Over the last couple of months we’ve spoken a lot about how varying portfolio factors, such as asset allocation and retirement length, affects safe withdrawal rate. And now we have a clearer view of how much we can withdraw from our portfolio without running our of money during retirement.
But we haven’t actually spoken about what market conditions determine safe withdrawal rates. Why are some periods associated with low safe withdrawal rates and others not?
So in this article we deep dive into the mathematics behind safe withdrawal rates to figure out what you want to stock market to be doing while you’re saving money and while you’re withdrawing money in retirement.
Interested in safe withdrawal rates and want to dive into the detail? You can check out the entire series here:
- Part 1: Introduction to Safe Withdrawal Rates
- Part 2: Building and Validating a Data Set
- Part 3: Initial Findings (Domestic Equities and Bonds)
- Part 4: Portfolio Optimisation (International and Domestic Equities and Bonds)
- Part 5: Extending Retirement Length
- Part 6: Targeting a Larger Final Portfolio Balance
- Part 7: Sequence of Returns Risk and Safe Withdrawal Rates
- Part 8: Summary (So Far)
What determines safe withdrawal rates?
The aim of this article is to mathematically test a couple of hypotheses about safe withdrawal rates, then try to confirm the results using our historical simulations.
Put simply, we have two main hypotheses as to what determines safe withdrawal rates:
- Low returns over the total length of retirement. It makes intuitive sense that portfolio returns might affect safe withdrawal rates, as portfolio balance in retirement is the tension between how much the portfolio is accumulating from asset returns and how much we are taking out as living expenses.
- The sequence of returns over the retirement period. The other possible determinant of safe withdrawal rate is the order in which returns occur. In other words, do we achieve high returns when our portfolio balance is high or when it’s still low?
Which is more important: low returns or sequence of returns?
To test our hypotheses, let’s replicate the work of Big ERN. We will use regression to compare the predictive value of low returns and sequence of returns on safe withdrawal rate.
First, let’s conduct a basic univariate linear regression. This simply tests how well the average returns over retirement (the independent variable) predicts a portfolio’s safe withdrawal rate (the dependent variable).
Then we will compare it to a multivariate linear regression that tests how well knowing returns and when they occurred (i.e. at the beginning of retirement vs the end of retirement) predicts a portfolio’s safe withdrawal rate.
The results of the regressions are shown in the tables above. It might look like gibberish to those of us without a statistics background but it’s fairly easy to explain.
According to the top table, average portfolio return explains only 7.2% of the variance in safe withdrawal rate (this is shown by the r-squared value). This tells us that it is not a good predictor of safe withdrawal rates.
The bottom table shows us that knowing the sequence of those returns explains 57.1% of the variance in safe withdrawal rates. Not quite as predictive as what Big ERN found for his data, but clearly sequence of returns is more predictive of safe withdrawal rate than just average portfolio return alone.
It’s also interesting to see how the model weights each five year window. The first window (0-5 Years) is the best predictor of safe withdrawal rate (look at the beta value in the table), and the predictive utility reduces as the windows move further away from the start of retirement.
In other words, returns in the early part of retirement are more important in predicting safe withdrawal rate.
How does sequence of return risk work?
So we now know that sequence of returns is the biggest determinant of safe withdrawal rates but let’s dive deeper into why.
In short, sequence of returns affects withdrawal rates because we are contributing to our portfolio (in the accumulation phase) or withdrawing from our portfolio (in the withdrawal phase). If we did neither of those things and simply held onto existing investments, then the sequence of returns doesn’t matter.
Let’s take three different portfolios that each returned a compounded -13% over two years. We can achieve the same compounded -13% with three different return profiles: (1) -13%, -13% (2) +50%, -50% and (3) -50%, +50%.
As you can see in the table below, for a buy and hold portfolio, the order of returns doesn’t affect the final value. This is because we didn’t contribute or withdraw any money.
On the other hand, let’s look at a portfolio that includes regular contributions or withdrawals. If we use the same returns profile as we used for the buy and hold portfolio, we can see that the final values differ as a function of the sequence of returns. This is despite the overall compounded returns remaining equal at -13%.
So, because we are regularly withdrawing a portion of our retirement portfolio during retirement, the sequence of returns matters. This applies to a portfolio irrespective of whether it is increasing in value or decreasing in value.
When is sequence of returns dangerous?
The more observant amongst us may have noticed something peculiar about the final values in the tables above. That is, the sum of the contributions portfolio and the withdrawals portfolio equal the buy and hold portfolio.
The implication here is that, no matter what sequence of returns does, it will always benefit one cohort and disadvantage another cohort. There is no objectively ‘bad’ sequence of returns; although needless to say it might be bad for you.
Fundamentally, we want highest returns when our balance is highest:
- On the one hand, our balance is highest at the end of the accumulation phase. So we want low returns at the beginning of saving and higher returns at the end of saving (i.e. near to retirement).
- On the other hand, our balance is highest at the beginning of the withdrawal phase. So we want high returns at the beginning of retirement and lower returns at the end of retirement.
Ideally, we’d have a low portfolio returns at the beginning of the accumulation phase and at the end of retirement, and a nice peak in portfolio returns just before and after we retire. In this case we’d benefit twice from sequence of returns.
But it’s also possible is that we get stung twice. A recession hits right before you want to retire and then lasts into the beginning of retirement. Right in the red zone of the chart above.
I suppose that could happen. But if you assume that you retire when you hit your savings number (e.g. 25-30x annual expenses), then you technically shouldn’t be hitting that number in the middle of a recession as your portfolio value is falling. AussieHIFIRE has done some analysis on that here.
More likely is that you ride a bull market into retirement, which helps you hit your retirement number. At some point after that, the market corrects and you experience a period of poor returns at the beginning of retirement. Well, at least you’re only stung once!
Relationship between sequence of returns and withdrawal rates
We’ve covered the theory behind sequence of returns risk, so let’s take a closer look at our historical simulations. It will be interesting to test whether the theory is reflected in the performance of actual retirement portfolios.
We will focus on the relationship between sequence of returns and withdrawal rates (this article is part of our Safe Withdrawal Rates series, after all!). And we will base the following calculations on a 30 year retirement portfolio with a 50/50 Australian and U.S. equities split. We are targeting a final balance of 100% of the initial balance.
Based on the theory we outlined above, we would expect that the average return over the first 10 years of retirement would be associated with a higher safe withdrawal rate. Let’s test this.
The scatterplot above plots average (geometric) return over the first 10 years against safe withdrawal rate. In this chart you can clearly see the positive correlation between safe withdrawal rate and portfolio return over the first 10 years of retirement.
Now let’s figure out which Aussie cohorts in our historical simulations were stung by poor returns in the early part of the retirement. Here we defined poor returns where average return over the first 10 years was 25% lower than the average return over the 30 year retirement.
You can see a few key periods where poor returns are associated with a low safe withdrawal rate. For example, the ‘Long Depression’ of the late 1800s, a couple of stock market panics in the 1900s, the Wall Street Crash of 1929/Great Depression, a flash crash and inflation crisis in the 60s, and the Dot-Com Bubble.
What did we learn?
Most importantly, we learnt that average portfolio returns don’t determine safe withdrawal rate. It’s the sequence of returns that matters.
To put this in context, the asset allocation (sequence of returns) determines the shape of the line on the ‘safe withdrawal rate over time’ chart. Adjusting the retirement length or the final portfolio balance shifts that line up or down on the y-axis.
For those of us still saving for retirement, we need to be careful of sequence of returns risk in both the accumulation and withdrawal phases. The unlucky amongst us will be hit by a couple of period of poor returns at the end of accumulation and then again at the beginning of withdrawal.
There’s not too much we can do about this, unfortunately. One idea is a bond tent, which might be a topic of another post. For now, I recommend that you check out Kitces’ blog on bond tents and Big ERN’s work on equity glidepaths.
Even if you can’t completely avoid sequence of return risk, just remember there’s always somebody on the other side of the equation that will be benefiting from the same market dynamics that punish you 🙂
As always, if you have any questions, comments or feedback, please email me or comment below. I’d love to hear your thoughts.