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 Airbnb.
Tasas de retorno
Airbnb Inc., tasas mensuales de retorno
| Airbnb Inc. (ABNB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioABNB,t1 | DividendoABNB,t1 | RABNB,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 dic. 2020 | $146.80 | 3,756.07 | ||||
| 1. | 31 ene. 2021 | $183.63 | 25.09% | 3,714.24 | -1.11% | |
| 2. | 28 feb. 2021 | $206.35 | 12.37% | 3,811.15 | 2.61% | |
| 3. | 31 mar. 2021 | $187.94 | -8.92% | 3,972.89 | 4.24% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 35. | 30 nov. 2023 | $126.34 | 6.81% | 4,567.80 | 8.92% | |
| 36. | 31 dic. 2023 | $136.14 | 7.76% | 4,769.83 | 4.42% | |
| Promedio (R): | 0.65% | 0.79% | ||||
| Desviación estándar: | 13.30% | 5.04% | ||||
| Airbnb Inc. (ABNB) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioABNB,t1 | DividendoABNB,t1 | RABNB,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 31 dic. 2020 | $146.80 | 3,756.07 | ||||
| 1. | 31 ene. 2021 | $183.63 | 25.09% | 3,714.24 | -1.11% | |
| 2. | 28 feb. 2021 | $206.35 | 12.37% | 3,811.15 | 2.61% | |
| 3. | 31 mar. 2021 | $187.94 | -8.92% | 3,972.89 | 4.24% | |
| 4. | 30 abr. 2021 | $172.71 | -8.10% | 4,181.17 | 5.24% | |
| 5. | 31 may. 2021 | $140.40 | -18.71% | 4,204.11 | 0.55% | |
| 6. | 30 jun. 2021 | $153.14 | 9.07% | 4,297.50 | 2.22% | |
| 7. | 31 jul. 2021 | $144.01 | -5.96% | 4,395.26 | 2.27% | |
| 8. | 31 ago. 2021 | $154.99 | 7.62% | 4,522.68 | 2.90% | |
| 9. | 30 sept. 2021 | $167.75 | 8.23% | 4,307.54 | -4.76% | |
| 10. | 31 oct. 2021 | $170.66 | 1.73% | 4,605.38 | 6.91% | |
| 11. | 30 nov. 2021 | $172.54 | 1.10% | 4,567.00 | -0.83% | |
| 12. | 31 dic. 2021 | $166.49 | -3.51% | 4,766.18 | 4.36% | |
| 13. | 31 ene. 2022 | $153.97 | -7.52% | 4,515.55 | -5.26% | |
| 14. | 28 feb. 2022 | $151.49 | -1.61% | 4,373.94 | -3.14% | |
| 15. | 31 mar. 2022 | $171.76 | 13.38% | 4,530.41 | 3.58% | |
| 16. | 30 abr. 2022 | $153.21 | -10.80% | 4,131.93 | -8.80% | |
| 17. | 31 may. 2022 | $120.87 | -21.11% | 4,132.15 | 0.01% | |
| 18. | 30 jun. 2022 | $89.08 | -26.30% | 3,785.38 | -8.39% | |
| 19. | 31 jul. 2022 | $110.98 | 24.58% | 4,130.29 | 9.11% | |
| 20. | 31 ago. 2022 | $113.12 | 1.93% | 3,955.00 | -4.24% | |
| 21. | 30 sept. 2022 | $105.04 | -7.14% | 3,585.62 | -9.34% | |
| 22. | 31 oct. 2022 | $106.91 | 1.78% | 3,871.98 | 7.99% | |
| 23. | 30 nov. 2022 | $102.14 | -4.46% | 4,080.11 | 5.38% | |
| 24. | 31 dic. 2022 | $85.50 | -16.29% | 3,839.50 | -5.90% | |
| 25. | 31 ene. 2023 | $111.11 | 29.95% | 4,076.60 | 6.18% | |
| 26. | 28 feb. 2023 | $123.28 | 10.95% | 3,970.15 | -2.61% | |
| 27. | 31 mar. 2023 | $124.40 | 0.91% | 4,109.31 | 3.51% | |
| 28. | 30 abr. 2023 | $119.67 | -3.80% | 4,169.48 | 1.46% | |
| 29. | 31 may. 2023 | $109.77 | -8.27% | 4,179.83 | 0.25% | |
| 30. | 30 jun. 2023 | $128.16 | 16.75% | 4,376.86 | 4.71% | |
| 31. | 31 jul. 2023 | $152.19 | 18.75% | 4,588.96 | 4.85% | |
| 32. | 31 ago. 2023 | $131.55 | -13.56% | 4,507.66 | -1.77% | |
| 33. | 30 sept. 2023 | $137.21 | 4.30% | 4,288.05 | -4.87% | |
| 34. | 31 oct. 2023 | $118.29 | -13.79% | 4,193.80 | -2.20% | |
| 35. | 30 nov. 2023 | $126.34 | 6.81% | 4,567.80 | 8.92% | |
| 36. | 31 dic. 2023 | $136.14 | 7.76% | 4,769.83 | 4.42% | |
| Promedio (R): | 0.65% | 0.79% | ||||
| Desviación estándar: | 13.30% | 5.04% | ||||
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 ABNB 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
Airbnb Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RABNB,t | RS&P 500,t | (RABNB,t–RABNB)2 | (RS&P 500,t–RS&P 500)2 | (RABNB,t–RABNB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 ene. 2021 | 25.09% | -1.11% | 597.48 | 3.62 | -46.54 |
| 2. | 28 feb. 2021 | 12.37% | 2.61% | 137.54 | 3.31 | 21.33 |
| 3. | 31 mar. 2021 | -8.92% | 4.24% | 91.52 | 11.93 | -33.04 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 35. | 30 nov. 2023 | 6.81% | 8.92% | 37.95 | 66.06 | 50.07 |
| 36. | 31 dic. 2023 | 7.76% | 4.42% | 50.58 | 13.20 | 25.84 |
| Total (Σ): | 6,195.02 | 889.77 | 1,107.74 | |||
| t | Fecha | RABNB,t | RS&P 500,t | (RABNB,t–RABNB)2 | (RS&P 500,t–RS&P 500)2 | (RABNB,t–RABNB)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 ene. 2021 | 25.09% | -1.11% | 597.48 | 3.62 | -46.54 |
| 2. | 28 feb. 2021 | 12.37% | 2.61% | 137.54 | 3.31 | 21.33 |
| 3. | 31 mar. 2021 | -8.92% | 4.24% | 91.52 | 11.93 | -33.04 |
| 4. | 30 abr. 2021 | -8.10% | 5.24% | 76.54 | 19.82 | -38.95 |
| 5. | 31 may. 2021 | -18.71% | 0.55% | 374.53 | 0.06 | 4.67 |
| 6. | 30 jun. 2021 | 9.07% | 2.22% | 71.05 | 2.05 | 12.06 |
| 7. | 31 jul. 2021 | -5.96% | 2.27% | 43.65 | 2.20 | -9.81 |
| 8. | 31 ago. 2021 | 7.62% | 2.90% | 48.71 | 4.45 | 14.72 |
| 9. | 30 sept. 2021 | 8.23% | -4.76% | 57.57 | 30.77 | -42.09 |
| 10. | 31 oct. 2021 | 1.73% | 6.91% | 1.19 | 37.51 | 6.67 |
| 11. | 30 nov. 2021 | 1.10% | -0.83% | 0.21 | 2.64 | -0.74 |
| 12. | 31 dic. 2021 | -3.51% | 4.36% | 17.23 | 12.75 | -14.83 |
| 13. | 31 ene. 2022 | -7.52% | -5.26% | 66.67 | 36.59 | 49.39 |
| 14. | 28 feb. 2022 | -1.61% | -3.14% | 5.09 | 15.41 | 8.86 |
| 15. | 31 mar. 2022 | 13.38% | 3.58% | 162.19 | 7.77 | 35.50 |
| 16. | 30 abr. 2022 | -10.80% | -8.80% | 130.99 | 91.89 | 109.71 |
| 17. | 31 may. 2022 | -21.11% | 0.01% | 473.21 | 0.62 | 17.07 |
| 18. | 30 jun. 2022 | -26.30% | -8.39% | 726.09 | 84.31 | 247.42 |
| 19. | 31 jul. 2022 | 24.58% | 9.11% | 573.10 | 69.25 | 199.21 |
| 20. | 31 ago. 2022 | 1.93% | -4.24% | 1.65 | 25.34 | -6.46 |
| 21. | 30 sept. 2022 | -7.14% | -9.34% | 60.65 | 102.61 | 78.89 |
| 22. | 31 oct. 2022 | 1.78% | 7.99% | 1.29 | 51.79 | 8.17 |
| 23. | 30 nov. 2022 | -4.46% | 5.38% | 26.08 | 21.02 | -23.42 |
| 24. | 31 dic. 2022 | -16.29% | -5.90% | 286.84 | 44.72 | 113.26 |
| 25. | 31 ene. 2023 | 29.95% | 6.18% | 858.97 | 29.00 | 157.83 |
| 26. | 28 feb. 2023 | 10.95% | -2.61% | 106.26 | 11.57 | -35.06 |
| 27. | 31 mar. 2023 | 0.91% | 3.51% | 0.07 | 7.37 | 0.72 |
| 28. | 30 abr. 2023 | -3.80% | 1.46% | 19.78 | 0.45 | -3.00 |
| 29. | 31 may. 2023 | -8.27% | 0.25% | 79.53 | 0.29 | 4.83 |
| 30. | 30 jun. 2023 | 16.75% | 4.71% | 259.47 | 15.40 | 63.20 |
| 31. | 31 jul. 2023 | 18.75% | 4.85% | 327.79 | 16.45 | 73.43 |
| 32. | 31 ago. 2023 | -13.56% | -1.77% | 201.84 | 6.56 | 36.40 |
| 33. | 30 sept. 2023 | 4.30% | -4.87% | 13.38 | 32.06 | -20.71 |
| 34. | 31 oct. 2023 | -13.79% | -2.20% | 208.34 | 8.93 | 43.13 |
| 35. | 30 nov. 2023 | 6.81% | 8.92% | 37.95 | 66.06 | 50.07 |
| 36. | 31 dic. 2023 | 7.76% | 4.42% | 50.58 | 13.20 | 25.84 |
| Total (Σ): | 6,195.02 | 889.77 | 1,107.74 | |||
Mostrar todo
VarianzaABNB = Σ(RABNB,t–RABNB)2 ÷ (36 – 1)
= 6,195.02 ÷ (36 – 1)
= 177.00
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (36 – 1)
= 889.77 ÷ (36 – 1)
= 25.42
CovarianzaABNB, S&P 500 = Σ(RABNB,t–RABNB)×(RS&P 500,t–RS&P 500) ÷ (36 – 1)
= 1,107.74 ÷ (36 – 1)
= 31.65
Estimación sistemática del riesgo (β)
| VarianzaABNB | 177.00 |
| VarianzaS&P 500 | 25.42 |
| CovarianzaABNB, S&P 500 | 31.65 |
| Coeficiente de correlaciónABNB, S&P 5001 | 0.47 |
| βABNB2 | 1.24 |
| αABNB3 | -0.34% |
Cálculos
1 Coeficiente de correlaciónABNB, S&P 500
= CovarianzaABNB, S&P 500 ÷ (Desviación estándarABNB × Desviación estándarS&P 500)
= 31.65 ÷ (13.30% × 5.04%)
= 0.47
2 βABNB
= CovarianzaABNB, S&P 500 ÷ VarianzaS&P 500
= 31.65 ÷ 25.42
= 1.24
3 αABNB
= PromedioABNB – βABNB × PromedioS&P 500
= 0.65% – 1.24 × 0.79%
= -0.34%
Tasa de rendimiento esperada
| Suposiciones | ||
| Tasa de rendimiento del LT Treasury Composite1 | RF | 4.65% |
| Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.79% |
| Riesgo sistemático de Airbnb acciones ordinarias | βABNB | 1.24 |
| Tasa de rendimiento esperada de las acciones ordinarias de Airbnb3 | E(RABNB) | 16.02% |
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(RABNB) = RF + βABNB [E(RM) – RF]
= 4.65% + 1.24 [13.79% – 4.65%]
= 16.02%