top of page

The Interplay Between Returns Risk and Sequence of Returns Risk

Investors are well acquainted with the risks stemming from poor returns. And most in the personal finance community are aware of what has come to be known as sequence of returns risk. But, in my view, there isn't enough discussion of the interplay between these risks in the real world, including the relative importance of these risks to different investors. My purpose in this post is to help readers understand that both returns risk and sequence of returns risk are important to all investors, including those contributing to their portfolio and those making withdrawals, but also that the relative magnitude of these risks changes over an investor's lifetime.

What are These Risks?

Returns risk is, put simply, the risk of investors experiencing poor returns from an investment or their entire portfolio. The returns of some investments are very predictable, such as the real return of a Treasury Inflation Protected Security (TIPS) bond held to its maturity, whereas other investments, such as stocks, have highly erratic returns. Many investors, especially those who are young, focus much of their attention on seeking after high returns with the reasoning that if they experience poor returns instead, they have enough time for the value of their investments to recover.

Sequence of returns risk (SORR) refers to the risk that the order in which returns occur may be disadvantageous to an investor. SORR only occurs when fixed contributions or withdrawals are made from a portfolio. If purely flexible contributions or withdrawals are made from a portfolio, then the sequence of those returns has no impact on the final balance.

As an illustration, let's assume that a retiree starts with a portfolio worth $1,000,000 and withdraws a fixed $50,000 from the portfolio at the end of every year (for the sake of simplicity, we'll ignore inflation and taxes). The portfolio goes on to return -10% each year for three years, then it returns +20% each year for the next three years. The final portfolio balance would be $843,568. If the returns were reversed (i.e., +20% for each of the first three years and -10% returns in each of the following three years), the final portfolio balance would be $991,534, a substantially better outcome. Note that in both instances, the average annualized returns (i.e., compounded) were identical. The disparity in the final portfolio balances in these examples is wholly due to sequence of returns risk.

Alternatively, a retiree can employ a purely flexible withdrawal method, such as withdrawing a fixed percentage of the portfolio each year. Using the same returns as above, if the retiree had withdrawn 5% of the portfolio's balance at the end of each year, the final portfolio balance at the end of the six years would be $926,004. And, importantly, this would be the final portfolio balance no matter how the portfolio's returns were arranged. This is due to the commutative property of multiplication; the product created by multiplying any set of numbers together remains the same no matter how the numbers are arranged.

However, purely flexible withdrawal methods like the one above have a major drawback: they 'move' the risk of a poor sequence of returns from the portfolio to the withdrawals. In the flexible scenario above, if the three years of good returns come first, the total amount withdrawn over the six years would be $378,785. In the other scenario, the total amount withdrawn would be $245,362. By comparison, $300,000 was withdrawn in both of the 'fixed' withdrawal scenarios.

But it is not only retirees making portfolio withdrawals who are impacted by returns risk and sequence of returns risk. Those still accumulating are exposed to both of these risks as well. I briefly discussed this in a previous post regarding the criticality of the decade before you retire, but I will cover the issue at greater length below.

Carcross Desert, Yukon Territory, Canada

Interplay Between These Risks

To demonstrate that both returns risk and sequence of returns risk impact all investors, below are examples of how both impacted those accumulating assets in their portfolio and those making withdrawals from their portfolio.

Consider an investor who started with a $1,000 portfolio and contributed an additional $1,000 every year for 30 years, beginning in 1940, and invested the funds in a portfolio of 60% U.S. total stock market and 40% U.S. total bond market. The average inflation-adjusted return for this portfolio over this period was 4.87%, so we would expect the investor to end the 30 year period with $69,139. But the investor would have actually ended the period with $81,903. In this instance, the accumulating investor benefited significantly from a favorable sequence of returns. Compare this to an identical investor who started accumulated from 1980 to 2009. Even though the real return over this period was 6.64%, meaning that the investor's expected portfolio value would have been expected to be $95,438 in 2009, the investor would have actually had $89,002. This means that this investor would have been somewhat harmed by sequence of returns risk.

To examine the impact of returns risk and sequence of returns risk on those withdrawing from their portfolio, let's examine the safe withdrawal rate for various portfolios. Since 1970, the 30 year safe withdrawal rate for a portfolio of 60% U.S. total stocks and 40% U.S. total bonds was 4.4%. The average real return for this portfolio was 5.6%. Many would expect a portfolio with a lower average real return to have a lower safe withdrawal rate, but this is not necessarily the case. For instance, over the same period, the Permanent Portfolio, which is comprised of 25% each in U.S. total stocks, long-term Treasury bonds, cash, and gold, had an average real return of 4.5% real, but its 30 year safe withdrawal rate was 5.4%. Even though its average real return was 20% lower than that of the 60/40 portfolio, its safe withdrawal rate was 23% higher! The reason for this counter-intuitive result is that the Permanent Portfolio was not as exposed to sequence of returns risk as the 60/40 portfolio was.

While there are no direct measures of sequence of returns risk, start-date sensitivity (SDS) is a good indirect measure of this risk. This metric is calculated by comparing the prior 10 years' returns of an asset class or portfolio to the forward 10 years' return over a long period of time, and the large differences in these returns will produce a high SDS. Since 1970, the 60/40 portfolio above has had an SDS of 23.8%. By comparison, the Permanent Portfolio's SDS was only 8.5%. So, even though the Permanent Portfolio had lower average returns, its far lower exposure to sequence of returns risk produced a substantially higher safe withdrawal rate.

This is not meant to be an endorsement of the Permanent Portfolio but rather an illustration that the income retirees can withdraw from their portfolio is driven at least as much by the sequence of their portfolio's returns as their average returns. This is why the the 30 year safe withdrawal rate for U.S. retirees only invested in the total stock market and the total bond market has been approximately 4% rather than the nearly 7% average real return that U.S. stocks have produced.

Even though returns risk and sequence of returns risk impact all investors, from my investigations, it appears that returns risk is greater for those still accumulating, while sequence of returns risk is greater for those withdrawing from their portfolio. The above example demonstrates this for those in the withdrawal phase, so let's look at an example of this for those in the accumulation phase. Since 1970, the safe saving rate (i.e., the lowest saving rate that would have always achieved a target portfolio value in a set number of years) for an investor earning $60,000 annually, targeting a $500,000 portfolio in 25 years, and invested in a 60/40 portfolio was 19%. This means that in all 25 year periods since 1970, this investor would have accumulated at least $500,000, in inflation-adjusted dollars, with a 19% savings rate. By comparison, had the investor been invested in the Permanent Portfolio instead, the safe saving rate would been 22%. The Permanent Portfolio's lower sequence of returns risk was more than offset by the higher average returns of the 60/40 portfolio.

That sequence of returns risk is so impactful to those in the withdrawal phase is very often lost in discussions of what the future safe withdrawal rate will be. I've read countless interchanges about this topic, and those forecasting lower safe withdrawal rates in the future than what have been seen in the past often believe that lower expected average returns will be the driving cause. There is some historic evidence of this assertion, but it ignores the reality that sequence of returns risk has historically mattered even more than returns risk.

The chart below, created by Boglehead's poster Siamond, demonstrates this point very well. The blue dots show the average inflation-adjusted returns (i.e., compounded annual growth rate or CAGR) of a 60/40 U.S. portfolio, and the pink dots show the 30 year safe withdrawal rate for each starting year.

Observe how often the safe withdrawal rate was substantially higher than the average return. For 30 year retirements starting in 1952, the average return was 3.8%, but the safe withdrawal rate was 7.4%! And while the average return over the 30 year period from 1966-1995 was higher at 4.5%, the safe withdrawal over that period was much lower at only 4.2%. Historically, when the average return over a 30 year period was around 4%, the corresponding safe withdrawal rate ranged from 4% to nearly 8%. The truly astounding implication of this is that even if we knew what the average returns over the next 30 years would be, due to sequence of returns risk, we still couldn't generate a good prediction of what the safe withdrawal rate would be!

Final Thoughts

While investors tend to focus on average returns, the above scenarios illustrate that both the average returns investors experience (i.e., returns risk) over a given period of time and the ordering of those returns (i.e., sequence of returns risk) have a significant impact on their portfolios and/or their retirement income.

Data over the last 50+ years suggest that, between these two risks, returns risk is of greater importance to those still accumulating assets for their portfolio, and sequence of returns risk is of greater importance to those making withdrawals from their portfolio. And there has been substantial variance across portfolios in their returns risk and sequence of returns risk. A potential takeaway from this is that an investor might wish to have one portfolio in the accumulation phase but a very different portfolio in the withdrawal phase.

I hope that this will help readers to better understand returns risk, sequence of returns risk, the interplay between these risks, and their real world implications.

bottom of page