Modelo de valoración de activos de capital (CAPM)

Nivel de dificultad medio

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

Las tasas de rendimiento
Varianza y covarianza
Estimación sistemática de riesgos (β)
Tasa de rendimiento esperada

Las tasas de rendimiento

Alphabet Inc., tasas de rendimiento mensuales

		Alphabet Inc. (GOOG)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_GOOG,t¹	Dividendo_GOOG,t¹	R_GOOG,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	31 ene. 2016	$742.95			1,940.24
1.	29 feb. 2016	$697.77		-6.08%	1,932.23	-0.41%
2.	31 mar. 2016	$744.95		6.76%	2,059.74	6.60%
3.	30 abr. 2016	$693.01		-6.97%	2,065.30	0.27%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
58.	30 nov. 2020	$1,760.74		8.62%	3,621.63	10.75%
59.	31 dic. 2020	$1,751.88		-0.50%	3,756.07	3.71%
Promedio (R):				1.65%		1.22%
Desviación típica:				6.18%		4.36%

Fuente: Alphabet Inc. (NASDAQ:GOOG) | CAPM (www.stock-analysis-on.net)

		Alphabet Inc. (GOOG)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_GOOG,t¹	Dividendo_GOOG,t¹	R_GOOG,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	31 ene. 2016	$742.95			1,940.24
1.	29 feb. 2016	$697.77		-6.08%	1,932.23	-0.41%
2.	31 mar. 2016	$744.95		6.76%	2,059.74	6.60%
3.	30 abr. 2016	$693.01		-6.97%	2,065.30	0.27%
4.	31 may. 2016	$735.72		6.16%	2,096.95	1.53%
5.	30 jun. 2016	$692.10		-5.93%	2,098.86	0.09%
6.	31 jul. 2016	$768.79		11.08%	2,173.60	3.56%
7.	31 ago. 2016	$767.05		-0.23%	2,170.95	-0.12%
8.	30 sept. 2016	$777.29		1.33%	2,168.27	-0.12%
9.	31 oct. 2016	$784.54		0.93%	2,126.15	-1.94%
10.	30 nov. 2016	$758.04		-3.38%	2,198.81	3.42%
11.	31 dic. 2016	$771.82		1.82%	2,238.83	1.82%
12.	31 ene. 2017	$796.79		3.24%	2,278.87	1.79%
13.	28 feb. 2017	$823.21		3.32%	2,363.64	3.72%
14.	31 mar. 2017	$829.56		0.77%	2,362.72	-0.04%
15.	30 abr. 2017	$905.96		9.21%	2,384.20	0.91%
16.	31 may. 2017	$964.86		6.50%	2,411.80	1.16%
17.	30 jun. 2017	$908.73		-5.82%	2,423.41	0.48%
18.	31 jul. 2017	$930.50		2.40%	2,470.30	1.93%
19.	31 ago. 2017	$939.33		0.95%	2,471.65	0.05%
20.	30 sept. 2017	$959.11		2.11%	2,519.36	1.93%
21.	31 oct. 2017	$1,016.64		6.00%	2,575.26	2.22%
22.	30 nov. 2017	$1,021.41		0.47%	2,647.58	2.81%
23.	31 dic. 2017	$1,046.40		2.45%	2,673.61	0.98%
24.	31 ene. 2018	$1,169.94		11.81%	2,823.81	5.62%
25.	28 feb. 2018	$1,104.73		-5.57%	2,713.83	-3.89%
26.	31 mar. 2018	$1,031.79		-6.60%	2,640.87	-2.69%
27.	30 abr. 2018	$1,017.33		-1.40%	2,648.05	0.27%
28.	31 may. 2018	$1,084.99		6.65%	2,705.27	2.16%
29.	30 jun. 2018	$1,115.65		2.83%	2,718.37	0.48%
30.	31 jul. 2018	$1,217.26		9.11%	2,816.29	3.60%
31.	31 ago. 2018	$1,218.19		0.08%	2,901.52	3.03%
32.	30 sept. 2018	$1,193.47		-2.03%	2,913.98	0.43%
33.	31 oct. 2018	$1,076.77		-9.78%	2,711.74	-6.94%
34.	30 nov. 2018	$1,094.43		1.64%	2,760.17	1.79%
35.	31 dic. 2018	$1,035.61		-5.37%	2,506.85	-9.18%
36.	31 ene. 2019	$1,116.37		7.80%	2,704.10	7.87%
37.	28 feb. 2019	$1,119.92		0.32%	2,784.49	2.97%
38.	31 mar. 2019	$1,173.31		4.77%	2,834.40	1.79%
39.	30 abr. 2019	$1,188.48		1.29%	2,945.83	3.93%
40.	31 may. 2019	$1,103.63		-7.14%	2,752.06	-6.58%
41.	30 jun. 2019	$1,080.91		-2.06%	2,941.76	6.89%
42.	31 jul. 2019	$1,216.68		12.56%	2,980.38	1.31%
43.	31 ago. 2019	$1,188.10		-2.35%	2,926.46	-1.81%
44.	30 sept. 2019	$1,219.00		2.60%	2,976.74	1.72%
45.	31 oct. 2019	$1,260.11		3.37%	3,037.56	2.04%
46.	30 nov. 2019	$1,304.96		3.56%	3,140.98	3.40%
47.	31 dic. 2019	$1,337.02		2.46%	3,230.78	2.86%
48.	31 ene. 2020	$1,434.23		7.27%	3,225.52	-0.16%
49.	29 feb. 2020	$1,339.33		-6.62%	2,954.22	-8.41%
50.	31 mar. 2020	$1,162.81		-13.18%	2,584.59	-12.51%
51.	30 abr. 2020	$1,348.66		15.98%	2,912.43	12.68%
52.	31 may. 2020	$1,428.92		5.95%	3,044.31	4.53%
53.	30 jun. 2020	$1,413.61		-1.07%	3,100.29	1.84%
54.	31 jul. 2020	$1,482.96		4.91%	3,271.12	5.51%
55.	31 ago. 2020	$1,634.18		10.20%	3,500.31	7.01%
56.	30 sept. 2020	$1,469.60		-10.07%	3,363.00	-3.92%
57.	31 oct. 2020	$1,621.01		10.30%	3,269.96	-2.77%
58.	30 nov. 2020	$1,760.74		8.62%	3,621.63	10.75%
59.	31 dic. 2020	$1,751.88		-0.50%	3,756.07	3.71%
Promedio (R):				1.65%		1.22%
Desviación típica:				6.18%		4.36%

Fuente: Alphabet Inc. (NASDAQ:GOOG) | CAPM (www.stock-analysis-on.net)

Mostrar todo

¹ Datos en dólares estadounidenses por acción ordinaria, ajustados por divisiones y dividendos en acciones.

² Tasa de rendimiento de las acciones ordinarias de GOOG 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

Alphabet Inc., cálculo de varianza y covarianza de retornos

t	Fecha	R_GOOG,t	R_{S&P 500,t}	(R_GOOG,t–R_GOOG)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_GOOG,t–R_GOOG)×(R_{S&P 500,t}–R_{S&P 500})
1.	29 feb. 2016	-6.08%	-0.41%	59.78	2.67	12.63
2.	31 mar. 2016	6.76%	6.60%	26.12	28.93	27.49
3.	30 abr. 2016	-6.97%	0.27%	74.36	0.90	8.19
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58.	30 nov. 2020	8.62%	10.75%	48.57	90.91	66.45
59.	31 dic. 2020	-0.50%	3.71%	4.64	6.21	-5.37
Total (Σ):				2,215.79	1,103.45	1,102.34

t	Fecha	R_GOOG,t	R_{S&P 500,t}	(R_GOOG,t–R_GOOG)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_GOOG,t–R_GOOG)×(R_{S&P 500,t}–R_{S&P 500})
1.	29 feb. 2016	-6.08%	-0.41%	59.78	2.67	12.63
2.	31 mar. 2016	6.76%	6.60%	26.12	28.93	27.49
3.	30 abr. 2016	-6.97%	0.27%	74.36	0.90	8.19
4.	31 may. 2016	6.16%	1.53%	20.36	0.10	1.41
5.	30 jun. 2016	-5.93%	0.09%	57.45	1.27	8.56
6.	31 jul. 2016	11.08%	3.56%	88.92	5.48	22.07
7.	31 ago. 2016	-0.23%	-0.12%	3.52	1.80	2.52
8.	30 sept. 2016	1.33%	-0.12%	0.10	1.81	0.42
9.	31 oct. 2016	0.93%	-1.94%	0.52	10.00	2.27
10.	30 nov. 2016	-3.38%	3.42%	25.29	4.83	-11.05
11.	31 dic. 2016	1.82%	1.82%	0.03	0.36	0.10
12.	31 ene. 2017	3.24%	1.79%	2.51	0.32	0.90
13.	28 feb. 2017	3.32%	3.72%	2.77	6.25	4.16
14.	31 mar. 2017	0.77%	-0.04%	0.77	1.59	1.11
15.	30 abr. 2017	9.21%	0.91%	57.14	0.10	-2.35
16.	31 may. 2017	6.50%	1.16%	23.53	0.00	-0.30
17.	30 jun. 2017	-5.82%	0.48%	55.78	0.55	5.52
18.	31 jul. 2017	2.40%	1.93%	0.55	0.51	0.53
19.	31 ago. 2017	0.95%	0.05%	0.49	1.36	0.82
20.	30 sept. 2017	2.11%	1.93%	0.21	0.50	0.32
21.	31 oct. 2017	6.00%	2.22%	18.90	1.00	4.34
22.	30 nov. 2017	0.47%	2.81%	1.40	2.52	-1.88
23.	31 dic. 2017	2.45%	0.98%	0.63	0.06	-0.19
24.	31 ene. 2018	11.81%	5.62%	103.13	19.34	44.66
25.	28 feb. 2018	-5.57%	-3.89%	52.20	26.16	36.95
26.	31 mar. 2018	-6.60%	-2.69%	68.12	15.28	32.26
27.	30 abr. 2018	-1.40%	0.27%	9.32	0.90	2.89
28.	31 may. 2018	6.65%	2.16%	25.00	0.89	4.70
29.	30 jun. 2018	2.83%	0.48%	1.38	0.54	-0.86
30.	31 jul. 2018	9.11%	3.60%	55.60	5.67	17.76
31.	31 ago. 2018	0.08%	3.03%	2.48	3.26	-2.84
32.	30 sept. 2018	-2.03%	0.43%	13.54	0.63	2.91
33.	31 oct. 2018	-9.78%	-6.94%	130.62	66.59	93.27
34.	30 nov. 2018	1.64%	1.79%	0.00	0.32	-0.01
35.	31 dic. 2018	-5.37%	-9.18%	49.36	108.11	73.05
36.	31 ene. 2019	7.80%	7.87%	37.79	44.20	40.87
37.	28 feb. 2019	0.32%	2.97%	1.78	3.07	-2.34
38.	31 mar. 2019	4.77%	1.79%	9.71	0.33	1.78
39.	30 abr. 2019	1.29%	3.93%	0.13	7.35	-0.97
40.	31 may. 2019	-7.14%	-6.58%	77.27	60.81	68.54
41.	30 jun. 2019	-2.06%	6.89%	13.76	32.18	-21.04
42.	31 jul. 2019	12.56%	1.31%	119.03	0.01	1.01
43.	31 ago. 2019	-2.35%	-1.81%	16.00	9.18	12.12
44.	30 sept. 2019	2.60%	1.72%	0.90	0.25	0.47
45.	31 oct. 2019	3.37%	2.04%	2.96	0.68	1.42
46.	30 nov. 2019	3.56%	3.40%	3.64	4.77	4.17
47.	31 dic. 2019	2.46%	2.86%	0.65	2.69	1.32
48.	31 ene. 2020	7.27%	-0.16%	31.58	1.91	-7.77
49.	29 feb. 2020	-6.62%	-8.41%	68.35	92.76	79.63
50.	31 mar. 2020	-13.18%	-12.51%	219.95	188.57	203.65
51.	30 abr. 2020	15.98%	12.68%	205.41	131.43	164.31
52.	31 may. 2020	5.95%	4.53%	18.49	10.94	14.23
53.	30 jun. 2020	-1.07%	1.84%	7.41	0.38	-1.68
54.	31 jul. 2020	4.91%	5.51%	10.60	18.40	13.96
55.	31 ago. 2020	10.20%	7.01%	73.04	33.48	49.45
56.	30 sept. 2020	-10.07%	-3.92%	137.40	26.45	60.28
57.	31 oct. 2020	10.30%	-2.77%	74.86	15.89	-34.49
58.	30 nov. 2020	8.62%	10.75%	48.57	90.91	66.45
59.	31 dic. 2020	-0.50%	3.71%	4.64	6.21	-5.37
Total (Σ):				2,215.79	1,103.45	1,102.34

Show all

Varianza_GOOG = Σ(R_GOOG,t–R_GOOG)² ÷ (59 – 1)
= 2,215.79 ÷ (59 – 1)
= 38.20

Varianza_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (59 – 1)
= 1,103.45 ÷ (59 – 1)
= 19.02

Covarianza_{GOOG, S&P 500} = Σ(R_GOOG,t–R_GOOG)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 1,102.34 ÷ (59 – 1)
= 19.01

Estimación sistemática de riesgos (β)

Varianza_GOOG	38.20
Varianza_{S&P 500}	19.02
Covarianza_{GOOG, S&P 500}	19.01
Coeficiente de correlación_{GOOG, S&P 500}¹	0.70
β_GOOG²	1.00
α_GOOG³	0.43%

Fuente: Alphabet Inc. (NASDAQ:GOOG) | CAPM (www.stock-analysis-on.net)

Cálculos

¹ Coeficiente de correlación_{GOOG, S&P 500}
= Covarianza_{GOOG, S&P 500} ÷ (Desviación típica_GOOG × Desviación típica_{S&P 500})
= 19.01 ÷ (6.18% × 4.36%)
= 0.70

² β_GOOG
= Covarianza_{GOOG, S&P 500} ÷ Varianza_{S&P 500}
= 19.01 ÷ 19.02
= 1.00

³ α_GOOG
= Promedio_GOOG – β_GOOG × Promedio_{S&P 500}
= 1.65% – 1.00 × 1.22%
= 0.43%

Tasa de rendimiento esperada

Supuestos
Tasa de rendimiento de LT Treasury Composite¹	R_F	2.03%
Tasa de rendimiento esperada de la cartera de mercado²	E(R_M)	11.89%
Riesgo sistemático de las acciones ordinarias de Alphabet	β_GOOG	1.00

Tasa de rendimiento esperada de las acciones ordinarias de Alphabet³	E(R_GOOG)	11.88%

Fuente: Alphabet Inc. (NASDAQ:GOOG) | CAPM (www.stock-analysis-on.net)

¹ Promedio no ponderado de los rendimientos de las ofertas de todos los bonos del Tesoro de EE. UU. De cupón fijo en circulación que no vencen ni son exigibles en menos de 10 años (proxy de tasa de rendimiento sin riesgo).

² Ver detalles »

³ E(R_GOOG) = R_F + β_GOOG [E(R_M) – R_F]
= 2.03% + 1.00 [11.89% – 2.03%]
= 11.88%