7.75 |
| 33. | 31 oct. 2020 | -2.93% | -2.77% | 21.26 | 11.79 | 15.83 |
| 34. | 30 nov. 2020 | 10.56% | 10.75% | 78.98 | 101.77 | 89.65 |
| 35. | 31 dic. 2020 | 1.50% | 3.71% | 0.03 | 9.28 | -0.52 |
| 36. | 31 ene. 2021 | -2.66% | -1.11% | 18.82 | 3.17 | 7.72 |
| 37. | 28 feb. 2021 | -8.44% | 2.61% | 102.26 | 3.77 | -19.64 |
| 38. | 31 mar. 2021 | -0.23% | 4.24% | 3.64 | 12.80 | -6.82 |
| 39. | 30 abr. 2021 | 3.95% | 5.24% | 5.19 | 20.94 | 10.42 |
| 40. | 31 may. 2021 | -0.05% | 0.55% | 2.97 | 0.01 | 0.20 |
| 41. | 30 jun. 2021 | -3.02% | 2.22% | 22.07 | 2.42 | -7.30 |
| 42. | 31 jul. 2021 | 7.28% | 2.27% | 31.41 | 2.59 | 9.01 |
| 43. | 31 ago. 2021 | -4.63% | 2.90% | 39.72 | 4.98 | -14.07 |
| 44. | 30 sept. 2021 | 1.56% | -4.76% | 0.01 | 29.42 | 0.64 |
| 45. | 31 oct. 2021 | -0.01% | 6.91% | 2.85 | 39.03 | -10.55 |
| 46. | 30 nov. 2021 | -9.63% | -0.83% | 127.93 | 2.25 | 16.97 |
| 47. | 31 dic. 2021 | 1.63% | 4.36% | 0.00 | 13.65 | -0.16 |
| 48. | 31 ene. 2022 | -11.22% | -5.26% | 166.41 | 35.11 | 76.43 |
| 49. | 28 feb. 2022 | -13.04% | -3.14% | 216.62 | 14.46 | 55.97 |
| 50. | 31 mar. 2022 | 9.18% | 3.58% | 56.29 | 8.47 | 21.84 |
| 51. | 30 abr. 2022 | -4.49% | -8.80% | 38.01 | 89.54 | 58.34 |
| 52. | 31 may. 2022 | -4.21% | 0.01% | 34.68 | 0.44 | 3.89 |
| 53. | 30 jun. 2022 | -0.87% | -8.39% | 6.48 | 82.06 | 23.06 |
| 54. | 31 jul. 2022 | 20.16% | 9.11% | 341.72 | 71.32 | 156.11 |
| 55. | 31 ago. 2022 | -4.06% | -4.24% | 32.95 | 24.11 | 28.19 |
| 56. | 30 sept. 2022 | 0.01% | -9.34% | 2.76 | 100.12 | 16.63 |
| 57. | 31 oct. 2022 | 18.77% | 7.99% | 292.03 | 53.58 | 125.08 |
| 58. | 30 nov. 2022 | -2.03% | 5.38% | 13.74 | 22.17 | -17.46 |
| 59. | 31 dic. 2022 | -4.64% | -5.90% | 39.89 | 43.08 | 41.46 |
| Total (Σ): | 3,711.35 | 1,691.48 | 1,478.53 | |||
Mostrar todo
VarianzaCSGP = Σ(RCSGP,t–RCSGP)2 ÷ (59 – 1)
= 3,711.35 ÷ (59 – 1)
= 63.99
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaCSGP, S&P 500 = Σ(RCSGP,t–RCSGP)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 1,478.53 ÷ (59 – 1)
= 25.49
Estimación sistemática del riesgo (β)
| VarianzaCSGP | 63.99 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaCSGP, S&P 500 | 25.49 |
| Coeficiente de correlaciónCSGP, S&P 5001 | 0.59 |
| βCSGP2 | 0.87 |
| αCSGP3 | 1.09% |
Cálculos
1 Coeficiente de correlaciónCSGP, S&P 500
= CovarianzaCSGP, S&P 500 ÷ (Desviación estándarCSGP × Desviación estándarS&P 500)
= 25.49 ÷ (8.00% × 5.40%)
= 0.59
2 βCSGP
= CovarianzaCSGP, S&P 500 ÷ VarianzaS&P 500
= 25.49 ÷ 29.16
= 0.87
3 αCSGP
= PromedioCSGP – βCSGP × PromedioS&P 500
= 1.68% – 0.87 × 0.67%
= 1.09%
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 CoStar Group acciones ordinarias | βCSGP | 0.87 |
| Tasa de rendimiento esperada de las acciones ordinarias de CoStar Group3 | E(RCSGP) | 12.64% |
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(RCSGP) = RF + βCSGP [E(RM) – RF]
= 4.67% + 0.87 [13.79% – 4.67%]
= 12.64%