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 los activos de riesgo como las acciones ordinarias de Oracle.

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

Las tasas de rendimiento

Oracle Corp., tasas de rendimiento mensuales

		Oracle Corp. (ORCL)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_ORCL,t¹	Dividendo_ORCL,t¹	R_ORCL,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	30 jun. 2014	$40.53			1,960.23
1.	31 jul. 2014	$40.39	$0.12	-0.05%	1,930.67	-1.51%
2.	31 ago. 2014	$41.53		2.82%	2,003.37	3.77%
3.	30 sept. 2014	$38.28		-7.83%	1,972.29	-1.55%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	30 abr. 2020	$52.97	$0.24	10.10%	2,912.43	12.68%
71.	31 may. 2020	$53.77		1.51%	3,044.31	4.53%
Promedio (R):				0.67%		0.70%
Desviación típica:				5.35%		4.05%

Fuente: Oracle Corp. (NYSE:ORCL) | CAPM (www.stock-analysis-on.net)

		Oracle Corp. (ORCL)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_ORCL,t¹	Dividendo_ORCL,t¹	R_ORCL,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	30 jun. 2014	$40.53			1,960.23
1.	31 jul. 2014	$40.39	$0.12	-0.05%	1,930.67	-1.51%
2.	31 ago. 2014	$41.53		2.82%	2,003.37	3.77%
3.	30 sept. 2014	$38.28		-7.83%	1,972.29	-1.55%
4.	31 oct. 2014	$39.05	$0.12	2.32%	2,018.05	2.32%
5.	30 nov. 2014	$42.41		8.60%	2,067.56	2.45%
6.	31 dic. 2014	$44.97		6.04%	2,058.90	-0.42%
7.	31 ene. 2015	$41.89	$0.12	-6.58%	1,994.99	-3.10%
8.	28 feb. 2015	$43.82		4.61%	2,104.50	5.49%
9.	31 mar. 2015	$43.15		-1.53%	2,067.89	-1.74%
10.	30 abr. 2015	$43.62	$0.15	1.44%	2,085.51	0.85%
11.	31 may. 2015	$43.49		-0.30%	2,107.39	1.05%
12.	30 jun. 2015	$40.30		-7.34%	2,063.11	-2.10%
13.	31 jul. 2015	$39.94	$0.15	-0.52%	2,103.84	1.97%
14.	31 ago. 2015	$37.09		-7.14%	1,972.18	-6.26%
15.	30 sept. 2015	$36.12		-2.62%	1,920.03	-2.64%
16.	31 oct. 2015	$38.84	$0.15	7.95%	2,079.36	8.30%
17.	30 nov. 2015	$38.97		0.33%	2,080.41	0.05%
18.	31 dic. 2015	$36.53		-6.26%	2,043.94	-1.75%
19.	31 ene. 2016	$36.31	$0.15	-0.19%	1,940.24	-5.07%
20.	29 feb. 2016	$36.78		1.29%	1,932.23	-0.41%
21.	31 mar. 2016	$40.91		11.23%	2,059.74	6.60%
22.	30 abr. 2016	$39.86	$0.15	-2.20%	2,065.30	0.27%
23.	31 may. 2016	$40.20		0.85%	2,096.95	1.53%
24.	30 jun. 2016	$40.93		1.82%	2,098.86	0.09%
25.	31 jul. 2016	$41.04	$0.15	0.64%	2,173.60	3.56%
26.	31 ago. 2016	$41.22		0.44%	2,170.95	-0.12%
27.	30 sept. 2016	$39.28		-4.71%	2,168.27	-0.12%
28.	31 oct. 2016	$38.42	$0.15	-1.81%	2,126.15	-1.94%
29.	30 nov. 2016	$40.19		4.61%	2,198.81	3.42%
30.	31 dic. 2016	$38.45		-4.33%	2,238.83	1.82%
31.	31 ene. 2017	$40.11	$0.15	4.71%	2,278.87	1.79%
32.	28 feb. 2017	$42.59		6.18%	2,363.64	3.72%
33.	31 mar. 2017	$44.61		4.74%	2,362.72	-0.04%
34.	30 abr. 2017	$44.96	$0.19	1.21%	2,384.20	0.91%
35.	31 may. 2017	$45.39		0.96%	2,411.80	1.16%
36.	30 jun. 2017	$50.14		10.46%	2,423.41	0.48%
37.	31 jul. 2017	$49.93	$0.19	-0.04%	2,470.30	1.93%
38.	31 ago. 2017	$50.33		0.80%	2,471.65	0.05%
39.	30 sept. 2017	$48.35		-3.93%	2,519.36	1.93%
40.	31 oct. 2017	$50.90	$0.19	5.67%	2,575.26	2.22%
41.	30 nov. 2017	$49.06		-3.61%	2,647.58	2.81%
42.	31 dic. 2017	$47.28		-3.63%	2,673.61	0.98%
43.	31 ene. 2018	$51.59	$0.19	9.52%	2,823.81	5.62%
44.	28 feb. 2018	$50.67		-1.78%	2,713.83	-3.89%
45.	31 mar. 2018	$45.75		-9.71%	2,640.87	-2.69%
46.	30 abr. 2018	$45.67	$0.19	0.24%	2,648.05	0.27%
47.	31 may. 2018	$46.72		2.30%	2,705.27	2.16%
48.	30 jun. 2018	$44.06		-5.69%	2,718.37	0.48%
49.	31 jul. 2018	$47.68	$0.19	8.65%	2,816.29	3.60%
50.	31 ago. 2018	$48.58		1.89%	2,901.52	3.03%
51.	30 sept. 2018	$51.56		6.13%	2,913.98	0.43%
52.	31 oct. 2018	$48.84	$0.19	-4.91%	2,711.74	-6.94%
53.	30 nov. 2018	$48.76		-0.16%	2,760.17	1.79%
54.	31 dic. 2018	$45.15		-7.40%	2,506.85	-9.18%
55.	31 ene. 2019	$50.23	$0.19	11.67%	2,704.10	7.87%
56.	28 feb. 2019	$52.13		3.78%	2,784.49	2.97%
57.	31 mar. 2019	$53.71		3.03%	2,834.40	1.79%
58.	30 abr. 2019	$55.33	$0.24	3.46%	2,945.83	3.93%
59.	31 may. 2019	$50.60		-8.55%	2,752.06	-6.58%
60.	30 jun. 2019	$56.97		12.59%	2,941.76	6.89%
61.	31 jul. 2019	$56.30	$0.24	-0.75%	2,980.38	1.31%
62.	31 ago. 2019	$52.06		-7.53%	2,926.46	-1.81%
63.	30 sept. 2019	$55.03		5.70%	2,976.74	1.72%
64.	31 oct. 2019	$54.49	$0.24	-0.55%	3,037.56	2.04%
65.	30 nov. 2019	$56.14		3.03%	3,140.98	3.40%
66.	31 dic. 2019	$52.98		-5.63%	3,230.78	2.86%
67.	31 ene. 2020	$52.45	$0.24	-0.55%	3,225.52	-0.16%
68.	29 feb. 2020	$49.46		-5.70%	2,954.22	-8.41%
69.	31 mar. 2020	$48.33		-2.28%	2,584.59	-12.51%
70.	30 abr. 2020	$52.97	$0.24	10.10%	2,912.43	12.68%
71.	31 may. 2020	$53.77		1.51%	3,044.31	4.53%
Promedio (R):				0.67%		0.70%
Desviación típica:				5.35%		4.05%

Fuente: Oracle Corp. (NYSE:ORCL) | 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 ORCL 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

Oracle Corp., cálculo de varianza y covarianza de retornos

t	Fecha	R_ORCL,t	R_{S&P 500,t}	(R_ORCL,t–R_ORCL)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ORCL,t–R_ORCL)×(R_{S&P 500,t}–R_{S&P 500})
1.	31 jul. 2014	-0.05%	-1.51%	0.52	4.89	1.59
2.	31 ago. 2014	2.82%	3.77%	4.64	9.38	6.59
3.	30 sept. 2014	-7.83%	-1.55%	72.16	5.08	19.16
.	.	.	.	.	.	.
.	.	.	.	.	.	.
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70.	30 abr. 2020	10.10%	12.68%	88.89	143.54	112.96
71.	31 may. 2020	1.51%	4.53%	0.71	14.63	3.22
Total (Σ):				2,005.72	1,148.02	1,047.08

t	Fecha	R_ORCL,t	R_{S&P 500,t}	(R_ORCL,t–R_ORCL)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ORCL,t–R_ORCL)×(R_{S&P 500,t}–R_{S&P 500})
1.	31 jul. 2014	-0.05%	-1.51%	0.52	4.89	1.59
2.	31 ago. 2014	2.82%	3.77%	4.64	9.38	6.59
3.	30 sept. 2014	-7.83%	-1.55%	72.16	5.08	19.16
4.	31 oct. 2014	2.32%	2.32%	2.74	2.61	2.68
5.	30 nov. 2014	8.60%	2.45%	62.97	3.06	13.88
6.	31 dic. 2014	6.04%	-0.42%	28.81	1.26	-6.02
7.	31 ene. 2015	-6.58%	-3.10%	52.58	14.50	27.61
8.	28 feb. 2015	4.61%	5.49%	15.51	22.90	18.85
9.	31 mar. 2015	-1.53%	-1.74%	4.83	5.97	5.37
10.	30 abr. 2015	1.44%	0.85%	0.59	0.02	0.11
11.	31 may. 2015	-0.30%	1.05%	0.94	0.12	-0.33
12.	30 jun. 2015	-7.34%	-2.10%	64.07	7.87	22.45
13.	31 jul. 2015	-0.52%	1.97%	1.42	1.61	-1.51
14.	31 ago. 2015	-7.14%	-6.26%	60.92	48.46	54.34
15.	30 sept. 2015	-2.62%	-2.64%	10.79	11.21	11.00
16.	31 oct. 2015	7.95%	8.30%	52.95	57.68	55.26
17.	30 nov. 2015	0.33%	0.05%	0.11	0.43	0.22
18.	31 dic. 2015	-6.26%	-1.75%	48.03	6.03	17.03
19.	31 ene. 2016	-0.19%	-5.07%	0.74	33.37	4.97
20.	29 feb. 2016	1.29%	-0.41%	0.39	1.25	-0.70
21.	31 mar. 2016	11.23%	6.60%	111.51	34.76	62.26
22.	30 abr. 2016	-2.20%	0.27%	8.23	0.19	1.24
23.	31 may. 2016	0.85%	1.53%	0.03	0.69	0.15
24.	30 jun. 2016	1.82%	0.09%	1.31	0.38	-0.70
25.	31 jul. 2016	0.64%	3.56%	0.00	8.16	-0.10
26.	31 ago. 2016	0.44%	-0.12%	0.05	0.68	0.19
27.	30 sept. 2016	-4.71%	-0.12%	28.90	0.68	4.45
28.	31 oct. 2016	-1.81%	-1.94%	6.13	7.00	6.55
29.	30 nov. 2016	4.61%	3.42%	15.51	7.37	10.69
30.	31 dic. 2016	-4.33%	1.82%	24.99	1.25	-5.58
31.	31 ene. 2017	4.71%	1.79%	16.31	1.18	4.38
32.	28 feb. 2017	6.18%	3.72%	30.40	9.10	16.63
33.	31 mar. 2017	4.74%	-0.04%	16.59	0.55	-3.02
34.	30 abr. 2017	1.21%	0.91%	0.29	0.04	0.11
35.	31 may. 2017	0.96%	1.16%	0.08	0.21	0.13
36.	30 jun. 2017	10.46%	0.48%	95.95	0.05	-2.18
37.	31 jul. 2017	-0.04%	1.93%	0.50	1.52	-0.87
38.	31 ago. 2017	0.80%	0.05%	0.02	0.42	-0.09
39.	30 sept. 2017	-3.93%	1.93%	21.19	1.50	-5.65
40.	31 oct. 2017	5.67%	2.22%	24.98	2.30	7.57
41.	30 nov. 2017	-3.61%	2.81%	18.35	4.43	-9.02
42.	31 dic. 2017	-3.63%	0.98%	18.47	0.08	-1.20
43.	31 ene. 2018	9.52%	5.62%	78.30	24.15	43.48
44.	28 feb. 2018	-1.78%	-3.89%	6.01	21.14	11.28
45.	31 mar. 2018	-9.71%	-2.69%	107.73	11.51	35.21
46.	30 abr. 2018	0.24%	0.27%	0.18	0.19	0.19
47.	31 may. 2018	2.30%	2.16%	2.66	2.12	2.38
48.	30 jun. 2018	-5.69%	0.48%	40.48	0.05	1.40
49.	31 jul. 2018	8.65%	3.60%	63.65	8.40	23.13
50.	31 ago. 2018	1.89%	3.03%	1.48	5.40	2.83
51.	30 sept. 2018	6.13%	0.43%	29.87	0.08	-1.50
52.	31 oct. 2018	-4.91%	-6.94%	31.09	58.43	42.62
53.	30 nov. 2018	-0.16%	1.79%	0.69	1.17	-0.90
54.	31 dic. 2018	-7.40%	-9.18%	65.17	97.64	79.77
55.	31 ene. 2019	11.67%	7.87%	121.06	51.34	78.84
56.	28 feb. 2019	3.78%	2.97%	9.69	5.15	7.07
57.	31 mar. 2019	3.03%	1.79%	5.58	1.19	2.57
58.	30 abr. 2019	3.46%	3.93%	7.81	10.42	9.02
59.	31 may. 2019	-8.55%	-6.58%	84.97	53.02	67.12
60.	30 jun. 2019	12.59%	6.89%	142.08	38.31	73.78
61.	31 jul. 2019	-0.75%	1.31%	2.03	0.37	-0.87
62.	31 ago. 2019	-7.53%	-1.81%	67.25	6.31	20.61
63.	30 sept. 2019	5.70%	1.72%	25.36	1.03	5.11
64.	31 oct. 2019	-0.55%	2.04%	1.47	1.79	-1.63
65.	30 nov. 2019	3.03%	3.40%	5.56	7.30	6.37
66.	31 dic. 2019	-5.63%	2.86%	39.67	4.65	-13.58
67.	31 ene. 2020	-0.55%	-0.16%	1.48	0.75	1.05
68.	29 feb. 2020	-5.70%	-8.41%	40.58	83.08	58.06
69.	31 mar. 2020	-2.28%	-12.51%	8.73	174.65	39.04
70.	30 abr. 2020	10.10%	12.68%	88.89	143.54	112.96
71.	31 may. 2020	1.51%	4.53%	0.71	14.63	3.22
Total (Σ):				2,005.72	1,148.02	1,047.08

Show all

Varianza_ORCL = Σ(R_ORCL,t–R_ORCL)² ÷ (71 – 1)
= 2,005.72 ÷ (71 – 1)
= 28.65

Varianza_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,148.02 ÷ (71 – 1)
= 16.40

Covarianza_{ORCL, S&P 500} = Σ(R_ORCL,t–R_ORCL)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 1,047.08 ÷ (71 – 1)
= 14.96

Estimación sistemática de riesgos (β)

Varianza_ORCL	28.65
Varianza_{S&P 500}	16.40
Covarianza_{ORCL, S&P 500}	14.96
Coeficiente de correlación_{ORCL, S&P 500}¹	0.69
β_ORCL²	0.91
α_ORCL³	0.03%

Fuente: Oracle Corp. (NYSE:ORCL) | CAPM (www.stock-analysis-on.net)

Cálculos

¹ Coeficiente de correlación_{ORCL, S&P 500}
= Covarianza_{ORCL, S&P 500} ÷ (Desviación típica_ORCL × Desviación típica_{S&P 500})
= 14.96 ÷ (5.35% × 4.05%)
= 0.69

² β_ORCL
= Covarianza_{ORCL, S&P 500} ÷ Varianza_{S&P 500}
= 14.96 ÷ 16.40
= 0.91

³ α_ORCL
= Promedio_ORCL – β_ORCL × Promedio_{S&P 500}
= 0.67% – 0.91 × 0.70%
= 0.03%

Tasa de rendimiento esperada

Supuestos
Tasa de rendimiento de LT Treasury Composite¹	R_F	2.15%
Tasa de rendimiento esperada de la cartera de mercado²	E(R_M)	11.70%
Riesgo sistemático de las acciones ordinarias de Oracle	β_ORCL	0.91

Tasa de rendimiento esperada de las acciones ordinarias de Oracle³	E(R_ORCL)	10.86%

Fuente: Oracle Corp. (NYSE:ORCL) | 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_ORCL) = R_F + β_ORCL [E(R_M) – R_F]
= 2.15% + 0.91 [11.70% – 2.15%]
= 10.86%