Some new thinking on the Safe Withdrawal Rate

Ever since the empirical findings of Bengen (1994) on the 4 percent rule and safe withdrawal rate, our knowledge and understanding of it has moved at a snail’s pace over the years. After 30 years, financial planners still bandy the idea of retirement planning using some version of this rule without fully understanding the need for inflation adjustment, or the fact that it has never worked outside of the US! For example, see Pfau (2010) and Anarkulova et al. (2023) test this on a wide sample of international asset markets and arrive at the conclusion that the 4% rule is basically a historical anomaly of the US stock market outperforming expectations! While some progress has been made, for example linking the Cyclically Adjusted Price-Earnings ratio (CAPE) to asset portfolio returns, and to safe withdrawal rates (see Kitces (2008)), most of the research has been solely based on historical US equity markets returns.

At its most fundamental, our understanding of the Safe Withdrawal Rate lacks a theoretical foundation, which can link expected asset portfolio returns to both sequence of returns risk and safe withdrawal rates. Without such a framework, all we can do is to simulate historical returns and link them to safe withdrawal rates. Since reliving the same 100 years of history (albeit in different sequence) does not make us 100X smarter, there is a limit to how much this sort of work can help us estimate safe withdrawal rates. And so, we need to arbitrarily put some measure of conservatism to it, for example, using 3.5% or even 3% as the safe withdrawal rate.

But recently, Bessembinder et al. (2024) have published some new thinking on measuring long-term returns to investors, and indirectly, provided us with a better framework for estimating safe withdrawal rates based on expected asset returns, expected volatility of returns, and the possibility of sequence of returns risk. Let’s take a look at some of the implications of this!

How Should Long-Term Investor Returns Be Measured?

Bessembinder et al. (2024) start off by reviewing the different measures of long-term returns typically used, such as the Arithmetic Return (AR), Geometric Return (GR), the Internal Rate of Return (IRR) and the Modified IRR (where the re-investment rate is based on another asset e.g. T-bills or T-bonds). They find that a useful measure of long term return for investors is the Sustainable Return (SR), or the stream of inflation-adjusted consumption which investors can enjoy from their investments without reducing the real value of the investment. This sounds very much like the safe withdrawal rate, except that:

The horizon for the withdrawal can be taken to be infinite (instead of just 30 years)
The investments maintain their real value (or more), rather than just ending up with positive value

However, these assumptions can be relaxed. The sustainable return or the safe withdrawal rate computed under these more stringent assumptions will represent the most conservative value amongst them.

How is the Sustainable Return Related to the Expect Returns of the Asset Portfolio?

Bessembinder et al. (2024) then go on to show that the expected Sustainable Return is essential similar to the expected Geometric Return over the long-term! In other words:

Graphically, their computations show that the expected Sustainable Return only diverges slightly from the expected Geometric Return at higher levels of asset returns volatility.

The relation between expected Geometric Return and expected Sustainable Return

Source: Bessembinder et al. (2024) Figure A1

This would imply that if we had a retirement asset portfolio that is expected to earn a geometric return of 8% a year, and 6% a year after inflation, then the safe withdrawal rate can be as high as 6%! Can this be possible?

Sequence of Returns Risk and Sustainable Return

What throws a spanner in the safe withdrawal rate estimation is, of course, sequence of returns risk. As Bessembinder et al. (2024) show, the expected Sustainable Return is based on the ex-ante expected Geometric Return, but the ex-post Geometric Return can be different, and also the sequence of the bad returns matter too.

Sustainable Returns and Sequence of Returns Risk

Source: Bessembinder et al. (2024) Figure 1

In the chart above, the expected Geometric Return is 6.18% and given the sequence of high (H) and low (L) returns experienced, the ex-post Geometric Return is also 6.18%. However, depending on the sequence of returns, e.g. LLHH or HHLL, and the volatility of these returns e.g. Range = 10% to 50%, the ex-post Sustainable Return or safe withdrawal rate can range from 4.71% for the 50%-range LLHH sequence, or as high as 7.88% for the 50%-range HHLL sequence!

Can the impact of the sequence of returns risk be quantified and the safe withdrawal rate adjusted accordingly? The answer appears to be YES! In their Appendix III, Bessembinder et al. (2024) derive the adjustment to the Sustainable Return due to sequence of returns risk to be:

where:

gr = Ln (1 + GR)

sr = Ln (1 + SR)

T = period over which the Low and High returns occur, e.g T = 4 -> LLHH, T = 6 -> LLLHHH

H = deviation from expected GR, e.g. GR = 5%, H = 10%, a Low return = -5%, and High return = +15%

Putting this into numbers, suppose we have a retirement asset portfolio where the expected Geometric Return is 5% after inflation. Suppose also we expect a bad sequence of returns to be LLLHHH, and the outcomes will be (-5%, -5%, -5%, +15%, +15% +15%). What will be the adjusted Sustainable Return, or safe withdrawal rate?

Running the numbers through the computer gives us 3.47%. Which is lower than the initial 5% safe withdrawal rate, thanks to the unfortunate sequence of returns. We can work out some of these numbers in a table:

Some examples of the impact of Sequence of Returns Risk on Safe Withdrawal Rates

Expected Real Return	Sequence of Returns	Low Return	High Return	Sustainable Return
5%	LLHH	0%	+10%	4.49%
5%	LLLHHH	0%	+10%	4.23%
5%	LLHH	-5%	+15%	3.98%
5%	LLLHHH	-5%	+15%	3.47%
5%	LLHH	-10%	+20%	3.47%
5%	LLLHHH	-10%	+20%	2.72%

A New Way Forward for Retirement Planning!

If these results from Bessembinder et al. (2024) hold true in practice (the mathematics work out, but translating from theory to the real world sometimes is not so straightforward), retirement finance and retirement planning can be changed for the better. For the first time, instead of relying on US historical data alone (which can be pretty irrelevant for non-US people), we have a way to link the expected return on our assets to the safe withdrawal rate and adjust for possible sequence of returns risk scenarios as well.

And this ties in with previous work on linking the Cyclically Adjusted PE ratio to asset returns as well, using the CAPE to forecast the returns on a portfolio of assets which fit out risk appetite, and then working out the safe withdrawal rates based on these forecasts. This would given retirees a much higher level of certainty than they would have now, and reduce reliance on conservatism which makes people work and save harder than they need to, and spend less than they can in retirement.

Financial planners, it is time to up your game!