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

El modelo de fijación de precios de activos de capital (CAPM, por sus siglas en inglés) indica cuál debería ser la tasa de rendimiento esperada o requerida en activos de riesgo como las acciones ordinarias de Align.

Tasas de retorno
Varianza y covarianza
Estimación sistemática del riesgo (β)
Tasa de rendimiento esperada

Tasas de retorno

Align Technology Inc., tasas mensuales de retorno

		Align Technology Inc. (ALGN)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_ALGN,t¹	Dividendo_ALGN,t¹	R_ALGN,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	31 ene. 2018	$262.00			2,823.81
1.	28 feb. 2018	$262.52		0.20%	2,713.83	-3.89%
2.	31 mar. 2018	$251.13		-4.34%	2,640.87	-2.69%
3.	30 abr. 2018	$249.85		-0.51%	2,648.05	0.27%
.	.	.	.	.	.	.
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.	.	.	.	.	.	.
58.	30 nov. 2022	$196.66		1.21%	4,080.11	5.38%
59.	31 dic. 2022	$210.90		7.24%	3,839.50	-5.90%
Promedio (R):				0.78%		0.67%
Desviación estándar:				14.90%		5.40%

		Align Technology Inc. (ALGN)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_ALGN,t¹	Dividendo_ALGN,t¹	R_ALGN,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	31 ene. 2018	$262.00			2,823.81
1.	28 feb. 2018	$262.52		0.20%	2,713.83	-3.89%
2.	31 mar. 2018	$251.13		-4.34%	2,640.87	-2.69%
3.	30 abr. 2018	$249.85		-0.51%	2,648.05	0.27%
4.	31 may. 2018	$331.95		32.86%	2,705.27	2.16%
5.	30 jun. 2018	$342.14		3.07%	2,718.37	0.48%
6.	31 jul. 2018	$356.65		4.24%	2,816.29	3.60%
7.	31 ago. 2018	$386.49		8.37%	2,901.52	3.03%
8.	30 sept. 2018	$391.22		1.22%	2,913.98	0.43%
9.	31 oct. 2018	$221.20		-43.46%	2,711.74	-6.94%
10.	30 nov. 2018	$229.89		3.93%	2,760.17	1.79%
11.	31 dic. 2018	$209.43		-8.90%	2,506.85	-9.18%
12.	31 ene. 2019	$248.95		18.87%	2,704.10	7.87%
13.	28 feb. 2019	$258.97		4.02%	2,784.49	2.97%
14.	31 mar. 2019	$284.33		9.79%	2,834.40	1.79%
15.	30 abr. 2019	$324.68		14.19%	2,945.83	3.93%
16.	31 may. 2019	$284.35		-12.42%	2,752.06	-6.58%
17.	30 jun. 2019	$273.70		-3.75%	2,941.76	6.89%
18.	31 jul. 2019	$209.08		-23.61%	2,980.38	1.31%
19.	31 ago. 2019	$183.11		-12.42%	2,926.46	-1.81%
20.	30 sept. 2019	$180.92		-1.20%	2,976.74	1.72%
21.	31 oct. 2019	$252.29		39.45%	3,037.56	2.04%
22.	30 nov. 2019	$277.34		9.93%	3,140.98	3.40%
23.	31 dic. 2019	$279.04		0.61%	3,230.78	2.86%
24.	31 ene. 2020	$257.10		-7.86%	3,225.52	-0.16%
25.	29 feb. 2020	$218.35		-15.07%	2,954.22	-8.41%
26.	31 mar. 2020	$173.95		-20.33%	2,584.59	-12.51%
27.	30 abr. 2020	$214.85		23.51%	2,912.43	12.68%
28.	31 may. 2020	$245.62		14.32%	3,044.31	4.53%
29.	30 jun. 2020	$274.44		11.73%	3,100.29	1.84%
30.	31 jul. 2020	$293.82		7.06%	3,271.12	5.51%
31.	31 ago. 2020	$296.98		1.08%	3,500.31	7.01%
32.	30 sept. 2020	$327.36		10.23%	3,363.00	-3.92%
33.	31 oct. 2020	$426.08		30.16%	3,269.96	-2.77%
34.	30 nov. 2020	$481.29		12.96%	3,621.63	10.75%
35.	31 dic. 2020	$534.38		11.03%	3,756.07	3.71%
36.	31 ene. 2021	$525.38		-1.68%	3,714.24	-1.11%
37.	28 feb. 2021	$567.11		7.94%	3,811.15	2.61%
38.	31 mar. 2021	$541.53		-4.51%	3,972.89	4.24%
39.	30 abr. 2021	$595.53		9.97%	4,181.17	5.24%
40.	31 may. 2021	$590.15		-0.90%	4,204.11	0.55%
41.	30 jun. 2021	$611.00		3.53%	4,297.50	2.22%
42.	31 jul. 2021	$695.80		13.88%	4,395.26	2.27%
43.	31 ago. 2021	$709.00		1.90%	4,522.68	2.90%
44.	30 sept. 2021	$665.43		-6.15%	4,307.54	-4.76%
45.	31 oct. 2021	$624.37		-6.17%	4,605.38	6.91%
46.	30 nov. 2021	$611.53		-2.06%	4,567.00	-0.83%
47.	31 dic. 2021	$657.18		7.46%	4,766.18	4.36%
48.	31 ene. 2022	$494.96		-24.68%	4,515.55	-5.26%
49.	28 feb. 2022	$511.46		3.33%	4,373.94	-3.14%
50.	31 mar. 2022	$436.00		-14.75%	4,530.41	3.58%
51.	30 abr. 2022	$289.91		-33.51%	4,131.93	-8.80%
52.	31 may. 2022	$277.64		-4.23%	4,132.15	0.01%
53.	30 jun. 2022	$236.67		-14.76%	3,785.38	-8.39%
54.	31 jul. 2022	$280.97		18.72%	4,130.29	9.11%
55.	31 ago. 2022	$243.70		-13.26%	3,955.00	-4.24%
56.	30 sept. 2022	$207.11		-15.01%	3,585.62	-9.34%
57.	31 oct. 2022	$194.30		-6.19%	3,871.98	7.99%
58.	30 nov. 2022	$196.66		1.21%	4,080.11	5.38%
59.	31 dic. 2022	$210.90		7.24%	3,839.50	-5.90%
Promedio (R):				0.78%		0.67%
Desviación estándar:				14.90%		5.40%

Mostrar todo

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

² Tasa de rendimiento de las acciones ordinarias de ALGN 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

Align Technology Inc., cálculo de la varianza y covarianza de los rendimientos

t	Fecha	R_ALGN,t	R_{S&P 500,t}	(R_ALGN,t–R_ALGN)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ALGN,t–R_ALGN)×(R_{S&P 500,t}–R_{S&P 500})
1.	28 feb. 2018	0.20%	-3.89%	0.34	20.81	2.67
2.	31 mar. 2018	-4.34%	-2.69%	26.25	11.26	17.19
3.	30 abr. 2018	-0.51%	0.27%	1.68	0.16	0.51
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58.	30 nov. 2022	1.21%	5.38%	0.18	22.17	2.02
59.	31 dic. 2022	7.24%	-5.90%	41.68	43.08	-42.38
Total (Σ):				12,875.12	1,691.48	2,637.01

t	Fecha	R_ALGN,t	R_{S&P 500,t}	(R_ALGN,t–R_ALGN)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_ALGN,t–R_ALGN)×(R_{S&P 500,t}–R_{S&P 500})
1.	28 feb. 2018	0.20%	-3.89%	0.34	20.81	2.67
2.	31 mar. 2018	-4.34%	-2.69%	26.25	11.26	17.19
3.	30 abr. 2018	-0.51%	0.27%	1.68	0.16	0.51
4.	31 may. 2018	32.86%	2.16%	1,028.81	2.23	47.93
5.	30 jun. 2018	3.07%	0.48%	5.22	0.03	-0.42
6.	31 jul. 2018	4.24%	3.60%	11.95	8.62	10.15
7.	31 ago. 2018	8.37%	3.03%	57.49	5.57	17.89
8.	30 sept. 2018	1.22%	0.43%	0.19	0.06	-0.10
9.	31 oct. 2018	-43.46%	-6.94%	1,957.49	57.87	336.56
10.	30 nov. 2018	3.93%	1.79%	9.88	1.25	3.52
11.	31 dic. 2018	-8.90%	-9.18%	93.79	96.91	95.34
12.	31 ene. 2019	18.87%	7.87%	327.09	51.87	130.25
13.	28 feb. 2019	4.02%	2.97%	10.50	5.32	7.47
14.	31 mar. 2019	9.79%	1.79%	81.14	1.27	10.14
15.	30 abr. 2019	14.19%	3.93%	179.74	10.66	43.77
16.	31 may. 2019	-12.42%	-6.58%	174.40	52.48	95.67
17.	30 jun. 2019	-3.75%	6.89%	20.52	38.77	-28.21
18.	31 jul. 2019	-23.61%	1.31%	595.09	0.42	-15.76
19.	31 ago. 2019	-12.42%	-1.81%	174.39	6.13	32.69
20.	30 sept. 2019	-1.20%	1.72%	3.92	1.11	-2.08
21.	31 oct. 2019	39.45%	2.04%	1,494.88	1.89	53.22
22.	30 nov. 2019	9.93%	3.40%	83.62	7.50	25.04
23.	31 dic. 2019	0.61%	2.86%	0.03	4.81	-0.38
24.	31 ene. 2020	-7.86%	-0.16%	74.78	0.69	7.17
25.	29 feb. 2020	-15.07%	-8.41%	251.43	82.40	143.94
26.	31 mar. 2020	-20.33%	-12.51%	446.01	173.67	278.32
27.	30 abr. 2020	23.51%	12.68%	516.56	144.43	273.14
28.	31 may. 2020	14.32%	4.53%	183.25	14.91	52.27
29.	30 jun. 2020	11.73%	1.84%	119.88	1.37	12.83
30.	31 jul. 2020	7.06%	5.51%	39.40	23.46	30.40
31.	31 ago. 2020	1.08%	7.01%	0.08	40.19	1.84
32.	30 sept. 2020	10.23%	-3.92%	89.21	21.06	-43.35
33.	31 oct. 2020	30.16%	-2.77%	862.70	11.79	-100.84
34.	30 nov. 2020	12.96%	10.75%	148.18	101.77	122.80
35.	31 dic. 2020	11.03%	3.71%	104.98	9.28	31.20
36.	31 ene. 2021	-1.68%	-1.11%	6.10	3.17	4.40
37.	28 feb. 2021	7.94%	2.61%	51.24	3.77	13.90
38.	31 mar. 2021	-4.51%	4.24%	28.04	12.80	-18.94
39.	30 abr. 2021	9.97%	5.24%	84.40	20.94	42.04
40.	31 may. 2021	-0.90%	0.55%	2.85	0.01	0.20
41.	30 jun. 2021	3.53%	2.22%	7.55	2.42	4.27
42.	31 jul. 2021	13.88%	2.27%	171.46	2.59	21.06
43.	31 ago. 2021	1.90%	2.90%	1.24	4.98	2.48
44.	30 sept. 2021	-6.15%	-4.76%	48.02	29.42	37.58
45.	31 oct. 2021	-6.17%	6.91%	48.37	39.03	-43.45
46.	30 nov. 2021	-2.06%	-0.83%	8.07	2.25	4.26
47.	31 dic. 2021	7.46%	4.36%	44.63	13.65	24.68
48.	31 ene. 2022	-24.68%	-5.26%	648.66	35.11	150.91
49.	28 feb. 2022	3.33%	-3.14%	6.50	14.46	-9.69
50.	31 mar. 2022	-14.75%	3.58%	241.44	8.47	-45.23
51.	30 abr. 2022	-33.51%	-8.80%	1,175.91	89.54	324.48
52.	31 may. 2022	-4.23%	0.01%	25.17	0.44	3.32
53.	30 jun. 2022	-14.76%	-8.39%	241.53	82.06	140.78
54.	31 jul. 2022	18.72%	9.11%	321.61	71.32	151.45
55.	31 ago. 2022	-13.26%	-4.24%	197.39	24.11	68.99
56.	30 sept. 2022	-15.01%	-9.34%	249.61	100.12	158.09
57.	31 oct. 2022	-6.19%	7.99%	48.58	53.58	-51.02
58.	30 nov. 2022	1.21%	5.38%	0.18	22.17	2.02
59.	31 dic. 2022	7.24%	-5.90%	41.68	43.08	-42.38
Total (Σ):				12,875.12	1,691.48	2,637.01

Mostrar todo

Varianza_ALGN = Σ(R_ALGN,t–R_ALGN)² ÷ (59 – 1)
= 12,875.12 ÷ (59 – 1)
= 221.98

Varianza_{S&P 500} = Σ(R_{S&P 500,t}–R_{S&P 500})² ÷ (59 – 1)
= 1,691.48 ÷ (59 – 1)
= 29.16

Covarianza_{ALGN, S&P 500} = Σ(R_ALGN,t–R_ALGN)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 2,637.01 ÷ (59 – 1)
= 45.47

Estimación sistemática del riesgo (β)

Varianza_ALGN	221.98
Varianza_{S&P 500}	29.16
Covarianza_{ALGN, S&P 500}	45.47
Coeficiente de correlación_{ALGN, S&P 500}¹	0.57
β_ALGN²	1.56
α_ALGN³	-0.25%

Cálculos

¹ Coeficiente de correlación_{ALGN, S&P 500}
= Covarianza_{ALGN, S&P 500} ÷ (Desviación estándar_ALGN × Desviación estándar_{S&P 500})
= 45.47 ÷ (14.90% × 5.40%)
= 0.57

² β_ALGN
= Covarianza_{ALGN, S&P 500} ÷ Varianza_{S&P 500}
= 45.47 ÷ 29.16
= 1.56

³ α_ALGN
= Promedio_ALGN – β_ALGN × Promedio_{S&P 500}
= 0.78% – 1.56 × 0.67%
= -0.25%

Tasa de rendimiento esperada

Suposiciones
Tasa de rendimiento del LT Treasury Composite¹	R_F	4.30%
Tasa de rendimiento esperada de la cartera de mercado²	E(R_M)	13.81%
Riesgo sistemático de Align acciones ordinarias	β_ALGN	1.56

Tasa de rendimiento esperada de las acciones ordinarias de Align³	E(R_ALGN)	19.12%

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

² Ver detalles »

³ E(R_ALGN) = R_F + β_ALGN [E(R_M) – R_F]
= 4.30% + 1.56 [13.81% – 4.30%]
= 19.12%

Align Technology Inc. (NASDAQ:ALGN)

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

Tasas de retorno

Varianza y covarianza

Estimación sistemática del riesgo (β)

Tasa de rendimiento esperada