# Sequence of Returns Risk: Decomposing Real Returns into Nominal Returns and Inflation to Find the Real Villain

The story of Sequence of Returns Risk is, at this point, well-trod. Looking at the average return over a period of time doesn’t tell you much about how good or bad a retirement during that period is.

In his exhaustive (and sometimes exhausting!) The Ultimate Guide to Safe Withdrawal Rates, EarlyRetirementNow devotes two installments to sequence of returns risk.

He gives us this table of three examples, showing us that average 30-year returns don’t tell us much about Safe Withdrawal Rates over that same period.

So far it’s the same old story. But then he does something cool and goes a step further. Instead of just examples he performs two regressions.

First he does a univariate regression on 30-year returns to show that the R² is only 31%. Then he breaks the 30-year returns into 5-year return chunks and performs a multivariate regression and find that this has an R² of 95%.

Precisely what I mean by SRR matters more than average returns: 31% of the fit is explained by the average return, an additional 64% is explained by the sequence of returns!

# Moving away from real returns

In the analysis above EarlyRetirementNow used real returns, which I think gives misleading results. It is misleading because

1. We know that equities aren’t correlated with inflation. So mixing up two uncorrelated things muddies the waters.
2. Nobody thinks in terms of real returns. Last year equities dropped -19% and inflation was 2% but did anyone call it a “real return” correction? Nope.
3. We don’t have any idea how much of the result is caused by equity returns and how much is controlled by inflation.

So let’s rerun an EarlyReturnNow-style multivariate analysis on Sequence of Returns Risk…but this time we’re going to separate out nominal equity returns and inflation into separate components.

## 30-year nominal returns

First let’s take a look at just doing a univariate regression on 30-year average nominal returns. There’s no surprise that this has even less explanatory power than real returns. But it is a surprise just how useless it is with an R² of just 8.7%. In other words, 91% of the explanation comes from something other than the 30-year average nominal return.

## 5-year chunks of nominal returns

This is what EarlyRetirementNow did, except instead of looking at real returns we’re looking at nominal returns. The first thing we notice is that while EarlyRetirementNow found an R² of 95.86%, our R² has dropped way down to 59.8%.

In other words over 40% of the Safe Withdrawal Rate is not explained by Sequence of Returns Risk, when we look at nominal equity returns.

## 3-year chunks of nominal returns

But why are we looking at 5-year chunks? Why not 7-year chunks or 3-year chunks? Or 1-year chunks?

We already know that a 30-year chunk (i.e. the whole thing) doesn’t tell us much. So we should expect that longer chunks are less explanatory and shorter chunks are more explanatory. And that’s what we see as we try various chunk sizes.

First notice, the massive jump — from 8.7% to 42.2% — just by splitting things up from a single 30-year period into two 15-year periods. But there’s also diminishing returns and it appears that we max out with an R² of 66%.

In other words, sequence of returns only explains 2/3rds of your Safe Withdrawal Rate.

## The missing variable: inflation

Remember, up until now we have ignored inflation. It isn’t exactly surprising that we aren’t able to fully explain Safe Withdrawal Rates without it. But now we have a better grasp of how important inflation is — and how much we should really worry about “a big stock crash” in the first few years of our retirement.

(To make the implicit explicit: I think that people over-worry about stock market crashes affecting their retirement and under-worry about inflation affecting their retirement.)

Let’s go back to 5-year chunks but this time throw in inflation. So we’re looking the the average return over 5-years and, separately, the average inflation over 5-years.

Now our R² has jumped from 60% to 90%. But also note the coefficients in the table below. We start with an intercept of 1.1%. Equity returns over the first five years have a coefficient of 0.258 and inflation over the first five years has a negative coefficient of -0.244.

## Diminishing returns

We all intuitively believe that the returns early in retirement are more important than the returns later in retirement. We can try to understand that dynamic better by looking at the impact of the first 2-years, the first 4-years, the first 6-years, etc on the R².

We can see that we quickly get to a point of diminishing returns. By Year 6 we’ve got most the information out of returns that we will. By Year 10 there’s really not much more to learn from returns; we’ve sucked out all the information there is and the next 20 years won’t tell us much more.

If we look at the same thing for but inflation we see a different picture. The first 2-, 4-, and even 6-years of inflation don’t matter that much. It takes until 12-years to have enough inflation information to understand its impact on Safe Withdrawal Rates. And we never plateau in quite the same was as we did with equity returns.

By Year 10 our equity returns R² has already reached 95% of final value. By contract, by Year 10 our inflation R² has only reached 95% of its final value in Year 22.

Inflation takes longer to make an impact but its has a long tail. Inflation over the first 12 years of your retirement has the same R² as equity returns over the first 2 years…but which one do you think retirees worry more about? A stock crash in the first 2 years after retiring? Or inflation over almost a decade?

And inflation over the full 30-years has almost the same R² as equity returns in the first four years of retirement.

Retirees aren’t crazy to worry about a big crash in the first 4- or 5-years of retirement. But they probably shouldn’t worry about it as much as they do, in light of the above. Instead, spare some worry for a long period of higher than normal inflation.

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