Low bond yields and high equity valuations suggest lower spending for retirees. Prior research forecasted the impact on safe-withdrawal rates (SWRs), but a more sophisticated model can improve the accuracy of those predictions. We show just how low the SWRs should be for today’s retirees.
SWR research, such as the well-known 4% rule, is based on a portfolio of stocks and bonds using historical return data. As we have shown in recent studies published in the Journal of Financial Planning, the Journal of Wealth Management1 and the Retirement Management Journal, the sustainability of retirement portfolios is highly sensitive to asset returns – particularly in the first decade of retirement. Even if bond yields rise, today’s retirees face greater shortfall risk because the value of portfolios invested in bonds will fall.
Equities are also not as safe as they have been historically. When prices are high (based on P/E ratios), future returns are more likely to be disappointing. In our paper published in the Retirement Management Journal, we demonstrated how using returns calibrated to current asset valuations instead of historical average returns leads to a much more pessimistic estimate of SWRs for retirees.
Most retirees don’t annuitize and most investment advisors don’t recommend annuities. Without an annuity, a retiree needs to select an amount to spend each year from a portfolio. A reasonable goal is to withdraw as much as possible from an investment portfolio without running out of money. In order to estimate how much can be safely withdrawn each year, an advisor must make a number of assumptions about things like life expectancy and portfolio returns, typically using historical return data for projections.
The problem with prior research
William Bengen developed the 4% rule-of-thumb for retirement withdrawals in 1994. He found that an individual could have withdrawn 4% of their retirement-date assets, with spending adjusted each year for inflation, over a 30-year retirement period using a portfolio invested in 50% to 75% stocks. The Trinity Study from 1998 updated this approach for a variety of scenarios and confirmed that a 4% withdrawal rate based on 20th century U.S. portfolio returns would have allowed a retiree to withdraw the same real income each year with only a small chance of failure.
A problem with using historical U.S. asset return data is that future market performance (and retirement outcomes) will depend on the price of stocks and bonds today. Stock returns depend on dividend income, earnings growth and changes in the valuation multiples placed on those earnings. If the current dividend yield is below its historical average, then history suggests that equity returns following periods of high valuations will also be lower than average. This is mainly because earnings growth is relatively stable. Stocks are priced based on supply and demand; higher prices indicate a lower required equity risk premium and/or a lower risk-free rate.
Returns on bonds depend on the current bond yield and on subsequent yield changes. Low bond yields predict lower holding period returns from less income and the heightened risk associated with capital losses if interest rates rise.
SWRs are directly related to the returns provided by the underlying investment portfolio. In particular, the returns experienced in early retirement will weigh disproportionately on the final outcome. Current market conditions are much more relevant than historical averages.
We question the relevance of research based on what worked in the past. The U.S. historical record is relatively slim for determining how much can be safely withdrawn from a rather aggressive investment portfolio. Past outcomes have little bearing on the unique situation facing today’s retirees.
This is much more than just an academic exercise. Relative to their historical averages, bond yields are very low and stock prices are high. Generally, low bond yields have coincided with flights to safety from stocks resulting in attractive equity valuations that subsequently bailed out a balanced portfolio. But today bond rates are low and equity valuations are high at the same time.
Fortunately, we do know how well bonds have done after a period of low yields. And we also know how equities have performed after a period of high valuations. We can simulate a portfolio that consists of expensive equities and low yielding bonds in the future to determine how such a portfolio will theoretically perform in the future, even if no expensive stocks and bonds existed simultaneously at today’s levels.
In this analysis, we’ll use bond yields to forecast bond returns and the cyclically-adjusted price-to-earnings (CAPE) ratio to forecast equity returns. Results provide guidance for advisors as to the appropriate SWR to recommend to clients.
Bond-return model
The yield on 10-year government bonds have averaged about 4.6% since 1871, but are approximately 2.2% today. To model the potential impact of low bond yields we use a simple autoregressive AR(1) model, where the forecasted yields change over time based on today’s low yields plus some randomness. The model we use is shown in equation 1, where 
is independent white noise that follows a normal distribution with a mean of 0% and a standard deviation of 1.25%.
After we determine the bond yield for a given year of a given simulation, we estimate the bond return using equation 2, where is assumed to have a mean of 0.0% and standard deviation of 1.5
The 1.5% standard deviation for the error term () is not the assumed standard deviation for the asset class (bonds in this case), but rather the standard deviation for the errors around the regression estimates. The actual standard deviation of bond returns using this model is approximately 6.0%. This is relatively similar to the long-term average. The actual standard deviation of bond returns is higher than 1.25% given the relative impact of change in bond yields on returns (equation 2).
CAPE-return model
Investing when CAPE ratios are high has historically resulted in lower 10-year equity returns than when stocks are valued closer to (or lower than) their historical average. Practically speaking, if prices are high, then dividend yields are comparatively low. We know from research by Robert Shiller and Eugene Fama (among others) that valuations based on either earnings or dividend yields have the power to predict future returns.
Rather than modeling the potential change in the CAPE ratio over time (as we did in our original model published in the RMJ), we seek to capture the relationship between the CAPE ratio at a certain point in time (t) and the return of the stock market in the future (t+n). For example, if the CAPE ratio is 20, what is the relation between this high CAPE ratio value and the return the following year (t+1), the year after that (t+2), etc? This approach allows us to adjust the future expected returns based on this past relationship. For each t+n year a regression is performed:
The figure below shows the coefficients for the next 15 years (from =1 to = 15)
Individual slope values are negative. We can see the slope for the year following the CAPE Ratio, for example, is approximately -.47%. This suggests that a higher CAPE ratio predicts a lower future return on stocks. The overall relationship between the CAPE ratio and future stock returns dissipates over time, meaning that the CAPE ratio is more predictive of returns next year than 10 years from now.
Given this model, it’s possible to run an analysis where the initial CAPE ratios are varied, which affects the future projected returns for equities. For example, if the base assumed return for equities is 10% and the CAPE ratio is near the historical average of 15, the assumed return would be higher than if the CAPE ratio were 27 as it is today.
Analysis
To illustrate the difference in SWRs when valuations are taken into account, we estimate the probability of success for a 4% initial withdrawal rate over 30 years for different equity allocations using a past-returns model. This model assumes an initial CAPE Ratio of 16 (the approximate long-term average), initial bond yields of 5.0%, no investment fees (as is common in retirement research) and an average equity return of 12% (consistent with the long-term arithmetic average historical total return of the S&P 500). We compared this to a forward-looking model that assumes an initial CAPE ratio of 27, an initial bond yield of 2.5%, an investment fee of 50 bps and an average future expected equity return of 9%. The figure below includes the probabilities of success for different equity allocations, from 0% to 100%, in 10% increments, for these two models.
As we can see in the figure, the probabilities of success for the forward-looking model are much lower than those based on historical returns. For example, using historical returns, the probability of success of a 4% SWR is approximately 95% (e.g., for a 50% equity allocation). In contrast, the probability of success using the forward-looking model for a 50% equity allocation is only 54%. It is as low as 1% for an all-bond portfolio.
Recall that we are still using asset-return data from the past to project SWRs. We are just using more information about current valuations and projecting future returns using a regression model estimated from historical data. Using these more realistic forward-looking assumptions, our simulation shows that SWRs suggested by past research are not nearly as safe as originally thought.
Which SWRs are safe? We estimated the probabilities of success for different equity allocations over various retirement periods using the forward-looking model. The assumptions are the same as in the previous analysis (CAPE ratio is 27, the initial bond yield is 2.5%, a 50 bps investment fee and the long-term average return on stocks is 9.0%). The values in the table below are the SWRs for a given target probability of success (PoS), retirement period and equity allocation based on 10,000 Monte Carlo simulations.
The SWRs diverged significantly based upon the desired probability of success, equity allocation and retirement period. More importantly, the rates are significantly lower than in past research.
One surprising result is that rates are lower for more aggressive asset allocations. This is inconsistent with other research showing that more aggressive portfolios allow for higher SWRs. This point becomes clearer in the following figure, which shows the probabilities of success for a 3% SWR over varying retirement periods and for varying equity allocations.
For a 25-year time horizon, a 0% equity allocation has the highest probabilities of success. While the optimal equity allocation increases slightly for longer time periods, to approximately 60% equities for a 40-year period, for a 30-year period it is only 10% equities.
To put the above values into perspective, here is the same analysis for a 4% SWR. Now, we see a very different relationship; higher equity allocations are associated with higher probabilities of success. This provides some insight into the idiosyncrasies of shortfall analysis when used as a yardstick to judge success. Bonds allow nearly all retirees to meet a modest spending goal, while equities (with both a higher average return and greater volatility) allow a greater chance of meeting a higher spending goal.
Conclusions
Portfolio return projections are based on information drawn from the past. By incorporating asset prices when making those projections, we can do a better job of selecting the right information to more accurately simulate how markets will perform and how different retirement-withdrawal strategies will fare.
Bond yields are relatively low by historical standards, suggesting lower potential bond returns. The stock market is relatively expensive based on metrics like the CAPE ratio. Taken together, the optimal SWR is lower than has been shown in prior research.
How should a planner use this information? Recognize that a 30-year time horizon is ideal for a hypothetical 65-year old retiree who dies at age 95. But remaining life expectancy at age 65 is less than 30 years, so many will die with money unspent. That represents a failure from being too conservative. Our simulation of 35- and 40-year retirements revealed very low SWRs, which will also increase the risk that the average retiree will die without spending as much as they could have. These low SWRs are not a prescription, especially since later-life spending shortfalls can be easily hedged by pooling risk through deferred-income annuities.
Most retirees will not need to spend the same amount every year. For couples, the longer-lived member won’t spend as much as a single-person household. Retirees generally decrease spending as they experience physical and mental limitations. In addition, most retirees are willing to cut spending a little when markets don’t do as well as they’d hoped. Incorporating variability into spending will increase the SWR significantly.
Lastly, the probability of success is only one way to measure outcomes for a retiree. It does not show the magnitude of the failures early in retirement, and it doesn’t consider the security of retirees who live well beyond the 30-year timeframe. Without considering the magnitude of failure, portfolio risk is increased, leaving retirees vulnerable to adverse market events, particularly those early in retirement.
Despite these shortcomings, financial advisors need to use lower SWRs than those shown in prior research, and adjust base returns in Monte Carlo simulations. The generous capital market returns of the prior century bolstered a comfortable and long-lasting retirement portfolio. But they will give 21st-century clients a false sense of security and prejudice products and strategies that would do a better job of meeting retirement income goals.
David M. Blanchett, CFA, CFP® is the head of retirement research for Morningstar Investment Management in Chicago, IL.
Michael Finke Ph.D., CFP® is a professor and director or retirement planning and living in the personal financial planning department at Texas Tech University in Lubbock, Texas.
Wade D. Pfau, Ph.D., CFA, is a professor of retirement income in the Ph.D. program in financial services and retirement planning at the American College in Bryn Mawr, Pennsylvania. He is also the director of retirement research for inStream Solutions and McLean Asset Management. He actively blogs about retirement research. See his Google+ profile for more information.
Read more articles by David Blanchett, Michael Finke and Wade Pfau
is independent white noise that follows a normal distribution with a mean of 0% and a standard deviation of 1.25%.
is assumed to have a mean of 0.0% and standard deviation of 1.5
coefficients for the next 15 years (from 
=1 to 
