You will be able to explain what Bengen and the Trinity study tested and what their results do and do not show.
Spend an evening reading about financial independence online and you will see the same two shortcuts again and again. Take out 4% a year and your money lasts. Save 25 times your spending and you are done. They are quoted so often that they sound like laws of nature, yet both come from a small number of studies on American data. Once you know what those studies tested, you can use the shortcut with your eyes open.
In module 1 you built a spending base. This module turns it into a number, and that needs the second input from lesson 1.1: how much you can take out of your investments each year without running out.
In 1994 William Bengen, a financial planner in the United States, published a study in the Journal of Financial Planning. His question was practical. A client retires with a portfolio and wants a steady income. How much can they take in the first year, and then raise each year in line with inflation, without the money running out over a thirty-year retirement?
To answer it, he used historical US market data. He imagined a retiree starting in each past year in turn, holding a mix of large American company shares and US government bonds, and he ran the withdrawals forward through what actually happened next. Some of those imaginary retirees started just before the Great Depression. Others started before the high inflation of the 1970s.
He was looking for the highest starting withdrawal that survived every one of those starting years, the worst of them included. The answer he found was about 4% of the starting portfolio. So, as an example, a retiree with S$1,000,000 would take S$40,000 in the first year, then S$40,000 plus inflation the next year, and so on, whatever the market did.
Two details matter. First, the 4% is a percentage of the starting balance only. After the first year, the withdrawal follows inflation and ignores the portfolio's value. Second, 4% was the rate that survived the worst historical start. In most starting years, the retiree would have died with plenty left over.
A few years later, three finance professors at Trinity University in Texas ran a broader test, now known as the Trinity study. They also used US historical data, but instead of searching for a single safe rate, they tested a range of withdrawal rates, over several retirement lengths and with different mixes of shares and bonds.
For each combination they reported how often the portfolio lasted the full period, so what came out was a table of success rates rather than one answer. Higher withdrawal rates, longer periods and lower shares in the mix all reduced the share of historical periods in which the money lasted.
Those tables are where much of the later talk of a "safe" 4% comes from. Read them with care, though. A high success rate means the portfolio survived most past US periods. It says nothing certain about the next thirty years in your own markets, with your own costs.
The arithmetic takes one line. If your first-year withdrawal of 4% has to equal your yearly spending, the portfolio must be 1 divided by 0.04 times that spending, and 1 divided by 0.04 is 25. So a 4% rate and a target of 25 times spending are the same statement in two forms.
The same works for any rate. At 3.5%, 1 divided by 0.035 gives about 28.6 times. At 3%, it gives about 33.3, usually rounded to 33. A lower rate means a larger multiple and a larger number.
Take Priya from module 1, whose spending base is S$44,000 a year at today's prices in this made-up example. At 25 times, her number is S$1,100,000. At 33 times, it is S$1,452,000. If you use the unrounded 33.3, it comes to about S$1,466,667. A single percentage point of withdrawal rate moves her target by over S$350,000.
The results tell you that, in US history, a retiree who started at about 4% and kept raising withdrawals for inflation would have got through thirty years in every period Bengen tested. They also make the trade-off plain: take more, and the chance of running out rises.
They cannot tell you that 4% is safe for you. The periods were thirty years. The data were American, from a century in which the US market did well. Most of the costs you pay today were left out. And the retiree in the model never adjusted spending, whatever happened. Lesson 2.2, Four reasons the rule may not fit you, goes through each of these in turn.
None of this makes the rule useless. It gives you a sensible starting point and a way to turn spending into a target in one step. The mistake is to treat it as a promise.
For the activity, you need only your spending base from lesson 1.4 and a calculator. Keep both figures it asks for, because lesson 2.4 uses them when you choose your own rate.
Multiply your yearly spending base by 25, and also by 33, which matches a 3% withdrawal, and write both figures down.
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