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Montecarlo Para Dummies​

La Simulación de Probabilidades, también conocida como el Método Montecarlo, se originó a mediados de la década de los 60 del siglo pasado. Sin embargo; su difusión y empleo se masifico recién a partir de la segunda mitad de los 90 gracias al advenimiento de hardware más potente y programas más amigables. Actualmente, el software necesario (Risk Simulator, Crystal Ball entre otros) corre dentro de programas de hojas de cálculo como el Excel. Si bien su ejecución es operativamente compleja y de ahí la necesidad de hardware más potente y software especializado, es bastante fácil de explicar.

El proceso de análisis consta de seis pasos, los que se describen a continuación:

Paso 1: Elaboración del modelo de pronóstico

Consiste en desarrollar las proyecciones financieras del proyecto. Dicho modelo debe ser efectuado en una hoja de cálculo en la que corra el programa (como, por ejemplo, Excel) y contar con un panel de variables de entrada en la que los valores de las variables estén vinculadas al estado de resultados, flujo de caja e indicadores de rentabilidad.

Paso 2: Selección de las variables de riesgo

Una vez elaborado el modelo de pronóstico, el evaluador debe seleccionar las variables de riesgo, esto es aquellas que se cree afectan en mayor medida a la rentabilidad del proyecto. La selección de las mismas debe basarse en i) la experiencia del evaluador y/o ii) como resultado del análisis de sensibilidad por variables.

Paso 3: Asignación de la distribución de probabilidades

Una vez seleccionadas las variables de riesgo, el paso siguiente consiste en asignar la distribución de probabilidades que más se adecue al comportamiento de las mismas. La mayoría de programas que corren esta clase de análisis tienen una función que permite introducir los valores observados o supuestos a fin que el programa le asigne la distribución más adecuada (por ejemplo, Fit Data). Adicionalmente, se deberán introducir datos complementarios como, por ejemplo, el valor promedio y los valores máximos y mínimos de cada una de las variables de riesgo.

Paso 4: Inclusión de correlación en las variables de riesgo

Una vez seleccionadas las variables de riesgo, los valores (promedio, máximo y mínimo) que estas pueden tomar y la distribución de probabilidades más adecuada toca establecer las correlaciones que puedan existir entre las variables seleccionadas. Por ejemplo, el evaluador puede colegir que existe una relación inversa entre precio y cantidad lo que implica introducir el valor del coeficiente de correlación respectivo.

Paso 5: Ejecución de la simulación

Este proceso puede resumirse de la manera siguiente:

  • El evaluador escoge el número de simulaciones que el programa efectuara. Nótese que el número mínimo para que el análisis sea significativo estadísticamente no debe ser menor de 200. El número máximo, por su parte, depende de la potencia de la computadora en la que se efectúa el análisis. En ese sentido, 10,000 simulaciones no es un número de repeticiones fuera de lo común.

 

  • Para la simulación 1, el programa escoge al azar, y de ahí que esta técnica sea conocida también como Montecarlo, valores de las variables de riesgo respetando las correlaciones, si las hubiera (así, por ejemplo, si hay correlación inversa entre precio y cantidad, el programa no escogería en ambas variables valores elevados) y las introduce al modelo de pronóstico obteniendo de esta manera el indicador de rentabilidad correspondiente (por ejemplo, el VPN).

 

  • Una vez hallado el VPN del primer escenario, el programa toma otros valores de las variables de riesgo incorporándolas al modelo y obteniendo de esta manera un segundo indicador de rentabilidad. El mismo proceso se repite una y otra vez hasta completar el número de simulaciones requeridas.

Paso 6: Análisis de resultados

Si se ejecutan “n” simulaciones (escenarios), se tendrán “n” indicadores de rentabilidad (por ejemplo, n VPN) cuya probabilidad de ocurrencia se estima en 1/n. Teniendo esos datos pueden hallarse el valor esperado, en este caso el VPNE, la varianza (σ2), la desviación estándar (σ), el coeficiente de variación (cv) y una serie de indicadores más (por ejemplo, la probabilidad de resultados negativos, pérdida esperada, ganancia esperada, valor máximo/mínimo del VPN, ratio de pérdida esperada, etc.)

 

Lo anterior permite al evaluador emitir una opinión sobre el riesgo del proyecto.

 

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