Stock Analysis on Net

Linde plc (NASDAQ:LIN)

Modelo de fijación de precios de activos de capital (CAPM) 

Microsoft Excel

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 Linde.


Tasas de retorno

Linde plc, tasas mensuales de retorno

Microsoft Excel
Linde plc (LIN) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioLIN,t1 DividendoLIN,t1 RLIN,t2 PrecioS&P 500,t RS&P 500,t3
31 ene. 2019 $163.01 2,704.10
1. 28 feb. 2019 $173.24 6.28% 2,784.49 2.97%
2. 31 mar. 2019 $175.93 $0.875 2.06% 2,834.40 1.79%
3. 30 abr. 2019 $180.26 2.46% 2,945.83 3.93%
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov. 2023 $413.77 8.27% 4,567.80 8.92%
59. 31 dic. 2023 $410.71 $1.275 -0.43% 4,769.83 4.42%
Promedio (R): 1.92% 1.11%
Desviación estándar: 6.50% 5.31%
Linde plc (LIN) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioLIN,t1 DividendoLIN,t1 RLIN,t2 PrecioS&P 500,t RS&P 500,t3
31 ene. 2019 $163.01 2,704.10
1. 28 feb. 2019 $173.24 6.28% 2,784.49 2.97%
2. 31 mar. 2019 $175.93 $0.875 2.06% 2,834.40 1.79%
3. 30 abr. 2019 $180.26 2.46% 2,945.83 3.93%
4. 31 may. 2019 $180.55 $0.875 0.65% 2,752.06 -6.58%
5. 30 jun. 2019 $200.80 11.22% 2,941.76 6.89%
6. 31 jul. 2019 $191.28 -4.74% 2,980.38 1.31%
7. 31 ago. 2019 $188.91 $0.875 -0.78% 2,926.46 -1.81%
8. 30 sept. 2019 $193.72 2.55% 2,976.74 1.72%
9. 31 oct. 2019 $198.35 2.39% 3,037.56 2.04%
10. 30 nov. 2019 $206.21 3.96% 3,140.98 3.40%
11. 31 dic. 2019 $212.90 $0.875 3.67% 3,230.78 2.86%
12. 31 ene. 2020 $203.13 -4.59% 3,225.52 -0.16%
13. 29 feb. 2020 $191.01 -5.97% 2,954.22 -8.41%
14. 31 mar. 2020 $173.00 $0.963 -8.92% 2,584.59 -12.51%
15. 30 abr. 2020 $183.99 6.35% 2,912.43 12.68%
16. 31 may. 2020 $202.34 9.97% 3,044.31 4.53%
17. 30 jun. 2020 $212.11 $0.963 5.30% 3,100.29 1.84%
18. 31 jul. 2020 $245.11 15.56% 3,271.12 5.51%
19. 31 ago. 2020 $249.74 1.89% 3,500.31 7.01%
20. 30 sept. 2020 $238.13 $0.963 -4.26% 3,363.00 -3.92%
21. 31 oct. 2020 $220.34 -7.47% 3,269.96 -2.77%
22. 30 nov. 2020 $256.42 16.37% 3,621.63 10.75%
23. 31 dic. 2020 $263.51 $0.963 3.14% 3,756.07 3.71%
24. 31 ene. 2021 $245.40 -6.87% 3,714.24 -1.11%
25. 28 feb. 2021 $244.27 -0.46% 3,811.15 2.61%
26. 31 mar. 2021 $280.14 $1.06 15.12% 3,972.89 4.24%
27. 30 abr. 2021 $285.84 2.03% 4,181.17 5.24%
28. 31 may. 2021 $300.60 5.16% 4,204.11 0.55%
29. 30 jun. 2021 $289.10 $1.06 -3.47% 4,297.50 2.22%
30. 31 jul. 2021 $307.39 6.33% 4,395.26 2.27%
31. 31 ago. 2021 $314.59 2.34% 4,522.68 2.90%
32. 30 sept. 2021 $293.38 $1.06 -6.41% 4,307.54 -4.76%
33. 31 oct. 2021 $319.20 8.80% 4,605.38 6.91%
34. 30 nov. 2021 $318.14 -0.33% 4,567.00 -0.83%
35. 31 dic. 2021 $346.43 $1.06 9.23% 4,766.18 4.36%
36. 31 ene. 2022 $318.68 -8.01% 4,515.55 -5.26%
37. 28 feb. 2022 $293.24 -7.98% 4,373.94 -3.14%
38. 31 mar. 2022 $319.43 $1.17 9.33% 4,530.41 3.58%
39. 30 abr. 2022 $311.96 -2.34% 4,131.93 -8.80%
40. 31 may. 2022 $324.68 4.08% 4,132.15 0.01%
41. 30 jun. 2022 $287.53 $1.17 -11.08% 3,785.38 -8.39%
42. 31 jul. 2022 $302.00 5.03% 4,130.29 9.11%
43. 31 ago. 2022 $282.86 -6.34% 3,955.00 -4.24%
44. 30 sept. 2022 $269.59 $1.17 -4.28% 3,585.62 -9.34%
45. 31 oct. 2022 $297.35 10.30% 3,871.98 7.99%
46. 30 nov. 2022 $336.48 13.16% 4,080.11 5.38%
47. 31 dic. 2022 $326.18 $1.17 -2.71% 3,839.50 -5.90%
48. 31 ene. 2023 $330.94 1.46% 4,076.60 6.18%
49. 28 feb. 2023 $348.37 5.27% 3,970.15 -2.61%
50. 31 mar. 2023 $355.44 $1.275 2.40% 4,109.31 3.51%
51. 30 abr. 2023 $369.45 3.94% 4,169.48 1.46%
52. 31 may. 2023 $353.66 -4.27% 4,179.83 0.25%
53. 30 jun. 2023 $381.08 $1.275 8.11% 4,376.86 4.71%
54. 31 jul. 2023 $390.67 2.52% 4,588.96 4.85%
55. 31 ago. 2023 $387.04 -0.93% 4,507.66 -1.77%
56. 30 sept. 2023 $372.35 $1.275 -3.47% 4,288.05 -4.87%
57. 31 oct. 2023 $382.16 2.63% 4,193.80 -2.20%
58. 30 nov. 2023 $413.77 8.27% 4,567.80 8.92%
59. 31 dic. 2023 $410.71 $1.275 -0.43% 4,769.83 4.42%
Promedio (R): 1.92% 1.11%
Desviación estándar: 6.50% 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 LIN 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

Linde plc, cálculo de la varianza y covarianza de los rendimientos

Microsoft Excel
t Fecha RLIN,t RS&P 500,t (RLIN,tRLIN)2 (RS&P 500,tRS&P 500)2 (RLIN,tRLIN)×(RS&P 500,tRS&P 500)
1. 28 feb. 2019 6.28% 2.97% 18.98 3.49 8.13
2. 31 mar. 2019 2.06% 1.79% 0.02 0.47 0.10
3. 30 abr. 2019 2.46% 3.93% 0.29 7.98 1.53
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov. 2023 8.27% 8.92% 40.36 61.03 49.63
59. 31 dic. 2023 -0.43% 4.42% 5.52 11.00 -7.80
Total (Σ): 2,453.29 1,634.30 1,499.15
t Fecha RLIN,t RS&P 500,t (RLIN,tRLIN)2 (RS&P 500,tRS&P 500)2 (RLIN,tRLIN)×(RS&P 500,tRS&P 500)
1. 28 feb. 2019 6.28% 2.97% 18.98 3.49 8.13
2. 31 mar. 2019 2.06% 1.79% 0.02 0.47 0.10
3. 30 abr. 2019 2.46% 3.93% 0.29 7.98 1.53
4. 31 may. 2019 0.65% -6.58% 1.62 59.04 9.78
5. 30 jun. 2019 11.22% 6.89% 86.44 33.49 53.80
6. 31 jul. 2019 -4.74% 1.31% 44.35 0.04 -1.38
7. 31 ago. 2019 -0.78% -1.81% 7.29 8.50 7.87
8. 30 sept. 2019 2.55% 1.72% 0.39 0.37 0.38
9. 31 oct. 2019 2.39% 2.04% 0.22 0.88 0.44
10. 30 nov. 2019 3.96% 3.40% 4.18 5.28 4.70
11. 31 dic. 2019 3.67% 2.86% 3.06 3.07 3.07
12. 31 ene. 2020 -4.59% -0.16% 42.35 1.61 8.26
13. 29 feb. 2020 -5.97% -8.41% 62.18 90.57 75.04
14. 31 mar. 2020 -8.92% -12.51% 117.58 185.44 147.66
15. 30 abr. 2020 6.35% 12.68% 19.66 134.06 51.34
16. 31 may. 2020 9.97% 4.53% 64.88 11.71 27.57
17. 30 jun. 2020 5.30% 1.84% 11.46 0.54 2.48
18. 31 jul. 2020 15.56% 5.51% 186.03 19.40 60.07
19. 31 ago. 2020 1.89% 7.01% 0.00 34.82 -0.18
20. 30 sept. 2020 -4.26% -3.92% 38.22 25.29 31.09
21. 31 oct. 2020 -7.47% -2.77% 88.16 15.00 36.36
22. 30 nov. 2020 16.37% 10.75% 208.98 93.10 139.48
23. 31 dic. 2020 3.14% 3.71% 1.49 6.79 3.18
24. 31 ene. 2021 -6.87% -1.11% 77.29 4.93 19.51
25. 28 feb. 2021 -0.46% 2.61% 5.66 2.26 -3.58
26. 31 mar. 2021 15.12% 4.24% 174.24 9.85 41.42
27. 30 abr. 2021 2.03% 5.24% 0.01 17.11 0.48
28. 31 may. 2021 5.16% 0.55% 10.53 0.31 -1.81
29. 30 jun. 2021 -3.47% 2.22% 29.07 1.24 -6.01
30. 31 jul. 2021 6.33% 2.27% 19.43 1.37 5.15
31. 31 ago. 2021 2.34% 2.90% 0.18 3.22 0.76
32. 30 sept. 2021 -6.41% -4.76% 69.29 34.37 48.80
33. 31 oct. 2021 8.80% 6.91% 47.36 33.74 39.98
34. 30 nov. 2021 -0.33% -0.83% 5.07 3.76 4.36
35. 31 dic. 2021 9.23% 4.36% 53.39 10.60 23.79
36. 31 ene. 2022 -8.01% -5.26% 98.58 40.51 63.19
37. 28 feb. 2022 -7.98% -3.14% 98.04 17.99 42.00
38. 31 mar. 2022 9.33% 3.58% 54.93 6.11 18.32
39. 30 abr. 2022 -2.34% -8.80% 18.12 98.04 42.15
40. 31 may. 2022 4.08% 0.01% 4.66 1.21 -2.38
41. 30 jun. 2022 -11.08% -8.39% 169.01 90.21 123.48
42. 31 jul. 2022 5.03% 9.11% 9.70 64.09 24.93
43. 31 ago. 2022 -6.34% -4.24% 68.17 28.62 44.17
44. 30 sept. 2022 -4.28% -9.34% 38.40 109.11 64.72
45. 31 oct. 2022 10.30% 7.99% 70.20 47.34 57.65
46. 30 nov. 2022 13.16% 5.38% 126.36 18.23 47.99
47. 31 dic. 2022 -2.71% -5.90% 21.46 49.04 32.44
48. 31 ene. 2023 1.46% 6.18% 0.21 25.70 -2.33
49. 28 feb. 2023 5.27% -2.61% 11.21 13.82 -12.45
50. 31 mar. 2023 2.40% 3.51% 0.23 5.76 1.14
51. 30 abr. 2023 3.94% 1.46% 4.09 0.13 0.72
52. 31 may. 2023 -4.27% 0.25% 38.35 0.74 5.31
53. 30 jun. 2023 8.11% 4.71% 38.38 13.02 22.35
54. 31 jul. 2023 2.52% 4.85% 0.36 13.99 2.24
55. 31 ago. 2023 -0.93% -1.77% 8.11 8.28 8.19
56. 30 sept. 2023 -3.47% -4.87% 29.00 35.73 32.19
57. 31 oct. 2023 2.63% -2.20% 0.51 10.92 -2.37
58. 30 nov. 2023 8.27% 8.92% 40.36 61.03 49.63
59. 31 dic. 2023 -0.43% 4.42% 5.52 11.00 -7.80
Total (Σ): 2,453.29 1,634.30 1,499.15

Mostrar todo

VarianzaLIN = Σ(RLIN,tRLIN)2 ÷ (59 – 1)
= 2,453.29 ÷ (59 – 1)
= 42.30

VarianzaS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,634.30 ÷ (59 – 1)
= 28.18

CovarianzaLIN, S&P 500 = Σ(RLIN,tRLIN)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,499.15 ÷ (59 – 1)
= 25.85


Estimación sistemática del riesgo (β)

Microsoft Excel
VarianzaLIN 42.30
VarianzaS&P 500 28.18
CovarianzaLIN, S&P 500 25.85
Coeficiente de correlaciónLIN, S&P 5001 0.75
βLIN2 0.92
αLIN3 0.90%

Cálculos

1 Coeficiente de correlaciónLIN, S&P 500
= CovarianzaLIN, S&P 500 ÷ (Desviación estándarLIN × Desviación estándarS&P 500)
= 25.85 ÷ (6.50% × 5.31%)
= 0.75

2 βLIN
= CovarianzaLIN, S&P 500 ÷ VarianzaS&P 500
= 25.85 ÷ 28.18
= 0.92

3 αLIN
= PromedioLIN – βLIN × PromedioS&P 500
= 1.92%0.92 × 1.11%
= 0.90%


Tasa de rendimiento esperada

Microsoft Excel
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 Linde acciones ordinarias βLIN 0.92
 
Tasa de rendimiento esperada de las acciones ordinarias de Linde3 E(RLIN) 12.85%

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).

2 Ver detalles »

3 E(RLIN) = RF + βLIN [E(RM) – RF]
= 4.43% + 0.92 [13.60%4.43%]
= 12.85%