El modelo de fijación de precios de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida sobre activos de riesgo como las acciones ordinarias de Pioneer.
Tasas de retorno
Pioneer Natural Resources Co. (PXD) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioPXD,t1 | DividendoPXD,t1 | RPXD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 ene. 2019 | $142.32 | 2,704.10 | ||||
1. | 28 feb. 2019 | $140.95 | -0.96% | 2,784.49 | 2.97% | |
2. | 31 mar. 2019 | $152.28 | $0.32 | 8.27% | 2,834.40 | 1.79% |
3. | 30 abr. 2019 | $166.46 | 9.31% | 2,945.83 | 3.93% | |
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58. | 30 nov. 2023 | $231.64 | $3.20 | -1.74% | 4,567.80 | 8.92% |
59. | 31 dic. 2023 | $224.88 | -2.92% | 4,769.83 | 4.42% | |
Promedio (R): | 1.96% | 1.11% | ||||
Desviación estándar: | 12.15% | 5.31% |
Pioneer Natural Resources Co. (PXD) | Standard & Poor’s 500 (S&P 500) | |||||
---|---|---|---|---|---|---|
t | Fecha | PrecioPXD,t1 | DividendoPXD,t1 | RPXD,t2 | PrecioS&P 500,t | RS&P 500,t3 |
31 ene. 2019 | $142.32 | 2,704.10 | ||||
1. | 28 feb. 2019 | $140.95 | -0.96% | 2,784.49 | 2.97% | |
2. | 31 mar. 2019 | $152.28 | $0.32 | 8.27% | 2,834.40 | 1.79% |
3. | 30 abr. 2019 | $166.46 | 9.31% | 2,945.83 | 3.93% | |
4. | 31 may. 2019 | $141.96 | -14.72% | 2,752.06 | -6.58% | |
5. | 30 jun. 2019 | $153.86 | 8.38% | 2,941.76 | 6.89% | |
6. | 31 jul. 2019 | $138.04 | -10.28% | 2,980.38 | 1.31% | |
7. | 31 ago. 2019 | $123.42 | -10.59% | 2,926.46 | -1.81% | |
8. | 30 sept. 2019 | $125.77 | $0.44 | 2.26% | 2,976.74 | 1.72% |
9. | 31 oct. 2019 | $123.02 | -2.19% | 3,037.56 | 2.04% | |
10. | 30 nov. 2019 | $127.84 | 3.92% | 3,140.98 | 3.40% | |
11. | 31 dic. 2019 | $151.37 | $0.44 | 18.75% | 3,230.78 | 2.86% |
12. | 31 ene. 2020 | $135.00 | -10.81% | 3,225.52 | -0.16% | |
13. | 29 feb. 2020 | $122.78 | -9.05% | 2,954.22 | -8.41% | |
14. | 31 mar. 2020 | $70.15 | $0.55 | -42.42% | 2,584.59 | -12.51% |
15. | 30 abr. 2020 | $89.31 | 27.31% | 2,912.43 | 12.68% | |
16. | 31 may. 2020 | $91.60 | 2.56% | 3,044.31 | 4.53% | |
17. | 30 jun. 2020 | $97.70 | $0.55 | 7.26% | 3,100.29 | 1.84% |
18. | 31 jul. 2020 | $96.92 | -0.80% | 3,271.12 | 5.51% | |
19. | 31 ago. 2020 | $103.93 | 7.23% | 3,500.31 | 7.01% | |
20. | 30 sept. 2020 | $85.99 | $0.55 | -16.73% | 3,363.00 | -3.92% |
21. | 31 oct. 2020 | $79.56 | -7.48% | 3,269.96 | -2.77% | |
22. | 30 nov. 2020 | $100.58 | 26.42% | 3,621.63 | 10.75% | |
23. | 31 dic. 2020 | $113.89 | $0.55 | 13.78% | 3,756.07 | 3.71% |
24. | 31 ene. 2021 | $120.90 | 6.16% | 3,714.24 | -1.11% | |
25. | 28 feb. 2021 | $148.57 | 22.89% | 3,811.15 | 2.61% | |
26. | 31 mar. 2021 | $158.82 | $0.56 | 7.28% | 3,972.89 | 4.24% |
27. | 30 abr. 2021 | $153.83 | -3.14% | 4,181.17 | 5.24% | |
28. | 31 may. 2021 | $152.19 | -1.07% | 4,204.11 | 0.55% | |
29. | 30 jun. 2021 | $162.52 | $0.56 | 7.16% | 4,297.50 | 2.22% |
30. | 31 jul. 2021 | $145.37 | -10.55% | 4,395.26 | 2.27% | |
31. | 31 ago. 2021 | $149.67 | 2.96% | 4,522.68 | 2.90% | |
32. | 30 sept. 2021 | $166.51 | $2.07 | 12.63% | 4,307.54 | -4.76% |
33. | 31 oct. 2021 | $186.98 | 12.29% | 4,605.38 | 6.91% | |
34. | 30 nov. 2021 | $178.32 | $3.02 | -3.02% | 4,567.00 | -0.83% |
35. | 31 dic. 2021 | $181.88 | $0.62 | 2.34% | 4,766.18 | 4.36% |
36. | 31 ene. 2022 | $218.89 | 20.35% | 4,515.55 | -5.26% | |
37. | 28 feb. 2022 | $239.60 | $3.78 | 11.19% | 4,373.94 | -3.14% |
38. | 31 mar. 2022 | $250.03 | 4.35% | 4,530.41 | 3.58% | |
39. | 30 abr. 2022 | $232.47 | -7.02% | 4,131.93 | -8.80% | |
40. | 31 may. 2022 | $277.94 | $7.38 | 22.73% | 4,132.15 | 0.01% |
41. | 30 jun. 2022 | $223.08 | -19.74% | 3,785.38 | -8.39% | |
42. | 31 jul. 2022 | $236.95 | 6.22% | 4,130.29 | 9.11% | |
43. | 31 ago. 2022 | $253.22 | 6.87% | 3,955.00 | -4.24% | |
44. | 30 sept. 2022 | $216.53 | $8.57 | -11.10% | 3,585.62 | -9.34% |
45. | 31 oct. 2022 | $256.41 | 18.42% | 3,871.98 | 7.99% | |
46. | 30 nov. 2022 | $235.99 | $5.71 | -5.74% | 4,080.11 | 5.38% |
47. | 31 dic. 2022 | $228.39 | -3.22% | 3,839.50 | -5.90% | |
48. | 31 ene. 2023 | $230.35 | 0.86% | 4,076.60 | 6.18% | |
49. | 28 feb. 2023 | $200.41 | -13.00% | 3,970.15 | -2.61% | |
50. | 31 mar. 2023 | $204.24 | $5.58 | 4.70% | 4,109.31 | 3.51% |
51. | 30 abr. 2023 | $217.55 | 6.52% | 4,169.48 | 1.46% | |
52. | 31 may. 2023 | $199.44 | $3.34 | -6.79% | 4,179.83 | 0.25% |
53. | 30 jun. 2023 | $207.18 | 3.88% | 4,376.86 | 4.71% | |
54. | 31 jul. 2023 | $225.67 | 8.92% | 4,588.96 | 4.85% | |
55. | 31 ago. 2023 | $237.93 | 5.43% | 4,507.66 | -1.77% | |
56. | 30 sept. 2023 | $229.55 | $1.84 | -2.75% | 4,288.05 | -4.87% |
57. | 31 oct. 2023 | $239.00 | 4.12% | 4,193.80 | -2.20% | |
58. | 30 nov. 2023 | $231.64 | $3.20 | -1.74% | 4,567.80 | 8.92% |
59. | 31 dic. 2023 | $224.88 | -2.92% | 4,769.83 | 4.42% | |
Promedio (R): | 1.96% | 1.11% | ||||
Desviación estándar: | 12.15% | 5.31% |
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 PXD 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
t | Fecha | RPXD,t | RS&P 500,t | (RPXD,t–RPXD)2 | (RS&P 500,t–RS&P 500)2 | (RPXD,t–RPXD)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 28 feb. 2019 | -0.96% | 2.97% | 8.57 | 3.49 | -5.46 |
2. | 31 mar. 2019 | 8.27% | 1.79% | 39.70 | 0.47 | 4.33 |
3. | 30 abr. 2019 | 9.31% | 3.93% | 53.99 | 7.98 | 20.76 |
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58. | 30 nov. 2023 | -1.74% | 8.92% | 13.73 | 61.03 | -28.94 |
59. | 31 dic. 2023 | -2.92% | 4.42% | 23.84 | 11.00 | -16.20 |
Total (Σ): | 8,558.51 | 1,634.30 | 2,158.61 |
t | Fecha | RPXD,t | RS&P 500,t | (RPXD,t–RPXD)2 | (RS&P 500,t–RS&P 500)2 | (RPXD,t–RPXD)×(RS&P 500,t–RS&P 500) |
---|---|---|---|---|---|---|
1. | 28 feb. 2019 | -0.96% | 2.97% | 8.57 | 3.49 | -5.46 |
2. | 31 mar. 2019 | 8.27% | 1.79% | 39.70 | 0.47 | 4.33 |
3. | 30 abr. 2019 | 9.31% | 3.93% | 53.99 | 7.98 | 20.76 |
4. | 31 may. 2019 | -14.72% | -6.58% | 278.30 | 59.04 | 128.18 |
5. | 30 jun. 2019 | 8.38% | 6.89% | 41.20 | 33.49 | 37.14 |
6. | 31 jul. 2019 | -10.28% | 1.31% | 149.97 | 0.04 | -2.53 |
7. | 31 ago. 2019 | -10.59% | -1.81% | 157.64 | 8.50 | 36.60 |
8. | 30 sept. 2019 | 2.26% | 1.72% | 0.09 | 0.37 | 0.18 |
9. | 31 oct. 2019 | -2.19% | 2.04% | 17.23 | 0.88 | -3.89 |
10. | 30 nov. 2019 | 3.92% | 3.40% | 3.82 | 5.28 | 4.49 |
11. | 31 dic. 2019 | 18.75% | 2.86% | 281.76 | 3.07 | 29.43 |
12. | 31 ene. 2020 | -10.81% | -0.16% | 163.30 | 1.61 | 16.21 |
13. | 29 feb. 2020 | -9.05% | -8.41% | 121.35 | 90.57 | 104.84 |
14. | 31 mar. 2020 | -42.42% | -12.51% | 1,969.72 | 185.44 | 604.38 |
15. | 30 abr. 2020 | 27.31% | 12.68% | 642.56 | 134.06 | 293.50 |
16. | 31 may. 2020 | 2.56% | 4.53% | 0.36 | 11.71 | 2.05 |
17. | 30 jun. 2020 | 7.26% | 1.84% | 28.04 | 0.54 | 3.88 |
18. | 31 jul. 2020 | -0.80% | 5.51% | 7.63 | 19.40 | -12.17 |
19. | 31 ago. 2020 | 7.23% | 7.01% | 27.76 | 34.82 | 31.09 |
20. | 30 sept. 2020 | -16.73% | -3.92% | 349.56 | 25.29 | 94.02 |
21. | 31 oct. 2020 | -7.48% | -2.77% | 89.15 | 15.00 | 36.56 |
22. | 30 nov. 2020 | 26.42% | 10.75% | 598.10 | 93.10 | 235.97 |
23. | 31 dic. 2020 | 13.78% | 3.71% | 139.62 | 6.79 | 30.80 |
24. | 31 ene. 2021 | 6.16% | -1.11% | 17.56 | 4.93 | -9.30 |
25. | 28 feb. 2021 | 22.89% | 2.61% | 437.75 | 2.26 | 31.45 |
26. | 31 mar. 2021 | 7.28% | 4.24% | 28.22 | 9.85 | 16.67 |
27. | 30 abr. 2021 | -3.14% | 5.24% | 26.07 | 17.11 | -21.12 |
28. | 31 may. 2021 | -1.07% | 0.55% | 9.18 | 0.31 | 1.69 |
29. | 30 jun. 2021 | 7.16% | 2.22% | 26.95 | 1.24 | 5.79 |
30. | 31 jul. 2021 | -10.55% | 2.27% | 156.67 | 1.37 | -14.63 |
31. | 31 ago. 2021 | 2.96% | 2.90% | 0.99 | 3.22 | 1.78 |
32. | 30 sept. 2021 | 12.63% | -4.76% | 113.86 | 34.37 | -62.56 |
33. | 31 oct. 2021 | 12.29% | 6.91% | 106.70 | 33.74 | 60.00 |
34. | 30 nov. 2021 | -3.02% | -0.83% | 24.81 | 3.76 | 9.66 |
35. | 31 dic. 2021 | 2.34% | 4.36% | 0.14 | 10.60 | 1.24 |
36. | 31 ene. 2022 | 20.35% | -5.26% | 337.99 | 40.51 | -117.01 |
37. | 28 feb. 2022 | 11.19% | -3.14% | 85.08 | 17.99 | -39.13 |
38. | 31 mar. 2022 | 4.35% | 3.58% | 5.71 | 6.11 | 5.90 |
39. | 30 abr. 2022 | -7.02% | -8.80% | 80.77 | 98.04 | 88.99 |
40. | 31 may. 2022 | 22.73% | 0.01% | 431.39 | 1.21 | -22.86 |
41. | 30 jun. 2022 | -19.74% | -8.39% | 470.99 | 90.21 | 206.12 |
42. | 31 jul. 2022 | 6.22% | 9.11% | 18.09 | 64.09 | 34.05 |
43. | 31 ago. 2022 | 6.87% | -4.24% | 24.03 | 28.62 | -26.23 |
44. | 30 sept. 2022 | -11.10% | -9.34% | 170.80 | 109.11 | 136.51 |
45. | 31 oct. 2022 | 18.42% | 7.99% | 270.72 | 47.34 | 113.21 |
46. | 30 nov. 2022 | -5.74% | 5.38% | 59.31 | 18.23 | -32.88 |
47. | 31 dic. 2022 | -3.22% | -5.90% | 26.88 | 49.04 | 36.31 |
48. | 31 ene. 2023 | 0.86% | 6.18% | 1.22 | 25.70 | -5.61 |
49. | 28 feb. 2023 | -13.00% | -2.61% | 223.85 | 13.82 | 55.61 |
50. | 31 mar. 2023 | 4.70% | 3.51% | 7.46 | 5.76 | 6.55 |
51. | 30 abr. 2023 | 6.52% | 1.46% | 20.73 | 0.13 | 1.63 |
52. | 31 may. 2023 | -6.79% | 0.25% | 76.62 | 0.74 | 7.51 |
53. | 30 jun. 2023 | 3.88% | 4.71% | 3.67 | 13.02 | 6.92 |
54. | 31 jul. 2023 | 8.92% | 4.85% | 48.45 | 13.99 | 26.03 |
55. | 31 ago. 2023 | 5.43% | -1.77% | 12.03 | 8.28 | -9.98 |
56. | 30 sept. 2023 | -2.75% | -4.87% | 22.21 | 35.73 | 28.17 |
57. | 31 oct. 2023 | 4.12% | -2.20% | 4.63 | 10.92 | -7.11 |
58. | 30 nov. 2023 | -1.74% | 8.92% | 13.73 | 61.03 | -28.94 |
59. | 31 dic. 2023 | -2.92% | 4.42% | 23.84 | 11.00 | -16.20 |
Total (Σ): | 8,558.51 | 1,634.30 | 2,158.61 |
Mostrar todo
VarianzaPXD = Σ(RPXD,t–RPXD)2 ÷ (59 – 1)
= 8,558.51 ÷ (59 – 1)
= 147.56
VarianzaS&P 500 = Σ(RS&P 500,t–RS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18
CovarianzaPXD, S&P 500 = Σ(RPXD,t–RPXD)×(RS&P 500,t–RS&P 500) ÷ (59 – 1)
= 2,158.61 ÷ (59 – 1)
= 37.22
Estimación sistemática del riesgo (β)
VarianzaPXD | 147.56 |
VarianzaS&P 500 | 28.18 |
CovarianzaPXD, S&P 500 | 37.22 |
Coeficiente de correlaciónPXD, S&P 5001 | 0.58 |
βPXD2 | 1.32 |
αPXD3 | 0.50% |
Cálculos
1 Coeficiente de correlaciónPXD, S&P 500
= CovarianzaPXD, S&P 500 ÷ (Desviación estándarPXD × Desviación estándarS&P 500)
= 37.22 ÷ (12.15% × 5.31%)
= 0.58
2 βPXD
= CovarianzaPXD, S&P 500 ÷ VarianzaS&P 500
= 37.22 ÷ 28.18
= 1.32
3 αPXD
= PromedioPXD – βPXD × PromedioS&P 500
= 1.96% – 1.32 × 1.11%
= 0.50%
Tasa de rendimiento esperada
Suposiciones | ||
Tasa de rendimiento del LT Treasury Composite1 | RF | 4.43% |
Tasa de rendimiento esperada de la cartera de mercado2 | E(RM) | 13.60% |
Riesgo sistemático de Pioneer acciones ordinarias | βPXD | 1.32 |
Tasa de rendimiento esperada de las acciones ordinarias de Pioneer3 | E(RPXD) | 16.55% |
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(RPXD) = RF + βPXD [E(RM) – RF]
= 4.43% + 1.32 [13.60% – 4.43%]
= 16.55%