The million dollar question for those seeking early retirement is:

How much money do I need to have saved up to retire?

The answer isâ€¦ the 4% rule. Dun, dun, dunnnn!

## The Trinity Study

In 1998, three professors at Trinity University conducted a study to determine what percentage of his total savings a retiree could withdraw annually if he was to live off his savings for the rest of his life.

The study used historical data from 1926 to 1995 to calculate the success rate of various withdrawal rates based on the combination of two variables:

• The composition of the retireeâ€™s portfolio
• The remaining life expectancy for the retiree

Five different portfolio compositions were considered:

• 100% stocks
• 75% stocks/25% bonds
• 50% stocks/50% bonds
• 25% stocks/75% bonds
• 100% bonds

Along with four remaining life expectancies:

• 15 years
• 20 years
• 25 years
• 30 years

At the end of this post I answer some questions I had while reading through the study, if youâ€™re confused at any point feel free to skim through them and then continue.

## What were the results of the study?

The study determined that a 4% withdrawal rate basically guaranteed a retiree would make it to the end of the 30 year period with money left over.

This is why the study has come to be known as the four percent rule.

Here are the results:

The study was updated in 2009 and the results were almost exactly the same:

Note that these results account for inflation, meaning if you retired with \$1,000 in savings, you would withdraw \$40 in the first year, but \$40 times the inflation rate in the second year.

## Why does this matter for early retirement?

This study is exciting as it helps answer two thorny questions:

• How much money do I need in order to retire?
• How should I divide my investments between stocks and bonds?

### How much money do I need in order to retire?

Since we know we can withdraw 4% from our savings ever year and never run out of money*, we can calculate how much we need in order to retire by determining what our annual expenses are.

For example, Sam currently spends \$2,000 a month between rent, food, Netflix, Tinder subscription, etc. This means he lives on \$24,000 per year.

So in order to able to spend \$24,000 for the rest of his life without having to work, Sam would need to have saved up \$600,000 (4% of \$600,000 is \$24,000)

An easy way to calculate this number is to multiply your annual expenses by 25 (as 100%/4% is 25).

In Samâ€™s case: \$24,000 * 25 = \$600,000

Annual Expenses * 25 = Savings Needed To Retire

But wait, Sam says, when I retire I want to live it up.

I want to travel and party, and, heck, throw a baby in there (Samâ€™s Tinder subscription has got to pay off at some point and he hears babies are expensive).

The four percent rule still works, but youâ€™ll have to estimate what your annual expenses will be.

If you currently spend \$2,000 a month, but you think youâ€™ll need \$4,000 when you retire (to buy yourself and your baby margaritas on the beach), then just multiply the predicted expenses, rather than your current expenses, by 25.

In this case: \$4,000 a month is \$48,000 a year and \$48,000 * 25 = \$1.2 million

### How should I allocate my portfolio between stocks and bonds?

The real (accounting for inflation) rate return of the stock market from 1950 to 2009 was 7%.

The real rate of return of bonds (US government bonds) from 1950 to 2009 was about 2%.

Stocks have a higher rate of return, but they are more volatile.

In times of recession, the stock market gets hammered, as you can see in the chart below (look at the Great Depression in the 1930â€™s and the Great Recession in the late 2000â€™s)

Currently, Iâ€™m all in on stocks. Iâ€™m young and have time to weather out any storms in the stock market.

A retiree, however, canâ€™t afford the volatility and needs to hedge her bets.

Consider the Great Recession of the late 2000â€™s.

If a retiree was all in on stocks and needed to withdraw money, she would have had to do so at a great loss.

The stock market eventually recovered, but the damage would have been done.

Some exposure to the bond market reduces volatility and improves the success rate.

A 75%/25% stock/bond allocation seems to capture the upside of the stock market while reducing volatility.

## How safe is the 4 percent rule?

The 4 percent rule is a great starting point, but it is not perfect.

As always, thereâ€™s some good news and some bad news.

• Though the study calculated success rates for up to 30 years, early retirees need their money to last for potentially 60-70 years, not just 30.
• A 98% success rate sounds greatâ€¦ unless you lived in that one period where you got f**ked over.

The Good

• The study does not include Social Security benefits. If you retire at 35, by the time the 30 year period ends you become eligible for Social Security.
• The study assumes you will never make another dollar for the rest of your life. Early retirement doesnâ€™t necessarily mean you (and your baby) will be on the beach sipping margaritas all day long. If you get a seasonal or part-time job or start a side business that brings in some money, your success rate goes way up.
• The period of data the study uses (1926-2009) includes the Great Depression. This accounts for many of the failed cases. Those retiring right before or during the Great Depression got the short end of the stick. Not saying this couldnâ€™t happen again, but worth mentioning.
• The study doesnâ€™t include any adjustments. We can adjust our withdrawal rate based on how the economy is doing, maybe withdraw only 3% on down years and 4% on others.

## Final considerations

The 4% rule is a simple heuristic we can use to get an idea of how much weâ€™ll need to have saved up to retire.

The two big takeaways are:

• To calculate your magic retirement number determine your estimated annual expenses and multiply by 25.
• While young, take advantage of the superior rates of return of the stock market with a 100% stock portfolio allocation since you have time to weather out any storms. When retired, reduce the volatility of your portfolio by using a 75%/25% stock/bond portfolio allocation.

What is a â€śportfolioâ€ť?

• A portfolio just refers to the grouping of all the different assets one owns. For example, a house, cash in a savings account, stocks, bonds, gold (if youâ€™re Scrooge McDuck), expensive art (if youâ€™re a bored billionaire), etc.
• If you have \$100 invested in stocks and \$100 invested in bonds, you have a portfolio worth \$200 with a 50%/50% stock/bond composition.

What is a â€świthdrawal rateâ€ť?

• A withdrawal rate is the percentage of money the retiree takes out every year.
• If a retiree has a portfolio worth \$100,000, a 4% withdrawal rate would mean she would withdraw \$4,000 every year.

How are â€śstocksâ€ť and â€śbondsâ€ť represented in the study?

• â€śStocksâ€ť are represented by the Standards and Poorâ€™s 500 index.
• â€śBondsâ€ť are represented by long-term, high-grade corporates.

What is the Standards and Poorâ€™s 500 index?

• The Standards and Poorâ€™s 500 index, often called the S&P 500 or just the S&P, is a measure of how the stock market is doing at any given time.
• The 500 in S&P 500 refers to the 500 companies that are tracked in the index.
• When the prices of the stocks of these 500 companies go up, the S&P goes up, when the prices go down, the S&P goes down.

What are long-term, high-grade corporate bonds?

• A bond is a promise to pay a specified amount of money on a specific date. For example, you let the government borrow \$1,000 and 30 years later they pay you \$2,000.
• Long-term means the bond has a duration of at least 15 years.
• High-grade means the bonds are low risk, i.e. it is highly unlikely that the borrower will not pay you back what you lent him.

How can I guarantee that my stocks match the S&P 500? Do I have to buy individual stocks of each of the 500 companies?

• Index funds (such as VTSAX) take care of this for you.

What are index funds?

• An index fund is a portfolio of stocks.
• An index fund â€śtracksâ€ť an index (such as the S&P 500), meaning it tries to duplicate the indexâ€™s performance.
• For example, an index fund tracking the S&P 500 is made up of shares of all the 500 different companies in the S&P.
• Instead of buying shares of each of the 500 different companies, you buy shares of the index fund.

What time periods were analyzed?

• The study analyzed every single 15, 20, 25, and 30 year period between 1926 and 1995.
• For example, there are 56 different 15 year periods between 1926 and 1995. The one starting in 1926 and ending in 1941, the one starting in 1927 and ending in 1942, the one starting in 1928 and ending in 1943, and so on.

How was the â€śsuccess rateâ€ť calculated?

• The success rate is simply the number of periods where there was money left over at the end of the period, i.e. the retiree never ran out of money, divided by the total number of periods.
• Letâ€™s say weâ€™re calculating the success rate of a 50%/50% stock/bond portfolio for a 15 year period.
• As we said above, there are 56 different 15 year periods between 1926 and 1995.
• So if the 50%/50% stock/bond portfolio had money remaining in it in 55 out of the 56 15 year-periods, then the success rate for a 50%/50% stock/bond portfolio over 15 years is 98%.

## Notes

* Never is my own extrapolation here as the study only went up to 30 years. You can play with different numbers here to see how different stock/bond allocations over different time horizons (30, 40, 50, etc. years) would play out. As far as I could tell, the 4% rule backed by a 75%/25% stock/bond allocation has a nearly 100% success rate.