I recently saw a Twitter thread discussing the best rate of stock returns to use for an early retirement projection. Would-be early retirees often rely on historical rates of return to estimate whether a portfolio can support retirement spending for decades into the future. Most people on the Twitter thread suggested using average or annualized average returns based on the entire history of the stock market, which equates to between 8 and 10% annual returns. Others suggested using 7% returns to make sure the projection was sufficiently conservative.
I pointed out that most recent return forecasts are calling for an even lower 4 to 6% annual return for the next 10 to 15 years, as I’ve summarized in my annual review of such forecasts. In response, someone wanted to see an early retirement projection using a 5% return in the first 10 years and the historical average of 9% for the remaining years. I thought that sounded like a great exercise for this post and a fitting sequel to some projections that I recently presented based on my retirement plan. These sorts of long-term retirement projections are a great way to illustrate and discuss one of the major risks associated with early retirement investing and spending: sequence of returns risk.
Constant Growth Projections
First, let’s start with the requested projection. I calculated the constant growth of a $1,000,000 dollar portfolio with an inflation-adjusted 4% annual withdrawal rate for a somewhat arbitrary 35-year retirement period. By 4% annual withdrawal, I mean that our hypothetical early retiree would withdraw $40,000 annually in “real” terms (increased each year by the rate of inflation). I assumed a 5% return for the first 10 years and then a 9% return for the following 25 years. I ran this projection using both 2% and 4% inflation rates for the adjustment to the annual withdrawal, to see how inflation impacts the portfolio over time. I also compared these projections to a constant 9% return rate that some people suggested in the Twitter thread.
Here’s a table showing the scenarios and some key results for each.
| Scenario | 10-Year Return | 25-Year Return | Inflation | Nominal CAGR | End Value | Lowest Value | Worst Draw Down |
| Constant 1 | 5% | 9% | 2% | 7.8% | $ 4,277,985 | $ 1,009,200 | None |
| Constant 1 | 5% | 9% | 4% | 7.8% | $ 1,376,979 | $ 1,008,400 | None |
| Constant 2 | 9% | 9% | 2% | 9.0% | $ 9,681,191 | $ 1,049,200 | None |
| Constant 2 | 9% | 9% | 4% | 9.0% | $ 6,712,693 | $ 1,048,400 | None |
“CAGR” is compound annualized growth rate (without withdrawals included). We can see that relatively poor 5% returns in the next 10 years would drag down the overall CAGR by more than one percent, as compared to a constant 9% growth rate. Here’s a graph of these four constant growth scenarios.
Nothing too surprising here. For growing money, a 9% growth rate is clearly better than a 5% growth rate in the first 10 years. And a lower inflation rate is better than a higher inflation rate, because less money is withdrawn from the portfolio each year to maintain the same purchasing power. On the downside, the worst-performing projection, using lower returns and higher inflation, results in almost no growth of the portfolio. On the upside, none of the scenarios run out of money by the end of the projection. So, you might reasonably conclude that it’s safe to retire for 35 years with a million dollars saved up and a plan to spend $40,000 in real terms each year. The expected poor performance of the stock market in the next decade seems like nothing much to worry about.
Variable Growth Projections
Someone else chimed in on Twitter that the average return is not as important as the “sequence of returns”. This is a great observation. I’ve recently devoted considerable blog space to evaluating exactly these type of sequence-of-return impacts to my portfolio. “Sequence of returns” is important because the stock market (or any market) never grows at a steady rate as assumed in the above “constant growth” projections. In fact, most experienced investors are all too familiar with the wild up and down gyrations of the stock market from year to year. It turns out that when you start to withdraw money from your portfolio, the sequence of returns you experience substantially impacts how much your portfolio grows (or shrinks) over time.
So, how would these projections change, if we instead used historical sequences of returns? Instead of assuming constant growth, we could use actual historical sequences of returns that generated about 5% annualized growth for 10 years and other sequences that generated about 9% annualized growth for 25 years. Further, we could splice these 5% and 9%-growth sequences together to generate an overall retirement sequence of 35 years. How likely is it that a bad sequence of returns, particularly in the first 10 years, would sink this relatively safe-sounding retirement plan?
When I looked in the Robert Shiller stock data going back to 1871, I found seven sequences of about 5% annualized returns over a 10-year time span. In contrast, I found many sequences generating about 9% annualized returns over 25 years. (This tells us that a 10-year period of only 5% annualized returns is a fairly rare event in stock market history, which is a pretty useful discovery by itself.) So, I picked seven of the 9% return sequences, essentially at random, and spliced them to the ends of the seven available 5% return sequences.
Here’s a similar data table for these variable growth scenarios. Remember that each scenario involves a different sequence of returns. Some start out of the gate fast and run out of steam toward the end, some are the opposite, and all have unique patterns of up and downs.
| Scenario | 10-Year Return | 25-Year Return | Inflation | Nominal CAGR | End Value | Lowest Value | Worst Draw Down |
| Variable 1 | 5% | 9% | 2% | 7.7% | $ 4,497,707 | $ 822,306 | 18% |
| Variable 1 | 5% | 9% | 4% | 7.7% | $ 1,716,422 | $ 819,995 | 18% |
| Variable 2 | 5% | 9% | 2% | 6.6% | $ 1,117,368 | $ 686,421 | 31% |
| Variable 2 | 5% | 9% | 4% | 6.6% | $ (1,856,317) | $ (1,856,317) | 100% |
| Variable 3 | 5% | 9% | 2% | 8.6% | $ 6,654,710 | $ 690,212 | 31% |
| Variable 3 | 5% | 9% | 4% | 8.6% | $ 3,812,307 | $ 687,958 | 31% |
| Variable 4 | 5% | 9% | 2% | 7.4% | $ 5,057,346 | $ 1,159,429 | None |
| Variable 4 | 5% | 9% | 4% | 7.4% | $ 2,700,568 | $ 1,099,505 | None |
| Variable 5 | 5% | 9% | 2% | 8.1% | $ 3,855,116 | $ 874,304 | 13% |
| Variable 5 | 5% | 9% | 4% | 8.1% | $ 266,051 | $ 266,051 | 73% |
| Variable 6 | 5% | 9% | 2% | 9.3% | $ 12,918,115 | $ 1,044,030 | None |
| Variable 6 | 5% | 9% | 4% | 9.3% | $ 10,368,607 | $ 1,014,055 | None |
| Variable 7 | 5% | 9% | 2% | 7.9% | $ 3,980,635 | $ 595,228 | 40% |
| Variable 7 | 5% | 9% | 4% | 7.9% | $ 1,185,928 | $ 580,221 | 42% |
And here’s two graphs of these same scenarios. The upper graph is for the 2% inflation scenarios and the lower graph is for the 4% inflation scenarios.
That’s a lot of information, so I’ll highlight a few things. First, from the table we can see that different sequences of return yield very different CAGR values, ranging from almost as low as 6.5% to over 9%. Clearly, a 5% annualized return in your first 10 years doesn’t always generate a horrible outcome. It’s also interesting that the draw downs of the portfolios vary widely. Some scenarios have almost no draw downs at all. But in one scenario you’d suffer through a stomach-turning 73% decline in your starting portfolio value. And in one extreme scenario, the portfolio runs completely out of money because of a particularly bad sequence of returns. Further, as we saw with the constant growth scenarios, higher inflation substantially erodes portfolio longevity. In the 4% inflation graph, one scenario ran out of money around year 28, another scenario is close to running out of money by year 35, and two other scenarios have barely grown at all in 35 years.
Conclusions
Constant growth calculations are simple to understand and conduct, but they are often misleading. If you stopped with just a few constant growth calculations, you might assume there’s almost no way you could run out of money in retirement. But this entirely ignores how sequence of returns might drive or impede your retirement success.
The other important takeaway is that we need to think of retirement plans in terms of probabilities. Most people hate making decisions based on probabilities, except for gamblers, who apparently have great fun with probabilistic decisions. Most people want a simple yes or no answer. Will my retirement “fail” or will it “succeed”? Unfortunately, the real world and the stock market rarely offers simple black and white decisions. Using our example million dollar portfolio, all we can say is that it seems unlikely to fail in the next 35 years. But there’s an outside chance that a particularly poor sequence of returns coupled with high inflation would cause a serious problem. And there’s a somewhat greater chance that this example portfolio would support a reasonable level of spending but hardly grow at all.
So, would you decide to retire today, if you had a million-dollar stock portfolio and could live on an inflation-adjusted $40,000 per year? Ultimately, this is a personal choice about how well you think you can live and sleep with these sorts of low failure probabilities. As I’ve discussed extensively at Mindfully Investing, mindfulness can help reduce our worries about bad outcomes that are unlikely. From a mindful perspective, this example retirement plan seems reasonable and prudent to me. And it’s actually pretty similar to the failure probabilities associated with my own retirement plan. If you find this example unacceptably scary, you might want to read some more about the concept of mindful investing and mindful personal finances here, here, and here.
