In today’s post I want to explain and demonstrate how modern retirement calculators work. There are two basic ways to calculate how much you can safely withdraw from your portfolio in retirement; looking backwards using historical data for past retirees and looking forward using possible future investment returns. On this blog I’ve pretty much only described the historical safe withdrawal rate (SWR) approach. That’s where the 4% SWR number comes from that you hear talked about all the time. Modern retirement calculators do not use this approach. They use a forward looking approach called Monte-Carlo analysis to come up with their SWRs. Lets see how these calculators work.

What’s wrong with using historical data to come up with SWRs? The problem is history only represents one outcome of all the possible future paths from that previous point. If you were back in 1966 looking forward to a 30 year retirement the actual outcome of your 30 year retirement period, which happened to become the worst in history, was only one of many possibilities. Modern retirement calculators eliminate this drawback by looking at many many possible future retirement outcomes. That’s the fundamental difference. The rest is calculation details. How do they do this? They assume that future investment returns follow some probability distribution, since the future is fundamentally indeterminate and probabilistic. So, for example, they assume that future investment returns are normally distributed (they also use some really fancy distributions like multi-variate log normal but the results are similar), i.e. follow a bell curve. They then randomly generate a time series of investment returns and use those investment returns to calculate what the SWR would be in each of those random series of returns. Since they can’t do this for the infinite variety of possible returns they usually stop at a sufficiently large number that generates statistically robust results. The generally accepted large enough number for these retirement calculators is 10,000 trials.

Now, here is the catch with these retirement calculators. They still involve some kind of bias or human forecasting under this seemingly unbiased random robust scientific method. For those assumed normal distributions you still need to pick a mean and a standard deviation to generate those random investment returns. And you still need to forecast inflation as well. You can’t model all possible potential future outcomes. Confused yet?

It’s really pretty simple, it’s just the calculations that get intense. I put together a simple retirement calculator in excel to illustrate how this is done. In one excel file I generated 1,000 random series of 30 year investment returns (note: every time you open, save, or make any changes to this file the random numbers change, unless you turn off automatic calc in options). I generated stock and bond returns independently. I then copied these results to another excel file where I did the work of calculating the SWR for those 1,000 random simulations. In this first pass I use the historical mean and standard deviations for US stocks and US 10 year government bonds from 1929 through 2013. I also used historical inflation. And this leads to the next important observation regarding retirement calculators. All of them define a successful SWR to one that has an 80% to 85% success rate. In a 10,000 trial simulation that means 1,500 to 2,000 of the possible time series of investment returns result in failure, i.e. running out of money. It’s just that those cases are lower probability events. Yet still possible. Using an 85% success rate my simple model yields and SWR of 3.92% for a 50/50 stock bond allocation. Pretty close to the historical SWRs for such a simple model.

But none of the modern retirement calculators I’ve seen use historical returns in their calculators. They all use a return forecast that is significantly lower than historical returns have been. I think the simplest and best retirement calculator is the one from Vanguard. I like it because there is no need for a ton of inputs on the user’s part. It just generates the SWR based on the retirement period and one of three asset allocations. All the gory details are behinds the scenes. Their future return assumptions are updated once a year and explained in the Vanguard Capital Markets Model. It’s well worth the read. Basically, they use diversified portfolio returns of 3-5% real going forward, less than returns have been in the past. For a 30 yr retirement period and a moderate asset allocation their model yields and SWR of 3.8%. I used these lower future expected returns in my simple model and that yielded an SWR of 3.30%. You can access those files here and here .

At the end of all this fancy analysis we have a tool that tells us that future SWRs will be lower than the past because we are forecasting future returns to be lower than historical returns. And specifically lower than the 30 year retirement period that started in 1966 which is what gave us the worst case historical SWR to begin with. Seems kind of obvious when you put it that way. So, basically this all relies on a forecast of the future which are notoriously inaccurate. But its the best tool we have. From today’s valuation levels and interest rates it is possible the SWRs will be slightly to a good deal lower than 4%. But they may not be.

That pretty much sums up how modern retirement calculators work. Now you can at least use these tools with an understanding of what’s under the hood. You can even generate your own models if you want.

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Note: the
T Rowe Price retirement calculator
is another very popular one. I find the added inputs and complexity unnecessary.
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So you think it’s a bad idea to assume a SWR greater than 4%? The GTAA Agg models have much higher SWR even after a 20% reduction to make up for not including 1966. I’ve used FireCalc’s Monte Carlo simulator with reduced returns, but same standard deviation of GTAA Agg. Perhaps I am being too ambitious…

Hi Jeff, I knew that question was coming… and thanks for asking it. In this post I just wanted to explain how these retirement calculators work and stop there. Basically, the retirement calculators are forecasting returns lower than the worst 30 yr period in history, 1966. 30 yr portfolio returns starting in 1966 for a 70/30 portfolio were 5.7% real. The killer was the first 15 years of this period which had portfolio returns of 1.2% real. Could the future be worse than this? Maybe. But we have better methods today, more asset class choices, etc… but since we lack any real long term history with these new things I think the best we can say is that they increase our odds of success. So, going with a globally diversified buy and hold portfolio and a flexible retirement spending model increases the chances of the 4% SWR working into the future. Going with a more active portfolio choice like the GTAA AGG models increases the chances of an SWR above 4% working. But these things may not compound. So taking the Vanguard monte carlo sim figures of 3.8% and adjusting up from there I’d be hard pressed to use any SWR above 5% especially in the early years. The SWR can always be adjusted upwards.

Paul

Thank you for framing it this way and also for posting about the differences in historical vs monte carlo retirement calculators. Sometimes it is tempting to get caught up in tweaking the numbers until it tells you what you want, while losing sight of how they work and other underlying factors/assumptions.

Absolutely true Jeff.

Paul, one of the issues I have with many of the retirement calculators is that they assume a set withdrawal rate (like 4%/year) from one’s investment portfolio over the entire duration of retirement. To some of us (and hopefully many) we hope to enjoy social security and possibly deferred pensions kicking in during out later years, thereby reducing the required withdrawals from our IRA’s and other investments. To deal with this, I have constructed spreadsheets which forecast the required (variable) cash withdrawals from my investment accounts by year…that is, that cash withdrawn each year to supplement what I anticipate receiving by year from social security and pensions. I forecast the investment returns each year based on a monte carlo routine, and then look at the probabilities of success for a 30 year retirement horizon from all the sources of income. Based on your prior postings, I’ve invested almost exclusively in the GTAA13, but use a conservative 8% average annual return estimate (and an 8% standard deviation). Does this approach make sense to you?

Regards.

Keith, your approach makes total sense. I do the same thing. I think its crucial to forecast yearly cashflows during retirement.

Paul

For early retirement calculation what do you think of the Flexible calculator – http://www.flexibleretirementplanner.com/ ?

Thanks for the tip. Wasn’t aware of that one. I like it. Simple but yet lets you model what you want. As with all Monte Carlo sims you still need to be aware of the portfolio return inputs but I like the approach that the calculator takes.

Paul