A controversial topic for today. Or maybe not controversial at all – we’ll see. This topic has been on my mind for a long time and I’ve mentioned this in passing in some of my posts over the last few months: The stock market isn’t really precisely a random walk! And just for the record: I am not saying that I am in possession of any kind of formula to perfectly predict tomorrow’s equity performance. My guess is just as good as anyone else’s. On a scale from 0 to 10, where 10 is a Random Walk and 0 is perfectly deterministic and forecastable, I’d still call the stock market a 9.9. But there are few peculiar features in the last 140+ years of equity returns that are clearly at odds with the Random Walk Hypothesis. So, let’s look at some of the small quirks I found and what they mean for us in the Personal Finance community…
Observation 1: “Simple Math” endogenous retirement timing lowers the sustainable Safe Withdrawal Rate
As we showed in Part 22 of the Safe Withdrawal Series, when retirees use the “Simple Math” method, i.e., they save until they reach a certain savings target (e.g., 25x annual expenditures) then the sustainable Safe Withdrawal Rates tend to be lower than for retirees who pick a retirement date at random. Here’s a chart from that post:
The top panel is the cumulative real total return of the S&P500. The red dots indicate when cohorts reached their savings goal. On the bottom chart is the sustainable withdrawal rate for each starting date, again with red dots indicating the retirement dates. Notice something? Everybody retires during bull markets and nobody retires at the bottom of the notable bear markets (1932, 1975, 1982, 2002/3, 2009). Which in turn means that if you retire in response to reaching a savings goal you’ll experience a noticeably lower safe withdrawal rate than those who retired without using the “Simple Math” timing.
Well, that’s in complete contradiction to the Random Walk Hypothesis, because with a true “memory-free” stochastic process, it doesn’t matter one little whiff how many months of above-average returns you might have experienced right before retirement. A Random Walk has no memory and thus random draws in the future should not be impacted by those in the past. It’s like in the casino: it doesn’t matter how many times red showed up for the upcoming roll of the roulette wheel. But the stock market appears to display some small degree of “memory” because as the bottom chart shows, the endogenous retirement decision reduces our SWRs.
Observation 2: The real cumulative equity return “hugs” the exponential trend line a bit “too closely”
Side Note: For the mathematically inclined, because of positive returns and compounding, the index level itself can’t be a random walk. Rather the logarithm of the S&P500 Real Total Return would be a random walk with drift. Drift, because stocks go up on average, and we use the logarithm of the Total Return to properly allow for compounding.
Let’s look at the actual returns (red line) the exponential trend line in black (here a straight line due to the log-scale vertical axis) and add 100 draws from simulated random walks with the same annualized risk as the S&P (blue lines). The random walks are rescaled so that they all have the same overall average return over the last 147 years to make the paths easier to compare.
Notice something peculiar? The red line tracks its trend line much more closely than the typical random walk. Random walks can have wildly different growth rates during any of their 30 or 40-year or even 70-year subperiods, while the red line is tracking its trend closely with a few wiggles around the big macroeconomic events (WW1, Great Depression, WW2, 1973-1982, 2001, 2008/9). It’s almost like there is a rubber band that pulls the red line back to the black trend line. And it should! Equity returns don’t rain down from heaven. They are not pulled from a computer random number generator.
Equity returns are tied to macroeconomic fundamentals!
Let’s look at the table from our equity return history post last year. S&P500 Returns largely came from two components: GDP growth and Dividends. The noise is created because earnings sometimes grow faster/slower than GDP and multiple expansion/contraction. Obviously, over really short horizons, stocks and GDP will deviate wildly. Peak to trough, the U.S. GDP dropped by less than one percent in 2001 but the stock market dropped by over 50%. But over long horizons, everything converges back to economic fundamentals. It’s what we call mean reversion and mean reversion is not something you should see in a true Random Walk!
Observation 3: Consecutive 15-year window returns are extremely negatively correlated
Here’s another observation that doesn’t quite jive with the Random Walk hypothesis: If real equity returns were above average during one 15-year window then they tend to be below average over the subsequent 15 years. Don’t believe me? Check out this chart below. The red line is the trailing 15-year average annualized S&P500 returns (dividends reinvested, CPI-adjusted) and the blue line is the return over the next 15-year window (and thus the red line is the blue line shifted by 15 years to the right). They seem to be negatively correlated! On the bottom half is a scatterplot with the same data and the correlation is a staggering -0.64.
How is that possible? Of course, it’s related to Observation 2 because if over long horizons (say 30 years, i.e., multiple business cycles) equity returns have to revert to some macroeconomically justified average return, then 15 years of substantially above average returns make it more likely to have 15 years of below average returns after that.
The correlation becomes even more negative when looking at the 1926-2017 time frame (recall that a lot of the other retirement withdrawal researchers, e.g., Trinity, Bengen, use returns only after 1926), see chart below:
Such a strong negative correlation is not what you’d normally find with truly random draws. For the math geeks, I simulated several thousand true random walk processes and only less than 2% of them displayed such a negative correlation of consecutive 15Y windows. It would have to be a pretty large coincidence that the observed equity returns came from a mathematically clean Random Walk! And I don’t believe in coincidences!
So, what does this all mean for Personal Finance? Here are some implications for us practitioners:
Implication 1: Savers shouldn’t stress out over corrections
When you talk to younger folks who are just starting out in their careers and ask them what’s holding them back from investing in stocks they’ll most likely say the fear of an equity market correction. But that fear is completely misplaced if you are still years away from retirement! In fact, listen to the two consecutive ChooseFI podcasts, Episode 34 (Jim Collins) and Episode 35 (yours truly, Big ERN) and you’ll find one almost identical quote, which I could paraphrase as:
“The best thing that can happen to young savers today is a stock market correction”
That quote, I promise, was not coordinated because the episodes are obviously pre-recorded and I had no idea what Jim Collins was going to say in the other recording. And this statement makes sense only because the stock market doesn’t follow a random walk. Remember, with a random walk, the outlook for future returns is independent of past returns. But the cumulative return chart shows that after a correction, the market would not just recover with some lame long-term average return (6.7% p.a. real) but with strong double-digit returns (see the 1980s, 1990s, 2010s!). God Bless Mean Reversion!
So, if you are just starting out saving for retirement and there is indeed a correction, don’t panic, enjoy the ride and pick up some cheap discounted stocks along the way. Make Sequence of Return Risk work in your favor!
Implication 2: Today’s retirees should be concerned about high equity valuations
Well, unfortunately, the flip side of Implication 1 is that the non-random-walk feature also bites you every once in a while. That “rubber band” behavior also works in reverse when equities are expensive (i.e., today!) and we should probably scale back our equity return expectations just a little bit. In other words, we should all recognize the logical inconsistency in the two statements below:
“Retirees have nothing to worry about; the stock market follows a random walk with 8% annual returns and there is no mean reversion after a long bull market.”
“Young savers have nothing to worry about because the stock market is not really a random walk and tends to mean revert after a correction.”
Both statements cannot be true at the same time but you’ll be surprised how often people in the personal finance community follow this wishful thinking of “Random Walk to the rescue” when equities are expensive and “Mean Reversion to the rescue” when equities are cheap. I wouldn’t go so far and predict 4% (nominal!) returns for equities like Jack Bogle did a while ago but I would certainly give that 8-10% equity return that some people are still using a bit of a “haircut!”
Implication 3: Beware of Monte-Carlo Simulations
I have talked about this issue before, most recently in the SWR Series, Part 20. I prefer to do my simulations with historical data (despite some of the disadvantages) because Monte Carlo cannot properly account for the mean reversion properties of equity returns. Modeling both equity and bond returns as Random Walks misses some of the important interactions between stocks and bonds (changing correlations) and the equity “rubber band.” For example, I showed in the SWR Series (Part 20) that the Kitces/Pfau glidepaths that behaved optimally in a Monte Carlo simulation are some of the worst performers when using historical returns.
Implication 4: Being too passive is going to cost you!
OK, maybe I haven’t said anything controversial enough yet, so let me drop a real bombshell now. The non-Random-Walk nature of equity returns means that there is a case for being more active with our financial decisions. More active than what the bogleheads prescribe, more active than what Jim Collins proposes in The Simple Path to Wealth, and more active than what most people in our personal finance community want to deal with. I’m not saying that anyone has to do any of this but here’s some food for thought if you are interested (if you may remember, these are related to items 3-5 in our post about active vs. passive investing):
- First, adjusting the safe withdrawal rate in response to equity valuations seems to be a way to somewhat soften the effect of Sequence Risk, see Part 18 of the SWR series. When stocks are expensive, for example, because the past 15Y return was high and the next 15Y return expectations are low, then the Safe Withdrawal Rate should be lower. But the opposite is true as well. After a big drop in stocks, you can probably raise the withdrawal rate to significantly above 4%!
- Second, glidepaths that increase the equity weight help with Sequence Risk, see Part 19 and Part 20 of the SWR series due to the negative correlation between the consecutive 15-year return windows.
- Third, since stocks don’t follow a precise Random Walk there is room for actively/tactically timing the stock exposure to manage risk. There is a huge benefit to being able to avoid some of the significant drawdowns like 2001 or 2008/9. Of course, nobody will ever be able to precisely time the market and sell equities at the peak and buy them back at the bottom. But even being able to avoid a small fraction of the drawdown can make the difference between a scary shaky retirement and a safe retirement. How do we do this? I’m not going to tell you today because we’re pushing 2,000 words already. But I’m working on a post, potentially a two-part series, to detail some of my thoughts on how to do this. Stay tuned!