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 sobre activos de riesgo como las acciones ordinarias de Ulta Beauty.
Tasas de retorno
Ulta Beauty Inc., tasas mensuales de retorno
| Ulta Beauty Inc. (ULTA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioULTA,t1 | DividendoULTA,t1 | RULTA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 28 feb. 2017 | $273.43 | 2,363.64 | ||||
| 1. | 31 mar. 2017 | $285.23 | 4.32% | 2,362.72 | -0.04% | |
| 2. | 30 abr. 2017 | $281.44 | -1.33% | 2,384.20 | 0.91% | |
| 3. | 31 may. 2017 | $304.84 | 8.31% | 2,411.80 | 1.16% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2022 | $469.07 | 0.91% | 3,839.50 | -5.90% | |
| 71. | 31 ene. 2023 | $513.96 | 9.57% | 4,076.60 | 6.18% | |
| Promedio (R): | 1.50% | 0.90% | ||||
| Desviación estándar: | 10.95% | 5.01% | ||||
| Ulta Beauty Inc. (ULTA) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioULTA,t1 | DividendoULTA,t1 | RULTA,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 28 feb. 2017 | $273.43 | 2,363.64 | ||||
| 1. | 31 mar. 2017 | $285.23 | 4.32% | 2,362.72 | -0.04% | |
| 2. | 30 abr. 2017 | $281.44 | -1.33% | 2,384.20 | 0.91% | |
| 3. | 31 may. 2017 | $304.84 | 8.31% | 2,411.80 | 1.16% | |
| 4. | 30 jun. 2017 | $287.34 | -5.74% | 2,423.41 | 0.48% | |
| 5. | 31 jul. 2017 | $251.21 | -12.57% | 2,470.30 | 1.93% | |
| 6. | 31 ago. 2017 | $221.01 | -12.02% | 2,471.65 | 0.05% | |
| 7. | 30 sept. 2017 | $226.06 | 2.28% | 2,519.36 | 1.93% | |
| 8. | 31 oct. 2017 | $201.79 | -10.74% | 2,575.26 | 2.22% | |
| 9. | 30 nov. 2017 | $221.71 | 9.87% | 2,647.58 | 2.81% | |
| 10. | 31 dic. 2017 | $223.66 | 0.88% | 2,673.61 | 0.98% | |
| 11. | 31 ene. 2018 | $222.10 | -0.70% | 2,823.81 | 5.62% | |
| 12. | 28 feb. 2018 | $203.35 | -8.44% | 2,713.83 | -3.89% | |
| 13. | 31 mar. 2018 | $204.27 | 0.45% | 2,640.87 | -2.69% | |
| 14. | 30 abr. 2018 | $250.91 | 22.83% | 2,648.05 | 0.27% | |
| 15. | 31 may. 2018 | $246.91 | -1.59% | 2,705.27 | 2.16% | |
| 16. | 30 jun. 2018 | $233.46 | -5.45% | 2,718.37 | 0.48% | |
| 17. | 31 jul. 2018 | $244.39 | 4.68% | 2,816.29 | 3.60% | |
| 18. | 31 ago. 2018 | $260.00 | 6.39% | 2,901.52 | 3.03% | |
| 19. | 30 sept. 2018 | $282.12 | 8.51% | 2,913.98 | 0.43% | |
| 20. | 31 oct. 2018 | $274.52 | -2.69% | 2,711.74 | -6.94% | |
| 21. | 30 nov. 2018 | $297.79 | 8.48% | 2,760.17 | 1.79% | |
| 22. | 31 dic. 2018 | $244.84 | -17.78% | 2,506.85 | -9.18% | |
| 23. | 31 ene. 2019 | $291.92 | 19.23% | 2,704.10 | 7.87% | |
| 24. | 28 feb. 2019 | $312.49 | 7.05% | 2,784.49 | 2.97% | |
| 25. | 31 mar. 2019 | $348.73 | 11.60% | 2,834.40 | 1.79% | |
| 26. | 30 abr. 2019 | $348.98 | 0.07% | 2,945.83 | 3.93% | |
| 27. | 31 may. 2019 | $333.38 | -4.47% | 2,752.06 | -6.58% | |
| 28. | 30 jun. 2019 | $346.89 | 4.05% | 2,941.76 | 6.89% | |
| 29. | 31 jul. 2019 | $349.25 | 0.68% | 2,980.38 | 1.31% | |
| 30. | 31 ago. 2019 | $237.73 | -31.93% | 2,926.46 | -1.81% | |
| 31. | 30 sept. 2019 | $250.65 | 5.43% | 2,976.74 | 1.72% | |
| 32. | 31 oct. 2019 | $233.15 | -6.98% | 3,037.56 | 2.04% | |
| 33. | 30 nov. 2019 | $233.86 | 0.30% | 3,140.98 | 3.40% | |
| 34. | 31 dic. 2019 | $253.14 | 8.24% | 3,230.78 | 2.86% | |
| 35. | 31 ene. 2020 | $267.91 | 5.83% | 3,225.52 | -0.16% | |
| 36. | 29 feb. 2020 | $257.09 | -4.04% | 2,954.22 | -8.41% | |
| 37. | 31 mar. 2020 | $175.70 | -31.66% | 2,584.59 | -12.51% | |
| 38. | 30 abr. 2020 | $217.92 | 24.03% | 2,912.43 | 12.68% | |
| 39. | 31 may. 2020 | $244.01 | 11.97% | 3,044.31 | 4.53% | |
| 40. | 30 jun. 2020 | $203.42 | -16.63% | 3,100.29 | 1.84% | |
| 41. | 31 jul. 2020 | $192.99 | -5.13% | 3,271.12 | 5.51% | |
| 42. | 31 ago. 2020 | $232.18 | 20.31% | 3,500.31 | 7.01% | |
| 43. | 30 sept. 2020 | $223.98 | -3.53% | 3,363.00 | -3.92% | |
| 44. | 31 oct. 2020 | $206.77 | -7.68% | 3,269.96 | -2.77% | |
| 45. | 30 nov. 2020 | $275.40 | 33.19% | 3,621.63 | 10.75% | |
| 46. | 31 dic. 2020 | $287.16 | 4.27% | 3,756.07 | 3.71% | |
| 47. | 31 ene. 2021 | $279.76 | -2.58% | 3,714.24 | -1.11% | |
| 48. | 28 feb. 2021 | $322.33 | 15.22% | 3,811.15 | 2.61% | |
| 49. | 31 mar. 2021 | $309.17 | -4.08% | 3,972.89 | 4.24% | |
| 50. | 30 abr. 2021 | $329.35 | 6.53% | 4,181.17 | 5.24% | |
| 51. | 31 may. 2021 | $345.36 | 4.86% | 4,204.11 | 0.55% | |
| 52. | 30 jun. 2021 | $345.77 | 0.12% | 4,297.50 | 2.22% | |
| 53. | 31 jul. 2021 | $335.80 | -2.88% | 4,395.26 | 2.27% | |
| 54. | 31 ago. 2021 | $387.31 | 15.34% | 4,522.68 | 2.90% | |
| 55. | 30 sept. 2021 | $360.92 | -6.81% | 4,307.54 | -4.76% | |
| 56. | 31 oct. 2021 | $367.36 | 1.78% | 4,605.38 | 6.91% | |
| 57. | 30 nov. 2021 | $383.95 | 4.52% | 4,567.00 | -0.83% | |
| 58. | 31 dic. 2021 | $412.34 | 7.39% | 4,766.18 | 4.36% | |
| 59. | 31 ene. 2022 | $363.74 | -11.79% | 4,515.55 | -5.26% | |
| 60. | 28 feb. 2022 | $374.50 | 2.96% | 4,373.94 | -3.14% | |
| 61. | 31 mar. 2022 | $398.22 | 6.33% | 4,530.41 | 3.58% | |
| 62. | 30 abr. 2022 | $396.80 | -0.36% | 4,131.93 | -8.80% | |
| 63. | 31 may. 2022 | $423.10 | 6.63% | 4,132.15 | 0.01% | |
| 64. | 30 jun. 2022 | $385.48 | -8.89% | 3,785.38 | -8.39% | |
| 65. | 31 jul. 2022 | $388.91 | 0.89% | 4,130.29 | 9.11% | |
| 66. | 31 ago. 2022 | $419.87 | 7.96% | 3,955.00 | -4.24% | |
| 67. | 30 sept. 2022 | $401.19 | -4.45% | 3,585.62 | -9.34% | |
| 68. | 31 oct. 2022 | $419.37 | 4.53% | 3,871.98 | 7.99% | |
| 69. | 30 nov. 2022 | $464.84 | 10.84% | 4,080.11 | 5.38% | |
| 70. | 31 dic. 2022 | $469.07 | 0.91% | 3,839.50 | -5.90% | |
| 71. | 31 ene. 2023 | $513.96 | 9.57% | 4,076.60 | 6.18% | |
| Promedio (R): | 1.50% | 0.90% | ||||
| Desviación estándar: | 10.95% | 5.01% | ||||
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 ULTA 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
Ulta Beauty Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RULTA,t | RS&P 500,t | (RULTA,t–RULTA)2 | (RS&P 500,t–RS&P 500)2 | (RULTA,t–RULTA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2017 | 4.32% | -0.04% | 7.91 | 0.87 | -2.63 |
| 2. | 30 abr. 2017 | -1.33% | 0.91% | 8.02 | 0.00 | -0.04 |
| 3. | 31 may. 2017 | 8.31% | 1.16% | 46.40 | 0.07 | 1.79 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 70. | 31 dic. 2022 | 0.91% | -5.90% | 0.35 | 46.14 | 4.03 |
| 71. | 31 ene. 2023 | 9.57% | 6.18% | 65.08 | 27.88 | 42.60 |
| Total (Σ): | 8,390.96 | 1,754.14 | 2,258.16 | |||
| t | Fecha | RULTA,t | RS&P 500,t | (RULTA,t–RULTA)2 | (RS&P 500,t–RS&P 500)2 | (RULTA,t–RULTA)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 mar. 2017 | 4.32% | -0.04% | 7.91 | 0.87 | -2.63 |
| 2. | 30 abr. 2017 | -1.33% | 0.91% | 8.02 | 0.00 | -0.04 |
| 3. | 31 may. 2017 | 8.31% | 1.16% | 46.40 | 0.07 | 1.79 |
| 4. | 30 jun. 2017 | -5.74% | 0.48% | 52.47 | 0.17 | 3.00 |
| 5. | 31 jul. 2017 | -12.57% | 1.93% | 198.15 | 1.08 | -14.63 |
| 6. | 31 ago. 2017 | -12.02% | 0.05% | 182.91 | 0.71 | 11.37 |
| 7. | 30 sept. 2017 | 2.28% | 1.93% | 0.61 | 1.07 | 0.81 |
| 8. | 31 oct. 2017 | -10.74% | 2.22% | 149.79 | 1.75 | -16.20 |
| 9. | 30 nov. 2017 | 9.87% | 2.81% | 70.04 | 3.66 | 16.01 |
| 10. | 31 dic. 2017 | 0.88% | 0.98% | 0.39 | 0.01 | -0.05 |
| 11. | 31 ene. 2018 | -0.70% | 5.62% | 4.84 | 22.30 | -10.39 |
| 12. | 28 feb. 2018 | -8.44% | -3.89% | 98.90 | 22.94 | 47.64 |
| 13. | 31 mar. 2018 | 0.45% | -2.69% | 1.10 | 12.84 | 3.76 |
| 14. | 30 abr. 2018 | 22.83% | 0.27% | 454.96 | 0.39 | -13.30 |
| 15. | 31 may. 2018 | -1.59% | 2.16% | 9.59 | 1.60 | -3.92 |
| 16. | 30 jun. 2018 | -5.45% | 0.48% | 48.30 | 0.17 | 2.86 |
| 17. | 31 jul. 2018 | 4.68% | 3.60% | 10.11 | 7.33 | 8.61 |
| 18. | 31 ago. 2018 | 6.39% | 3.03% | 23.86 | 4.54 | 10.41 |
| 19. | 30 sept. 2018 | 8.51% | 0.43% | 49.07 | 0.22 | -3.26 |
| 20. | 31 oct. 2018 | -2.69% | -6.94% | 17.61 | 61.40 | 32.88 |
| 21. | 30 nov. 2018 | 8.48% | 1.79% | 48.63 | 0.79 | 6.21 |
| 22. | 31 dic. 2018 | -17.78% | -9.18% | 371.86 | 101.46 | 194.24 |
| 23. | 31 ene. 2019 | 19.23% | 7.87% | 314.22 | 48.63 | 123.61 |
| 24. | 28 feb. 2019 | 7.05% | 2.97% | 30.73 | 4.32 | 11.52 |
| 25. | 31 mar. 2019 | 11.60% | 1.79% | 101.90 | 0.80 | 9.06 |
| 26. | 30 abr. 2019 | 0.07% | 3.93% | 2.05 | 9.22 | -4.34 |
| 27. | 31 may. 2019 | -4.47% | -6.58% | 35.68 | 55.85 | 44.64 |
| 28. | 30 jun. 2019 | 4.05% | 6.89% | 6.50 | 35.97 | 15.29 |
| 29. | 31 jul. 2019 | 0.68% | 1.31% | 0.68 | 0.17 | -0.34 |
| 30. | 31 ago. 2019 | -31.93% | -1.81% | 1,117.84 | 7.31 | 90.42 |
| 31. | 30 sept. 2019 | 5.43% | 1.72% | 15.46 | 0.68 | 3.24 |
| 32. | 31 oct. 2019 | -6.98% | 2.04% | 71.99 | 1.32 | -9.74 |
| 33. | 30 nov. 2019 | 0.30% | 3.40% | 1.44 | 6.30 | -3.01 |
| 34. | 31 dic. 2019 | 8.24% | 2.86% | 45.45 | 3.86 | 13.24 |
| 35. | 31 ene. 2020 | 5.83% | -0.16% | 18.77 | 1.12 | -4.58 |
| 36. | 29 feb. 2020 | -4.04% | -8.41% | 30.71 | 86.61 | 51.57 |
| 37. | 31 mar. 2020 | -31.66% | -12.51% | 1,099.65 | 179.75 | 444.60 |
| 38. | 30 abr. 2020 | 24.03% | 12.68% | 507.46 | 138.98 | 265.57 |
| 39. | 31 may. 2020 | 11.97% | 4.53% | 109.61 | 13.20 | 38.03 |
| 40. | 30 jun. 2020 | -16.63% | 1.84% | 328.96 | 0.89 | -17.11 |
| 41. | 31 jul. 2020 | -5.13% | 5.51% | 43.96 | 21.30 | -30.60 |
| 42. | 31 ago. 2020 | 20.31% | 7.01% | 353.59 | 37.35 | 114.91 |
| 43. | 30 sept. 2020 | -3.53% | -3.92% | 25.35 | 23.21 | 24.26 |
| 44. | 31 oct. 2020 | -7.68% | -2.77% | 84.39 | 13.41 | 33.64 |
| 45. | 30 nov. 2020 | 33.19% | 10.75% | 1,004.17 | 97.21 | 312.43 |
| 46. | 31 dic. 2020 | 4.27% | 3.71% | 7.66 | 7.93 | 7.80 |
| 47. | 31 ene. 2021 | -2.58% | -1.11% | 16.64 | 4.04 | 8.20 |
| 48. | 28 feb. 2021 | 15.22% | 2.61% | 188.07 | 2.94 | 23.50 |
| 49. | 31 mar. 2021 | -4.08% | 4.24% | 31.20 | 11.21 | -18.70 |
| 50. | 30 abr. 2021 | 6.53% | 5.24% | 25.24 | 18.90 | 21.84 |
| 51. | 31 may. 2021 | 4.86% | 0.55% | 11.28 | 0.12 | -1.16 |
| 52. | 30 jun. 2021 | 0.12% | 2.22% | 1.92 | 1.76 | -1.84 |
| 53. | 31 jul. 2021 | -2.88% | 2.27% | 19.24 | 1.90 | -6.05 |
| 54. | 31 ago. 2021 | 15.34% | 2.90% | 191.45 | 4.02 | 27.73 |
| 55. | 30 sept. 2021 | -6.81% | -4.76% | 69.16 | 31.95 | 47.01 |
| 56. | 31 oct. 2021 | 1.78% | 6.91% | 0.08 | 36.23 | 1.69 |
| 57. | 30 nov. 2021 | 4.52% | -0.83% | 9.08 | 2.99 | -5.21 |
| 58. | 31 dic. 2021 | 7.39% | 4.36% | 34.71 | 12.01 | 20.42 |
| 59. | 31 ene. 2022 | -11.79% | -5.26% | 176.60 | 37.87 | 81.78 |
| 60. | 28 feb. 2022 | 2.96% | -3.14% | 2.12 | 16.25 | -5.87 |
| 61. | 31 mar. 2022 | 6.33% | 3.58% | 23.34 | 7.19 | 12.96 |
| 62. | 30 abr. 2022 | -0.36% | -8.80% | 3.46 | 93.91 | 18.02 |
| 63. | 31 may. 2022 | 6.63% | 0.01% | 26.27 | 0.79 | -4.56 |
| 64. | 30 jun. 2022 | -8.89% | -8.39% | 108.04 | 86.25 | 96.53 |
| 65. | 31 jul. 2022 | 0.89% | 9.11% | 0.38 | 67.51 | -5.04 |
| 66. | 31 ago. 2022 | 7.96% | -4.24% | 41.70 | 26.41 | -33.19 |
| 67. | 30 sept. 2022 | -4.45% | -9.34% | 35.42 | 104.75 | 60.92 |
| 68. | 31 oct. 2022 | 4.53% | 7.99% | 9.17 | 50.28 | 21.48 |
| 69. | 30 nov. 2022 | 10.84% | 5.38% | 87.23 | 20.07 | 41.84 |
| 70. | 31 dic. 2022 | 0.91% | -5.90% | 0.35 | 46.14 | 4.03 |
| 71. | 31 ene. 2023 | 9.57% | 6.18% | 65.08 | 27.88 | 42.60 |
| Total (Σ): | 8,390.96 | 1,754.14 | 2,258.16 | |||
Mostrar todo
VarianzaULTA = Σ(RULTA,t–RULTA)2 ÷ (71 – 1)
= 8,390.96 ÷ (71 – 1)
= 119.87
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (71 – 1)
= 1,754.14 ÷ (71 – 1)
= 25.06
CovarianzaULTA, S&P 500 = Σ(RULTA,t–RULTA)×(RS&P 500,t–RS&P 500) ÷ (71 – 1)
= 2,258.16 ÷ (71 – 1)
= 32.26
Estimación sistemática del riesgo (β)
| VarianzaULTA | 119.87 |
| VarianzaS&P 500 | 25.06 |
| CovarianzaULTA, S&P 500 | 32.26 |
| Coeficiente de correlaciónULTA, S&P 5001 | 0.59 |
| βULTA2 | 1.29 |
| αULTA3 | 0.35% |
Cálculos
1 Coeficiente de correlaciónULTA, S&P 500
= CovarianzaULTA, S&P 500 ÷ (Desviación estándarULTA × Desviación estándarS&P 500)
= 32.26 ÷ (10.95% × 5.01%)
= 0.59
2 βULTA
= CovarianzaULTA, S&P 500 ÷ VarianzaS&P 500
= 32.26 ÷ 25.06
= 1.29
3 αULTA
= PromedioULTA – βULTA × PromedioS&P 500
= 1.50% – 1.29 × 0.90%
= 0.35%
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 Ulta Beauty acciones ordinarias | βULTA | 1.29 |
| Tasa de rendimiento esperada de las acciones ordinarias de Ulta Beauty3 | E(RULTA) | 16.41% |
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(RULTA) = RF + βULTA [E(RM) – RF]
= 4.67% + 1.29 [13.79% – 4.67%]
= 16.41%