**Update Dec 21, 2016: Check our new series on safe withdrawal rates: **

- The Ultimate Guide to Safe Withdrawal Rates – Part 1: Introduction
- The Ultimate Guide to Safe Withdrawal Rates – Part 2: Capital Preservation vs. Capital Depletion
- The Ultimate Guide to Safe Withdrawal Rates – Part 3: Equity Valuation

The sustainability of the 4% withdrawal rule depends on returns we can expect going forward. Backward looking simulations may be quite entertaining but they still require the usual disclaimer “Past returns are no guarantee of future returns.” How comfortable can we be assuming today’s retirees will enjoy the same average returns as in the last 145 years, the time span used by the cFIREsim site? Or the Trinity study, which uses data since 1926?

Nobody ever expects low equity returns (just like in Monty Python, nobody expects the Spanish Inquisition). But there are some signs that equity expected returns may be lower than the average we observed in the last few decades (and bond returns too, more on that in a future post). This is the first part in a multi-part series on the (so-called) safe withdrawal rate, dealing with equity expected returns.

## Part 1: Equity Expected Returns

The S&P500 yielded around 8.60% in nominal terms (dividends reinvested) and 6.57% after inflation in the time span Jan-1871 to Mar-2016. Not surprisingly then, the 4% rule works on average in portfolios with a high equity weight. Moreover, the 2.5% gap between the withdrawal rate and the average real return acted as enough of a cushion to weather the market volatility. But even with this cushion, there were some pretty tense and scary periods, for example, 1965-1982, and 2000-2013. We want to make the case that in the future we may have much less of a cushion, or maybe none at all.

### The Shiller CAPE ratio: a valuation signal for equity returns

Economics Nobel Prize Winner Robert Shiller posts his data on the CAPE (Cyclically Adjusted Price Earnings) Ratio. He found that if you divide today’s stock price not by *current* earnings (the usual PE ratio), but by a 10-year rolling *average* of inflation-adjusted earnings to smooth out business cycle fluctuations you get a more reliable measure of how over/undervalued the market is.

We started with Shiller’s data and added some of our own calculations:

- We fill in the first 10 years of data (1871-1880) with expanding window average earnings. Shiller starts his computations only in 1881
- We fill in the earnings data all the way to Q1 of 2016, with data on quarterly earnings from S&P
- Instead of a CAPE ratio we compute the inverse, i.e., the earnings yield (average real earnings divided by price). So, we calculate a CAEY, Cyclically Adjusted Earnings Yield, which tells us how much in average real earnings you received over the last 10 years per $100 invested today

In the chart below we plot the current CAEY versus the 10-year forward real (CPI-adjusted ) annualized equity return. Thus, the last observation is the CAEY in March 2006 (x-axis) and the March 2006 to March 2016 annualized real return of the S&P500 index (y-axis). We were really amazed how something as random as future stock returns can have such a strong positive correlation (about +0.59) with something observable today.

Also notice that at the 3/31/2016 earnings yield of just under 4%, the linear regression line of the 10 year forward returns is below the 4% mark, somewhere around 3.0-3.5%. True, there were plenty of past observations where the earnings yield was around 4% and subsequently, the equity market returned an annualized 6%. But the 10-year realized return also looked a lot worse, even negative, on many occasions when the earnings yield was this low.

If the scatter plot is a bit too noisy and messy we can also look at how the future 10-year returns turned out when the earnings yield fell into specific earnings yield buckets, see chart below. Currently, we’re in the 3-4% bucket in earnings yield. Equity returns in the past have ranged from about -2% to about +6.5%, with a mean of +3.5% when the earnings yield was this low. The 6.5% mean return assumption as in the overall mean of the 1871-2016 era you would be using in your cFIRESim is not impossible, but it would be an extreme upper outlier, given today’s market valuation. Crossing your fingers and hoping for a record run in equity returns is not a good retirement strategy!

Not surprisingly then, the failure probabilities increase significantly if we go from the unconditional failure probabilities to those conditional on observing low earnings yield in year 1. In the chart below we contrast the failure probabilities at a 30, 40, and 50-year horizon. This is for a 4% withdrawal rate and equity shares of 100%, 80% and 60%, annual fee 0.05%, according to cFIREsim. We already saw from our previous post that failure probabilities rise when going to 40 and 50-year horizons. Nothing new there, these are the three lines at the bottom. But if we plot the failure probabilities for the years when the CAEY was below 5% (currently it’s just below 4%), even the 30-year horizon failure probabilities are elevated. In fact, one can show at the 30-year horizon, *every single failure* has occurred when the CAEY was below 5% in the initial year. Thus, the failure probabilities are significantly higher, about 17-25% after 30 years. How can the probability jump this high? Very simple: only one in 8 retirement cohorts had a CAEY below 5%. Since all failures occur in cohorts with this low CAEY, the conditional probability has to be eight times as high as the unconditional, hence, roughly 17-25% compared to the original (rounded) 2-3%. Ouch! But it gets even worse, the failure probability goes up to 42%-83% after 50 years. Suddenly, the 4% safe withdrawal rate is not so safe anymore.

The Trinity Study, Kitces & Co. all look at the unconditional probabilities only, thus conveniently ignoring the currently unusually low earnings yield. That’s a little bit like telling you that you have a low probability of being stuck in traffic by averaging traffic jam probabilities over the entire 24 hours of the day. That number, of course, is pretty useless if you already know that you’ll be driving at 5pm.

Well, to give credit to Michael Kitces, he did look at CAPE-based equity valuations and medium-term equity returns and proposed basing withdrawal rates on equity earnings regimes. Not many details on how that’s supposed to be done in practice. But in the lengthy post, he rightly states that the valuation-driven lower returns will likely not last for the entire 30 years. Even if returns will likely bounce back after 10 or 15 years, you cannot ignore the temporarily lower returns due to the “sequence or return risk.” But one can afford to lower the SWR by much less than the expected return shortfall, which is very much in line with the cFIREsim default assumptions of a 0.5% reduction of the SWR for each 1% reduction in the earnings yield.

Then what expected equity returns do we assume? To be sure, some people who want to grab attention and headlines use the low CAEY (i.e. high CAPE ratio) as the harbinger of an equity market crash. That’s scaremongering. Unless the CAEY falls into the low 3% or even below 3%, we should not fear doom and gloom, at least not from this valuation metric. We personally assume a 3.5% real equity expected return, a full 3 percentage point below the long-term average. To give us a bit of a cushion we target a 2.5%-3% initial withdrawal rate. That’s for a 100% equity portfolio. For investors turned off by too much equity volatility who want to mix in a substantial share of bonds, the portfolio expected return will be substantially lower than 3.5%, due to extremely low bond yields. We will write more about that in a future post, in Part 2 of this series!

### Stay tuned for future parts of this series!

Intro: Pros and cons of different withdrawal rate rules

**Part 1: Equity expected returns**

Part 3: The small-sample problem in historical simulations

Great post! I have been planning my own retirement (http://www.smellingfreedom.com/2016/04/financial-independence-am-i-there-yet/)

and am targeting an equity/bond split of 70/30. I absolutely do not feel comfortable basing my retirement on a 4% withdrawal rate and so far have assumed a 3% withdrawal and 6% growth. I will run my model using your numbers to see if my numbers pass the test.

I am also incorporating different passive income streams into my plan (freelance work, rental income) and as time goes by I will be able to cover the great majority of my costs from this income, while my withdrawals will go down to the 1% range. I am hoping that this will give me the margin of safety I need to guarantee 40 to 50 years of retirement income.

Agree, it’s important to have some other uncorrelated income streams, for example rental income. Again, equity withdrawals should accommodate 4% on average, just not right now. So we are planning only 2.5-3% in the beginning