Difference between revisions of "Retirement Planning"
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A fixed amount is already paid in at the beginning of the simulation and a fixed amount is invested each year in January. The results from the stock portfolio are standard normally distributed and are calculated on a monthly basis. However, a distinction must be made between two scenarios. A mean and a standard deviation are required for months in which a black swan event occurs and for months in which no black swan event occurs. In addition, a probability must be given for the occurrence of a Black Swan month. The simulation then randomly determines whether a month is a Black Swan month or not. The results of the Monte Carlo simulation record how many Black Swan months occurred in a simulation. This makes it possible to examine the results afterwards for the number of Black Swan months.The Stock portfolio is simulated 1000 times. | A fixed amount is already paid in at the beginning of the simulation and a fixed amount is invested each year in January. The results from the stock portfolio are standard normally distributed and are calculated on a monthly basis. However, a distinction must be made between two scenarios. A mean and a standard deviation are required for months in which a black swan event occurs and for months in which no black swan event occurs. In addition, a probability must be given for the occurrence of a Black Swan month. The simulation then randomly determines whether a month is a Black Swan month or not. The results of the Monte Carlo simulation record how many Black Swan months occurred in a simulation. This makes it possible to examine the results afterwards for the number of Black Swan months.The Stock portfolio is simulated 1000 times. | ||
| − | The stock portfolio consists of a mixture of an investment in the S&P 500 and a portfolio of 4 DAX stocks. The optimal weights for both portfolios were determined using a Monte Carlo simulation. Random weights are assigned to the individual stocks and the respective expected return and variance are calculated from the combination. Since the portfolio is a retirement plan, the weights were chosen in such a way that the portfolio has a minimum risk (minimum variance / standard deviation). | + | The stock portfolio consists of a mixture of an investment in the S&P 500 and a portfolio of 4 DAX stocks. The optimal weights for both portfolios were determined using a Monte Carlo simulation. Random weights are assigned to the individual stocks and the respective expected return and variance are calculated from the combination. Since the portfolio is a retirement plan, the weights were chosen in such a way that the portfolio has a minimum risk (minimum variance / standard deviation). 1000 different weights are choosen for both optimisations. |
== Input Variables == | == Input Variables == | ||
Revision as of 18:38, 19 January 2021
Contents
Problem Definition
In retirement planning, there are different investment options that are associated with different risks. Therefore, this simulation is intended to help compare different investment options and evaluate their risk. For this purpose, it is assumed that a fixed amount is already invested in one of the options and that a fixed amount will be invested over the next 30 years. Two different options are compared, an investment in a chosen stock portfolio or an investment in bonds. To make the model more realistic, it is assumed that the stock markets are repeatedly shaken by black swan events. Black swan events are, for example, financial crises that occur irregularly and without warning. In addition, inflation is simulated over the next 30 years and the result is adjusted for it.
Method
The chosen simulation method is a Monte Carlo simulation in Excel.
Model
Inflation
Inflation is assumed to be normally distributed. For the simulation, both a mean value and the standard deviation must be determined. Then the discount factors for each simulation are calculated. The result of the two investment options is in the end adjusted by a selection from these discount factors. The worst case scenario, the mean, the median and the 5%, 10%, 15%, 20% percentile (5% percentile is the value that is not exceeded with 95% certainty) were chosen. Inflation is simulated 1000 times.
Stock Portfolio
A fixed amount is already paid in at the beginning of the simulation and a fixed amount is invested each year in January. The results from the stock portfolio are standard normally distributed and are calculated on a monthly basis. However, a distinction must be made between two scenarios. A mean and a standard deviation are required for months in which a black swan event occurs and for months in which no black swan event occurs. In addition, a probability must be given for the occurrence of a Black Swan month. The simulation then randomly determines whether a month is a Black Swan month or not. The results of the Monte Carlo simulation record how many Black Swan months occurred in a simulation. This makes it possible to examine the results afterwards for the number of Black Swan months.The Stock portfolio is simulated 1000 times.
The stock portfolio consists of a mixture of an investment in the S&P 500 and a portfolio of 4 DAX stocks. The optimal weights for both portfolios were determined using a Monte Carlo simulation. Random weights are assigned to the individual stocks and the respective expected return and variance are calculated from the combination. Since the portfolio is a retirement plan, the weights were chosen in such a way that the portfolio has a minimum risk (minimum variance / standard deviation). 1000 different weights are choosen for both optimisations.
