Tuesday, May 10, 2011

Can We Predict the Sustainable Withdrawal Rate for New Retirees? Supplemental Materials

Let me summarize the purpose of the article, but for those of you who came here to find the accompanying spreadsheet, here it is. The spreadsheet lets you enter values for EY10, DY10, and I (explained more below as well as in the article), and then provides you with the predicted maximum sustainable withdrawal rate for a variety of asset allocations for stocks and bonds. For those of you with more technical inclinations, the estimates provided in the spreadsheet are based on the table of regression coefficients shown in the bottom of this blog entry.

Now, about the article.  It serves as a sequel to “Safe Savings Rates: A New Approach to Retirement Planning over the Lifecycle,” as it uses the basic underlying idea from that article, about how sustainable withdrawal rates relate to whether there was a bull or bear market prior to retirement, to provide some indication about how much a retiree may be able to reasonably expect to withdraw from retirement savings in a sustainable manner.

Retirees now frequently base their retirement decisions on the portfolio success rates found in research such as the Trinity study. Studies such as those are fine for what they accomplish: they show how successful different withdrawal rate strategies were in the historical data. But it must be clear that this is not the information that current and prospective retirees need for making their withdrawal rate decisions. John Bogle makes clear why in his 2009 book, Enough. Though he was speaking about stock returns, the same idea applies to sustainable withdrawal rates, since they are related to the returns of the underlying portfolio of stocks and bonds. He wrote, “My concern is that too many of us make the implicit assumption that stock market history repeats itself when we know, deep down, that the only valid prism through which to view the market’s future is the one that takes into account not history, but the sources of stock returns” (page 102, original emphasis).

Future stock returns (and, therefore, future sustainable withdrawal rates) depend on the sources of returns: dividend income, growth of the underlying earnings, and changes in the valuation multiples placed on those earnings. The historical average success rate for a withdrawal strategy is not the information retirees need to know when determining their forward-looking sustainable withdrawal rate. As Mr. Bogle also writes, “But no, the contribution of dividend yields to returns depends, not on historic norms, but on the dividend yield that actually exists at the time of the projection of future returns. With the dividend yield at 2.3 percent in July 2008, of what use are historical statistics that reflect a dividend yield that averaged 5 percent - more than twice the present yield? (Answer: None.)”

I use this idea to develop a regression model in which I attempt to predict the maximum sustainable withdrawal rates that a person can use with their retirement savings to obtain inflation-adjusted income over a 30-year period, for a 60/40 asset allocation of large-capitalization stocks and 10-year government bonds. The regression model explains and predicts the withdrawal rate including variables for the cyclically-adjusted earnings yield (100 / PE10), a 10-year moving average of the dividend yield, and the nominal bond yield at the retirement date. The regression framework includes variables to predict long-term stock returns, bond returns, and inflation (the components driving a retiree's remaining portfolio balance). It produces estimates that fit the historical data well. The past model fit and the predictions for sustainable 30-year inflation-adjusted withdrawal rates for the years since 1981 can be seen below:

This study suggests that a 4 percent withdrawal rate cannot be considered as safe for U.S. retirees in recent years when the cyclically-adjusted price-earnings ratio has experienced historical highs and the dividend yield has experienced historical lows. What must be clear, as I explain at length in the article, is that the events that have taken place since about 1990 have very little impact on the results of the updated Trinity study, even though it uses data through 2009. What we have experienced in terms of record-high PE10 levels and record-low dividend yields during the past 15 years explain why the model predicts sustainable withdrawal rates falling below 3 percent since 1999, and even below two percent in the years since 2003.

I do have hope that withdrawal rates in recent years will not actually fall this low. In the past 15 years, financial markets have really been sailing in uncharted waters. We have never experienced such high valuation multiples and such low dividend yields. This makes it difficult for the model to make predictions for withdrawal rates, as it must make predictions outside the range of historical observation. Hopefully withdrawal rates will not fall as low as shown in the above figure. But the real lesson here is that even though the Trinity study indicates that a 4% withdrawal rate had a historical 96% success rate for a 50-50 portfolio with inflation-adjustments over 30 years, this success rate does not really apply to the situation in recent years.

This post also covers one other issue that is referenced in the paper. With regard to fees, with a 60/40 asset allocation, a one percent account fee charged at the end of each year would, an average, result in a 0.63 percentage point reduction in the MWR, which represents an average reduction in retiree annual spending power of 11 percent (compared to the MWR) from her wealth portfolio. The next two figures show the outcomes for all the historical data points.


Finally, here is a table of the regression coefficients:

Regression Results for Various Asset Allocations
( % Stocks /  % Bonds )

Adj R2


  1. Pretty tight fit with past realities. Two questions.

    1) Is this a case of data-snooping, or does this have predictive value? I understand there are math tests to determine this.

    2) A lot of people will pounce on this as proof that their own preferred portfolio's attributes will generate a more safe retirement. They will use their own (e.g.) lower PE and higher div in your equation. How do you feel about the transferability of the conclusion to data that is NOT the full market (but is just one person's portfolio choices)?

  2. Third question: The US market is very cyclical, probably because it is large enough to be very diversified. This cyclicality allows for predictability. How do you feel your equation would work in (say) the Canadian market which is very UN-cyclical? Compare Sheets 8 and 18 of spreadsheets http://www.retailinvestor.org/StatsCan.xls

  3. Thanks for the comments!

    1) On the issue of data snooping, for the final published paper I had to cut a lot out. I did play around with things like assuming it is 1950 and fitting the data up to that point to see how well the predictions compare to the actual historical experience since 1950. It didn't do too bad. A longer and more technical version of this paper can be found here:


    2) This is a good point. I didn't really think about it. The idea I had in mind about the spreadsheet was that people could update more recent values for the underlying indices. But I suppose people might want to test for the characteristics of their own portfolios. Having not thought about that, I must say that I would discourage transferring these results to portfolios that are not the full market. There could be other risks involved, and these results may not adequately reflect the characteristics of non-indexed portfolios.

    3) I looked at the Canadian Shiller P/E sheet. But how are you concluding it is uncyclical? These results do rely on cyclical P/E reverting to its historical mean. I would like to study more about other countries to see if it holds up. But mostly I can only find P/E data since the 1950s for a small sample of countries. I'd like to have longer data periods. That is quite an interesting spreadsheet. May I ask, what is your source for Canadian P/E data? I am aware that the data is collected by Global Financial Data, but I wonder if there is also some other data source I am missing. Thanks.

  4. The data page is Sheet 1. The Cdn PE is column BB. The source is a monthly report from our central Bank of Canada with the data code v122629 http://www.bankofcanada.ca/en/bfsgen.html
    The other references are listed at the bottom of column B. You will see from Sheet 1 that the data from various sources is often contradictory, or vaguely different. The 'best' choices have been highlighted in yellow.

    This metric is uses the Dec 31 valuation of the stock index and the earnings that have been reported at that date. So the earnings are more like the Q3 rolling 12 months, NOT the eventual Q4 number like S&P uses for US data.

    It is this difference that explains some of the lagging you see on many of the chart comparisons between US and Cdn data.

    Sheet 20 shows the Cdn PE over time. Don't see any cyclicality there. Personally I don't put much store in Shiller's calculation (Sheet 28) showing cyclicality. The act of creating averages by its very nature creates the impression of cycles because each individual year's metric get weighted in 5 different data-points.

  5. Can you tell me what the variables EY10,DY10 and I are? Also PE10.I can't find a straightforward definition in your paper.

  6. I develop a regression model to predict the 30-year MWR for a retiree based on market information freely available at the start of retirement. I choose one regression specification to cover the various asset allocations, which suggests that the specification must include variables to predict real stock and bond returns and inflation. Campbell and Shiller established a link between real stock returns, PE10, and DY, suggesting that these variables belong in the model. PE10 is the stock price in January divided by the average real earnings on a monthly basis over the previous 10 years. Campbell and Shiller justified this measure as a way to remove cyclical factors from earnings, though there is no particular theoretical reason to choose precisely 10 years. The cyclically adjusted earnings yield (EY10) is 100 divided by PE10. I use EY10 rather than PE10 for the main predictions and forecasting, as the out-of-sample predictions of MWRs from simple one-variable regressions show that the EY10 regression is more forgiving of low EY10 values than the PE10 regression is of corresponding high PE10 values. PE10 predicts worse MWR outcomes in recent years, but is more vulnerable to out-of-sample estimation errors. For this reason, predictions for recent MWRs should rely more on EY10 than PE10.

    The dividend yield (DY) is aggregate dividends divided by the stock price. I find that a 10-year moving average for the dividend yield (DY10) provides a better model fit. This can be justified as a way to obtain the underlying trend in dividend payments after removing the cyclical trend in stock prices. Unlike EY10, the 10-year moving average for DY is not the average of previous dividends over current price, but rather the average dividend yield. Because EY10 already includes the current price, another variable with current price is not needed.

    Nominal bond yields (I) are for 10-year government bonds. For bond returns, this yield may provide reasonable predictive power, as a high yield implies both that current income from the bond will be high and that any subsequent shift toward lower yields will raise bond prices and boost returns. Through the Fisher effect, the nominal bond yield consists of a real yield and expected inflation, and it may provide insight into future inflation rates, because both real rates and inflation tend to show persistence. Together, this suggests using a parsimonious model in which the 30-year MWRs are explained and predicted by the values of EY10, DY10, and I at the retirement date. The model is estimated with data from 1883 to 1980.

  7. Thank goodness for your work! There is so much crapola spread by self-appointed experts (that includes the Bogleheads) that people are being seriously mislead I fear. Kudos, Fred