# Safe withdrawal rates

A safe withdrawal rate (SWR) is the quantity of money, expressed as a percentage of the initial investment, which you can withdraw per year from a portfolio, for a given quantity of time, including adjustments for inflation, without portfolio failure, where 'without failure' is a 95% probability of not running out of money at any time within the specified period.

Usage: A "safe withdrawal rate" is typically an approximation of the probability that a given portfolio can support a given annual spending component for a required period, with a reasonable confidence. To do this, you would use variables such as the allocation of assets within a model portfolio, the beginning balance, and/or the number of years expected in retirement are varied, apply a model to them, and then compare the results of altering these variables to optimize for the best outcome.

Controversy: Unfortunately, the term "safe withdrawal rate" is ambiguous. This is because initial methods used historical data to statically determine what would have been safe, given the actual results that past portfolios would have generated with the variables given. The next logical step, of course, was to use that information to predict future SWRs. Either use is technically correct, but to avoid unnecessary arguments, you need to be clear if you use the term for past SWRs or projected SWRs.

## Studies and papers

### Trinity study

Philip L. Cooley, Carl M. Hubbard and Daniel T. Walz authored an early and influential paper, Retirement Savings: Choosing a Withdrawal Rate That Is Sustainable.[1] Because the authors were professors at Trinity University in San Antonio, Texas, it is often referred to as "the Trinity study." The authors studied actual historical stock and bond returns from 1926 through 1995 to determine sustainable withdrawal rates. The study has gained renewed significance in light of recent turbulent economy.

Using all of the historical data, the professors looked at five possible portfolio compositions, from 100 percent stocks to 100 percent bonds - the three other portfolios had a stock/bond allocation of: 75/25, 50/50, and 25/75 - and evaluated the impact of fixed annual withdrawals ranging from three percent to twelve percent. The S&P 500 index represented stocks, and long-term high grade domestic bonds represented bonds.

Payout periods were in five-year intervals, from 15 to 30 years. In the study, the professors considered a portfolio successful if it ended a particular withdrawal period with a positive (not zero, and not negative) value.

The study produced a number of conclusions, including:

• Withdrawal periods longer than fifteen years dramatically reduced the probability of success at withdrawal rates exceeding five percent.
• Bonds increase the success rate for lower to mid level withdrawal rates, but most retirees would benefit with at least a 50 percent allocation to stocks.
• Retirees who want inflation-adjusted withdrawals must expect a substantially lower withdrawal rate from the initial portfolio.
• Stock-dominated portfolios using a three to four percent withdrawal rate may create rich heirs at the expense of the retiree's current standard of living.
• For a payout of fifteen years or less, a withdrawal rate of eight to nine percent from a stock-dominated portfolio appears sustainable.[2][3]

#### The Trinity study numbers

• Table 1 shows the success rate of various portfolios for different time periods measured against the full time span of the studied data, 1926-1995.
• Table 2 shows the success rate of various portfolios for different time periods measured against the post-World War II markets, 1946-1995.
• Table 3 shows the success rate of various portfolios for different time periods measured against the full time span of the studied data, 1926-1995. However, unlike Table 1 which covers the same time period, this data is adjusted for inflation and deflation.
Trinity Study portfolio success rates
Table 1: 1926-1995 Table 2: 1946-1995 Table 3: 1926-1995, adjusted

(Click on each table for a larger view with additional details)

### Limitations of the Trinity study

One scenario backtested in the Trinity study suggests that a retiree with a suitably allocated \$1 million portfolio could withdraw \$40,000 the first year, give themselves a cost-of-living adjustment every year afterwards, and have a 98% chance of the portfolio lasting at least 30 years.

Taken literally, such a plan has been criticized as unrealistic. Even if the tests showed that the plan had a 98% success rate over all past time periods, would a prudent person blindly go on steadily increasing withdrawals in a prolonged bear market? It also leads to apparent absurdities. Suppose retirees Alice and Bob have saved \$1 million in 2008, and the market crash reduces their portfolios to \$800,000 in 2009. Alice, however, retires in 2008 while Bob waits until 2009. The Trinity study bases withdrawals the dollar value of the portfolio at the start of retirement. The value fluctuates with the vagaries of the stock market. As a result, even though their situations are almost identical, in the Trinity scenario, because Alice retired in 2008 she is allowed to withdraw \$40,000 plus COLA in 2009; while Bob, despite being in an almost identical situation, would be allowed only \$32,000.

The authors of the paper, however, did not mean for their scenarios to be applied rigidly or uncritically. The article makes this very important statement:

The word planning is emphasized because of the great uncertainties in the stock and bond markets. Mid-course corrections likely will be required, with the actual dollar amounts withdrawn adjusted downward or upward relative to the plan. The investor needs to keep in mind that selection of a withdrawal rate is not a matter of contract but rather a matter of planning.

Nisiprius requested clarification from Professor Philip L. Cooley, senior author of the Trinity study:[4]

What the "4% SWR" means is not that you can treat a portfolio as if it were a guaranteed annuity. I think all the [Trinity] authors meant is that if it is late 2008 and your stocks halve in value, you don't need to halve your spending instantly. It's OK to cross your fingers and continue spending according to the 4%-then-COLAed plan, even though it means dipping into capital, and it's OK to go on doing that for a while.

Professor Cooley's response:[5]

You have hit the nail on the head! I've tried to explain that thought to journalists but they don't seem to get it. You've got it. Stay flexible my friend!, which is the advice we should give to retirees.

### Trinity study update, April 2011

The original Trinity Study authors have updated their results through 2009.[6]

See Trinity study update for a comprehensive discussion on the implications of the Trinity study to investors.

## Papers

At the onset of retirement, investment advisors make crucial recommendations to clients concerning asset allocation, as well as dollar amounts they can safely withdraw annually, so clients will not outlive their money.... It employs graphical interpretations of the data to determine the maximum safe withdrawal rate (as a percentage of initial portfolio value), and establishes a range of stock and bond asset allocations that is optimal for virtually all retirement portfolios.

(Quoting Bernstein:) "Two percent is bullet-proof, 3% is probably safe, 4% is pushing it and, at 5%, you're eating Alpo in your old age," reckons William Bernstein, an investment adviser in North Bend, Ore. "If you take out 5% and you live into your 90s, there's a 50% chance you will run out of money."

(Clements said:) [Using a two-act retirement plan] if you're short on savings... will give you a fair amount of income, your heirs will inherit a decent sum if you die before age 85 and, if you live longer than that, you should be comfortable enough.

... provides a more robust calculation of "safe" withdrawal rates for retirement and provides a graphic method for better understanding the interrelationship among withdrawal strategies, risk tolerance, and asset allocation.

The 4% rule is the advice most often given to retirees for managing spending and investing. This rule and its variants finance a constant, non-volatile spending plan using a risky, volatile investment strategy. As a result, retirees accumulate unspent surpluses when markets outperform and face spending shortfalls when markets underperform. The previous work on this subject has focused on the probability of short falls and optimal portfolio mixes. We will focus on the rule’s inefficiencies—the price paid for funding its unspent surpluses and the overpayments made to purchase its spending policy. We show that a typical rule allocates 10%-20% of a retiree’s initial wealth to surpluses and an additional 2%-4% to overpayments. Further, we argue that even if retirees were to recoup these costs, the 4% rule’s spending plan often remains wasteful, since many retirees may actually prefer a different, cheaper spending plan.

If history is any guide, a 4% withdrawal rate means your portfolio will be able to withstand a market meltdown of the worst magnitude we’ve experienced in the last 80 years as well as support you for an exceptionally long life. William Bengen, a U.S. researcher, has back-tested a 4% withdrawal rate with a balanced portfolio of U.S. stocks and government bonds earning overall market returns and found that you would have been able to safely withdraw 4% of your portfolio over any 30-year period since 1926.

...most [SWR] research has centered on withdrawal rules that are quite static... yet most retirees have the ability to modify their annual spending, at least to some degree. Would the ability to make small systematic modifications if investment performance is poor increase the safety of an investment portfolio and allow for slightly higher withdrawal rates?