Question

The annual rate of return of a savings portfolio is assumed to be distributed N(9%,692) An investor starts with a $1MM investment. The investor withdraws $10K per year. Simulate this and display the distribution of how much the investor has after ten years.

a. If the investor wants to have a 90% chance of having 1M or more at the end of the 10 years, what size withdrawl would create that?

Answer 1

The student's question about investment portfolio simulation can be addressed using a Monte Carlo simulation or similar numerical methods to find the withdrawal amount that would provide a 90% chance of maintaining at least $1 million after ten years.

Step-by-step explanation:

The question involves simulating the future value of an investment portfolio given a normal distribution of annual returns and a constant withdrawal amount. To determine the future value after ten years, with a specific confidence level of 90% for having at least $1 million, Monte Carlo simulation or another numerical method would typically be used to model the portfolio performance under random sampling of the annual returns.

To find the maximum withdrawal amount that allows the investor to have a 90% chance of maintaining at least $1 million after ten years, one would adjust the withdrawal amount in the simulation until the 10th percentile (or the 90th percentile from the other direction) of the ending portfolio values is at or above $1 million.

Monte Carlo simulation, numerical method, and portfolio performance are key concepts in approaching this problem.

For the given normal distribution N(9%, 692), the mean annual return would be 9% and the standard deviation would be 692. After generating the random returns, we can calculate the ending portfolio value for each simulation, taking into account the annual withdrawals of $10,000. Finally, we can analyze the distribution to find the withdrawal amount that would result in a 90% chance of having $1 million or more at the end of 10 years.