Stock Analysis on Net

3M Co. (NYSE:MMM)

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

Microsoft Excel

El modelo de fijación de precios de activos de capital (CAPM) indica cuál debería ser la tasa de rendimiento esperada o requerida de los activos de riesgo, como las acciones ordinarias de 3M.


Tasas de retorno

3M Co., tasas mensuales de retorno

Microsoft Excel
3M Co. (MMM) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioMMM,t1 DividendoMMM,t1 RMMM,t2 PrecioS&P 500,t RS&P 500,t3
31 ene. 2017 $174.82 2,278.87
1. 28 feb. 2017 $186.35 $1.175 7.27% 2,363.64 3.72%
2. 31 mar. 2017 $191.33 2.67% 2,362.72 -0.04%
3. 30 abr. 2017 $195.83 2.35% 2,384.20 0.91%
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov. 2021 $170.04 $1.48 -4.01% 4,567.00 -0.83%
59. 31 dic. 2021 $177.63 4.46% 4,766.18 4.36%
Promedio (R): 0.46% 1.36%
Desviación estándar: 6.03% 4.48%
3M Co. (MMM) Standard & Poor’s 500 (S&P 500)
t Fecha PrecioMMM,t1 DividendoMMM,t1 RMMM,t2 PrecioS&P 500,t RS&P 500,t3
31 ene. 2017 $174.82 2,278.87
1. 28 feb. 2017 $186.35 $1.175 7.27% 2,363.64 3.72%
2. 31 mar. 2017 $191.33 2.67% 2,362.72 -0.04%
3. 30 abr. 2017 $195.83 2.35% 2,384.20 0.91%
4. 31 may. 2017 $204.47 $1.175 5.01% 2,411.80 1.16%
5. 30 jun. 2017 $208.19 1.82% 2,423.41 0.48%
6. 31 jul. 2017 $201.17 -3.37% 2,470.30 1.93%
7. 31 ago. 2017 $204.32 $1.175 2.15% 2,471.65 0.05%
8. 30 sept. 2017 $209.90 2.73% 2,519.36 1.93%
9. 31 oct. 2017 $230.19 9.67% 2,575.26 2.22%
10. 30 nov. 2017 $243.14 $1.175 6.14% 2,647.58 2.81%
11. 31 dic. 2017 $235.37 -3.20% 2,673.61 0.98%
12. 31 ene. 2018 $250.50 6.43% 2,823.81 5.62%
13. 28 feb. 2018 $235.51 $1.36 -5.44% 2,713.83 -3.89%
14. 31 mar. 2018 $219.52 -6.79% 2,640.87 -2.69%
15. 30 abr. 2018 $194.39 -11.45% 2,648.05 0.27%
16. 31 may. 2018 $197.23 $1.36 2.16% 2,705.27 2.16%
17. 30 jun. 2018 $196.72 -0.26% 2,718.37 0.48%
18. 31 jul. 2018 $212.32 7.93% 2,816.29 3.60%
19. 31 ago. 2018 $210.92 $1.36 -0.02% 2,901.52 3.03%
20. 30 sept. 2018 $210.71 -0.10% 2,913.98 0.43%
21. 31 oct. 2018 $190.26 -9.71% 2,711.74 -6.94%
22. 30 nov. 2018 $207.92 $1.36 10.00% 2,760.17 1.79%
23. 31 dic. 2018 $190.54 -8.36% 2,506.85 -9.18%
24. 31 ene. 2019 $200.30 5.12% 2,704.10 7.87%
25. 28 feb. 2019 $207.39 $1.44 4.26% 2,784.49 2.97%
26. 31 mar. 2019 $207.78 0.19% 2,834.40 1.79%
27. 30 abr. 2019 $189.51 -8.79% 2,945.83 3.93%
28. 31 may. 2019 $159.75 $1.44 -14.94% 2,752.06 -6.58%
29. 30 jun. 2019 $173.34 8.51% 2,941.76 6.89%
30. 31 jul. 2019 $174.72 0.80% 2,980.38 1.31%
31. 31 ago. 2019 $161.72 $1.44 -6.62% 2,926.46 -1.81%
32. 30 sept. 2019 $164.40 1.66% 2,976.74 1.72%
33. 31 oct. 2019 $164.99 0.36% 3,037.56 2.04%
34. 30 nov. 2019 $169.77 $1.44 3.77% 3,140.98 3.40%
35. 31 dic. 2019 $176.42 3.92% 3,230.78 2.86%
36. 31 ene. 2020 $158.66 -10.07% 3,225.52 -0.16%
37. 29 feb. 2020 $149.24 $1.47 -5.01% 2,954.22 -8.41%
38. 31 mar. 2020 $136.51 -8.53% 2,584.59 -12.51%
39. 30 abr. 2020 $151.92 11.29% 2,912.43 12.68%
40. 31 may. 2020 $156.44 $1.47 3.94% 3,044.31 4.53%
41. 30 jun. 2020 $155.99 -0.29% 3,100.29 1.84%
42. 31 jul. 2020 $150.47 -3.54% 3,271.12 5.51%
43. 31 ago. 2020 $163.02 $1.47 9.32% 3,500.31 7.01%
44. 30 sept. 2020 $160.18 -1.74% 3,363.00 -3.92%
45. 31 oct. 2020 $159.96 -0.14% 3,269.96 -2.77%
46. 30 nov. 2020 $172.73 $1.47 8.90% 3,621.63 10.75%
47. 31 dic. 2020 $174.79 1.19% 3,756.07 3.71%
48. 31 ene. 2021 $175.66 0.50% 3,714.24 -1.11%
49. 28 feb. 2021 $175.06 $1.48 0.50% 3,811.15 2.61%
50. 31 mar. 2021 $192.68 10.07% 3,972.89 4.24%
51. 30 abr. 2021 $197.14 2.31% 4,181.17 5.24%
52. 31 may. 2021 $203.04 $1.48 3.74% 4,204.11 0.55%
53. 30 jun. 2021 $198.63 -2.17% 4,297.50 2.22%
54. 31 jul. 2021 $197.94 -0.35% 4,395.26 2.27%
55. 31 ago. 2021 $194.74 $1.48 -0.87% 4,522.68 2.90%
56. 30 sept. 2021 $175.42 -9.92% 4,307.54 -4.76%
57. 31 oct. 2021 $178.68 1.86% 4,605.38 6.91%
58. 30 nov. 2021 $170.04 $1.48 -4.01% 4,567.00 -0.83%
59. 31 dic. 2021 $177.63 4.46% 4,766.18 4.36%
Promedio (R): 0.46% 1.36%
Desviación estándar: 6.03% 4.48%

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1 Datos en US$ por acción de acciones ordinarias, ajustados por escisiones y dividendos de acciones.

2 Tasa de rendimiento de las acciones ordinarias de MMM 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

3M Co., cálculo de varianza y covarianza de rendimientos

Microsoft Excel
t Fecha RMMM,t RS&P 500,t (RMMM,tRMMM)2 (RS&P 500,tRS&P 500)2 (RMMM,tRMMM)×(RS&P 500,tRS&P 500)
1. 28 feb. 2017 7.27% 3.72% 46.30 5.58 16.07
2. 31 mar. 2017 2.67% -0.04% 4.88 1.95 -3.09
3. 30 abr. 2017 2.35% 0.91% 3.57 0.20 -0.85
. . . . . . .
. . . . . . .
. . . . . . .
58. 30 nov. 2021 -4.01% -0.83% 19.98 4.80 9.80
59. 31 dic. 2021 4.46% 4.36% 16.01 9.02 12.02
Total (Σ): 2,109.95 1,164.17 1,113.30
t Fecha RMMM,t RS&P 500,t (RMMM,tRMMM)2 (RS&P 500,tRS&P 500)2 (RMMM,tRMMM)×(RS&P 500,tRS&P 500)
1. 28 feb. 2017 7.27% 3.72% 46.30 5.58 16.07
2. 31 mar. 2017 2.67% -0.04% 4.88 1.95 -3.09
3. 30 abr. 2017 2.35% 0.91% 3.57 0.20 -0.85
4. 31 may. 2017 5.01% 1.16% 20.69 0.04 -0.91
5. 30 jun. 2017 1.82% 0.48% 1.84 0.77 -1.19
6. 31 jul. 2017 -3.37% 1.93% 14.71 0.33 -2.21
7. 31 ago. 2017 2.15% 0.05% 2.85 1.70 -2.20
8. 30 sept. 2017 2.73% 1.93% 5.14 0.33 1.30
9. 31 oct. 2017 9.67% 2.22% 84.70 0.74 7.92
10. 30 nov. 2017 6.14% 2.81% 32.19 2.10 8.23
11. 31 dic. 2017 -3.20% 0.98% 13.39 0.14 1.37
12. 31 ene. 2018 6.43% 5.62% 35.58 18.15 25.41
13. 28 feb. 2018 -5.44% -3.89% 34.86 27.59 31.01
14. 31 mar. 2018 -6.79% -2.69% 52.60 16.37 29.35
15. 30 abr. 2018 -11.45% 0.27% 141.86 1.18 12.94
16. 31 may. 2018 2.16% 2.16% 2.88 0.64 1.36
17. 30 jun. 2018 -0.26% 0.48% 0.52 0.76 0.63
18. 31 jul. 2018 7.93% 3.60% 55.76 5.04 16.76
19. 31 ago. 2018 -0.02% 3.03% 0.23 2.78 -0.80
20. 30 sept. 2018 -0.10% 0.43% 0.32 0.86 0.52
21. 31 oct. 2018 -9.71% -6.94% 103.39 68.86 84.38
22. 30 nov. 2018 10.00% 1.79% 90.89 0.18 4.08
23. 31 dic. 2018 -8.36% -9.18% 77.83 111.00 92.94
24. 31 ene. 2019 5.12% 7.87% 21.71 42.39 30.33
25. 28 feb. 2019 4.26% 2.97% 14.41 2.61 6.13
26. 31 mar. 2019 0.19% 1.79% 0.08 0.19 -0.12
27. 30 abr. 2019 -8.79% 3.93% 85.67 6.62 -23.82
28. 31 may. 2019 -14.94% -6.58% 237.37 62.97 122.26
29. 30 jun. 2019 8.51% 6.89% 64.71 30.64 44.52
30. 31 jul. 2019 0.80% 1.31% 0.11 0.00 -0.02
31. 31 ago. 2019 -6.62% -1.81% 50.12 10.03 22.42
32. 30 sept. 2019 1.66% 1.72% 1.43 0.13 0.43
33. 31 oct. 2019 0.36% 2.04% 0.01 0.47 -0.07
34. 30 nov. 2019 3.77% 3.40% 10.94 4.19 6.77
35. 31 dic. 2019 3.92% 2.86% 11.93 2.25 5.18
36. 31 ene. 2020 -10.07% -0.16% 110.88 2.31 16.01
37. 29 feb. 2020 -5.01% -8.41% 29.96 95.43 53.47
38. 31 mar. 2020 -8.53% -12.51% 80.87 192.37 124.73
39. 30 abr. 2020 11.29% 12.68% 117.19 128.29 122.62
40. 31 may. 2020 3.94% 4.53% 12.11 10.05 11.03
41. 30 jun. 2020 -0.29% 1.84% 0.56 0.23 -0.36
42. 31 jul. 2020 -3.54% 5.51% 16.01 17.24 -16.62
43. 31 ago. 2020 9.32% 7.01% 78.40 31.91 50.02
44. 30 sept. 2020 -1.74% -3.92% 4.86 27.89 11.64
45. 31 oct. 2020 -0.14% -2.77% 0.36 17.01 2.48
46. 30 nov. 2020 8.90% 10.75% 71.22 88.30 79.30
47. 31 dic. 2020 1.19% 3.71% 0.53 5.54 1.72
48. 31 ene. 2021 0.50% -1.11% 0.00 6.11 -0.09
49. 28 feb. 2021 0.50% 2.61% 0.00 1.57 0.05
50. 31 mar. 2021 10.07% 4.24% 92.20 8.33 27.71
51. 30 abr. 2021 2.31% 5.24% 3.43 15.09 7.19
52. 31 may. 2021 3.74% 0.55% 10.76 0.65 -2.65
53. 30 jun. 2021 -2.17% 2.22% 6.94 0.75 -2.28
54. 31 jul. 2021 -0.35% 2.27% 0.66 0.84 -0.74
55. 31 ago. 2021 -0.87% 2.90% 1.77 2.38 -2.05
56. 30 sept. 2021 -9.92% -4.76% 107.83 37.39 63.50
57. 31 oct. 2021 1.86% 6.91% 1.95 30.87 7.75
58. 30 nov. 2021 -4.01% -0.83% 19.98 4.80 9.80
59. 31 dic. 2021 4.46% 4.36% 16.01 9.02 12.02
Total (Σ): 2,109.95 1,164.17 1,113.30

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VarianzaMMM = Σ(RMMM,tRMMM)2 ÷ (59 – 1)
= 2,109.95 ÷ (59 – 1)
= 36.38

VarianzaS&P 500 = Σ(RS&P 500,tRS&P 500)2 ÷ (59 – 1)
= 1,164.17 ÷ (59 – 1)
= 20.07

CovarianzaMMM, S&P 500 = Σ(RMMM,tRMMM)×(RS&P 500,tRS&P 500) ÷ (59 – 1)
= 1,113.30 ÷ (59 – 1)
= 19.19


Estimación sistemática del riesgo (β)

Microsoft Excel
VarianzaMMM 36.38
VarianzaS&P 500 20.07
CovarianzaMMM, S&P 500 19.19
Coeficiente de correlaciónMMM, S&P 5001 0.71
βMMM2 0.96
αMMM3 -0.84%

Cálculos

1 Coeficiente de correlaciónMMM, S&P 500
= CovarianzaMMM, S&P 500 ÷ (Desviación estándarMMM × Desviación estándarS&P 500)
= 19.19 ÷ (6.03% × 4.48%)
= 0.71

2 βMMM
= CovarianzaMMM, S&P 500 ÷ VarianzaS&P 500
= 19.19 ÷ 20.07
= 0.96

3 αMMM
= PromedioMMM – βMMM × PromedioS&P 500
= 0.46%0.96 × 1.36%
= -0.84%


Tasa de rendimiento esperada

Microsoft Excel
Suposiciones
Tasa de rendimiento de LT Treasury Composite1 RF 3.62%
Tasa de rendimiento esperada de la cartera de mercado2 E(RM) 12.55%
Riesgo sistemático de acciones ordinarias 3M βMMM 0.96
 
Tasa de rendimiento esperada de las acciones ordinarias de 3M3 E(RMMM) 12.16%

1 Promedio no ponderado de los rendimientos de las ofertas en todos los bonos del Tesoro de los Estados Unidos con cupón fijo pendientes, ni vencidos ni exigibles en menos de 10 años (proxy de tasa de rendimiento libre de riesgo).

2 Ver detalles »

3 E(RMMM) = RF + βMMM [E(RM) – RF]
= 3.62% + 0.96 [12.55%3.62%]
= 12.16%