How can I find a maximum withdrawal rate of a portfolio?

Hi everyone,

I’m new to Matlab and I need help solving a simple investment problem.

I have a function which takes an initial portfolio amount (e.g. $100,000) and a withdrawal rate (e.g. 4%) and calculates the value of the portfolio at the end of a given period for a set of returns (generated randomly). It assumes that you withdraw a fixed percentage from the initial portfolio amount at each period.

function [portfolioEOP] = wtdFixedFlat(initPortAmt, wtdPerc)
% initPortAmt: initial value of the portfolio (e.g. 100000)
% wtdPerc: withdrawal percentage at each period (must be between 0 and 1)

[myReturns] = simulateReturns(); % get random set of returns

% Initialize vectors, assume 30 periods
portfolioSOP = zeros(30,1);
portfolioEOP = zeros(30,1);
wtdAmt = zeros(30,1);

% Set first period
portfolioSOP(1,1) = initPortAmt*(1-wtdPerc)*(1+myReturns(1,1)/100);
wtdAmt(1,1) = initPortAmt*wtdPerc;
portfolioEOP(1,1) = portfolioSOP(1,1)-wtdAmt(1,1);

% Loop through all other periods
for i=2:30
  portfolioSOP(i,1)=(1+myReturns(i,1)/100)*portfolioEOP(i-1,1);
  wtdAmt(i,1) = initPortAmt*wtdPerc;
  portfolioEOP(i,1)=portfolioSOP(i,1)-wtdAmt(i,1);
end

I want to find the maximum withdrawal rate such that I am at least 90% certain that I will not run out of money at the end of the 30 periods.

I tried doing this by returning an indicator: 1 if portfolioEOP(30,1) > 0, 0 otherwise

Then, for a given withdrawal rate, I loop through the function 1000 times and if the mean of the indicators is > 90% then I keep that as a possible withdrawal rate. I then used fmincon to find the best withdrawal rate.

This seems very inefficient and I’m not sure whether I’m using the appropriate optimization method. Is there a better way of doing this? Any help would be greatly appreciated. Thank you!