In 1999, a study was published detailing the effects of a range of nominal and inflation-adjusted withdrawal rates on investment portfolios for payout periods up to 30 years. Within finance, investment advising and retirement planning this study is informally known as the Trinity Study.

The study suggests that portfolios of at least 75% stocks provide a 4% to 5% inflation-adjusted withdrawal. In other words, if you have a portfolio of $1 million, you can withdraw annually $40.000 to $50.000 adjusted for inflation without the risk of running out of money, at least, for the coming 30 years.

After reading this study, I was inspired to extend the work of this paper. As a result, I have written a python script that follows the methodology described in this study to determine a sustainable withdrawal rate for any investment portfolio (assuming that there is sufficient historical data).

This article is comprised of the following sections, first, I will explain the data and methodology. Second, I will elaborate on the Python implementation and explain how to use it. Lastly, a conclusion is presented regarding the determination of a safe withdrawal rate.

Data and Methodology

In order to determine a sustainable withdrawal rate, the study used a ratio called the portfolio success rate. This ratio is used to compare all the portfolio compositions with different withdrawal rates and payout periods. The portfolio success rate, is defined as the number of portfolio successes divided by the number of simulations. A portfolio is considered a success if it completes the payout period with an end of period value greater than or equal to zero.

The data used in the study were the total monthly returns of the Standard & Poor’s 500 Index and the Salomon Brothers Long-Term High-Grade Corporate Bond Index. Total monthly return is the actual return of an investment for a given period, this includes interest, capital gains, dividends and distributions.

Using these historical total monthly returns, simulations are derived by using an overlapping years method for different payout periods. This method is elaborated in the figure below:

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