Modelo de fijación de precios de activos de capital (CAPM)
El modelo de valoración 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 Palantir.
Tasas de retorno
Palantir Technologies Inc., tasas mensuales de retorno
| Palantir Technologies Inc. (PLTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioPLTR,t1 | DividendoPLTR,t1 | RPLTR,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 sept. 2020 | $9.50 | 3,363.00 | ||||
| 1. | 31 oct. 2020 | $10.13 | 6.63% | 3,269.96 | -2.77% | |
| 2. | 30 nov. 2020 | $27.11 | 167.62% | 3,621.63 | 10.75% | |
| 3. | 31 dic. 2020 | $23.55 | -13.13% | 3,756.07 | 3.71% | |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 38. | 30 nov. 2023 | $20.05 | 35.47% | 4,567.80 | 8.92% | |
| 39. | 31 dic. 2023 | $17.17 | -14.36% | 4,769.83 | 4.42% | |
| Promedio (R): | 5.51% | 1.03% | ||||
| Desviación estándar: | 35.26% | 5.15% | ||||
| Palantir Technologies Inc. (PLTR) | Standard & Poor’s 500 (S&P 500) | |||||
|---|---|---|---|---|---|---|
| t | Fecha | PrecioPLTR,t1 | DividendoPLTR,t1 | RPLTR,t2 | PrecioS&P 500,t | RS&P 500,t3 |
| 30 sept. 2020 | $9.50 | 3,363.00 | ||||
| 1. | 31 oct. 2020 | $10.13 | 6.63% | 3,269.96 | -2.77% | |
| 2. | 30 nov. 2020 | $27.11 | 167.62% | 3,621.63 | 10.75% | |
| 3. | 31 dic. 2020 | $23.55 | -13.13% | 3,756.07 | 3.71% | |
| 4. | 31 ene. 2021 | $35.18 | 49.38% | 3,714.24 | -1.11% | |
| 5. | 28 feb. 2021 | $23.90 | -32.06% | 3,811.15 | 2.61% | |
| 6. | 31 mar. 2021 | $23.29 | -2.55% | 3,972.89 | 4.24% | |
| 7. | 30 abr. 2021 | $23.04 | -1.07% | 4,181.17 | 5.24% | |
| 8. | 31 may. 2021 | $22.95 | -0.39% | 4,204.11 | 0.55% | |
| 9. | 30 jun. 2021 | $26.36 | 14.86% | 4,297.50 | 2.22% | |
| 10. | 31 jul. 2021 | $21.71 | -17.64% | 4,395.26 | 2.27% | |
| 11. | 31 ago. 2021 | $26.34 | 21.33% | 4,522.68 | 2.90% | |
| 12. | 30 sept. 2021 | $24.04 | -8.73% | 4,307.54 | -4.76% | |
| 13. | 31 oct. 2021 | $25.88 | 7.65% | 4,605.38 | 6.91% | |
| 14. | 30 nov. 2021 | $20.65 | -20.21% | 4,567.00 | -0.83% | |
| 15. | 31 dic. 2021 | $18.21 | -11.82% | 4,766.18 | 4.36% | |
| 16. | 31 ene. 2022 | $13.71 | -24.71% | 4,515.55 | -5.26% | |
| 17. | 28 feb. 2022 | $11.85 | -13.57% | 4,373.94 | -3.14% | |
| 18. | 31 mar. 2022 | $13.73 | 15.86% | 4,530.41 | 3.58% | |
| 19. | 30 abr. 2022 | $10.40 | -24.25% | 4,131.93 | -8.80% | |
| 20. | 31 may. 2022 | $8.68 | -16.54% | 4,132.15 | 0.01% | |
| 21. | 30 jun. 2022 | $9.07 | 4.49% | 3,785.38 | -8.39% | |
| 22. | 31 jul. 2022 | $10.35 | 14.11% | 4,130.29 | 9.11% | |
| 23. | 31 ago. 2022 | $7.72 | -25.41% | 3,955.00 | -4.24% | |
| 24. | 30 sept. 2022 | $8.13 | 5.31% | 3,585.62 | -9.34% | |
| 25. | 31 oct. 2022 | $8.79 | 8.12% | 3,871.98 | 7.99% | |
| 26. | 30 nov. 2022 | $7.50 | -14.68% | 4,080.11 | 5.38% | |
| 27. | 31 dic. 2022 | $6.42 | -14.40% | 3,839.50 | -5.90% | |
| 28. | 31 ene. 2023 | $7.78 | 21.18% | 4,076.60 | 6.18% | |
| 29. | 28 feb. 2023 | $7.84 | 0.77% | 3,970.15 | -2.61% | |
| 30. | 31 mar. 2023 | $8.45 | 7.78% | 4,109.31 | 3.51% | |
| 31. | 30 abr. 2023 | $7.75 | -8.28% | 4,169.48 | 1.46% | |
| 32. | 31 may. 2023 | $14.71 | 89.81% | 4,179.83 | 0.25% | |
| 33. | 30 jun. 2023 | $15.33 | 4.21% | 4,376.86 | 4.71% | |
| 34. | 31 jul. 2023 | $19.84 | 29.42% | 4,588.96 | 4.85% | |
| 35. | 31 ago. 2023 | $14.98 | -24.50% | 4,507.66 | -1.77% | |
| 36. | 30 sept. 2023 | $16.00 | 6.81% | 4,288.05 | -4.87% | |
| 37. | 31 oct. 2023 | $14.80 | -7.50% | 4,193.80 | -2.20% | |
| 38. | 30 nov. 2023 | $20.05 | 35.47% | 4,567.80 | 8.92% | |
| 39. | 31 dic. 2023 | $17.17 | -14.36% | 4,769.83 | 4.42% | |
| Promedio (R): | 5.51% | 1.03% | ||||
| Desviación estándar: | 35.26% | 5.15% | ||||
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 PLTR 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
Palantir Technologies Inc., cálculo de la varianza y covarianza de los rendimientos
| t | Fecha | RPLTR,t | RS&P 500,t | (RPLTR,t–RPLTR)2 | (RS&P 500,t–RS&P 500)2 | (RPLTR,t–RPLTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 oct. 2020 | 6.63% | -2.77% | 1.25 | 14.41 | -4.24 |
| 2. | 30 nov. 2020 | 167.62% | 10.75% | 26,278.84 | 94.58 | 1,576.53 |
| 3. | 31 dic. 2020 | -13.13% | 3.71% | 347.64 | 7.20 | -50.02 |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| . | . | . | . | . | . | . |
| 38. | 30 nov. 2023 | 35.47% | 8.92% | 897.57 | 62.23 | 236.34 |
| 39. | 31 dic. 2023 | -14.36% | 4.42% | 395.12 | 11.52 | -67.46 |
| Total (Σ): | 47,256.37 | 1,008.01 | 2,744.07 | |||
| t | Fecha | RPLTR,t | RS&P 500,t | (RPLTR,t–RPLTR)2 | (RS&P 500,t–RS&P 500)2 | (RPLTR,t–RPLTR)×(RS&P 500,t–RS&P 500) |
|---|---|---|---|---|---|---|
| 1. | 31 oct. 2020 | 6.63% | -2.77% | 1.25 | 14.41 | -4.24 |
| 2. | 30 nov. 2020 | 167.62% | 10.75% | 26,278.84 | 94.58 | 1,576.53 |
| 3. | 31 dic. 2020 | -13.13% | 3.71% | 347.64 | 7.20 | -50.02 |
| 4. | 31 ene. 2021 | 49.38% | -1.11% | 1,924.65 | 4.59 | -94.02 |
| 5. | 28 feb. 2021 | -32.06% | 2.61% | 1,412.04 | 2.50 | -59.36 |
| 6. | 31 mar. 2021 | -2.55% | 4.24% | 65.06 | 10.33 | -25.93 |
| 7. | 30 abr. 2021 | -1.07% | 5.24% | 43.39 | 17.75 | -27.75 |
| 8. | 31 may. 2021 | -0.39% | 0.55% | 34.86 | 0.23 | 2.84 |
| 9. | 30 jun. 2021 | 14.86% | 2.22% | 87.33 | 1.42 | 11.14 |
| 10. | 31 jul. 2021 | -17.64% | 2.27% | 536.10 | 1.55 | -28.84 |
| 11. | 31 ago. 2021 | 21.33% | 2.90% | 250.06 | 3.50 | 29.57 |
| 12. | 30 sept. 2021 | -8.73% | -4.76% | 202.93 | 33.48 | 82.43 |
| 13. | 31 oct. 2021 | 7.65% | 6.91% | 4.58 | 34.63 | 12.60 |
| 14. | 30 nov. 2021 | -20.21% | -0.83% | 661.63 | 3.47 | 47.91 |
| 15. | 31 dic. 2021 | -11.82% | 4.36% | 300.31 | 11.10 | -57.74 |
| 16. | 31 ene. 2022 | -24.71% | -5.26% | 913.56 | 39.54 | 190.05 |
| 17. | 28 feb. 2022 | -13.57% | -3.14% | 364.05 | 17.35 | 79.48 |
| 18. | 31 mar. 2022 | 15.86% | 3.58% | 107.15 | 6.49 | 26.38 |
| 19. | 30 abr. 2022 | -24.25% | -8.80% | 886.07 | 96.53 | 292.46 |
| 20. | 31 may. 2022 | -16.54% | 0.01% | 486.29 | 1.05 | 22.58 |
| 21. | 30 jun. 2022 | 4.49% | -8.39% | 1.04 | 88.76 | 9.61 |
| 22. | 31 jul. 2022 | 14.11% | 9.11% | 73.94 | 65.32 | 69.50 |
| 23. | 31 ago. 2022 | -25.41% | -4.24% | 956.30 | 27.81 | 163.07 |
| 24. | 30 sept. 2022 | 5.31% | -9.34% | 0.04 | 107.51 | 2.10 |
| 25. | 31 oct. 2022 | 8.12% | 7.99% | 6.78 | 48.40 | 18.12 |
| 26. | 30 nov. 2022 | -14.68% | 5.38% | 407.60 | 18.89 | -87.74 |
| 27. | 31 dic. 2022 | -14.40% | -5.90% | 396.54 | 47.98 | 137.93 |
| 28. | 31 ene. 2023 | 21.18% | 6.18% | 245.56 | 26.48 | 80.64 |
| 29. | 28 feb. 2023 | 0.77% | -2.61% | 22.49 | 13.25 | 17.26 |
| 30. | 31 mar. 2023 | 7.78% | 3.51% | 5.14 | 6.13 | 5.61 |
| 31. | 30 abr. 2023 | -8.28% | 1.46% | 190.37 | 0.19 | -6.00 |
| 32. | 31 may. 2023 | 89.81% | 0.25% | 7,105.31 | 0.61 | -65.84 |
| 33. | 30 jun. 2023 | 4.21% | 4.71% | 1.69 | 13.58 | -4.78 |
| 34. | 31 jul. 2023 | 29.42% | 4.85% | 571.50 | 14.57 | 91.24 |
| 35. | 31 ago. 2023 | -24.50% | -1.77% | 900.56 | 7.85 | 84.06 |
| 36. | 30 sept. 2023 | 6.81% | -4.87% | 1.68 | 34.83 | -7.65 |
| 37. | 31 oct. 2023 | -7.50% | -2.20% | 169.35 | 10.42 | 42.00 |
| 38. | 30 nov. 2023 | 35.47% | 8.92% | 897.57 | 62.23 | 236.34 |
| 39. | 31 dic. 2023 | -14.36% | 4.42% | 395.12 | 11.52 | -67.46 |
| Total (Σ): | 47,256.37 | 1,008.01 | 2,744.07 | |||
Mostrar todo
VarianzaPLTR = Σ(RPLTR,t–RPLTR)2 ÷ (39 – 1)
= 47,256.37 ÷ (39 – 1)
= 1,243.59
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (39 – 1)
= 1,008.01 ÷ (39 – 1)
= 26.53
CovarianzaPLTR, S&P 500 = Σ(RPLTR,t–RPLTR)×(RS&P 500,t–RS&P 500) ÷ (39 – 1)
= 2,744.07 ÷ (39 – 1)
= 72.21
Estimación sistemática del riesgo (β)
| VarianzaPLTR | 1,243.59 |
| VarianzaS&P 500 | 26.53 |
| CovarianzaPLTR, S&P 500 | 72.21 |
| Coeficiente de correlaciónPLTR, S&P 5001 | 0.40 |
| βPLTR2 | 2.72 |
| αPLTR3 | 2.71% |
Cálculos
1 Coeficiente de correlaciónPLTR, S&P 500
= CovarianzaPLTR, S&P 500 ÷ (Desviación estándarPLTR × Desviación estándarS&P 500)
= 72.21 ÷ (35.26% × 5.15%)
= 0.40
2 βPLTR
= CovarianzaPLTR, S&P 500 ÷ VarianzaS&P 500
= 72.21 ÷ 26.53
= 2.72
3 αPLTR
= PromedioPLTR – βPLTR × PromedioS&P 500
= 5.51% – 2.72 × 1.03%
= 2.71%
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) | 13.77% |
| Riesgo sistemático de Palantir acciones ordinarias | βPLTR | 2.72 |
| Tasa de rendimiento esperada de las acciones ordinarias de Palantir3 | E(RPLTR) | 29.44% |
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(RPLTR) = RF + βPLTR [E(RM) – RF]
= 4.67% + 2.72 [13.77% – 4.67%]
= 29.44%