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 Accenture.

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

Las tasas de rendimiento

Accenture PLC, tasas de rendimiento mensuales

		Accenture PLC (ACN)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_ACN,t¹	Dividendo_ACN,t¹	R_ACN,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	30 sept. 2014	$81.32			1,972.29
1.	31 oct. 2014	$81.12	$1.02	1.01%	2,018.05	2.32%
2.	30 nov. 2014	$86.33		6.42%	2,067.56	2.45%
3.	31 dic. 2014	$89.31		3.45%	2,058.90	-0.42%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	31 jul. 2020	$224.78	$0.80	5.06%	3,271.12	5.51%
71.	31 ago. 2020	$239.93		6.74%	3,500.31	7.01%
Promedio (R):				1.85%		0.90%
Desviación típica:				5.50%		4.12%

Fuente: Accenture PLC (NYSE:ACN) | CAPM (www.stock-analysis-on.net)

		Accenture PLC (ACN)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_ACN,t¹	Dividendo_ACN,t¹	R_ACN,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	30 sept. 2014	$81.32			1,972.29
1.	31 oct. 2014	$81.12	$1.02	1.01%	2,018.05	2.32%
2.	30 nov. 2014	$86.33		6.42%	2,067.56	2.45%
3.	31 dic. 2014	$89.31		3.45%	2,058.90	-0.42%
4.	31 ene. 2015	$84.03		-5.91%	1,994.99	-3.10%
5.	28 feb. 2015	$90.03		7.14%	2,104.50	5.49%
6.	31 mar. 2015	$93.69		4.07%	2,067.89	-1.74%
7.	30 abr. 2015	$92.65	$1.02	-0.02%	2,085.51	0.85%
8.	31 may. 2015	$96.04		3.66%	2,107.39	1.05%
9.	30 jun. 2015	$96.78		0.77%	2,063.11	-2.10%
10.	31 jul. 2015	$103.11		6.54%	2,103.84	1.97%
11.	31 ago. 2015	$94.27		-8.57%	1,972.18	-6.26%
12.	30 sept. 2015	$98.26		4.23%	1,920.03	-2.64%
13.	31 oct. 2015	$107.20	$1.10	10.22%	2,079.36	8.30%
14.	30 nov. 2015	$107.22		0.02%	2,080.41	0.05%
15.	31 dic. 2015	$104.50		-2.54%	2,043.94	-1.75%
16.	31 ene. 2016	$105.54		1.00%	1,940.24	-5.07%
17.	29 feb. 2016	$100.26		-5.00%	1,932.23	-0.41%
18.	31 mar. 2016	$115.40		15.10%	2,059.74	6.60%
19.	30 abr. 2016	$112.92	$1.10	-1.20%	2,065.30	0.27%
20.	31 may. 2016	$118.97		5.36%	2,096.95	1.53%
21.	30 jun. 2016	$113.29		-4.77%	2,098.86	0.09%
22.	31 jul. 2016	$112.81		-0.42%	2,173.60	3.56%
23.	31 ago. 2016	$115.00		1.94%	2,170.95	-0.12%
24.	30 sept. 2016	$122.17		6.23%	2,168.27	-0.12%
25.	31 oct. 2016	$116.24	$1.21	-3.86%	2,126.15	-1.94%
26.	30 nov. 2016	$119.43		2.74%	2,198.81	3.42%
27.	31 dic. 2016	$117.13		-1.93%	2,238.83	1.82%
28.	31 ene. 2017	$113.87		-2.78%	2,278.87	1.79%
29.	28 feb. 2017	$122.50		7.58%	2,363.64	3.72%
30.	31 mar. 2017	$119.88		-2.14%	2,362.72	-0.04%
31.	30 abr. 2017	$121.30	$1.21	2.19%	2,384.20	0.91%
32.	31 may. 2017	$124.47		2.61%	2,411.80	1.16%
33.	30 jun. 2017	$123.68		-0.63%	2,423.41	0.48%
34.	31 jul. 2017	$128.82		4.16%	2,470.30	1.93%
35.	31 ago. 2017	$130.76		1.51%	2,471.65	0.05%
36.	30 sept. 2017	$135.07		3.30%	2,519.36	1.93%
37.	31 oct. 2017	$142.36	$1.33	6.38%	2,575.26	2.22%
38.	30 nov. 2017	$148.01		3.97%	2,647.58	2.81%
39.	31 dic. 2017	$153.09		3.43%	2,673.61	0.98%
40.	31 ene. 2018	$160.70		4.97%	2,823.81	5.62%
41.	28 feb. 2018	$161.01		0.19%	2,713.83	-3.89%
42.	31 mar. 2018	$153.50		-4.66%	2,640.87	-2.69%
43.	30 abr. 2018	$151.20	$1.33	-0.63%	2,648.05	0.27%
44.	31 may. 2018	$155.74		3.00%	2,705.27	2.16%
45.	30 jun. 2018	$163.59		5.04%	2,718.37	0.48%
46.	31 jul. 2018	$159.33		-2.60%	2,816.29	3.60%
47.	31 ago. 2018	$169.07		6.11%	2,901.52	3.03%
48.	30 sept. 2018	$170.20		0.67%	2,913.98	0.43%
49.	31 oct. 2018	$157.62	$1.46	-6.53%	2,711.74	-6.94%
50.	30 nov. 2018	$164.52		4.38%	2,760.17	1.79%
51.	31 dic. 2018	$141.01		-14.29%	2,506.85	-9.18%
52.	31 ene. 2019	$153.55		8.89%	2,704.10	7.87%
53.	28 feb. 2019	$161.38		5.10%	2,784.49	2.97%
54.	31 mar. 2019	$176.02		9.07%	2,834.40	1.79%
55.	30 abr. 2019	$182.67	$1.46	4.61%	2,945.83	3.93%
56.	31 may. 2019	$178.07		-2.52%	2,752.06	-6.58%
57.	30 jun. 2019	$184.77		3.76%	2,941.76	6.89%
58.	31 jul. 2019	$192.58		4.23%	2,980.38	1.31%
59.	31 ago. 2019	$198.17		2.90%	2,926.46	-1.81%
60.	30 sept. 2019	$192.35		-2.94%	2,976.74	1.72%
61.	31 oct. 2019	$185.42	$0.80	-3.19%	3,037.56	2.04%
62.	30 nov. 2019	$201.16		8.49%	3,140.98	3.40%
63.	31 dic. 2019	$210.57		4.68%	3,230.78	2.86%
64.	31 ene. 2020	$205.21	$0.80	-2.17%	3,225.52	-0.16%
65.	29 feb. 2020	$180.59		-12.00%	2,954.22	-8.41%
66.	31 mar. 2020	$163.26		-9.60%	2,584.59	-12.51%
67.	30 abr. 2020	$185.19	$0.80	13.92%	2,912.43	12.68%
68.	31 may. 2020	$201.62		8.87%	3,044.31	4.53%
69.	30 jun. 2020	$214.72		6.50%	3,100.29	1.84%
70.	31 jul. 2020	$224.78	$0.80	5.06%	3,271.12	5.51%
71.	31 ago. 2020	$239.93		6.74%	3,500.31	7.01%
Promedio (R):				1.85%		0.90%
Desviación típica:				5.50%		4.12%

Fuente: Accenture PLC (NYSE:ACN) | 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 ACN 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

Accenture PLC, cálculo de varianza y covarianza de retornos

t	Fecha	R_ACN,t	R_{S&P 500,t}	(R_ACN,t–R_ACN)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ACN,t–R_ACN)×(R_{S&P 500,t}–R_{S&P 500})
1.	31 oct. 2014	1.01%	2.32%	0.71	2.03	-1.20
2.	30 nov. 2014	6.42%	2.45%	20.91	2.43	7.12
3.	31 dic. 2014	3.45%	-0.42%	2.57	1.73	-2.11
.	.	.	.	.	.	.
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70.	31 jul. 2020	5.06%	5.51%	10.29	21.29	14.80
71.	31 ago. 2020	6.74%	7.01%	23.92	37.34	29.88
Total (Σ):				2,115.87	1,190.16	1,242.84

t	Fecha	R_ACN,t	R_{S&P 500,t}	(R_ACN,t–R_ACN)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ACN,t–R_ACN)×(R_{S&P 500,t}–R_{S&P 500})
1.	31 oct. 2014	1.01%	2.32%	0.71	2.03	-1.20
2.	30 nov. 2014	6.42%	2.45%	20.91	2.43	7.12
3.	31 dic. 2014	3.45%	-0.42%	2.57	1.73	-2.11
4.	31 ene. 2015	-5.91%	-3.10%	60.24	16.00	31.04
5.	28 feb. 2015	7.14%	5.49%	27.99	21.10	24.30
6.	31 mar. 2015	4.07%	-1.74%	4.91	6.95	-5.84
7.	30 abr. 2015	-0.02%	0.85%	3.50	0.00	0.08
8.	31 may. 2015	3.66%	1.05%	3.27	0.02	0.28
9.	30 jun. 2015	0.77%	-2.10%	1.16	8.98	3.23
10.	31 jul. 2015	6.54%	1.97%	22.01	1.16	5.06
11.	31 ago. 2015	-8.57%	-6.26%	108.63	51.18	74.56
12.	30 sept. 2015	4.23%	-2.64%	5.68	12.53	-8.44
13.	31 oct. 2015	10.22%	8.30%	70.03	54.80	61.95
14.	30 nov. 2015	0.02%	0.05%	3.35	0.71	1.55
15.	31 dic. 2015	-2.54%	-1.75%	19.24	7.02	11.62
16.	31 ene. 2016	1.00%	-5.07%	0.73	35.63	5.10
17.	29 feb. 2016	-5.00%	-0.41%	46.95	1.71	8.97
18.	31 mar. 2016	15.10%	6.60%	175.60	32.53	75.58
19.	30 abr. 2016	-1.20%	0.27%	9.27	0.39	1.91
20.	31 may. 2016	5.36%	1.53%	12.31	0.41	2.23
21.	30 jun. 2016	-4.77%	0.09%	43.87	0.65	5.33
22.	31 jul. 2016	-0.42%	3.56%	5.17	7.10	-6.06
23.	31 ago. 2016	1.94%	-0.12%	0.01	1.04	-0.09
24.	30 sept. 2016	6.23%	-0.12%	19.23	1.04	-4.47
25.	31 oct. 2016	-3.86%	-1.94%	32.64	8.06	16.21
26.	30 nov. 2016	2.74%	3.42%	0.80	6.36	2.26
27.	31 dic. 2016	-1.93%	1.82%	14.25	0.85	-3.49
28.	31 ene. 2017	-2.78%	1.79%	21.46	0.80	-4.14
29.	28 feb. 2017	7.58%	3.72%	32.83	7.98	16.18
30.	31 mar. 2017	-2.14%	-0.04%	15.91	0.87	3.73
31.	30 abr. 2017	2.19%	0.91%	0.12	0.00	0.00
32.	31 may. 2017	2.61%	1.16%	0.58	0.07	0.20
33.	30 jun. 2017	-0.63%	0.48%	6.17	0.17	1.03
34.	31 jul. 2017	4.16%	1.93%	5.32	1.08	2.40
35.	31 ago. 2017	1.51%	0.05%	0.12	0.71	0.29
36.	30 sept. 2017	3.30%	1.93%	2.09	1.07	1.50
37.	31 oct. 2017	6.38%	2.22%	20.54	1.75	6.00
38.	30 nov. 2017	3.97%	2.81%	4.49	3.66	4.05
39.	31 dic. 2017	3.43%	0.98%	2.51	0.01	0.14
40.	31 ene. 2018	4.97%	5.62%	9.74	22.30	14.74
41.	28 feb. 2018	0.19%	-3.89%	2.74	22.95	7.94
42.	31 mar. 2018	-4.66%	-2.69%	42.43	12.85	23.35
43.	30 abr. 2018	-0.63%	0.27%	6.16	0.39	1.55
44.	31 may. 2018	3.00%	2.16%	1.33	1.60	1.46
45.	30 jun. 2018	5.04%	0.48%	10.18	0.17	-1.31
46.	31 jul. 2018	-2.60%	3.60%	19.83	7.32	-12.05
47.	31 ago. 2018	6.11%	3.03%	18.18	4.54	9.08
48.	30 sept. 2018	0.67%	0.43%	1.39	0.22	0.55
49.	31 oct. 2018	-6.53%	-6.94%	70.27	61.40	65.69
50.	30 nov. 2018	4.38%	1.79%	6.39	0.79	2.25
51.	31 dic. 2018	-14.29%	-9.18%	260.48	101.48	162.58
52.	31 ene. 2019	8.89%	7.87%	49.61	48.62	49.11
53.	28 feb. 2019	5.10%	2.97%	10.56	4.31	6.75
54.	31 mar. 2019	9.07%	1.79%	52.16	0.80	6.48
55.	30 abr. 2019	4.61%	3.93%	7.61	9.21	8.37
56.	31 may. 2019	-2.52%	-6.58%	19.08	55.85	32.64
57.	30 jun. 2019	3.76%	6.89%	3.66	35.97	11.47
58.	31 jul. 2019	4.23%	1.31%	5.65	0.17	0.99
59.	31 ago. 2019	2.90%	-1.81%	1.11	7.32	-2.85
60.	30 sept. 2019	-2.94%	1.72%	22.91	0.68	-3.94
61.	31 oct. 2019	-3.19%	2.04%	25.36	1.32	-5.78
62.	30 nov. 2019	8.49%	3.40%	44.08	6.29	16.66
63.	31 dic. 2019	4.68%	2.86%	8.00	3.85	5.55
64.	31 ene. 2020	-2.17%	-0.16%	16.12	1.12	4.25
65.	29 feb. 2020	-12.00%	-8.41%	191.73	86.62	128.87
66.	31 mar. 2020	-9.60%	-12.51%	131.00	179.77	153.46
67.	30 abr. 2020	13.92%	12.68%	145.76	138.97	142.33
68.	31 may. 2020	8.87%	4.53%	49.32	13.19	25.51
69.	30 jun. 2020	6.50%	1.84%	21.60	0.89	4.38
70.	31 jul. 2020	5.06%	5.51%	10.29	21.29	14.80
71.	31 ago. 2020	6.74%	7.01%	23.92	37.34	29.88
Total (Σ):				2,115.87	1,190.16	1,242.84

Show all

Varianza_ACN = Σ(R_ACN,t–R_ACN)² ÷ (71 – 1)
= 2,115.87 ÷ (71 – 1)
= 30.23

Varianza_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,190.16 ÷ (71 – 1)
= 17.00

Covarianza_{ACN, S&P 500} = Σ(R_ACN,t–R_ACN)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 1,242.84 ÷ (71 – 1)
= 17.75

Estimación sistemática de riesgos (β)

Varianza_ACN	30.23
Varianza_{S&P 500}	17.00
Covarianza_{ACN, S&P 500}	17.75
Coeficiente de correlación_{ACN, S&P 500}¹	0.78
β_ACN²	1.04
α_ACN³	0.91%

Fuente: Accenture PLC (NYSE:ACN) | CAPM (www.stock-analysis-on.net)

Cálculos

¹ Coeficiente de correlación_{ACN, S&P 500}
= Covarianza_{ACN, S&P 500} ÷ (Desviación típica_ACN × Desviación típica_{S&P 500})
= 17.75 ÷ (5.50% × 4.12%)
= 0.78

² β_ACN
= Covarianza_{ACN, S&P 500} ÷ Varianza_{S&P 500}
= 17.75 ÷ 17.00
= 1.04

³ α_ACN
= Promedio_ACN – β_ACN × Promedio_{S&P 500}
= 1.85% – 1.04 × 0.90%
= 0.91%

Tasa de rendimiento esperada

Supuestos
Tasa de rendimiento de LT Treasury Composite¹	R_F	2.25%
Tasa de rendimiento esperada de la cartera de mercado²	E(R_M)	11.73%
Riesgo sistemático de las acciones ordinarias de Accenture	β_ACN	1.04

Tasa de rendimiento esperada de las acciones ordinarias de Accenture³	E(R_ACN)	12.15%

Fuente: Accenture PLC (NYSE:ACN) | 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_ACN) = R_F + β_ACN [E(R_M) – R_F]
= 2.25% + 1.04 [11.73% – 2.25%]
= 12.15%