The ‘super safe withdrawal rate” calculator below estimates certainty-equivalent returns and the Merton share.
You can use these certainty-equivalent returns as ultraconservative safe withdrawal rates. And the Merton share as the optimal allocation to stocks in your portfolio.
Click Calculate to see example calculations using historical averages. Or follow the instructions below the calculator to make your own personalized calculations.
Note: The initial default inputs use U.S. historical real average returns and volatility with one simplification: While the historical volatility of intermediate US treasury bonds equals 5 percent. I set this input to 0 (zero) to match the typical textbook treatment.
Equity Arithmetic Mean (%):
Riskfree Arithmetic Mean (%):
Equity Premium (%):
How Calculator Works
The super safe withdrawal rate calculator steps through three calculations.
First, it takes the average geometric returns expected from equities and risk-free assets and adjusts these percentages so they approximate arithmetic mean returns. (Mechanically, the formulas add one-half the squared volatility.)
Second, the calculator estimates the equity premium. (If equities return 7 percent and risk-free bonds return 2 percent, the equity premium equals 5 percent.)
Third, finally, the super safe withdrawal rate calculator estimates the certainty-equivalent returns (CERs) as well as the resulting Merton “equity allocation” shares suggested for the standard set of risk tolerances.
Personalized Super Safe Withdrawal Rate
To calculate a personal super safe withdrawal rate, replace the default annual average “geometric mean” returns for equities and risk-free bonds with your forecasted returns. And then also estimate the volatilty, or standard deviation, for both asset classes.
You may aleady have estimates for these inputs. But if you don’t? No problem. The large investment services also provide this information regularly. (See here, for example, for the December 2024 Market Outlook from Vanguard.)
Certainty-equivalent Returns and Merton Shares in a Picture
A simple line chart accurately shows how Merton shares and certainty-equivalent returns work (see below).
The blue line shows the average expected arithmetic returns for portfolios using a variety of stock allocations: 0%, 10%, 20%, 30% and so on. If the portfolio holds only risk-free assets, for example, the expected return equals the risk-free return. If the portfolio holds only equities, the expected return equals the equity return. In between those equity percentages, the expected return reflects a weighted average.
The line chart hints at the portfolio risks using those two dashed grey lines. They show the 25th and the 75th percentile returns. (All of these calculations reflect the historical real returns of US stocks and risk-free assets and their volatility. Also, in this chart to make it make sense, I did set the standard deviation of the risk-free assets to 5%.)
That green line shows the certainty-equivalent returns, or CERs, and graphically shows the utility the investor enjoys at various stock allocations. The green line flattens as the investor increases the allocation to stocks. That visually signals the diminished marginal utility. In effect, the formulas assume there’s a risk penalty diminishing the expected value.
By the way, the green line reflects a good guess as to the utility. The Python script that draws the line chart uses the standard utility function, or formula, economists think does a pretty good job. But the main takeaway here for non-economists? Sure, you and I get larger returns by allocating ever larger percentages to stocks (see the blue line). But risks explode as we do this (see the two grey dashed lines.) The utility we enjoy (see the green line) essentially tops out at the Merton share.
Historical Context Helps
Using the historical default numbers, which is what the line chart does, the Merton share formula suggests a 62.5% allocation to stocks based on a constant relative risk aversion equal to 2. (More on this constant in a minute.) So very close to the orthodox 60-percent stocks and 40-percent bonds asset allocation. Furthermore, the certainty-equivalent return per the formula equals about 3.56%. Which is interestingly close to the cannonical four percent safe withdrawal rate.
Personalizing Your Relative Risk Aversion
For practical purposes, the super safe withdrawal calculator above assumes your personal relative risk aversion equals 1, 2, 3, 4 or 5. The way the Merton share and CER formulas work, those values are sort of the standard “shoe sizes.”
Most people, according to the research, feel a constant relative risk aversion equal to 2 or 3.
A constant relative risk aversion equal to 1 might signal someone comfortable with a leveraged portfolio in many economic scenarios. (In late December 2024, a constant relative risk aversion equal to 1 would mean an investor focusing on only US stocks might invest between 60 and 65 percent of their portfolio in US equities.)
A constant relative risk aversion equal to 4 or 5 would suggest in the current market an allocation to US equities of maybe 10 percent to 15 percent.
Use CER as a Super Safe Withdrawal Rate?
The $64 question: Can you or I really use certainty-equivalent returns as a “safer” safe withdrawal rate? Good question. And one worth chewing over a bit.
Certainty-equivalent returns can provide a good safe withdrawal rate number. As noted, if you make the calculations using historical averages? The resulting Merton shares and CERs mesh with the almost canonical 4 percent rule and popular 60-percent stocks and 40-percent bonds asset allocation. But you need to be careful here.
True, using CERs as a super safe withdrawal rate delivers some unique benefits. The approach considers the risks of a particular portfolio. It explicitly addresses periods where expected returns going forward will probably be lower. (If you don’t like the idea of forecasting lower expected equity returns, you can surely see it makes sense to forecast lower expected bond returns if interest rates have dropped.) Further for investors with long retirements and who want to preserve their wealth? The ultraconservative nature of CERs mean they’re almost guaranteed not to fail. (If this sounds implausible, consider the CER percentages start lower. And then if portfolios shrink in value, that CER percentage probably increases but it also gets multiplied by the new year’s lower portfolio value.)
However, using the CER as a super safe withdrawal rate may not make sense in many situations. Currently, the formula returns a very low withdrawal rate for investors who limit their equity investments to US stocks. (The certainty-equivalent return in late 2024 might suggest a super safe withdrawal rate of less than 2 percent for an all US stocks investor.) The CER formula would also often result in investors simply not spending much of their retirement nest egg. (That doesn’t really make sure.) And the formula would tend to restrict a retiree’s spending. (That doesn’t sound great.)
Two Final Thoughts
A couple of other thoughts before I end.
First, if you’ve been using the four percent safe withdrawal rate, one way to maybe benefit from the super safe withdrawal rate calculator is to make the calculations for your portfolio. And then think about an average of the CER percentage and that four percent figure. That hybrid approach hedges your bets a bit.
A second idea: Calculating CERs and Merton shares may help you think about diversifying away from US stocks. (Adding more international stocks will make the numbers work better.) And doing the arithmetic may also help you more unemotionally calibrate your portfolio risks. (The CERs and Merton share math help you quantatively adjust your portfolio risk.) Those effects? Arguably pretty good.
Related Resources
This companion calculator and discussion may be interesting as you’re learning about this stuff: Merton Share Estimator.
This related discusion of the variability of portfolio returns may provide nice context: Retirement Plan B: Why You Need One.
I like the insights the Merton share and certainty-equivalent returns provide when thinking about retirement. But personally? I think it makes more sense to do Monte Carlo simulations to think about the risks. That topic is discussed in more detail here: Monte Carlo Safe Withdrawal Rates for Low Expected Returns.
Finally, if you’re struggling with the math and logic of certainty-equivalent returns and how lower-returning bonds can possibly help? Check this blog post: Monte Carlo Simulations Show How Bonds Dampen Retirement Risk. It provides a visual approach to exploring how risk-free assets can mostly dial down your risks during retirement.