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 comunes de Autodesk.

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

Las tasas de rendimiento

Autodesk Inc., tasas de rendimiento mensuales

		Autodesk Inc. (ADSK)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_ADSK,t¹	Dividendo_ADSK,t¹	R_ADSK,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	28 feb. 2015	$64.24			2,104.50
1.	31 mar. 2015	$58.64		-8.72%	2,067.89	-1.74%
2.	30 abr. 2015	$56.83		-3.09%	2,085.51	0.85%
3.	31 may. 2015	$54.15		-4.72%	2,107.39	1.05%
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	31 dic. 2020	$305.34		8.96%	3,756.07	3.71%
71.	31 ene. 2021	$277.43		-9.14%	3,714.24	-1.11%
Promedio (R):				2.58%		0.89%
Desviación típica:				10.14%		4.30%

Fuente: Autodesk Inc. (NASDAQ:ADSK) | CAPM (www.stock-analysis-on.net)

		Autodesk Inc. (ADSK)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_ADSK,t¹	Dividendo_ADSK,t¹	R_ADSK,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	28 feb. 2015	$64.24			2,104.50
1.	31 mar. 2015	$58.64		-8.72%	2,067.89	-1.74%
2.	30 abr. 2015	$56.83		-3.09%	2,085.51	0.85%
3.	31 may. 2015	$54.15		-4.72%	2,107.39	1.05%
4.	30 jun. 2015	$50.08		-7.52%	2,063.11	-2.10%
5.	31 jul. 2015	$50.58		1.00%	2,103.84	1.97%
6.	31 ago. 2015	$46.75		-7.57%	1,972.18	-6.26%
7.	30 sept. 2015	$44.14		-5.58%	1,920.03	-2.64%
8.	31 oct. 2015	$55.19		25.03%	2,079.36	8.30%
9.	30 nov. 2015	$63.47		15.00%	2,080.41	0.05%
10.	31 dic. 2015	$60.93		-4.00%	2,043.94	-1.75%
11.	31 ene. 2016	$46.82		-23.16%	1,940.24	-5.07%
12.	29 feb. 2016	$51.74		10.51%	1,932.23	-0.41%
13.	31 mar. 2016	$58.31		12.70%	2,059.74	6.60%
14.	30 abr. 2016	$59.82		2.59%	2,065.30	0.27%
15.	31 may. 2016	$58.27		-2.59%	2,096.95	1.53%
16.	30 jun. 2016	$54.14		-7.09%	2,098.86	0.09%
17.	31 jul. 2016	$59.45		9.81%	2,173.60	3.56%
18.	31 ago. 2016	$67.40		13.37%	2,170.95	-0.12%
19.	30 sept. 2016	$72.33		7.31%	2,168.27	-0.12%
20.	31 oct. 2016	$72.28		-0.07%	2,126.15	-1.94%
21.	30 nov. 2016	$72.61		0.46%	2,198.81	3.42%
22.	31 dic. 2016	$74.01		1.93%	2,238.83	1.82%
23.	31 ene. 2017	$81.34		9.90%	2,278.87	1.79%
24.	28 feb. 2017	$86.30		6.10%	2,363.64	3.72%
25.	31 mar. 2017	$86.47		0.20%	2,362.72	-0.04%
26.	30 abr. 2017	$90.07		4.16%	2,384.20	0.91%
27.	31 may. 2017	$111.77		24.09%	2,411.80	1.16%
28.	30 jun. 2017	$100.82		-9.80%	2,423.41	0.48%
29.	31 jul. 2017	$110.79		9.89%	2,470.30	1.93%
30.	31 ago. 2017	$114.46		3.31%	2,471.65	0.05%
31.	30 sept. 2017	$112.26		-1.92%	2,519.36	1.93%
32.	31 oct. 2017	$124.96		11.31%	2,575.26	2.22%
33.	30 nov. 2017	$109.70		-12.21%	2,647.58	2.81%
34.	31 dic. 2017	$104.83		-4.44%	2,673.61	0.98%
35.	31 ene. 2018	$115.62		10.29%	2,823.81	5.62%
36.	28 feb. 2018	$117.47		1.60%	2,713.83	-3.89%
37.	31 mar. 2018	$125.58		6.90%	2,640.87	-2.69%
38.	30 abr. 2018	$125.90		0.25%	2,648.05	0.27%
39.	31 may. 2018	$129.10		2.54%	2,705.27	2.16%
40.	30 jun. 2018	$131.09		1.54%	2,718.37	0.48%
41.	31 jul. 2018	$128.44		-2.02%	2,816.29	3.60%
42.	31 ago. 2018	$154.35		20.17%	2,901.52	3.03%
43.	30 sept. 2018	$156.11		1.14%	2,913.98	0.43%
44.	31 oct. 2018	$129.25		-17.21%	2,711.74	-6.94%
45.	30 nov. 2018	$144.50		11.80%	2,760.17	1.79%
46.	31 dic. 2018	$128.61		-11.00%	2,506.85	-9.18%
47.	31 ene. 2019	$147.20		14.45%	2,704.10	7.87%
48.	28 feb. 2019	$163.01		10.74%	2,784.49	2.97%
49.	31 mar. 2019	$155.82		-4.41%	2,834.40	1.79%
50.	30 abr. 2019	$178.21		14.37%	2,945.83	3.93%
51.	31 may. 2019	$160.91		-9.71%	2,752.06	-6.58%
52.	30 jun. 2019	$162.90		1.24%	2,941.76	6.89%
53.	31 jul. 2019	$156.17		-4.13%	2,980.38	1.31%
54.	31 ago. 2019	$142.82		-8.55%	2,926.46	-1.81%
55.	30 sept. 2019	$147.70		3.42%	2,976.74	1.72%
56.	31 oct. 2019	$147.36		-0.23%	3,037.56	2.04%
57.	30 nov. 2019	$180.90		22.76%	3,140.98	3.40%
58.	31 dic. 2019	$183.46		1.42%	3,230.78	2.86%
59.	31 ene. 2020	$196.85		7.30%	3,225.52	-0.16%
60.	29 feb. 2020	$190.88		-3.03%	2,954.22	-8.41%
61.	31 mar. 2020	$156.10		-18.22%	2,584.59	-12.51%
62.	30 abr. 2020	$187.13		19.88%	2,912.43	12.68%
63.	31 may. 2020	$210.38		12.42%	3,044.31	4.53%
64.	30 jun. 2020	$239.19		13.69%	3,100.29	1.84%
65.	31 jul. 2020	$236.43		-1.15%	3,271.12	5.51%
66.	31 ago. 2020	$245.70		3.92%	3,500.31	7.01%
67.	30 sept. 2020	$231.01		-5.98%	3,363.00	-3.92%
68.	31 oct. 2020	$235.54		1.96%	3,269.96	-2.77%
69.	30 nov. 2020	$280.23		18.97%	3,621.63	10.75%
70.	31 dic. 2020	$305.34		8.96%	3,756.07	3.71%
71.	31 ene. 2021	$277.43		-9.14%	3,714.24	-1.11%
Promedio (R):				2.58%		0.89%
Desviación típica:				10.14%		4.30%

Fuente: Autodesk Inc. (NASDAQ:ADSK) | 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 ADSK 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

Autodesk Inc., cálculo de varianza y covarianza de retornos

t	Fecha	R_ADSK,t	R_{S&P 500,t}	(R_ADSK,t–R_ADSK)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ADSK,t–R_ADSK)×(R_{S&P 500,t}–R_{S&P 500})
1.	31 mar. 2015	-8.72%	-1.74%	127.63	6.94	29.76
2.	30 abr. 2015	-3.09%	0.85%	32.11	0.00	0.24
3.	31 may. 2015	-4.72%	1.05%	53.23	0.02	-1.13
.	.	.	.	.	.	.
.	.	.	.	.	.	.
.	.	.	.	.	.	.
70.	31 dic. 2020	8.96%	3.71%	40.71	7.94	17.98
71.	31 ene. 2021	-9.14%	-1.11%	137.37	4.03	23.54
Total (Σ):				7,204.46	1,292.68	2,010.27

t	Fecha	R_ADSK,t	R_{S&P 500,t}	(R_ADSK,t–R_ADSK)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ADSK,t–R_ADSK)×(R_{S&P 500,t}–R_{S&P 500})
1.	31 mar. 2015	-8.72%	-1.74%	127.63	6.94	29.76
2.	30 abr. 2015	-3.09%	0.85%	32.11	0.00	0.24
3.	31 may. 2015	-4.72%	1.05%	53.23	0.02	-1.13
4.	30 jun. 2015	-7.52%	-2.10%	101.93	8.98	30.25
5.	31 jul. 2015	1.00%	1.97%	2.50	1.17	-1.71
6.	31 ago. 2015	-7.57%	-6.26%	103.07	51.16	72.62
7.	30 sept. 2015	-5.58%	-2.64%	66.63	12.52	28.89
8.	31 oct. 2015	25.03%	8.30%	504.18	54.81	166.24
9.	30 nov. 2015	15.00%	0.05%	154.32	0.71	-10.49
10.	31 dic. 2015	-4.00%	-1.75%	43.32	7.01	17.43
11.	31 ene. 2016	-23.16%	-5.07%	662.43	35.62	153.61
12.	29 feb. 2016	10.51%	-0.41%	62.86	1.71	-10.37
13.	31 mar. 2016	12.70%	6.60%	102.38	32.54	57.72
14.	30 abr. 2016	2.59%	0.27%	0.00	0.39	-0.01
15.	31 may. 2016	-2.59%	1.53%	26.74	0.41	-3.30
16.	30 jun. 2016	-7.09%	0.09%	93.47	0.65	7.77
17.	31 jul. 2016	9.81%	3.56%	52.24	7.11	19.27
18.	31 ago. 2016	13.37%	-0.12%	116.48	1.03	-10.97
19.	30 sept. 2016	7.31%	-0.12%	22.42	1.04	-4.82
20.	31 oct. 2016	-0.07%	-1.94%	7.02	8.05	7.52
21.	30 nov. 2016	0.46%	3.42%	4.51	6.36	-5.36
22.	31 dic. 2016	1.93%	1.82%	0.43	0.86	-0.60
23.	31 ene. 2017	9.90%	1.79%	53.64	0.80	6.55
24.	28 feb. 2017	6.10%	3.72%	12.37	7.98	9.94
25.	31 mar. 2017	0.20%	-0.04%	5.68	0.87	2.22
26.	30 abr. 2017	4.16%	0.91%	2.51	0.00	0.02
27.	31 may. 2017	24.09%	1.16%	462.78	0.07	5.66
28.	30 jun. 2017	-9.80%	0.48%	153.19	0.17	5.12
29.	31 jul. 2017	9.89%	1.93%	53.42	1.08	7.60
30.	31 ago. 2017	3.31%	0.05%	0.54	0.71	-0.62
31.	30 sept. 2017	-1.92%	1.93%	20.27	1.07	-4.66
32.	31 oct. 2017	11.31%	2.22%	76.26	1.75	11.56
33.	30 nov. 2017	-12.21%	2.81%	218.80	3.66	-28.31
34.	31 dic. 2017	-4.44%	0.98%	49.27	0.01	-0.62
35.	31 ene. 2018	10.29%	5.62%	59.49	22.31	36.43
36.	28 feb. 2018	1.60%	-3.89%	0.96	22.94	4.69
37.	31 mar. 2018	6.90%	-2.69%	18.70	12.84	-15.49
38.	30 abr. 2018	0.25%	0.27%	5.41	0.39	1.45
39.	31 may. 2018	2.54%	2.16%	0.00	1.60	-0.05
40.	30 jun. 2018	1.54%	0.48%	1.08	0.17	0.43
41.	31 jul. 2018	-2.02%	3.60%	21.17	7.33	-12.46
42.	31 ago. 2018	20.17%	3.03%	309.51	4.54	37.50
43.	30 sept. 2018	1.14%	0.43%	2.07	0.22	0.67
44.	31 oct. 2018	-17.21%	-6.94%	391.48	61.39	155.02
45.	30 nov. 2018	11.80%	1.79%	84.99	0.79	8.22
46.	31 dic. 2018	-11.00%	-9.18%	184.32	101.45	136.75
47.	31 ene. 2019	14.45%	7.87%	141.00	48.63	82.81
48.	28 feb. 2019	10.74%	2.97%	66.59	4.32	16.96
49.	31 mar. 2019	-4.41%	1.79%	48.87	0.81	-6.28
50.	30 abr. 2019	14.37%	3.93%	138.98	9.22	35.80
51.	31 may. 2019	-9.71%	-6.58%	150.99	55.84	91.82
52.	30 jun. 2019	1.24%	6.89%	1.80	35.98	-8.06
53.	31 jul. 2019	-4.13%	1.31%	45.04	0.17	-2.81
54.	31 ago. 2019	-8.55%	-1.81%	123.84	7.31	30.09
55.	30 sept. 2019	3.42%	1.72%	0.70	0.68	0.69
56.	31 oct. 2019	-0.23%	2.04%	7.90	1.32	-3.23
57.	30 nov. 2019	22.76%	3.40%	407.25	6.30	50.65
58.	31 dic. 2019	1.42%	2.86%	1.36	3.86	-2.29
59.	31 ene. 2020	7.30%	-0.16%	22.26	1.12	-4.99
60.	29 feb. 2020	-3.03%	-8.41%	31.50	86.60	52.23
61.	31 mar. 2020	-18.22%	-12.51%	432.68	179.74	278.87
62.	30 abr. 2020	19.88%	12.68%	299.23	139.00	203.94
63.	31 may. 2020	12.42%	4.53%	96.91	13.20	35.77
64.	30 jun. 2020	13.69%	1.84%	123.53	0.89	10.49
65.	31 jul. 2020	-1.15%	5.51%	13.94	21.30	-17.23
66.	31 ago. 2020	3.92%	7.01%	1.80	37.35	8.19
67.	30 sept. 2020	-5.98%	-3.92%	73.25	23.21	41.23
68.	31 oct. 2020	1.96%	-2.77%	0.38	13.41	2.27
69.	30 nov. 2020	18.97%	10.75%	268.74	97.22	161.64
70.	31 dic. 2020	8.96%	3.71%	40.71	7.94	17.98
71.	31 ene. 2021	-9.14%	-1.11%	137.37	4.03	23.54
Total (Σ):				7,204.46	1,292.68	2,010.27

Show all

Varianza_ADSK = Σ(R_ADSK,t–R_ADSK)² ÷ (71 – 1)
= 7,204.46 ÷ (71 – 1)
= 102.92

Varianza_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (71 – 1)
= 1,292.68 ÷ (71 – 1)
= 18.47

Covarianza_{ADSK, S&P 500} = Σ(R_ADSK,t–R_ADSK)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (71 – 1)
= 2,010.27 ÷ (71 – 1)
= 28.72

Estimación sistemática de riesgos (β)

Varianza_ADSK	102.92
Varianza_{S&P 500}	18.47
Covarianza_{ADSK, S&P 500}	28.72
Coeficiente de correlación_{ADSK, S&P 500}¹	0.66
β_ADSK²	1.56
α_ADSK³	1.19%

Fuente: Autodesk Inc. (NASDAQ:ADSK) | CAPM (www.stock-analysis-on.net)

Cálculos

¹ Coeficiente de correlación_{ADSK, S&P 500}
= Covarianza_{ADSK, S&P 500} ÷ (Desviación típica_ADSK × Desviación típica_{S&P 500})
= 28.72 ÷ (10.14% × 4.30%)
= 0.66

² β_ADSK
= Covarianza_{ADSK, S&P 500} ÷ Varianza_{S&P 500}
= 28.72 ÷ 18.47
= 1.56

³ α_ADSK
= Promedio_ADSK – β_ADSK × Promedio_{S&P 500}
= 2.58% – 1.56 × 0.89%
= 1.19%

Tasa de rendimiento esperada

Supuestos
Tasa de rendimiento de LT Treasury Composite¹	R_F	2.28%
Tasa de rendimiento esperada de la cartera de mercado²	E(R_M)	11.75%
Riesgo sistemático de las acciones ordinarias de Autodesk	β_ADSK	1.56

Tasa de rendimiento esperada de las acciones ordinarias de Autodesk³	E(R_ADSK)	17.01%

Fuente: Autodesk Inc. (NASDAQ:ADSK) | 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_ADSK) = R_F + β_ADSK [E(R_M) – R_F]
= 2.28% + 1.56 [11.75% – 2.28%]
= 17.01%