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//////////8AAP////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////8AAP////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////8AAP////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////4AAP////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////4AAP////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////8AAP////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //8AAP////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////8AAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////8AAP////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////8A AP////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////8AAP////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////8AAP////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////8AAP// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////8AAP////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////8AAP////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////8AAP////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////8AAP////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////8AAP////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////8AAP////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////8AAP////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////8AAP////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////8AAP////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////8AAP////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////8AAP////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////8AAP////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //8AAP////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////8AAP////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////8AAP////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////8A 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//////////////////////////////////////////////////////////////////8AAP////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////8AAP////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////8AAP////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////8AAP////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////8AAP////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////8AAP////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////8AAP////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////8AAP////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////4AAP////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////8AAP////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //8AAP////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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//////////////////////////////////////////////////////////////////////////// //////////////////4AAP////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////8AAP////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////4AAP////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////8AAP////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////8AAP////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////4AAP////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////8AAP////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////4AAP////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////8AAP////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////4AAP////////////////////////////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// //////////////////////////////8AAP////////////////////////////////////////// //////////////////////////////////////////////////////////////////////////// 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FACULTAD DE NEGOCIOSCon Reconocimiento de Validez Oficial de Estudios de la Secretaría de Educación Pública según acuerdo número No 954315 de fecha 30 de octubre de 1995

TESIS

Desarrollo de un fondo de inversión a largo plazo llamado “Fondo Crece” para elevar el ahorro en las familias mexicanas PARA OBTENER EL GRADO DE MAESTRO EN INGENIERÍA ECONÓMICA Y FINANCIERA PRESENTA:Juan José De Amirola FernándezDirector de Tesis: Dr. Héctor Alonso Olivares Aguayo

Ciudad de México a

Agosto

de 2024

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Agradecimientos y

edicatoria

A mi madre, por haber sido tanto padre como madre, por estar a mi lado en cada situación y por brindarme la oportunidad de una educación profesional. Gracias por apoyarme desde mis primeros pasos hasta el día de hoy, siendo el pilar fundamental que me ha formado como la persona que soy.

A mi compañera de vida, por su amor incondicional, por estar a mi lado en cada etapa de nuestra vida, por su paciencia, por formar parte de nuestro proyecto de vida y por ser un soporte esencial en mi vida.

A mi hija, por ser mi mayor fuente de inspiración y motivación,

impulsándome

cada día a esforzarme por ser un mejor padre y una mejor persona.

Al Dr. Héctor Alonso Olivares Aguayo, por su apoyo constante, profesionalismo y amistad. Gracias por acompañarme en este proyecto y por ser una pieza clave para llevarlo a cabo. Sin su ayuda y aliento, no habría sido posible completar este trabajo.

Índice

General

TOC \o "1-3" \h \z \u

IntroducciónCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgANgA5AAAA PAGEREF _Toc171025869 \h 1

Capítulo 1 Planteamiento del ProblemaCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgANwAwAAAA PAGEREF _Toc171025870 \h 3

1.1

Justificación del ProyectoCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgANwAxAAAA PAGEREF _Toc171025871 \h 3

1.2

¿Qué significa tener salud financiera?CNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgANwA0AAAA PAGEREF _Toc171025874 \h 6

1.2.1

¿Qué es la salud financiera?CNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgANwA1AAAA PAGEREF _Toc171025875 \h 7

1.3

El Capital Privado o Private Equity8

Capítulo 2 AntecedentesCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOAAxAAAA PAGEREF _Toc171025881 \h 10

2.1

Definición e historia del ahorroCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOAAyAAAA PAGEREF _Toc171025882 \h 10

2.2

Determinantes del AhorroCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOAAzAAAA PAGEREF _Toc171025883 \h 11

2.3

Relación entre Ahorro y DesarrolloCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOQAwAAAA PAGEREF _Toc171025890 \h 12

2.4

Portafolios de InversiónCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOQAzAAAA PAGEREF _Toc171025893 \h 13

2.5

Desventajas del portafolio de MarkowitzCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOQA0AAAA PAGEREF _Toc171025894 \h 15

2.6

El sistema de Ahorro para el Retiro (SAR)CNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOQA1AAAA PAGEREF _Toc171025895 \h 15

Capítulo 3 Metodología del ModeloCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOQA2AAAA PAGEREF _Toc171025896 \h 17

3.1

Metodología para la Evaluación de los Portafolios de InversiónCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOQA3AAAA PAGEREF _Toc171025897 \h 19

3.1.1

RendimientoCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOQA4AAAA PAGEREF _Toc171025898 \h 19

3.2

El ratio o índice de SharpeCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADgAOQA5AAAA PAGEREF _Toc171025899 \h 21

3.3 Tasa Libre de Riesgo “CeteS”CNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAAwAAAA PAGEREF _Toc171025900 \h 21

3.4 RiesgoCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAAxAAAA PAGEREF _Toc171025901 \h 22

3.4.1

Desviación EstándarCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAAyAAAA PAGEREF _Toc171025902 \h 24

3.4.2

Riesgo SistemáticoCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAAzAAAA PAGEREF _Toc171025903 \h 25

3.4.3

Riesgo No SistemáticoCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAA0AAAA PAGEREF _Toc171025904 \h 26

3.4.4

BetaCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAA1AAAA PAGEREF _Toc171025905 \h 27

3.5

Mercado de CapitalesCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAA2AAAA PAGEREF _Toc171025906 \h 28

3.5.1

Línea de Mercado de CapitalesCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAA3AAAA PAGEREF _Toc171025907 \h 28

3.5.2

Tipos de inversionesCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAA4AAAA PAGEREF _Toc171025908 \h 29

3.5.3

Portafolio EquiponderadoCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMAA5AAAA PAGEREF _Toc171025909 \h 29

3.5.4

Portafolio de Mínima VarianzaCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMQAwAAAA PAGEREF _Toc171025910 \h 30

3.6 Metodología del Fondo32

Resultados ObtenidosCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMQAyAAAA PAGEREF _Toc171025912 \h 33

4.1

S&P/BMV IPCCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMQAzAAAA PAGEREF _Toc171025913 \h 34

4.2

Elaboración de los Portafolios: Equiponderado, mínima varianza y SharpeCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMQA0AAAA PAGEREF _Toc171025914 \h 36

4.3

Comparación de los Portafolios: Equiponderado, mínima varianza y SharpeCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMQA1AAAA PAGEREF _Toc171025915 \h 388

4.4 Simulación de Ganancia entre los tres tipos de portafolios y TLR 2007 – 2022CNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMQA2AAAA PAGEREF _Toc171025916 \h 39

Conclusiones40

5.1

Limitantes en los portafoliosCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMQA4AAAA PAGEREF _Toc171025918 \h 41

BibliografíaCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMQA5AAAA PAGEREF _Toc171025919 \h 42

AnexosCNDJ6nn5us4RjIIAqgBLqQsCAAAACAAAAA4AAABfAFQAbwBjADEANwAxADAAMgA1ADkAMgAwAAAA PAGEREF _Toc171025920 \h 44

Índice

de tablas

TOC \t "Tablas,1"

Tabla No.

Simulación del Fondo

-----------------------------------------------------------------------------------

----

--------3

Tabla No. 4

Empresas que componen S&P/BMV IPC ---------------------------------------------------------

------------

Tabla No.

4.2

Comparativo entre los tres tipos de portafolio

S&P/BMV IPC 2005 - 2007

Tabla No. 4.3

Comparativo entre los tres tipos de portafolio

y TLR 2007

2022

------------------------------

--------

Índice

de Gráficas

Gráfica No. 1.1

Población de 18 a 70 años con formas de ahorro informal por sexo 2021

---------------------------

Gráfica No. 1.2

Población de 18 a 70 años con formas de ahorro informal por sexo 2015 - 2021

-------------

----

Gráfica No. 1.3

Población de 18 a 70 años que tienen una cuenta de ahorro formal según sexo 2015 - 2021

TOC \t "Tablas,1"

Gráfica

No.

3.1

Línea de mercado de capitales

Gráfica

No. 4.2

Comparativo entre los tres tipos de portafolio

S&P/BMV IPC 2005 - 2007

IVPAGE \* MERGEFORMAT16

IntroducciónEl presente proyecto de investigación examina la relevancia del ahorro como medio para beneficiar a individuos, específicamente en la creación de un fondo de Capital Privado denominado "Crece" en México, con el propósito de acumular fondos para sufragar estudios universitarios futuros. Los fondos de capital privado se orientan hacia la captación de recursos de inversionistas sofisticados, destinados a ser invertidos en diversas compañías privadas o proyectos con alto potencial de crecimiento. Estos fondos proporcionan a los inversionistas la garantía de una gestión adecuada del negocio, dado que están sujetos a regulaciones por parte de diferentes firmas, en algunos casos respaldados por diferentes tipos de fideicomisos.Cuando una compañía alcanza su horizonte de inversión y adquiere mayor valor, el fondo ejecuta una estrategia de desinversión con el fin de retribuir a los inversionistas sus ganancias y obtener una rentabilidad para todos los participantes involucrados. La problemática asociada al ahorro en México radica en que una parte de la población ahorra de manera informal y con enfoque a corto plazo, siendo que casi el 40% de la población no realiza ningún tipo de ahorro.Ahorrar de manera informal conlleva riesgos significativos debido a la ausencia de una planificación financiera estructurada. La falta de un presupuesto mensual de gastos y ahorros conlleva a que las familias mexicanas, para enfrentar imprevistos, la mayoría de las familias mexicanas utilizan métodos como tandas, cajas de ahorro, cuentas bancarias e incluso guardar el efectivo debajo del colchón. Esta preferencia se atribuye en gran medida a la falta de información y al hecho de que menos del 50% de los mexicanos utilizan servicios bancarios.La presente investigación tiene como objetivo explorar la importancia del ahorro a largo plazo diseñando un Fondo que beneficie a las personas desde una edad temprana, promoviendo el ahorro para el financiamiento de sus estudios universitarios futuros. Para lograrlo, se busca promover el ahorro a través del fondo iniciando el plan de ahorro para la universidad, para eso se necesita construir portafolios: equiponderados, mínima varianza y de máximo índice de Sharpe. Se pretende evaluar mediante el diseño de estos portafolios cuál método de ejecución resulta más eficiente. Se busca generar conciencia sobre la necesidad de implementar mecanismos de ahorro que actualmente no existen en el panorama financiero.El enfoque del trabajo se centra en la creación de un fondo de ahorro innovador, destinado a beneficiar a las personas desde una edad temprana hasta su ingreso a la universidad. Este proyecto, denominado fondo "Crece", tiene como meta principal acumular recursos suficientes para cubrir los costos educativos mediante un esquema de aportaciones mensuales, que podrían ser obligatorias por parte de las instituciones educativas y manejadas como deducibles de impuestos.El proyecto contempla el inicio de las contribuciones desde el nacimiento del individuo hasta cumplir al menos 18 años, con el propósito de establecer un sólido fondo de ahorro para respaldar la educación superior. Este enfoque novedoso busca proporcionar una solución integral para garantizar el acceso a la educación universitaria sin incurrir en deudas excesivas.Las dificultades financieras en México tienen diversas causas, entre las que se destaca la falta de una cultura financiera arraigada, exacerbada por el constante incremento del costo de vida y los cambios de inflación que afectan los precios de bienes y servicios. Además, el aumento de la necesidad de adquirir bienes no esenciales contribuye a esta problemática. A esto se suma el desequilibrio entre ingresos y gastos, lo cual proporciona justificaciones para no ahorrar.En cuanto a las estrategias de inversión del fondo de capital privado propuesto, se enfocará en activos como infraestructura, bienes raíces y energía, aprovechando proyectos gubernamentales a través de fideicomisos para garantizar la gestión eficiente de los recursos. Respecto a la metodología de Markowitz, este trabajo incluirá el cálculo del riesgo del portafolio considerando tanto el riesgo sistemático como no sistemático, especialmente en períodos de alta volatilidad debido a eventos como la pandemia y conflictos internacionales.Cuando una compañía alcanza su horizonte de inversión y adquiere mayor valor, el fondo ejecuta una estrategia de desinversión con el fin de retribuir a los inversionistas sus ganancias y obtener una rentabilidad para todos los participantes involucrados. La problemática asociada al ahorro en México radica en que una parte de la población ahorra de manera informal y con enfoque a corto plazo, siendo que casi el 40% de la población no realiza ningún tipo de ahorro.

apítulo

Planteamiento del

Problema

Justificación

del Proyecto

problemática derivada del ahorro

México en el cual

la mayoría

de los

mexicanos

prefieren

ahorr

de manera

muy

informal

prefiriendo

guardar dinero pensando

en el corto plazo.

Es que

asi el 40% de las personas en México no guarda dinero p

reviniendo

el futuro.

Ahorrar de manera informal conlleva riesgos

ya que no existe una planificación

y al no haber un presupuesto mensu

de gastos y de ahorro,

la preferencia

en las familias mexicanas

para generar ahorro para cubrir algún impr

visto es la utilización de

tandas

o en

cajas de ahorro

a razón por la que muchos mexicanos guardan su dinero en casa o debajo del colchón es porque no están bien informados sobre

los servicios financieros

. Además, menos del 50% de la población utiliza servicios bancarios.

Gran parte de los mexicanos son

analfabetas financier

población no bancarizada

com

o se puede observar en la Gráfica

1.1

, desconoce

los beneficios que podría obtener al ahorrar, invertir y administrar de mejor manera su dinero.

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Gráfica

Población

de 18 a 70 años con formas de ahorro informal por sexo 2021

Nota

: INEGI. Encuesta Nacional de inclusión Financiera (ENIF). Ediciones 2015, 2018 y 2021.

Muchas personas dicen que no ahorran porque sus ingresos

solo les alcanza para cubrir sus necesidades básicas e incluso que no les alcanza el recurso y se ven en la necesidad de

pedir prestado

, como se observa en la Gráfica

1.2.

Por otro lado,

ahorra pensando

obtener

en el corto plazo

algo que

se desea

y la meta es alcanzarlo o

para cubrir emergencias

metas personales inmediatas; sin embargo, si

se hicieran

aportaciones

de dinero de forma recurrente

en una institución financiera, con montos

accesibles para

iniciar

inversion

mínima

se pudiera fo

mentar

un ahorro considerable de miles

incluso millones

de pesos, dependiendo el horizonte

Gráfica

Población de 18 a 70 años con formas de ahorro informal por sexo 2015

–

2021

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Nota

: INEGI

. Encuesta Nacional de inclusión Financiera (ENIF). Ediciones 2015, 20

18 y 2021.

Hay que distinguir entre el "ahorro", que es guardar dinero de manera segura y con la posibilidad de acceder a él rápidamente; y la "inversión", que busca generar ganancias o rentabilidad a corto, mediano o largo plazo, considerando las fluctuaciones del mercado y asumiendo cierto riesgo con la expectativa de aumentar el capital con el tiempo. Al evaluar esta distinción, es importante tener en cuenta varios consejos para el ahorro e inversión

(Guerrini, 2013)

Es importante destinar una parte de

dinero cada mes, trimestre, semestre o año para imprevistos. Esto ayudará a estar preparado y protegido ante cualquier situación inesperada que pueda surgir.

En la Gráfica

1.3, se muestra

el porcentaje de personas

tanto hombres como mujeres

que

tienen una cuenta formal en México, incluy

e cuentas

nómina, de pensión

, para recepción de ayudas de gobierno, cuentas de ahorro, cuentas de cheques, depósitos fijos, fondos de inversió

n, cuentas

internet.

Gráfica

Población de 18 a 70 años

que tienen una cuenta de ahorro formal

según

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Nota

: INEGI. Encuesta Nacional de inclusión Financiera (ENIF). Ediciones 2015, 2018 y 2021.

Un producto que se adapte perfectamente a

las

necesidades

de la persona,

se elige basándose en varios factores importantes

de acuerdo con

meta de ahorro

que tiene cada persona

se tiene que elaborar un

perfil de riesgo y

pendiendo

la capacidad de ahorro

que uno tenga

revisando los ingresos y

los egresos

que una persona tenga;

podría

uscar la ayuda de alguien especializado en el tema

que

permitirá obtener consejos valiosos de alguien con experiencia y conocimientos profundos en el área

para

ayudar

con una planeación patrimonial

de manera integral

una planeación financiera

para

construcción

de una estrategia

para el futuro

mejor

establecer un objetivo o meta, medible y trazable en el tiempo

esto dependerá de

l horizonte de inversión, la

adversidad al riesgo

ya que existe volatilidad en el mercado y

se debe diversificar la inversión

esto reducirá el riesgo

¿Qué significa tener salud financiera?

El bienestar financiero se define como el estado de salud financiera que abarca tanto la satisfacción con los aspectos tangibles como intangibles de la situación económica de una persona, así como la percepción de estabilidad financiera, incluyendo la suficiencia de recursos, tanto materiales como inmateriales, disponibles para cada individuo.

(Joo 1998).

Se señala que el bienestar financiero es esencialmente el resultado de llevar a cabo una gestión financiera integral que engloba actitudes, conocimientos y comportamientos financieros promovidos por la educación financiera. Se ha observado que aquellos con una base sólida en educación financiera tienden a disfrutar de una mejor salud financiera, experimentan menos estrés económico y reportan una mayor satisfacción financiera en general.

Los resultados de esta investigación resaltan que la falta de salud financiera impacta de manera más significativa a aquellos que enfrentan desafíos financieros en su vida. Las personas que tienen deudas o carecen de ahorros para imprevistos son especialmente vulnerables.

Por ejemplo, aquellos con deudas comprometen una parte de sus ingresos futuros para pagar sus obligaciones mensuales. Esto significa que disponen de menos dinero para otras necesidades. Además, la ausencia de un fondo de emergencia, incluso si es modesto, hace que cualquier contratiempo represente un desequilibrio financiero significativo. En muchos casos, las personas se ven obligadas a recurrir a nuevas deudas para hacer frente a estas situaciones inesperadas.

¿Qué es la salud finan

era?

Administrar adecuadamente

os recursos económicos implica gastar menos de lo que

se gana

, lo cual abarca todos

os gastos.

Tener deudas sanas como la hipoteca

limita la

libertad a corto plazo, pero se está generando un patrimonio a largo plazo, sin embargo,

reduce la

capacidad de ahorro.

Es fundamental disponer de un fondo de reserva para emergencias que permita hacer frente a imprevistos financieros. Además, es importante contar con diversos tipos de seguros, como los de vida, educación, salud y automóvil, para proteger

a estabilidad financiera ante diferentes eventualidades.

Existen múltiples aspectos que influyen en la salud financiera, como el hábito de ahorrar para alcanzar metas prioritarias y la inversión inteligente de esos ahorros, considerando

horizonte temporal y tolerancia al riesgo. Sin embargo, cada individuo parte de una situación financiera diferente.

enc

uentra

actualmente endeu

dada la persona

debido a compras innecesarias con tarjetas de crédito, no

se tendrá

la posibilidad de invertir. En cambio,

e necesita

disminuir la

situación de deuda.

¿Cómo mejorar la salud financiera?

Gastos

Mantener un gasto que no supere

los

ingresos.

Ahorro

Tener suficientes ahorros cubrir

los

gastos y emergencias.

Tener suficientes activos de largo plazo.

Seguros.

Deuda

Tener un nivel de deuda saludable

Tener un buen buró de crédito

Plan

Contar con un seguro adecuado.

Tener una planeación de gastos.

Personalmente

, considero que la mejor manera de mejor

ar la salud financiera incluye:

Gestionar los gastos de manera eficiente y planificar el presupuesto, no solo para reducir gastos, sino para utilizar el dinero de manera más inteligente.

Incrementar los ahorros y las inversiones en bienes raíces u otros activos que generen ingresos pasivos consistentes. Esto aumenta el flujo de ingresos a largo plazo.

Disminuir las deudas pendientes.

Realizar una planificación financiera que incluya metas claras y herramientas para controlar activos, pasivos, ingresos y gastos futuros.

Diversificar las fuentes de ingresos, como alquilar propiedades, invertir en el mercado de valores o iniciar un negocio propio.

El Capital Privado o Private Equity

Consiste en desempeñar el papel de intermediario financiero, canalizando fondos de inversionistas hacia empresas y proyectos con un gran potencial de crecimiento, pero que no cotizan en

olsa

. El objetivo principal es aumentar el valor de estas empresas a lo largo del tiempo, generando retornos para sus accionistas e inversionistas a mediano y largo plazo.

fondo de

Capital Privado proporciona liquidez a empresas que tienen planes de crecimiento y expansión, así como a aquellas que están desarrollando nuevos proyectos. Estos fondos actúan como inversionistas, aportando capital en distintas etapas de desarrollo de una empresa, a cambio de una

participación en sus ganancias. Esta participación proporciona seguridad a los inversionistas sobre la gestión de los fondos y les permite calcular los rendimientos esperados.

Es importante destacar que los fondos de capital privado no buscan especular a corto plazo, sino que los inversionistas invierten en proyectos o empresas con una visión a largo plazo, que puede variar desde un mínimo de tres años hasta quince años, dependiendo de la naturaleza del proyecto.

Capítulo

Antecedentes

Definición e historia del ahorro

El ahorro se refiere a la parte del ingreso que no se destina al consumo inmediato. Este concepto ha sido practicado desde tiempos antiguos por civilizaciones como las de Egipto, China y la Inca, que almacenaban semillas para asegurar una futura cosecha. Este acto implicaba renunciar al consumo presente en favor de tener recursos para el futuro. Debido a la incertidumbre sobre las condiciones climáticas y la garantía de una buena cosecha, el ahorro empezó a ser visto como una forma de protegerse ante posibles contratiempos

futuros

en el proceso productivo. Además, una parte de los recursos ahorrados se destinaba al intercambio de bienes con comunidades vecinas, lo que dio origen al sistema de trueque y más tarde al uso del dinero debido a las limitaciones del trueque y el desarrollo económico.

Recuperado a partir de

l problema originado en las cuestiones sociales, constituye uno de los más graves y complejos que afectan al mundo en los actuales momentos, siendo a la vez, el punto céntrico y de mayor discusión, al que se relaciona con los Aspectos del Salario

(

Stolla

1953).

A pesar del esfuerzo colectivo de los trabajadores de todo el mundo y a lo largo de la historia, de las victorias conseguidas a costa de sus vidas y su sangre, así como de las leyes sociales que se supone los respaldan y protegen contra la explotación y la injusticia, estas siguen existiendo. Se manifiestan y se resumen en el salario, que muchas veces no es más que una burla irónica, una falsa apariencia de equidad con la que se engaña al trabajador, dándole una migaja de pan como si fuera una limosna, después de que ya ha agotado toda su energía y potencial.

partir

del

banco Nacional da

fomento de la facultad de captar los ahorros de la comunidad, mediante un adecuado sistema de emisión y venta pública de valores, para colocarlo en condiciones de planear, plantear y resolver los problemas de inversión que, de acuerdo con un Plan General de Desarrollo Económico Nacional, se lleve a la práctica por la i

niciativa privada y el gobierno

en beneficio del

incremento productivo del pa

ís. Además, del desarrollo del Mercado de V

alores, complemento indispensable en la organización bancaria moderna

(Naranjo, 1953).

Determinantes del Ahorro

Según la cultura China, la palabra crisis se compone de dos ideogramas: peligro y oportunidad. Esto implica que arriesgarse implica superar los miedos, aunque el resultado final sea desconocido. Esta distinción es crucial para diferenciar entre incertidumbre e inseguridad. Al fluir con lo que está por venir, se recibe con sabiduría y se transforma la perspectiva del curso de los acontecimientos, lo cual facilita la vida. Entre estos elementos determinantes se encuentran varios factores, tales como:

(

Saving Trust S.A et al., 2006)

Vivienda

curre porque las familias buscan satisfacer sus necesidades y asegurar un lugar seguro al que puedan llamar hogar.

Educación

ara aquellos que buscan continuar aprendiendo de manera constante.

Jubilación

ara todas las personas que

al final de

la edad cumplida por ley dejan de trabajar y se les otorga una pensión

Vacaciones

s un ahorro en el corto plazo

para

viajar

dentro de territorio nacional y

por el mundo

Seguros

e utilizan para ofrecer una cobertura a los familiares por

muerte, invalidez o enfermedad por lo general

, como también es un método de ahorro para

el retiro o alguna meta en lo personal.

Otros

de acuerdo con

las necesidades

planes de cada

quien

deben estar impulsado

por

n propósito o una meta, sea a corto, mediano o largo

plazo, esto

facilitará el alcance de sus objetivos y garantizará una cobertura adecuada para enfrentar imprevistos. Esto brinda una sensación de seguridad y preparación para el futuro.

Relación entre Ahorro y Desarrollo

Cada año, las Naciones Unidas elaboran el Índice de Desarrollo Humano (IDH), una herramienta que evalúa el progreso de un país. Más allá de simplemente medir el crecimiento económico, el IDH considera factores como la salud (representada por la esperanza de vida al nacer), la educación (basada en los años de escolarización para todas las edades) y los ingresos.

Esto se combina en un coeficiente que permite comparar de manera equitativa entre diferentes naciones. Según el informe más reciente publicado en 2023, que abarcó 193 países, Suiza y Noruega destacaron como los países con el IDH más alto, mientras que Sudán del Sur y Somalia se encontra

ron entre los más rezagados en D

esarrollo

umano.

La relación entre ahorro y desarrollo económico es fundamental y compleja, con múltiples dimensiones que afectan el crecimiento y la prosperidad de una sociedad. Aquí se exploran algunos aspectos clave de esta relación:

Financiamiento de la inversión:

El ahorro proporciona los recursos necesarios para la inversión en capital físico (como infraestructura, maquinaria) y capital humano (educación, formación). Una mayor tasa de ahorro suele estar asociada con mayores niveles de inversión, lo cual puede impulsar el crecimiento económico a largo plazo.

Estabilidad macroeconómica:

Los niveles adecuados de ahorro pueden contribuir a la estabilidad macroeconómica al proporcionar un colchón financiero que ayude a mitigar shocks económicos. Esto se logra a través de la acumulación de reservas y la reducción de la dependencia de la deuda externa.

Desigualdad y distribución de ingresos:

El ahorro y su acceso pueden influir en la desigualdad económica. Aquellos con mayores ingresos tienden a ahorrar más, lo que puede perpetuar diferencias de riqueza y oportunidades entre diferentes grupos sociales si no se maneja adecuadamente.

Innovación y desarrollo tecnológico:

El ahorro también financia la investigación y el desarrollo (I+D), así como la adopción de tecnologías avanzadas. Esto es crucial para mejorar la productividad y la competitividad económica a largo plazo.

Política fiscal y ahorro público:

El ahorro del gobierno (superávit presupuestario) puede liberar recursos para la inversión privada o para la reducción de la deuda pública, mejorando así la sostenibilidad fiscal y fortaleciendo la confianza en la economía.

Acceso a servicios financieros:

La disponibilidad de instituciones financieras y productos de ahorro adecuados es crucial para fomentar el ahorro a nivel individual y empresarial. Esto incluye el acceso a cuentas de ahorro, préstamos accesibles y seguros.

Crecimiento inclusivo y desarrollo humano:

Cuando el ahorro se canaliza adecuadamente, puede contribuir al desarrollo humano al mejorar el acceso a la educación, la salud y otras oportunidades que son fundamentales para reducir la pobreza y promover el bienestar general.

Portafolios de Inversión

enfoque desarrollado por

Markowitz

(1952)

, conocido como el

modelo

Media-

Varianza

, transformó el ámbito de las finanzas al introducir principios fundamentales para la construcción de

portafolios

de inversión. Conceptos como los portafolios eficientes, propuestos por Markowitz, continúan siendo pilares en numerosos modelos de gestión de

portafolios

, manteniendo la esencia de su idea original.

Markowitz definió un portafolio eficiente como aque

l que ofrece un nivel de rendimie

máximo para un determinado nivel de riesgo, o viceversa, un nivel

mínimo de riesgo para un rendimiento

dado. Uno de los métodos para identificar estos portafolios eficientes es a través de un modelo que busca minimizar la varianza del portafolio, presentado como un prob

lema de programación no lineal.

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Una vez que se ha aplicado

esta

técnica

para resolver un problema de

programación

lineal

se puede calcular la proporción de cada activo en la cartera de inversiones que cumple con las restricciones del modelo. Sin embargo, este proceso no considera automáticamente las condiciones de no negatividad para las ponderaciones de los activos. En este estudio, se soluciona este problema utilizando la técnica de Multiplicadores de Lagrange.

El modelo de Markowitz requiere ciertos datos de entrada, como los rendimientos esperados de los activos que formarán parte de

l portafolio

y la matriz de varianza-covarianza entre estos rendimientos.

El rendimiento promedio o

espe

rado, se estima de la

manera

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del activo

al tiempo

es el período o ventana de tiempo sobre la cual se está considerando el rendimiento promedio.

La matriz de varianza-covarianza es crucial para comprender y gestionar el riesgo asociado a los activos financieros, ya que representa toda la variabilidad entre ellos. En el contexto del modelo de media-varianza, su estimación precisa es esen

cial para determinar un portafolio

eficiente. Esta matriz proporciona información sobre la volatilidad de los activos y las relaciones entre ellos.

Una crítica común al modelo es su suposición de que la volatilidad de una serie financiera es constante en el tiempo (homocedasticidad), mientras que en la realidad es más común observar cambios sistemáticos en la volatilidad a lo largo del tiempo (heterocedasticidad).

Desventajas del portafolio

de Markowitz

Aunque el modelo de Markowitz representó un avance significativo al abordar integralmente la construcción de portafolios de inversión, varios investigadores han señalado desafíos importantes:

El uso de series históricas de rendimientos para estimar los parámetros esperados introduce sesgos significativos. Esto conduce a la formación de portafolios eficientes compuestos por activos con alta rentabilidad,

baja varianza y correlación

entre sí, resultando en una concentración alta en unos pocos títulos (poca diversificación y alto riesgo).

No obstante, esta dificultad puede mitigarse mediante la introducción de restricciones adicionales que limiten el porcentaje máximo de recursos invertidos en cada título. Además, el modelo se basa en datos históricos, lo que supone que el mercado se comportará de manera similar a como lo hizo en el pasado, asumiendo una estabilidad que no siempre es garantizada.

(Michaud, 1989; Haugen, 1993).

El sistema de Ahorro para el Retiro (SAR)

De acuerdo con el artículo 3°, fracción X de la Ley de los Sistemas de Ahorro para el Retiro, se establece un sistema regulado por la Ley del Seguro Social, en el cual trabajadores, empleadores y el Gobierno Federal realizan aportaciones a cuentas individuales pertenecientes a los trabajadores. El propósito es acumular fondos para pensiones y seguridad social.

Este sistema tiene como objetivo que tanto los trabajadores, como los empleadores y el Gobierno Federal contribuyan a cuentas personales de los trabajadores. Al final de su vida laboral, el trabajador podrá acceder a una pensión. En caso de fallecimiento del trabajador, sus beneficiarios (ascendientes, cónyuge, pareja en concubinato e hijos menores de 16 años) podrán recibir una pensión, siempre que cumplan con los requisitos y condiciones establecidos por la ley.

En 1992 se implementó el Sistema de Ahorro para el Retiro (SAR) como parte de una reforma a las leyes del Seguro Social y del INFONAVIT. Este sistema complementa las pensiones del régimen de Beneficio Definido, destinando contribuciones equivalentes al 2% del Salario Base de Cotización (IMSS) o del Sueldo Básico (ISSSTE) a una cuenta individual de ahorro a nombre del trabajador (SAR 92), que es administrada por el Banco de México.

En 1994 se creó la Comisión Nacional del Sistema de Ahorro para el Retiro (CONSAR) con el fin de regular este sistema. Finalmente, el 1 de julio de 1997, entró en vigor una reforma a la Ley del Seguro Social que dio lugar a las Administradoras de Fondos para el Retiro (AFORE), completando así la estructura del SAR.

Capítulo 3

Metodología del

Modelo

El diseño de este trabajo es de carácter exploratorio,

para crear conciencia de la importancia de ahorrar a largo plazo

, para beneficiar a las personas desde sus edades tempranas generando el ahorro para el pago de sus estudios universitarios futuros

. En la actualidad no existe ningún mecanismo de ahorro parecido al que se

propone

Con el fin de describir las fuentes de financiación utilizadas

por el presente trabajo

se tiene

como objetivo

ahorrar un salario mínimo por mes

suponiendo que

las escuelas

realizan

dicha aportación extra y que s

e maneje como deducible de impuestos.

El proyecto inicia

desde el nacimiento

de la persona

hasta

la edad de 18 años

como mínimo

, inicialmente se recolectan

aportaci

ones

, esto con el fin de

obtener

un ahorro y así

poder pagar los

estudios

futuros

a través del

Fondo de Capital Privado

, llamado “Crece”

preveen

3 eventos de liquidez

Cuando

alcance la mayoría de edad, al menos a los 18 años,

podrá disponer

de los recursos para financiar

los

estudios universitarios.

Al iniciar el Posgrado

Para la compra de vivienda

Ventajas

Fomenta el ahorro

Diversificación

Las aportaciones serán utilizadas para el pago de universidades

Aumenta el patrimonio y la segurid

No existe nada igual en el mercado

Des

entajas:

No puedes decidir

cómo

administra

r el

recurso.

No tiene

liquidez.

Alto riesgo de que cambien las leyes.

enfoque estratégico implica utilizar el

S&P/BMV IPC

como punto de referencia principal para evaluar el rendimiento del fondo. Este enfoque nos permite

mantener

al tanto de los movimientos del mercado y ajustar

el portafolio

en consecuencia para mitigar riesgos innecesarios y maximizar los rendimientos.

Para garantizar la eficiencia y la segurida

d de nuestras operaciones, se ha

establecido un proceso de rebalanceo diario, lo que significa que

se realiza un monitoreo

ajuste diario a

la composición del fondo para

estar

alineados

con

los

objetivos de inversión y evitar riesgos innecesarios.

Además,

se ha

implementado un programa de inyección de capital mensual, diseñado para fortalecer y hacer crecer el fondo de manera constante. Esta estrategia permite aprovechar oportunidades de inversión a largo plazo y fomentar un aumento sostenible en el ahorro de

los

inversionistas.

Para garantizar la transparencia y la integridad en

la gestión

de los fondos,

se optó

por canalizar los recursos a través de un fideicomiso. Esta estructura proporciona una capa adicional de seguridad y supervisión, asegurando que los fondos se utilicen de manera adecuada y en línea con los intereses de

los

inversionistas.

Además,

estableci

una asociación estratégica con el Gobierno de México para aprovechar sinergias y maximizar el impacto de

las

inversiones. Los recursos aportados al fideicomiso no solo beneficiarán a nuestros inversionistas, sino que también se utilizarán para financiar proyectos de infraestructura clave en colaboración con el gobierno. Esta asociación permite contribuir al desarrollo económico y social del país, mientras

mayores

sean los

rendimientos atractivos para

los

inversionistas.

Metodología para la Evaluación de

los Portafolios de Inversión

Rendimiento

Según Gitman (2012) El rendimiento es la plusvalía

o minusvalía que experimenta

cualquier instrumento de inversión en un periodo especifico

donde en el presente trabajo se calculará de la manera siguiente:

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donde,

R: Rendimiento diario

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Precio

del activo

Se calcula

n distin

tos rendimientos diarios para

conformar

una serie de tiempo det

erminada

de la misma emisora

y se calcula el

rendimiento promedio:

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: Rendimiento

promedio

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Rendimiento diario del instrumento en el día t

Número de

observaciones

En el presente trabajo se

necesit

calcular el rendimiento anual esperado con la fórmula

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: Rendimiento promedio diario t.

Se realiza

una multiplicación de 251

, de

a la cantidad de días hábiles que cotizan el mercado de valore

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: Rendimiento

anual

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Rendimiento

anual esperado

Distribución

de fondos que se

invierte

ratio o índice de Sharpe

El ratio

o índice

de Sharpe,

fue creado

por William Sharpe de la Universidad de Stanford, se emplea para evaluar la rentabilidad ajustada al riesgo de un fondo de inversión. Este indicador permite comparar la calidad de un fondo con otros activos de su misma categoría. Tradicionalmente, se evalúa la calidad de un fondo según su rentabilidad, pero es igualmente importante considerar el nivel de riesgo asociado.

El ratio de Sharpe es una herramienta que permite evaluar la relación más favorable entre la rentabilidad y el riesgo de un fondo de inversión. En otras palabras, no solo se considera la rentabilidad del activo, sino también el nivel de riesgo que implica invertir en él.

Para calcular el ratio de Sharpe, solo se requieren tres datos: el rendimiento del fondo, la tasa libre de riesgo y la volatilidad o desviación estándar del fondo. La fórmula para calcularlo es la siguiente:

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Rendimiento

del activo i-ésimo.

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olatilidad del activo i-ésimo.

Tasa Libre de Riesgo “CETES

”

Los Certificados de la Tesorería de la Federación (CETES) son instrumentos de deuda emitidos por el Gobierno Federal de México, y se consideran uno de los activos financieros más antiguos en este

ámbito. Fueron introducidos por primera vez en 1978 y, desde entonces, han sido esenciales en el mercado de dinero del país.

Estos certificados pertenecen a la categoría de bonos cupón cero, los cuales se venden con descuento

en relación con

su valor nominal y no devengan intereses periódicos. En su lugar, el rendimiento se recibe en su totalidad al momento de su vencimiento.

Los plazos de emisión de los CETES varían, habiéndose emitido con plazos mínimos de 7 días y plazos

máximos de 728 días

. En la actualidad,

generalmente

los CETES suelen emitirse y colocarse con plazos de 28 y 91 días

, la subasta de dich

os títulos se realiza los días m

artes y se liquidan lo

s días j

ueves.

Riesgo

En el contexto de la

epidemia

, el concepto de "riesgo" se refiere a la probabilidad de que ocurra un evento no deseado junto con sus posibles consecuencias negativas. En otras palabras, el riesgo implica una incertidumbre asociada a la posibilidad de que algo ocurra y pueda resultar en pérdidas.

El concepto de riesgo es fundamental en economía y finanzas, y su comprensión es crucial para entender cómo influye en diversas decisiones económicas y en el desarrollo de una economía. Aquí se desarrollan diferentes aspectos del riesgo:

Riesgo financiero:

Hace referencia a la probabilidad de sufrir pérdidas económicas debido a variaciones en los mercados financieros, tasas de interés, tipos de cambio, entre otros factores.

Riesgo económico: Relacionado con la incertidumbre en el entorno económico que podría afectar los ingresos, costos o condiciones de mercado de una empresa o un país.

Riesgo empresarial: Incluye factores como la competencia, cambios tecnológicos, regulaciones gubernamentales, entre otros, que pueden afectar la rentabilidad y el crecimiento de las empresas.

Riesgo sistémico: Refiere a riesgos que afectan a todo el sistema financiero o económico, como crisis financieras, colapsos bancarios o recesiones globales.

Medición del riesgo:

Medidas estadísticas: Se utilizan diversas herramientas como la desviación estándar, el VaR (Value at Risk) y el CVaR (Conditional Value at Risk) para cuantificar la probabilidad y la magnitud de posibles pérdidas.

Análisis cualitativo: Considera factores subjetivos y no cuantificables, como la percepción del riesgo político o el impacto de la reputación de una empresa.

Gestión del riesgo:

Diversificación: Reducir el riesgo al invertir en una variedad de activos o sectores.

Hedging (cobertura): Utilizar instrumentos financieros para protegerse contra riesgos específicos, como contratos de futuros

opciones.

Seguro: Transferir el riesgo a una entidad aseguradora a cambio de una prima.

Impacto del riesgo en la economía:

Incentivos y decisiones: El riesgo puede afectar las decisiones de inversión, consumo y ahorro de individuos y empresas.

Crecimiento económico: La aversión al riesgo puede limitar la inversión y la innovación, afectando el potencial de crecimiento económico a largo plazo.

Estabilidad financiera: Los eventos de riesgo sistémico pueden desencadenar crisis financieras que afectan la estabilidad y el bienestar económico general.

Riesgo y desarrollo económico:

Un entorno con riesgos bien gestionados puede fomentar la inversión y la innovación, impulsando el desarrollo económico.

Sin embargo, un exceso de riesgo o una gestión inadecuada pueden llevar a crisis que obstaculizan el crecimiento y el desarrollo.

Desviación Estándar

La “desviación estándar” se define como la raíz cuadrada de la varianza

de una variable

se aplica

en el presente trabaj

o para calcular el riesgo de los rendim

ientos diarios con la

fórmula

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donde,

: Riesgo diario

R: Rendimiento diario

día t

: Rendimiento promedio diario

N: Número de observaciones

Se calcula el riesgo anual

con la fórmula

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donde,

A: Riesgo Anual

: Riesgo diario del portafolio

Riesgo Sistemático

El riesgo sistemático, también conocido como riesgo no diversificable o riesgo de mercado, se refiere a la parte de la variabilidad de los rendimientos de un activo financiero que no puede ser eliminada mediante

la diversificación del portafolio

. Este tipo de riesgo afecta a todos los activos dentro de un mercado o una economía en general, en lugar de estar vinculado específicamente a características individuales de un activo

particular.

Puntos clave del riesgo sistemático:

Influencia Externa: Este riesgo proviene de factores macroeconómicos y eventos que afectan a todos los activos financieros dentro de una clase de activo o mercado. Por ejemplo, cambios en las tasas de interés, fluctuaciones económicas generales, políticas gubernamentales, crisis financieras, eventos geopolíticos, etc.

No Diversificable: A diferencia del riesgo específico (o riesgo no sistemático), que puede ser mitigado mediante la diversificación de la cartera, el riesgo sistemático no se puede eliminar de manera individual. Esto se debe a que afecta a todos los activos en el mismo mercado o clase de activos al mismo tiempo.

Beta como medida: La medida más común del riesgo sistemático de un activo es su beta. La beta representa la sensibil

idad de un activo o un portafolio

a los movimientos en el mercado en gene

ral. Un activo con una beta alta

tendrá movimientos más amplios en respuesta a cambios en el mercado, mientras

que un activo con una beta baja

tendrá menos sensibilidad a esos cambios.

Importancia en la gestión de riesgos: Comprender y gestionar el riesgo sistemático es fundamental para los i

nversores y gestores de portafolios

. Aunque no se puede eliminar, se puede gestionar a través de estrategias de asignación de activos, coberturas financieras y otras técnicas que buscan mitigar su impacto en

los portafolios

de inversión.

Riesgo No Sistemático

El riesgo no sistemático, también llamado riesgo específico, diversificable o único, hace referencia a la parte de la variabilidad en el rendimiento de un activo financiero que es particular de ese activo y que puede ser reducida mediante una adecuada diversificación de la cartera. Este tipo de riesgo está relacionado con factores y eventos que afectan a una empresa o activo de manera individual, y no al mercado en su totalidad.

Puntos clave del riesgo no sistemático:

Origen del riesgo: Este riesgo surge de factores internos a una empresa o activo financiero específico. Pueden incluir problemas de gestión, cambios en la estructura de costos, innovaciones tecnológicas específicas de la industria, fluctuaciones en la demanda de productos, cambios en la estructura de capital de la empresa, entre otros.

Diversificación: A diferencia del riesgo sistemático, el riesgo no sistemático puede ser mitigado o eliminado a través de

la diversificación del portafolio

. Al invertir en una variedad de activos o empresas que no están correlacionados entre sí, los inversores pueden reducir el impacto de eventos específicos que afectan a una sola empresa.

Impacto en la inversión: Los inversores pueden gestionar el riesgo no sistemático eligiendo una combinación adecuada de activos para su

portafolio

. Esto implica seleccionar activos que tengan diferentes características y no estén expuestos a los mismos riesgos específicos. Por ejemplo, invertir en empresas de diferentes sectores industriales o en diferentes regiones geográficas.

Medición: A diferencia del riesgo sistemático, que se mide generalmente a través de la beta, el riesgo no sistemático es más difícil de cuantificar de manera precisa porque está asociado a eventos específicos y variables que afectan a cada empresa de manera diferente.

Importancia de la diversificación: La diversificación adecuada es fundamental para mitigar el riesgo no sistemático. Al distribuir los fondos entre diferentes clases de activos y empresas, los inversores pueden reducir la volatilidad de su cartera y

protegerse mejor contra pérdidas significativas debido a eventos específicos que afectan a una sola inversión.

Beta

La beta de un portafolio es una medida de sensibilidad

de variación de la rentabilidad de una emisora, realizada en cada activo

que facilita el cálculo del riesgo sistémico y no sistémico de un portafolio, la

beta si es

igual a

1 es neutral se mueve de la misma manera que el índice, si es

mayor que

considera un activo riesgoso

y si

es menor que

1 uno de bajo riesgo

Cuanto mayor sea la desviación estándar en los rendimientos históricos de las

acciones,

mayor será su volatilidad

su riesgo.

La beta del portafolio

se obtiene

de la manera

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: Peso

en los portafolio

Mercado de Capitales

El mercado de capitales es un componente clave del sistema financiero que facilita la compra y venta de instrumentos financieros a largo plazo, como acciones, bonos y otros valores, con el objetivo de proporcionar liquidez al mercado.

Su función principal es ofrecer a las empresas y entidades gubernamentales una vía para obtener financiamiento a largo plazo para sus proyectos de inversión, mientras que los inversionistas tienen la oportunidad de diversificar sus carteras y generar rendimientos mediante la compra y venta de estos activos. E

mercado de capitales es un espacio donde se negocian instrumentos financieros a largo plazo.

Línea de Mercado de Capitales

La línea de mercado de capitales es un gráfico que ilustra cómo varía el rendimiento esperado en relación con el riesgo de varios activos financieros dentro del mercado de capitales. E

ste concepto es esencial en la T

eoría de

Portafolios de I

nversión

y se fundamenta en el Modelo de Valoración de Activos de Capital (CAPM, por sus siglas en inglés). En esta línea, cada punto representa un activo individual o un

portafolio

de activos, y la pendiente de la línea indica el rendimiento adicional esperado por cada unidad de riesgo asumido.

a línea de mercado de capitales ayuda a los inversores a evaluar la relación entre riesgo y rendimiento de los activos financieros disponibles en el mercado

como se observa en la Gráfica 3.1

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Gráfica 3.1 Línea de mercado de capitales.

Nota

Julie Bang

Investopedia 2022

Tipos de inversiones

Existen diversos tipos de rentabilidades, las cuales están determinadas por el rendimiento o beneficio que genera una inversión.

Entre

stas, se encuentran las rentabilidades fija

y variable

. La renta fija implica un pago constante acordado en un tiempo determinado, mientras que la renta variable está sujeta a fluctuaciones y puede aumentar o disminuir, dependiendo de los movimientos del mercado. En resumen, la rentabilidad fija ofrece pagos preestablecidos, mientras que la rentabilidad variable está sujeta a cambios en el mercado.

Portafolio

Equiponderad

El portafolio

equiponderado

es el portafolio donde la distribución de las emisoras a invertir e

s la misma

proporción

en todas,

mo se muestra en

la fórmula

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Portafolio equiponderado

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3.9

donde,

Número de emisora

Portafolio de

Mínima Varianza

Fue desarrollado por Markowitz (1952)

, para obtener una rentabilidad con el menor riesgo posible en el mercado

se puede calcular con la fórmula

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donde,

Min

: Mí

nima varianza del portafolio

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: Covarianza entre los rendimientos de los valores

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: R

entabilidad esperad

a, con proporciones que minimizan el riesgo

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: R

dimiento esperado

V: P

arámetro

Portafolio de Máximo Sharpe

A diferencia del portafolio de Markowitz, en el portafolio de máximo Sharpe se desea maximizar el índice de Sharpe del portafolio

con la fórmula

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.11

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donde,

Max

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Máximo Índice de Sharpe

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Riesgo del portafolio

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: R

endimiento

esperad

o del portafolio.

De lo anterior se desprende la metodología propuesta para e

l fondo, como se muestra en la t

abla 3.1.

Tabla

Simulación del Fondo

Rendimientos Portafolios

Número de Años

Equiponderado

Mínima Varianza

Sharp

Equiponderado

Mínima Varianza

Sharp

Equiponderado

Mínima Varianza

Sharp

PE(R1*R2)

Min σ² (R1*R2)

IS (R1*R2)

X(PE)

Y(Min σ²)

Z(IS)

PE(R1*R2)

Min σ² (R1*R2)

IS (R1*R2)

X1(PE)

Y1(Minσ²)

Z1(IS)

X16

Y16

Z16

PE(R1*R2)

Min σ² (R1*R2)

IS (R1*R2)

X1(PE)

Y1(Minσ²)

Z1(IS)

Nota

aboración generada por el autor.

En las ecuaciones 3.8, 3.1.0 y 3.4 se observa el rendimiento por año de cada uno de los diferentes portafolios de inversión, la tasa libre de riesgo es

benchmarck

para ver

que tan eficientes resultaron los portafolios de inversión.

Para poder conocer la eficiencia de los portafolios analizados en esta investigación se tuvo que construir una tabla de simulación de r

endimiento por año contra la tasa libre de riesgo

, donde se demuestra la efi

iencia de los tres portafolios que generaron

más

rendimiento que la

tasa libre de riesgo.

Lo anterior se puede resumir en la tabla de simulación, la cual, para cada periodo de tiempo muestra el número de años (X, Y, Z) justo después se multiplica

X(PE)

por el rendimiento para así conocer la utilidad o pérdida del ejercicio de forma

más general, se muestra en la t

abla 4.3

Resultados Obtenidos

El proceso de desarrollo

del fondo Crece se basa en la Teoría de los P

ortafoli

os de I

nversión de Markowitz. Para llevar a cabo este análisis, se emplean datos del

S&P/ BMV IPC

desde el 27 de septiembre de 2005 hasta el 27 de septiembre de 2022, momento en el que se completa la construcción del portafolio y se realiza la inversión. Como punto de referencia para evaluar su desempeño, se utiliza la tasa libre de riesgo

(CETES)

Según la teoría de Markowitz, creada en 1952, la diversificación es clave para obtener una óptima relación entre riesgo y rendimiento. Esto implica crear combinaciones de activos que minimicen el riesgo asociado con la inversión en un solo activo. Aunque la diversificación puede reducir el riesgo, no es posible eliminarlo por completo debido a los factores macroeconómicos que afectan a todas las empresas.

En este estudio, se utiliza el ratio de Sharpe o índice de Sharpe, que compara el rendimiento adicional de un fondo de inversión con respecto a un activo libre de riesgo, teniendo en cuenta su volatilidad medida por su desviación estándar.

S&P/BMV IPC

En la

abla

4.1

se muestra el listado

de las empresas que conforman actualmente el

S&P/

BMV

IPC

Tabla 4.1 Empresas que componen S&P/

BMV IPC

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Nota

S&P/BMV

IPC.

En la t

abla 4.1 se puede observar las empresas que

se utilizan

y que cotizan

en el S&P/BMV

IPC

cual

tiene como objetivo

buscar y medir el desempeño

de las emisoras más liquida

s y más grandes del

país

Después se

descargó

la información diaria

de las emisoras que componen el

S&P/

BMV IPC (

atos descargados de Investing, 2023), iniciando

27 de septiembre del 2005 hasta el 27 de Septiembre de 2022

;

mediante la fórmula 3.1 se

calculó

el rendimiento diario

Se toman en cuenta

las emisoras del 2005 del S&P/

BMV IPC

y como método de descarte

se utiliza las

que correspondan del 2005 al 2023, las que no están de forma constante se descartan, (Datos descargados de Investing, 2005 - 2023)

Una vez obtenido el rendimiento diario

se calcula

iesgo

mediante la fórmula 3.1.2

y se calcula la beta mediante la fórmula 3.1.4

Para el análisis de las emisoras que pertenecen al portafolio de inversió

se calcula

Índice

Sharpe con la fórmula 3.5

, La tasa libre de riesgo utilizada

fue la correspondiente a CETES

364 días, tomada de Banco de

México

(2005 – 2023)

Con el cálculo del Índice de Sharpe para cada una de las emisoras

, los valores arrojados de forma positiva se

consideran para el portafolio y las negativas se rechazan

pues solo se consideran los activos que ofrecen rendimientos superiores a ll tasa de referencia CETES 364

ya con

las emisoras que conforman el portafolio se proced

e a elaborar la matriz de correlación, así como las varianzas y

el rendimiento anual del portafolio

utilizando las ecuaciones 3.

6.3

Elaboración

de los Portafolios

Equiponderado, Mínima V

arianza y Sharpe

2005 - 2007

En la tabla 4.2

se aprecia el comparativo entre los portafolios

analizados

para

rendimiento del portafolio se

utilizó

la aplicación de la ecuación 3.1

, la beta se calculó

mediante la ecuación 3.1.4

Para determinar los diferentes portafolios del 1 al 6 s

e calculó el rendimiento esperado

con portafolios de

ínima

arianza de Markowitz, lo anterior se puede apreciar en la

tabla

4.2

Tabla 4.

Comparativo entre lo

s tres tipos de portafolio

S&P/BMV IPC

2005 - 2007

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing.

a gráfica

4.2

se puede apreciar en el punto donde se crea una curva ahí empieza el portafolio de mínimo riesgo.

La eficiencia del portafolio la podemos observar cuando se junta la frontera eficiente

y en

la línea verde (Capital Market Line)

Gráfica

Comparativo entre los tres tipos de portafolio

S&P/BMV IPC

2005 -2007

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing.

En la gráfica 4.2 se muestra

tres

portafolios que son

portafolio equiponderado,

Mínima V

arianza

y Sharp, incluyendo el

S&P/

BMV IPC.

S&P/

BMV

IPC

es el que muestra un rendimiento intermedio

del 32%

aunque con un riesgo medio, el portafolio con menor riesgo es

el portafolio de Markowitz de Mínima V

arianz

con un rendimiento esperado del 25%

, en lo que representa el portafolio de Sharpe

es el mejor rendimiento esperado

con 52%

Comparación de los Portafolios

Equiponderado

, Mínima V

arianza y Sharpe

En la tabla 4.

realizó

ejercicio donde la inversión inicial es de $100,000 pesos y

análisis comprobó

que,

comparación entre los tres portafolios

: E

quiponderado,

ínima

arianza y

Máximo

Sharp en los periodos analizados

los tres

tipos de

portafolios

generan rendimientos superiores a CETES 365

Demostrando que a largo

plazo

se tiene

mejor

rendimiento

en renta

varia

ble

El portafolio

de Sharpe

que maximiza la

rentabilidad

tiene

una mayor variación

respecto al de Mínima Varianza de

Markowitz, el instrumento con

menor rendimiento fue la tasa libre de riesg

CETES 365

4.4

Simulación de Ganancia entre los tres tipos de portafolio

y TLR 2007 – 2022

Tabla 4.

Comparativo entre los tres tipos de portafolio

TLR

- 20

Rendimientos Portafolios

Año

Equiponderado

Mínima Varianza

Sharp

TLR

Equiponderado

Mínima Varianza

Sharp

TLR

Equiponderado

Mínima Varianza

Sharp

TLR

2007$ 100,000.00$ 100,000.00$ 100,000.00$ 100,000.00-11.14%-3.61% -20.34%7.68%-$ 11,143.51-$ 3,606.31-$ 20,342.16$ 7,680.00

2008$ 88,856.49$ 96,393.69$ 79,657.84$ 107,680.0011.38%8.34%13.80%8.66%$ 11,380.78$ 8,043.50$ 12,258.95$ 8,660.00

2009$ 100,237.27$ 104,437.19$ 91,916.79$ 116,340.0023.32%20.64%-7.64%5.35%$ 23,323.44$ 21,559.63-$ 7,657.37$ 5,350.00

2010$ 123,560.71$ 125,996.82$ 84,259.42$ 121,690.0016.82%15.43%12.12%4.74%$ 16,815.34$ 19,442.68$ 14,980.61$ 4,740.00

2011$ 140,376.05$ 145,439.50$ 99,240.03$ 126,430.0026.02%48.43%49.66%5.35%$ 26,018.33$ 70,442.94$ 69,710.56$ 5,350.00

2012$ 166,394.38$ 215,882.44$ 168,950.59$ 131,780.0013.78%12.57%13.74%4.59%$ 13,777.63$ 27,127.43$ 22,870.47$ 4,590.00

2013$ 180,172.01$ 243,009.87$ 191,821.05$ 136,370.0010.24%7.30%16.57%3.70%$ 10,236.95$ 17,733.48$ 29,849.97$ 3,700.00

2014$ 190,408.96$ 260,743.35$ 221,671.02$ 140,070.003.96%10.89%21.44%3.09%$ 3,955.42$ 28,394.36$ 40,815.94$ 3,090.00

2015$ 194,364.38$ 289,137.71$ 262,486.96$ 143,160.0015.08%13.93%12.49%3.71%$ 15,076.57$ 40,277.34$ 24,269.25$ 3,710.00

2016$ 209,440.96$ 329,415.05$ 286,756.21$ 146,870.00-2.99%1.44%5.88%4.87%-$ 2,990.72$ 4,754.37$ 12,319.93$ 4,870.00

2017$ 206,450.23$ 334,169.42$ 299,076.14$ 151,740.00-1.61%2.65%-3.17%7.18%-$ 1,614.44$ 8,844.16-$ 6,551.34$ 7,180.00

2018$ 204,835.79$ 343,013.58$ 292,524.80$ 158,920.00-9.01%-17.48%8.38%8.26%-$ 9,008.45-$ 59,964.35$ 17,174.49$ 8,260.00

2019$ 195,827.34$ 283,049.22$ 309,699.29$ 167,180.00-15.19%-20.65%-6.43%7.39%-$ 15,185.38-$ 58,441.19-$ 12,595.56$ 7,390.00

2020$ 180,641.96$ 224,608.04$ 297,103.73$ 174,570.0017.99%16.85%18.69%4.36%$ 17,992.03$ 37,851.11$ 33,753.21$ 4,360.00

2021$ 198,634.00$ 262,459.14$ 330,856.94$ 178,930.00-18.66%-28.47%-21.46%5.50%-$ 18,663.71-$ 74,729.52-$ 42,636.44$ 5,500.00

2022$ 179,970.29$ 187,729.62$ 288,220.51$ 184,430.0020.12%12.79%17.08%10.34%$ 20,117.59$ 24,012.76$ 30,735.90$ 10,340.00

Total$ 200,087.88$ 211,742.38$ 318,956.40$ 194,770.00

Depósito inicial

100,000.00

Nota

Elaboración

generada por el autor

basada en datos extraídos por investing

Conclusiones

Este proyecto propone una metodología innovadora y efectiva para abordar el desafío del ahorro en México, brindando a los usuarios una base sólida para financiar sus futuros estudios universitarios o de posgrado, según

sus preferencias y necesidades individuales.

Para lograr este objetivo,

emplea un enfoque

meticuloso en la selección del portafolio de acciones, basado en la combinación de diversos criterios de riesgo y rentabilidad. Esta metodología permite identificar y seleccionar las mejores oportunidades de inversión, optimizando así el rendimiento de la cartera mientras se controla el riesgo.

Los

resultados muestran que esta metodología no solo es efectiva en el contexto mexicano, sino que también puede ser aplicada con éxito en otros mercados bursátiles. Siguiendo los principios de la teoría de Markowitz,

se evalúa

la eficiencia

del portafolio, definiendo esta eficiencia como el conjunto de acciones que ofrece el mayor rendimiento esperado para cualquier nivel de riesgo dado. En nuestro estudio,

se aplica

estos principios al mercado de valores mexicano, demostrando su aplicabilidad y utilidad en este contexto específico.

Además, este proyecto resalta la importancia del esfuerzo y la planificación a largo plazo en el proceso de ahorro y planificación financiera.

Se muestra

que con dedicación y una estrategia bien definida, es posible alcanzar metas financieras significativas, como asegurar el financiamiento de la educación universitaria para las generaciones futuras. Al mismo tiempo, este enfoque contribuye al desarrollo económico y social del país al fomentar una cultura de ahorro e inversión responsable.

estudio piloto, basado en una muestra de 16 años, confirma la eficacia de

las

estrategias de inversión. Los portafolios

equiponderados, de Mínima V

arianza y de Sharpe, demostraron consistentemente rendimientos superiores a la tasa libre de riesgo, validando así

metodología y enfoque de inversión.

Limitantes en los portafolios

La principal limitante se apoya en supuestos simplificados acerca de los mercados financieros, como la eficiencia de los mercados, la distribución normal de los rendimientos y la estabilidad de las correlaciones entre activos. Sin embargo, en la práctica, estos supuestos pueden no ser válidos en todos los escenarios, lo que limita la capacidad de los modelos de cartera para prever con precisión el comportamiento del mercado y los resultados de inversión.

Es importante tener en cuenta es

tas limitaciones al aplicar la T

eoría de

ortafolio

de Inversión

en entornos reales, ya que

las condiciones del mercado pueden variar y los supuestos simplificados pueden no ser suficientes para capturar la complejidad del mundo financiero.

Los análisis de portafolio dependen en gran medida de datos históricos para calcular rendimientos esperados, volatilidades y correlaciones entre activos. Sin embargo, los datos pasados no siempre predicen el futuro de manera precisa, especialmente en entornos volátiles o en periodos

atípicos

ya que

o considera adecuadamente eventos extremos o "cisnes negros", que son eventos raros pero impactantes que pueden afectar significativamente el rendimiento de los activos. Estos eventos pueden tener un impacto desproporcionado en los resultados del

portafolio

Las correlaciones entre activos pueden cambiar con el tiempo, especialmente durante períodos de crisis o cambios en las condiciones macroeconómicas. Esto puede afectar la eficacia de las estrategias de diversificación y la estabilidad d

e los

portafolio

Los rendimientos de los activos financieros pueden no ser lineales, lo que significa que las relaciones entre rendimiento y riesgo pueden ser más complejas de lo que sugieren los modelos de

portafolio

estándar.

En este proyecto se demuestra que con un poco de esfuerzo se puede lograr la meta que se obtenga. Un beneficio de ahorro desde el nacimiento para el pago de los estudios universitarios futuros, al mismo tiempo se pueda convertir en un país próspero.

En resumen, est

a tesis

representa un paso significativo hacia el empoderamiento financiero de los individuos y el desarrollo económico del país, al ofrecer una solución innovadora y efectiva para el desafío del ahorro y la plan

ificación financiera en México.

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http://bibliotecadigital.uca.edu.ar/repositorio/revistas/importancia-ahorro-teoria-historia.pdf

Sharpe, W. F (2024)

https://www.estrategiasdeinversion.com/herramientas/diccionario/mercados/ratio-de-sharpe-t-402

Sharpe, W. F. (1998). The sharpe ratio.

Streetwise–the Best of the Journal of Portfolio Management

, 169-185.

Trullols, J., & People, F. (2013). La importancia del ratio de Sharpe a la hora de seleccionar fondos.

Boletín Mensual

Villarreal, C. (2013). Oferta pública inicial y underpricing en el mercado de capitales mexicano.

Journal of Economics Finance and Administrative Science

(35), 97-107.

Anexos

Anexo 1 Elaboración de los Portafolios 2006 - 2008

Tabla

Comparativo entre los tres tipos de portafolio S&P/

BMV IPC

2006 -2008

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.2759148713%0.1618102070.50072162620.1639084826%1.0599934220.44183200330.1580460239%1.9161379510.42441744840.1752031852%2.4653322720.42251565350.2134491265%2.6284045040.48145649460.3411099878%2.0231778980.583697362

MINIMA VAR0.15736960.3582455031.7261625150.428764531

SHARPE0.208660590.6353763252.6299950590.470713842

S&P_BMV IPC0.223459990.081726079-0.0218111571

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

Comparativo entre los tres tipos de portafolio

S&P/BMV IPC

2006 - 2008

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

se muestra tres portafolios que son portafolio equiponderado, mínima varianza y Sharp, incluyendo el

S&P/BMV IPC.

S&P/BMV

es el que muestra el rendimiento más bajo del 8% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Markowitz de

Mínima V

arianza con un rendimiento esperado del 35%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 63%.

Anexo 2 Elaboración de los Portafolios 2007

–

2009

Tabla

Comparativo entre los tres tipos de portafolio S&P/

BMV IPC

2007 - 2009

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.384919798%0.0721390970.81218868820.2822458116%0.3604192770.74898399730.2925809523%0.6004693060.74196252840.3273856430%0.7625415950.73391316150.3826414338%0.8457108180.72281558760.4695626845%0.8466666370.688456715

MINIMA VAR0.282051620.163999390.3917700980.748151153

SHARPE0.426992180.420544460.8596046360.729517084

S&P_BMV IPC0.32631068-0.01882847-0.2216552471

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2007 - 2009

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

se muestra tres portafolios que son portafolio equiponderado,

ínima

arianza y Sharp, incluyendo el

S&P/

BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento más bajo del -0

1% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Markowitz de mínima varianza con un rendimiento esperado del 16%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 42%.

Anexo 3 Elaboración de los Portafolios 2008

–

2010

Tabla

Comparativo entre los tres tipos de portafolio S&P/

BMV IPC

2008 - 2010

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.2926579088%0.1094895010.5663284720.17300976117%0.7083987770.34484793830.17792197326%1.1975852530.39099659640.28162768135%1.0779965520.72605306550.43001154144%0.916511881.11694763460.60188664753%0.8051802391.455984813

MINIMA VAR0.1601780740.2106753781.0193366340.321924139

SHARPE0.1867110390.2721607361.2037892180.429164544

S&P_BMV IPC0.2975398930.1291883650.2748820151

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

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Xc4XAAAAAElFTkSuQmCC

Gráfica

Comparativo entre los tres tipos de portafolio

S&P/BMV IPC

2008 - 2010

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/

BMV IPC.

S&P/BMV

es el que muestra el rendimiento más bajo del 12% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Markowitz de mínima varianza con un rendimiento esperado del 21%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 27%.

Anexo 4 Elaboración de los Portafolios 2009

–

2011

Tabla

Comparativo entre los tres tipos de portafolio

S&P/BMV IPC

2009 - 2011

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.1635452723%1.0710840330.5725812220.1647191925%1.2144732430.57035995630.1721013728%1.3069205670.62137850240.228933830%1.0911393430.78365234850.3619222733%0.7589334431.02506715660.6363211735%0.4707536721.173701972

MINIMA VAR0.163540690.230103861.0798772150.571952257

SHARPE0.174485510.282593871.3129678280.635403234

S&P_BMV IPC0.168813120.080018310.1570867631

Fuente: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2009 - 2011

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

se muestra tres portafolios que son portafolio equiponderado,

Mínima V

arianza y Sharp, incluyendo el

S&P/BMV IPC.

S&P/BMV

IPC

es el que muestra el rendimiento más bajo del 0.8% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Markowitz de

Mínima V

arianza con un rendimiento esperado del 23%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 28%

Anexo 5 Elaboración de los Portafolios 2010 - 2012

Tabla

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2010 - 2012

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.224615176%0.0549317780.70901808620.1400112213%0.6316314480.67298146330.111788121%1.4718235130.47764843740.1097183229%2.1931545860.41357048650.1435893636%2.205776880.52682614260.304639244%1.2894695221.234825243

MINIMA VAR0.107940030.254606421.9335405590.431279653

SHARPE0.119266350.331491342.3945677290.422073625

S&P_BMV IPC0.161744990.103780260.3578488531

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

Comparativo entre los tres tipos de portafolio

S&P/

BMV IP

C 2010 -2012

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

A.5

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/

BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento más bajo del 10% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Markowitz de mínima varianza con un rendimiento esperado del 25%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 33%

Anexo 6 Elaboración de los Portafolios 2011

–

2013

Tabla

A.6

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2011 - 2013

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.253951716%0.0924050320.91189599920.1118280617%1.21039130.27056691230.0952888428%2.5946900160.16120827640.1116297240%3.2171924260.14986190750.1591348651%2.9599019370.01690603560.3062251762%1.903543242-0.04752239

MINIMA VAR0.093679380.26472182.4308637230.210557099

SHARPE0.121400330.431191643.2470392320.133115626

S&P_BMV IPC0.160756470.092768140.3469107211

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

A.6

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2011 - 2013

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

A.6

se muestra tres portafolios que

son portafolio equiponderado, M

ínima

arianza y Sharp, incluyendo el

S&P/

BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento más bajo del 0.9% aunque con un riesgo alto, el portafolio con menor riesgo es

el portafolio de Markowitz de Mínima V

arianza con un rendimiento esperado del 26%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 43%.

Anexo 7 Elaboración de los Portafolios 2012

–

2014

Tabla

A.7

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2012 - 2014

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.283152864%0.0415556211.05963858720.1349910117%1.0341135170.73437611530.1194009630%2.2397275840.61168942940.1317717243%2.9995426710.54166131250.1760385155%2.9714157240.50176593260.2815764868%2.3116766740.429852927

MINIMA VAR0.119338880.307071422.3141780740.606489156

SHARPE0.14639570.478259983.0558273820.518587609

S&P_BMV IPC0.13503550.048954110.1336990291

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

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Gráfica

A.7

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2012 - 2014

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

A.7

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/

BMV IPC.

S&P/BMV

IPC

es el que muestra el rendimiento más bajo del 0.4% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Ma

rkowitz de Mínima V

arianza con un rendimiento esperado del 30%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 47%.

Anexo 8 Elaboración de los Portafolios 2013 - 2015

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.224700856%0.1181229520.79249898220.1190355317%1.080300660.67603795230.1218018827%1.8936166670.57964016140.1452863937%2.2899457450.50372845550.1882837147%2.3090144680.49099149560.2701162257%1.9872971840.71329252

MINIMA VAR0.117412040.204146821.4227401330.639703088

SHARPE0.164788150.422517932.3388692950.48160193

S&P_BMV IPC0.132182810.01197967-0.1900422981

Tabla

A.8

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2013 - 2015

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

A.8

Comparativo entre los tres tipos de portafolio S&P/

BMV IPC 2013 - 2015

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

A.8

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento más bajo del 0.1% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Markowitz de mínima varianza con un rendimiento esperado del 11%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 16%.

Anexo 9

Elaboración de los Portafolios 2014 – 2016

Tabla

A.9

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2014 - 2016

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.230580648%0.1565849930.79794959420.1333929613%0.6011645920.7301620430.1155843217%1.0752043580.62060635340.1171208622%1.4375114370.56942798550.1426920326%1.4888570850.50734852660.2675491531%0.9588283490.721566377

MINIMA VAR0.113975470.191900471.2564147450.593475072

SHARPE0.129711830.245381681.51629720.539226431

S&P_BMV IPC0.136672080.0309384-0.1299577641

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

A.9

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2014 - 2016

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

A.9

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/

BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento más bajo del 0.3% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Markowitz de mínima varianza con un rendimiento esperado del 19%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 24%

Anexo 10

Elaboración de los Portafolios 2015 – 2017

Tabla

A.10

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2015 - 2017

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.23316337%0.0054187260.52005661120.1082733417%0.8958918460.61162822530.1379120326%1.3975500280.64877660940.1932719336%1.4925949420.66550032450.2707579446%1.4190330.66267562760.400192955%1.1993021540.430568002

MINIMA VAR0.107162570.148982240.7202350640.618165527

SHARPE0.184940560.348123651.4941213760.66477474

S&P_BMV IPC0.124095840.090669940.1520594061

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

A.10

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2015 - 2017

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica A

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento más bajo del 0.9% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Ma

rkowitz de Mínima V

arianza con un rendimiento esperado del 14%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 34%

Anexo 11

Elaboración de los Portafolios 2016 – 2018

Tabla

A.11

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2016 - 2018

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.29035831510%0.0694629911.07782343720.14071572522%0.9865611550.50438919230.14491922533%1.7767151430.51313826140.1690507545%2.2249887790.5828741250.21610912157%2.2895433620.73929285860.37274613769%1.6457493370.910082178

MINIMA VAR0.1387493760.25515051.2854147850.500932531

SHARPE0.1934648720.5247657722.3154889460.668514193

S&P_BMV IPC0.2120835260.3273039031.1811568171

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

A.11

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2016 - 20

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica A

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento intermedio del 32% aunque con un riesgo alto, el portafolio con menor riesgo es

el portafolio de Markowitz de Mínima V

arianza con un rendimiento esperado del 25%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 52%

Anexo 12

Elaboración de los Portafolios 2017 – 2019

Tabla

A.12

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2017 - 2019

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.286453888%0.0166345721.36120649320.2421366910%0.1051914441.24241262730.2118050212%0.2180128931.12361751940.201865214%0.3313196561.00482251850.215162116%0.4070767690.88602807460.2479852418%0.4366909660.767234556

MINIMA VAR0.201799310.139245220.3238128741.013638998

SHARPE0.247985240.182192910.4366909660.767234556

S&P_BMV IPC0.14714127-0.07891589-1.0385658051

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

A.12

Comparativo entre los tres tipos de portafolio

S&P/BMV IPC

2017 - 2019

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Nota

: Elaboración generada por el autor basada en datos extraídos por investin

En la gráfica

A.12

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento más bajo del -0.7% aunque con un riesgo alto, el portafolio con menor riesgo es

el portafolio de Markowitz de Mínima V

arianza con un rendimiento esperado del 13%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 18%

Anexo 13

Elaboración de los Portafolios 2018 – 2020

Tabla

A.13

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2018 - 2020

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.568354916%0.0289943271.41646643220.2259033110%0.2468683980.64969334430.1600785414%0.5938197850.42590752840.1584701918%0.8477756150.32627484550.2241558222%0.7746233950.41340626260.3840771626%0.5543825440.593589511

MINIMA VAR0.153743190.159523820.754009450.366993994

SHARPE0.170862590.194862620.8852881440.306047756

S&P_BMV IPC0.20706075-0.14359037-0.9040361

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

A.13

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2018 - 2020

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

A.13

se muestra tres portafolios que son

portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento más bajo del -14% aunque con un riesgo alto, el portafolio con menor riesgo es el portafolio de Markowitz de mínima varianza con un rendimiento esperado del 15%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 19%.

Anexo

Elaboración de los Portafolios 2019 – 2021

Tabla

A.14

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2019 - 2021

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.111257026%0.0278919470.05488150720.1064110411%0.5506109830.33124669930.1554497117%0.7338643720.56509718240.219948922%0.7709377610.81871752350.2941716128%0.7650460391.12922419460.4654206634%0.6027724171.428870308

MINIMA VAR0.091339190.07034730.1680253050.183844682

SHARPE0.262560020.258494660.7750405440.982943985

S&P_BMV IPC0.203149920.093175070.1879157591

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

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Gráfica

A.14

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2019 - 2021

Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

A.14

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento intermedio del 0.9% aunque con un riesgo alto, el portafolio con menor riesgo es

el portafolio de Markowitz de Mínima V

arianza con un rendimiento esperado del 0.7%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 25%.

Anexo 15

Elaboración de los Portafolios 2020 – 2022

Tabla

A.15

Comparativo entre los tres tipos de portafolio S&P/

BMV IPC 20

- 20

PORTAFOLIO DE MARKOWITZ

DESVIACIÓN ESTANDAR

RENDIMIENTO ESPERADO

ÍNDICE DE SHARPE

BETA DEL PORTAFOLIO

10.3868151412%0.0301796921.41370003720.1894465916%0.2980453670.8855642730.1433321420%0.7064244090.61347372240.1475619825%0.9897060970.60934003850.1937071729%0.9851606140.752907760.3300522734%0.7138940641.099401633

MINIMA VAR0.14108880.221432740.83658480.6045237

SHARPE0.162161460.270162111.0283707850.654744885

S&P_BMV IPC0.160001820.09576037-0.0477471571

Fuente: Elaboración generada por el autor basada en datos extraídos por investing

Gráfica

A.15

Comparativo entre los tres tipos de portafolio

S&P/

BMV IPC

2020 – 2022

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Nota

: Elaboración generada por el autor basada en datos extraídos por investing

En la gráfica

A.15

se muestra tres portafolios que

son portafolio equiponderado, Mínima V

arianza y Sharp, incluyendo el

S&P/

BMV IPC.

S&P/

BMV

IPC

es el que muestra el rendimiento más bajo del 0.09% aunque con un riesgo alto, el portafolio con menor riesgo es

el portafolio de Markowitz de Mínima V

arianza con un rendimiento esperado del 22%, en lo que representa el portafolio de Sharpe es el mejor rendimiento esperado con 27%