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 Paycom.
Tasas de retorno
Paycom Software Inc., tasas mensuales de retorno
| Paycom Software Inc. (PAYC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioPAYC,t1 | DividendoPAYC,t1 | RPAYC,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $91.64 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $98.92 | 7.94% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $107.39 | 8.56% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $114.21 | 6.35% | 2,648.05 | 0.27% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | $339.10 | -1.99% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $310.31 | -8.49% | 3,839.50 | -5.90% | |
| Promedio (R): | 2.98% | 0.67% | ||||
| Desviación estándar: | 13.66% | 5.40% | ||||
| Paycom Software Inc. (PAYC) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioPAYC,t1 | DividendoPAYC,t1 | RPAYC,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 ene. 2018 | $91.64 | 2,823.81 | ||||
| 1. | 28 feb. 2018 | $98.92 | 7.94% | 2,713.83 | -3.89% | |
| 2. | 31 mar. 2018 | $107.39 | 8.56% | 2,640.87 | -2.69% | |
| 3. | 30 abr. 2018 | $114.21 | 6.35% | 2,648.05 | 0.27% | |
| 4. | 31 may. 2018 | $105.47 | -7.65% | 2,705.27 | 2.16% | |
| 5. | 30 jun. 2018 | $98.83 | -6.30% | 2,718.37 | 0.48% | |
| 6. | 31 jul. 2018 | $106.25 | 7.51% | 2,816.29 | 3.60% | |
| 7. | 31 ago. 2018 | $155.12 | 46.00% | 2,901.52 | 3.03% | |
| 8. | 30 sept. 2018 | $155.41 | 0.19% | 2,913.98 | 0.43% | |
| 9. | 31 oct. 2018 | $125.20 | -19.44% | 2,711.74 | -6.94% | |
| 10. | 30 nov. 2018 | $132.77 | 6.05% | 2,760.17 | 1.79% | |
| 11. | 31 dic. 2018 | $122.45 | -7.77% | 2,506.85 | -9.18% | |
| 12. | 31 ene. 2019 | $148.24 | 21.06% | 2,704.10 | 7.87% | |
| 13. | 28 feb. 2019 | $181.73 | 22.59% | 2,784.49 | 2.97% | |
| 14. | 31 mar. 2019 | $189.13 | 4.07% | 2,834.40 | 1.79% | |
| 15. | 30 abr. 2019 | $202.53 | 7.09% | 2,945.83 | 3.93% | |
| 16. | 31 may. 2019 | $212.10 | 4.73% | 2,752.06 | -6.58% | |
| 17. | 30 jun. 2019 | $226.72 | 6.89% | 2,941.76 | 6.89% | |
| 18. | 31 jul. 2019 | $240.75 | 6.19% | 2,980.38 | 1.31% | |
| 19. | 31 ago. 2019 | $250.12 | 3.89% | 2,926.46 | -1.81% | |
| 20. | 30 sept. 2019 | $209.49 | -16.24% | 2,976.74 | 1.72% | |
| 21. | 31 oct. 2019 | $211.53 | 0.97% | 3,037.56 | 2.04% | |
| 22. | 30 nov. 2019 | $276.81 | 30.86% | 3,140.98 | 3.40% | |
| 23. | 31 dic. 2019 | $264.76 | -4.35% | 3,230.78 | 2.86% | |
| 24. | 31 ene. 2020 | $318.16 | 20.17% | 3,225.52 | -0.16% | |
| 25. | 29 feb. 2020 | $282.65 | -11.16% | 2,954.22 | -8.41% | |
| 26. | 31 mar. 2020 | $202.01 | -28.53% | 2,584.59 | -12.51% | |
| 27. | 30 abr. 2020 | $261.02 | 29.21% | 2,912.43 | 12.68% | |
| 28. | 31 may. 2020 | $297.23 | 13.87% | 3,044.31 | 4.53% | |
| 29. | 30 jun. 2020 | $309.73 | 4.21% | 3,100.29 | 1.84% | |
| 30. | 31 jul. 2020 | $284.37 | -8.19% | 3,271.12 | 5.51% | |
| 31. | 31 ago. 2020 | $299.46 | 5.31% | 3,500.31 | 7.01% | |
| 32. | 30 sept. 2020 | $311.30 | 3.95% | 3,363.00 | -3.92% | |
| 33. | 31 oct. 2020 | $364.09 | 16.96% | 3,269.96 | -2.77% | |
| 34. | 30 nov. 2020 | $417.08 | 14.55% | 3,621.63 | 10.75% | |
| 35. | 31 dic. 2020 | $452.25 | 8.43% | 3,756.07 | 3.71% | |
| 36. | 31 ene. 2021 | $379.74 | -16.03% | 3,714.24 | -1.11% | |
| 37. | 28 feb. 2021 | $374.24 | -1.45% | 3,811.15 | 2.61% | |
| 38. | 31 mar. 2021 | $370.06 | -1.12% | 3,972.89 | 4.24% | |
| 39. | 30 abr. 2021 | $384.41 | 3.88% | 4,181.17 | 5.24% | |
| 40. | 31 may. 2021 | $329.60 | -14.26% | 4,204.11 | 0.55% | |
| 41. | 30 jun. 2021 | $363.47 | 10.28% | 4,297.50 | 2.22% | |
| 42. | 31 jul. 2021 | $400.00 | 10.05% | 4,395.26 | 2.27% | |
| 43. | 31 ago. 2021 | $488.90 | 22.23% | 4,522.68 | 2.90% | |
| 44. | 30 sept. 2021 | $495.75 | 1.40% | 4,307.54 | -4.76% | |
| 45. | 31 oct. 2021 | $547.85 | 10.51% | 4,605.38 | 6.91% | |
| 46. | 30 nov. 2021 | $437.48 | -20.15% | 4,567.00 | -0.83% | |
| 47. | 31 dic. 2021 | $415.19 | -5.10% | 4,766.18 | 4.36% | |
| 48. | 31 ene. 2022 | $335.30 | -19.24% | 4,515.55 | -5.26% | |
| 49. | 28 feb. 2022 | $339.21 | 1.17% | 4,373.94 | -3.14% | |
| 50. | 31 mar. 2022 | $346.38 | 2.11% | 4,530.41 | 3.58% | |
| 51. | 30 abr. 2022 | $281.47 | -18.74% | 4,131.93 | -8.80% | |
| 52. | 31 may. 2022 | $284.34 | 1.02% | 4,132.15 | 0.01% | |
| 53. | 30 jun. 2022 | $280.12 | -1.48% | 3,785.38 | -8.39% | |
| 54. | 31 jul. 2022 | $330.49 | 17.98% | 4,130.29 | 9.11% | |
| 55. | 31 ago. 2022 | $351.20 | 6.27% | 3,955.00 | -4.24% | |
| 56. | 30 sept. 2022 | $329.99 | -6.04% | 3,585.62 | -9.34% | |
| 57. | 31 oct. 2022 | $346.00 | 4.85% | 3,871.98 | 7.99% | |
| 58. | 30 nov. 2022 | $339.10 | -1.99% | 4,080.11 | 5.38% | |
| 59. | 31 dic. 2022 | $310.31 | -8.49% | 3,839.50 | -5.90% | |
| Promedio (R): | 2.98% | 0.67% | ||||
| Desviación estándar: | 13.66% | 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 PAYC 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
Paycom Software Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RPAYC,t | RS&P 500,t | (RPAYC,t–RPAYC)2 | (RS&P 500,t–RS&P 500)2 | (RPAYC,t–RPAYC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | 7.94% | -3.89% | 24.68 | 20.81 | -22.66 |
| 2. | 31 mar. 2018 | 8.56% | -2.69% | 31.20 | 11.26 | -18.74 |
| 3. | 30 abr. 2018 | 6.35% | 0.27% | 11.38 | 0.16 | -1.33 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 58. | 30 nov. 2022 | -1.99% | 5.38% | 24.71 | 22.17 | -23.41 |
| 59. | 31 dic. 2022 | -8.49% | -5.90% | 131.48 | 43.08 | 75.26 |
| Total (Σ): | 10,822.04 | 1,691.48 | 2,299.49 | |||
| t | Fecha | RPAYC,t | RS&P 500,t | (RPAYC,t–RPAYC)2 | (RS&P 500,t–RS&P 500)2 | (RPAYC,t–RPAYC)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 28 feb. 2018 | 7.94% | -3.89% | 24.68 | 20.81 | -22.66 |
| 2. | 31 mar. 2018 | 8.56% | -2.69% | 31.20 | 11.26 | -18.74 |
| 3. | 30 abr. 2018 | 6.35% | 0.27% | 11.38 | 0.16 | -1.33 |
| 4. | 31 may. 2018 | -7.65% | 2.16% | 112.98 | 2.23 | -15.88 |
| 5. | 30 jun. 2018 | -6.30% | 0.48% | 85.97 | 0.03 | 1.69 |
| 6. | 31 jul. 2018 | 7.51% | 3.60% | 20.53 | 8.62 | 13.30 |
| 7. | 31 ago. 2018 | 46.00% | 3.03% | 1,850.61 | 5.57 | 101.51 |
| 8. | 30 sept. 2018 | 0.19% | 0.43% | 7.78 | 0.06 | 0.66 |
| 9. | 31 oct. 2018 | -19.44% | -6.94% | 502.45 | 57.87 | 170.51 |
| 10. | 30 nov. 2018 | 6.05% | 1.79% | 9.42 | 1.25 | 3.44 |
| 11. | 31 dic. 2018 | -7.77% | -9.18% | 115.55 | 96.91 | 105.82 |
| 12. | 31 ene. 2019 | 21.06% | 7.87% | 327.07 | 51.87 | 130.25 |
| 13. | 28 feb. 2019 | 22.59% | 2.97% | 384.76 | 5.32 | 45.24 |
| 14. | 31 mar. 2019 | 4.07% | 1.79% | 1.20 | 1.27 | 1.23 |
| 15. | 30 abr. 2019 | 7.09% | 3.93% | 16.88 | 10.66 | 13.41 |
| 16. | 31 may. 2019 | 4.73% | -6.58% | 3.06 | 52.48 | -12.67 |
| 17. | 30 jun. 2019 | 6.89% | 6.89% | 15.34 | 38.77 | 24.39 |
| 18. | 31 jul. 2019 | 6.19% | 1.31% | 10.32 | 0.42 | 2.08 |
| 19. | 31 ago. 2019 | 3.89% | -1.81% | 0.84 | 6.13 | -2.27 |
| 20. | 30 sept. 2019 | -16.24% | 1.72% | 369.44 | 1.11 | -20.21 |
| 21. | 31 oct. 2019 | 0.97% | 2.04% | 4.01 | 1.89 | -2.76 |
| 22. | 30 nov. 2019 | 30.86% | 3.40% | 777.54 | 7.50 | 76.35 |
| 23. | 31 dic. 2019 | -4.35% | 2.86% | 53.72 | 4.81 | -16.07 |
| 24. | 31 ene. 2020 | 20.17% | -0.16% | 295.59 | 0.69 | -14.26 |
| 25. | 29 feb. 2020 | -11.16% | -8.41% | 199.87 | 82.40 | 128.34 |
| 26. | 31 mar. 2020 | -28.53% | -12.51% | 992.66 | 173.67 | 415.21 |
| 27. | 30 abr. 2020 | 29.21% | 12.68% | 688.27 | 144.43 | 315.28 |
| 28. | 31 may. 2020 | 13.87% | 4.53% | 118.72 | 14.91 | 42.08 |
| 29. | 30 jun. 2020 | 4.21% | 1.84% | 1.51 | 1.37 | 1.44 |
| 30. | 31 jul. 2020 | -8.19% | 5.51% | 124.64 | 23.46 | -54.07 |
| 31. | 31 ago. 2020 | 5.31% | 7.01% | 5.43 | 40.19 | 14.77 |
| 32. | 30 sept. 2020 | 3.95% | -3.92% | 0.95 | 21.06 | -4.48 |
| 33. | 31 oct. 2020 | 16.96% | -2.77% | 195.48 | 11.79 | -48.00 |
| 34. | 30 nov. 2020 | 14.55% | 10.75% | 134.04 | 101.77 | 116.79 |
| 35. | 31 dic. 2020 | 8.43% | 3.71% | 29.77 | 9.28 | 16.62 |
| 36. | 31 ene. 2021 | -16.03% | -1.11% | 361.37 | 3.17 | 33.84 |
| 37. | 28 feb. 2021 | -1.45% | 2.61% | 19.58 | 3.77 | -8.60 |
| 38. | 31 mar. 2021 | -1.12% | 4.24% | 16.76 | 12.80 | -14.64 |
| 39. | 30 abr. 2021 | 3.88% | 5.24% | 0.81 | 20.94 | 4.12 |
| 40. | 31 may. 2021 | -14.26% | 0.55% | 297.04 | 0.01 | 2.03 |
| 41. | 30 jun. 2021 | 10.28% | 2.22% | 53.28 | 2.42 | 11.35 |
| 42. | 31 jul. 2021 | 10.05% | 2.27% | 50.04 | 2.59 | 11.38 |
| 43. | 31 ago. 2021 | 22.23% | 2.90% | 370.50 | 4.98 | 42.97 |
| 44. | 30 sept. 2021 | 1.40% | -4.76% | 2.48 | 29.42 | 8.54 |
| 45. | 31 oct. 2021 | 10.51% | 6.91% | 56.74 | 39.03 | 47.06 |
| 46. | 30 nov. 2021 | -20.15% | -0.83% | 534.65 | 2.25 | 34.68 |
| 47. | 31 dic. 2021 | -5.10% | 4.36% | 65.15 | 13.65 | -29.82 |
| 48. | 31 ene. 2022 | -19.24% | -5.26% | 493.65 | 35.11 | 131.65 |
| 49. | 28 feb. 2022 | 1.17% | -3.14% | 3.28 | 14.46 | 6.88 |
| 50. | 31 mar. 2022 | 2.11% | 3.58% | 0.74 | 8.47 | -2.51 |
| 51. | 30 abr. 2022 | -18.74% | -8.80% | 471.59 | 89.54 | 205.48 |
| 52. | 31 may. 2022 | 1.02% | 0.01% | 3.83 | 0.44 | 1.29 |
| 53. | 30 jun. 2022 | -1.48% | -8.39% | 19.90 | 82.06 | 40.41 |
| 54. | 31 jul. 2022 | 17.98% | 9.11% | 225.15 | 71.32 | 126.72 |
| 55. | 31 ago. 2022 | 6.27% | -4.24% | 10.82 | 24.11 | -16.16 |
| 56. | 30 sept. 2022 | -6.04% | -9.34% | 81.29 | 100.12 | 90.21 |
| 57. | 31 oct. 2022 | 4.85% | 7.99% | 3.52 | 53.58 | 13.73 |
| 58. | 30 nov. 2022 | -1.99% | 5.38% | 24.71 | 22.17 | -23.41 |
| 59. | 31 dic. 2022 | -8.49% | -5.90% | 131.48 | 43.08 | 75.26 |
| Total (Σ): | 10,822.04 | 1,691.48 | 2,299.49 | |||
Mostrar todo
VarianzaPAYC = Σ(RPAYC,t–RPAYC)2 ÷ (59 – 1)
= 10,822.04 ÷ (59 – 1)
= 186.59
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16
CovarianzaPAYC, S&P 500 = Σ(RPAYC,t–RPAYC)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,299.49 ÷ (59 – 1)
= 39.65
Estimación sistemática del riesgo (β)
| VarianzaPAYC | 186.59 |
| VarianzaS&P 500 | 29.16 |
| CovarianzaPAYC, S&P 500 | 39.65 |
| Coeficiente de correlaciónPAYC, S&P 5001 | 0.54 |
| βPAYC2 | 1.36 |
| αPAYC3 | 2.07% |
Cálculos
1 Coeficiente de correlaciónPAYC, S&P 500
= CovarianzaPAYC, S&P 500 ÷ (Desviación estándarPAYC × Desviación estándarS&P 500)
= 39.65 ÷ (13.66% × 5.40%)
= 0.54
2 βPAYC
= CovarianzaPAYC, S&P 500 ÷ VarianzaS&P 500
= 39.65 ÷ 29.16
= 1.36
3 αPAYC
= PromedioPAYC – βPAYC × PromedioS&P 500
= 2.98% – 1.36 × 0.67%
= 2.07%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.62% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.69% |
| Riesgo sistemático de Paycom acciones ordinarias | βPAYC | 1.36 |
| Tasa de rendimiento esperada de las acciones ordinarias de Paycom3 | E(RPAYC) | 16.95% |
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(RPAYC) = RF + βPAYC [E(RM) – RF]
= 4.62% + 1.36 [13.69% – 4.62%]
= 16.95%