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 IQVIA.

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

Tasas de retorno

IQVIA Holdings Inc., tasas mensuales de retorno

		IQVIA Holdings Inc. (IQV)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_IQV,t¹	Dividendo_IQV,t¹	R_IQV,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	31 ene. 2018	$102.19			2,823.81
1.	28 feb. 2018	$98.33		-3.78%	2,713.83	-3.89%
2.	31 mar. 2018	$98.11		-0.22%	2,640.87	-2.69%
3.	30 abr. 2018	$95.76		-2.40%	2,648.05	0.27%
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58.	30 nov. 2022	$218.02		3.98%	4,080.11	5.38%
59.	31 dic. 2022	$204.89		-6.02%	3,839.50	-5.90%
Promedio (R):				1.59%		0.67%
Desviación estándar:				9.20%		5.40%

		IQVIA Holdings Inc. (IQV)			Standard & Poor’s 500 (S&P 500)
t	Fecha	Precio_IQV,t¹	Dividendo_IQV,t¹	R_IQV,t²	Precio_{S&P 500,t}	R_{S&P 500,t}³
	31 ene. 2018	$102.19			2,823.81
1.	28 feb. 2018	$98.33		-3.78%	2,713.83	-3.89%
2.	31 mar. 2018	$98.11		-0.22%	2,640.87	-2.69%
3.	30 abr. 2018	$95.76		-2.40%	2,648.05	0.27%
4.	31 may. 2018	$98.93		3.31%	2,705.27	2.16%
5.	30 jun. 2018	$99.82		0.90%	2,718.37	0.48%
6.	31 jul. 2018	$121.94		22.16%	2,816.29	3.60%
7.	31 ago. 2018	$127.09		4.22%	2,901.52	3.03%
8.	30 sept. 2018	$129.74		2.09%	2,913.98	0.43%
9.	31 oct. 2018	$122.93		-5.25%	2,711.74	-6.94%
10.	30 nov. 2018	$125.07		1.74%	2,760.17	1.79%
11.	31 dic. 2018	$116.17		-7.12%	2,506.85	-9.18%
12.	31 ene. 2019	$129.01		11.05%	2,704.10	7.87%
13.	28 feb. 2019	$140.10		8.60%	2,784.49	2.97%
14.	31 mar. 2019	$143.85		2.68%	2,834.40	1.79%
15.	30 abr. 2019	$138.90		-3.44%	2,945.83	3.93%
16.	31 may. 2019	$135.85		-2.20%	2,752.06	-6.58%
17.	30 jun. 2019	$160.90		18.44%	2,941.76	6.89%
18.	31 jul. 2019	$159.17		-1.08%	2,980.38	1.31%
19.	31 ago. 2019	$155.15		-2.53%	2,926.46	-1.81%
20.	30 sept. 2019	$149.38		-3.72%	2,976.74	1.72%
21.	31 oct. 2019	$144.42		-3.32%	3,037.56	2.04%
22.	30 nov. 2019	$145.98		1.08%	3,140.98	3.40%
23.	31 dic. 2019	$154.51		5.84%	3,230.78	2.86%
24.	31 ene. 2020	$155.25		0.48%	3,225.52	-0.16%
25.	29 feb. 2020	$139.49		-10.15%	2,954.22	-8.41%
26.	31 mar. 2020	$107.86		-22.68%	2,584.59	-12.51%
27.	30 abr. 2020	$142.59		32.20%	2,912.43	12.68%
28.	31 may. 2020	$149.52		4.86%	3,044.31	4.53%
29.	30 jun. 2020	$141.88		-5.11%	3,100.29	1.84%
30.	31 jul. 2020	$158.39		11.64%	3,271.12	5.51%
31.	31 ago. 2020	$163.75		3.38%	3,500.31	7.01%
32.	30 sept. 2020	$157.63		-3.74%	3,363.00	-3.92%
33.	31 oct. 2020	$153.99		-2.31%	3,269.96	-2.77%
34.	30 nov. 2020	$168.99		9.74%	3,621.63	10.75%
35.	31 dic. 2020	$179.17		6.02%	3,756.07	3.71%
36.	31 ene. 2021	$177.80		-0.76%	3,714.24	-1.11%
37.	28 feb. 2021	$192.79		8.43%	3,811.15	2.61%
38.	31 mar. 2021	$193.14		0.18%	3,972.89	4.24%
39.	30 abr. 2021	$234.69		21.51%	4,181.17	5.24%
40.	31 may. 2021	$240.16		2.33%	4,204.11	0.55%
41.	30 jun. 2021	$242.32		0.90%	4,297.50	2.22%
42.	31 jul. 2021	$247.70		2.22%	4,395.26	2.27%
43.	31 ago. 2021	$259.73		4.86%	4,522.68	2.90%
44.	30 sept. 2021	$239.54		-7.77%	4,307.54	-4.76%
45.	31 oct. 2021	$261.42		9.13%	4,605.38	6.91%
46.	30 nov. 2021	$259.13		-0.88%	4,567.00	-0.83%
47.	31 dic. 2021	$282.14		8.88%	4,766.18	4.36%
48.	31 ene. 2022	$244.90		-13.20%	4,515.55	-5.26%
49.	28 feb. 2022	$230.12		-6.04%	4,373.94	-3.14%
50.	31 mar. 2022	$231.21		0.47%	4,530.41	3.58%
51.	30 abr. 2022	$217.99		-5.72%	4,131.93	-8.80%
52.	31 may. 2022	$215.25		-1.26%	4,132.15	0.01%
53.	30 jun. 2022	$216.99		0.81%	3,785.38	-8.39%
54.	31 jul. 2022	$240.27		10.73%	4,130.29	9.11%
55.	31 ago. 2022	$212.66		-11.49%	3,955.00	-4.24%
56.	30 sept. 2022	$181.14		-14.82%	3,585.62	-9.34%
57.	31 oct. 2022	$209.67		15.75%	3,871.98	7.99%
58.	30 nov. 2022	$218.02		3.98%	4,080.11	5.38%
59.	31 dic. 2022	$204.89		-6.02%	3,839.50	-5.90%
Promedio (R):				1.59%		0.67%
Desviación estándar:				9.20%		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 IQV 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

IQVIA Holdings Inc., cálculo de la varianza y covarianza de los rendimientos

t	Fecha	R_IQV,t	R_{S&P 500,t}	(R_IQV,t–R_IQV)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_IQV,t–R_IQV)×(R_{S&P 500,t}–R_{S&P 500})
1.	28 feb. 2018	-3.78%	-3.89%	28.78	20.81	24.47
2.	31 mar. 2018	-0.22%	-2.69%	3.28	11.26	6.08
3.	30 abr. 2018	-2.40%	0.27%	15.86	0.16	1.57
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58.	30 nov. 2022	3.98%	5.38%	5.74	22.17	11.28
59.	31 dic. 2022	-6.02%	-5.90%	57.90	43.08	49.95
Total (Σ):				4,912.14	1,691.48	2,339.53

t	Fecha	R_IQV,t	R_{S&P 500,t}	(R_IQV,t–R_IQV)²	(R_{S&P 500,t}–R_{S&P 500})²	(R_IQV,t–R_IQV)×(R_{S&P 500,t}–R_{S&P 500})
1.	28 feb. 2018	-3.78%	-3.89%	28.78	20.81	24.47
2.	31 mar. 2018	-0.22%	-2.69%	3.28	11.26	6.08
3.	30 abr. 2018	-2.40%	0.27%	15.86	0.16	1.57
4.	31 may. 2018	3.31%	2.16%	2.97	2.23	2.57
5.	30 jun. 2018	0.90%	0.48%	0.47	0.03	0.13
6.	31 jul. 2018	22.16%	3.60%	423.24	8.62	60.39
7.	31 ago. 2018	4.22%	3.03%	6.95	5.57	6.22
8.	30 sept. 2018	2.09%	0.43%	0.25	0.06	-0.12
9.	31 oct. 2018	-5.25%	-6.94%	46.73	57.87	52.00
10.	30 nov. 2018	1.74%	1.79%	0.02	1.25	0.17
11.	31 dic. 2018	-7.12%	-9.18%	75.74	96.91	85.68
12.	31 ene. 2019	11.05%	7.87%	89.60	51.87	68.17
13.	28 feb. 2019	8.60%	2.97%	49.13	5.32	16.16
14.	31 mar. 2019	2.68%	1.79%	1.19	1.27	1.23
15.	30 abr. 2019	-3.44%	3.93%	25.28	10.66	-16.42
16.	31 may. 2019	-2.20%	-6.58%	14.31	52.48	27.41
17.	30 jun. 2019	18.44%	6.89%	284.00	38.77	104.93
18.	31 jul. 2019	-1.08%	1.31%	7.09	0.42	-1.72
19.	31 ago. 2019	-2.53%	-1.81%	16.91	6.13	10.18
20.	30 sept. 2019	-3.72%	1.72%	28.15	1.11	-5.58
21.	31 oct. 2019	-3.32%	2.04%	24.08	1.89	-6.76
22.	30 nov. 2019	1.08%	3.40%	0.26	7.50	-1.39
23.	31 dic. 2019	5.84%	2.86%	18.11	4.81	9.33
24.	31 ene. 2020	0.48%	-0.16%	1.23	0.69	0.92
25.	29 feb. 2020	-10.15%	-8.41%	137.79	82.40	106.56
26.	31 mar. 2020	-22.68%	-12.51%	588.67	173.67	319.75
27.	30 abr. 2020	32.20%	12.68%	937.10	144.43	367.89
28.	31 may. 2020	4.86%	4.53%	10.71	14.91	12.64
29.	30 jun. 2020	-5.11%	1.84%	44.85	1.37	-7.85
30.	31 jul. 2020	11.64%	5.51%	100.99	23.46	48.67
31.	31 ago. 2020	3.38%	7.01%	3.23	40.19	11.39
32.	30 sept. 2020	-3.74%	-3.92%	28.35	21.06	24.44
33.	31 oct. 2020	-2.31%	-2.77%	15.18	11.79	13.38
34.	30 nov. 2020	9.74%	10.75%	66.48	101.77	82.25
35.	31 dic. 2020	6.02%	3.71%	19.69	9.28	13.51
36.	31 ene. 2021	-0.76%	-1.11%	5.53	3.17	4.19
37.	28 feb. 2021	8.43%	2.61%	46.84	3.77	13.29
38.	31 mar. 2021	0.18%	4.24%	1.98	12.80	-5.03
39.	30 abr. 2021	21.51%	5.24%	397.04	20.94	91.18
40.	31 may. 2021	2.33%	0.55%	0.55	0.01	-0.09
41.	30 jun. 2021	0.90%	2.22%	0.47	2.42	-1.07
42.	31 jul. 2021	2.22%	2.27%	0.40	2.59	1.02
43.	31 ago. 2021	4.86%	2.90%	10.69	4.98	7.30
44.	30 sept. 2021	-7.77%	-4.76%	87.62	29.42	50.77
45.	31 oct. 2021	9.13%	6.91%	56.96	39.03	47.15
46.	30 nov. 2021	-0.88%	-0.83%	6.07	2.25	3.69
47.	31 dic. 2021	8.88%	4.36%	53.18	13.65	26.94
48.	31 ene. 2022	-13.20%	-5.26%	218.63	35.11	87.61
49.	28 feb. 2022	-6.04%	-3.14%	58.10	14.46	28.99
50.	31 mar. 2022	0.47%	3.58%	1.24	8.47	-3.24
51.	30 abr. 2022	-5.72%	-8.80%	53.36	89.54	69.12
52.	31 may. 2022	-1.26%	0.01%	8.09	0.44	1.88
53.	30 jun. 2022	0.81%	-8.39%	0.61	82.06	7.05
54.	31 jul. 2022	10.73%	9.11%	83.57	71.32	77.20
55.	31 ago. 2022	-11.49%	-4.24%	171.04	24.11	64.22
56.	30 sept. 2022	-14.82%	-9.34%	269.25	100.12	164.19
57.	31 oct. 2022	15.75%	7.99%	200.59	53.58	103.67
58.	30 nov. 2022	3.98%	5.38%	5.74	22.17	11.28
59.	31 dic. 2022	-6.02%	-5.90%	57.90	43.08	49.95
Total (Σ):				4,912.14	1,691.48	2,339.53

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Varianza_IQV = Σ(R_IQV,t–R_IQV)² ÷ (59 – 1)
= 4,912.14 ÷ (59 – 1)
= 84.69

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_{IQV, S&P 500} = Σ(R_IQV,t–R_IQV)×(R_{S&P 500,t}–R_{S&P 500}) ÷ (59 – 1)
= 2,339.53 ÷ (59 – 1)
= 40.34

Estimación sistemática del riesgo (β)

Varianza_IQV	84.69
Varianza_{S&P 500}	29.16
Covarianza_{IQV, S&P 500}	40.34
Coeficiente de correlación_{IQV, S&P 500}¹	0.81
β_IQV²	1.38
α_IQV³	0.67%

Cálculos

¹ Coeficiente de correlación_{IQV, S&P 500}
= Covarianza_{IQV, S&P 500} ÷ (Desviación estándar_IQV × Desviación estándar_{S&P 500})
= 40.34 ÷ (9.20% × 5.40%)
= 0.81

² β_IQV
= Covarianza_{IQV, S&P 500} ÷ Varianza_{S&P 500}
= 40.34 ÷ 29.16
= 1.38

³ α_IQV
= Promedio_IQV – β_IQV × Promedio_{S&P 500}
= 1.59% – 1.38 × 0.67%
= 0.67%

Tasa de rendimiento esperada

Suposiciones
Tasa de rendimiento del LT Treasury Composite¹	R_F	4.62%
Tasa de rendimiento esperada de la cartera de mercado²	E(R_M)	13.69%
Riesgo sistemático de IQVIA acciones ordinarias	β_IQV	1.38

Tasa de rendimiento esperada de las acciones ordinarias de IQVIA³	E(R_IQV)	17.16%

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_IQV) = R_F + β_IQV [E(R_M) – R_F]
= 4.62% + 1.38 [13.69% – 4.62%]
= 17.16%

IQVIA Holdings Inc. (NYSE:IQV)

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