Understanding modern retirement calculators

August 31, 2014

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.

Note: the T Rowe Price retirement calculator is another very popular one. I find the added inputs and complexity unnecessary.

The impact of realistic spending on your retirement

May 28, 2014

In a post last week I showed that for the majority of retirees the standard recommended spending model in retirement does not match reality. Spending  in retirement actually grows by less than inflation over time. In this post I want to show you how using a more realistic sending model impacts how much you can withdraw from your portfolio in retirement.

If we go back and use the same model we used to calculate SWRs, we can adjust annual spending to see the impact of using a more realistic spending model on SWRs. For this post I simply changed the annual spending adjustment in retirement to grow by 1% less than inflation during the 30 year retirement periods (-1% per year real spending). This is actually pretty conservative compared to the actual retiree data.

Second, I took at look at combining a realistic spending model with a flexible spending model I’ve discussed in the past. The Floor Ceiling method basically allows spending adjustments in retirement based on the performance of the portfolio. For this post I used a floor ceiling model with unlimited upside and a max floor of -10% to inflation adjusted spending.

The results are shown in the table below for 30 year retirement periods, a 70-30 SP500 10yr UST bond stock portfolio with data going back to 1929.

SWRs for base vs realistic vs fcm model may 2014

The standard retirement model says your SWR is 4.39% for this portfolio. By simply using a more realistic spending model the SWR for the portfolio goes up to 4.90% an increase of almost 12%. The FCM model with its flexible spending says your SWR is 4.84% for this portfolio. By combining both approaches the SWR for the portfolio goes up to 5.39%, an increase of over 22%! That’s a raise of 22% per year in retirement simply by being more realistic and flexible. Very powerful stuff.

For those still building for retirement the implications are perhaps even more impactful. The percentage increases in SWR are equivalent to a reduction in the amount you need to fund your retirement. If you can spend 22% more with these models in retirement it also means you would need 22% less to retire. That could translate into several years of work or no work in this case.


Spending Realities in Retirement

May 20, 2014

It’s usually worthwhile to question conventional wisdom. At the minimum you usually learn where that wisdom came from. Often you learn the conventional wisdom is not the best approach. This happens to apply rather well to the topic of retirement spending. Lets take a look at the conventional wisdom regarding retirement spending and see why it may not be the best approach.

All the standard retirement models tell retirees to adjust spending every year for inflation right? This how the SWR (Safe Withdrawal Rate) model works. You pick a percentage of the portfolio to withdraw in year 1 and then adjust that spending every year for inflation. Simple enough. The theory being that at the minimum we want to maintain the same ‘standard of living’, i.e. real spending, from year to year. The biggest question to ask is this model actually how retiree spending evolves over time?

Anectodally, this model has always felt a bit off to me. For one, I meet a lot of retirees and speak to them quite a bit about finances and spending. Many I’ve met have held spending constant for years while maintaining their quality of life. In my personal situation, on average spending has either stayed the same or declined every year. What gives?

Fortunately, some recent research has shed some light on this topic. Michael Kitces has a great post covering this research which I highly recommend. I’ll just highlight a few points from the post. Lets first look at how retirees actually spend. Here is the data:

Annual Real Change in Consumption for Retirees May 20 2014

The orange line in the graph above is spending adjusted for inflation, real spending. This is the line all retirees fall on according to the recommended retirement models. The reality is somewhat different. For the majority of retirees real, inflation adjusted spending declines in retirement. Even towards the end of life. The declines are on the order of 1% a year, growing to 2% a year, then back to 1% a year in the later years but still never positive. Definitely a different reality than the models portray. An important point: this is real spending. Actual spending may still actually increase. For example, inflation is 3%, spending goes up 2%, real spending is then down 1%. Now lets look at how you can use this in your retirement.

I think the best way to use this research is to take a look at your retirement in stages. Michael also talks about this in his post but basically the idea is to divide retirement into three spending stages. Like pictured here;

three stage retirement model may 2014


Each of the three stages can be modeled with a different change in retirement spending. For first stage, say 60 to 70, -1% per year in real spending could be used (or conservatively the standard model’s o% per year), for the second stage, 70 to 85, -2% per year, and for the third stage back to -1% per year. This can be tailored to be fit your specific circumstances which is also much better than the standard retirement model.

OK, so far all we’ve done is match the retirement model to a better representation of retirees’ actual experiences. Now for the punchline. Being that realistic scenario is less spending than the model means one of several things. One, the standard SWRs are too conservative. Two, retirees need less money to retire to being with. Three, worst case, the SWRs from the standard retirement model plus a more realistic spending outlook means a much higher probability of success in retirement. I’ll take a look at some of these implications in later posts.

Standing on the edge: diversified portfolios & the modern retiree

May 16, 2014

What’s the hardest part of the retirement decision? For many its taking the leap of faith that financially what’s worked in the past will continue to work in the future. And often the start of every single year, during those early years of retirement, brings the anxiety right back again. I’m in my ninth year of withdrawals and while the anxiety has lessened by orders of magnitude, it is still there. Someday I may recount the year by year story, maybe after year 10. In today’s post I want to look back a bit in order to look forward. We’ll go back to the beginning of the year 2000 and the year 2008 and look at the decisions facing those retirees. Then we’ll look at how those portfolio decisions performed through the end of 2013.

For every retiree since 1996 the retirement decision matrix, SWR decisions vs stock allocation, has looked exactly the same. The table below shows what those choices are:

SWRs by allocation May 2014

Why have the historical SWRs not changed since 1996? Because, as I show in this post, the SWR is solely determined by the worst case retiree in history which happens to be the 1966 retiree. That 1966 was the worst case period was not know until that 30 year retirement period was over in 1996. Lets assume that the 2000 and the 2008 retiree chose an SWR of 4.39%. They then were faced with several investment portfolios offering different levels of diversification and risk management. They used data similar to what I presented in this post. I’ll use the various diversified IVY portfolios, their timing relatives, and the Permanent Portfolio. How have the 2000 and the 2008 retiree fared if they chose one of those portfolios? Here is the data.

Diviersified portfolios and the modern retiree

First, lets look at the year 2000 retiree, 14 years later. Everyone of these portfolio choices would have worked out just fine compared to the worst case 1966 retiree. In every case the more diversified portfolios did even better and the timing/trend following portfolios did even better. Only the the retiree that chose the standard 70% US stock, 30% US Bond portfolio, ended with less money than when they started with. Several of the portfolio choices would also have given the 2000 retiree the opportunity to adjust their withdrawal rates higher due to the great performance. Diversification works and it paid off in spades. All as expected.

Now, lets turn to the 2008 retiree. Hmm, notice something interesting here. For the last 6 years, diversification has basically failed to give a portfolio much benefit. The bull market in US stocks has been quite powerful. Only the two most aggressive portfolios, that combine timing and momentum (GTAA 3 and GTAA 6) beat the standard 70/30 portfolio substantially. What should we make of this? Time to abandon diversification all together? I hope you don’t think so. The last 6 years of US market out performance does not trump the long term historical data. Nor should it. If anything I think it suggests the diversified portfolios are set to outperform going forward. And so far, in 2014, that is proving itself out. But hey, that’s forecasting and who knows.

There is something more important here to take away. While it may be intellectually easy to say, stick with diversification, emotionally, while looking at your portfolio statements, it is a different story for most people. Any strategy you choose will have periods where it under performs other strategies. And those periods of under performance can be significant. This uncertainty can make taking the leap into retirement quite scary. How do you deal with this?

This is a concept called base rates which I’ve discussed in my quant strategy posts but the concept applies here as well. How best to deal with base rates less than 100%, i.e. that your portfolio choice will under perform for various periods often a lot longer than you feel comfortable with? The best way is not to go with one strategy all or nothing. A part of your retirement portfolio could be a standard 70/30 stock bond portfolio, another part could be more broadly diversified IVY B&H 13 for example, etc.. This way during any given period part of your portfolio is outperforming. This I think is the best way to deal with the emotional factors involved in retirement investing.

In summary, the 2000 and the 2008 retiree while both doing just fine with any of the various retirement portfolios discussed here have had quite a different experience. While for one diversification has been a boon, for the other it has been mostly a meh. This is quite the exhibit of the uncertainty in retirement. It is important I think to let the long term record speak for itself but at the same time choose a few of the strategies to make the emotional aspect of retirement investing easier to deal with and thereby increase the chances of success.


Revisiting the worst times to retire in history (2013 update)

May 12, 2014

Today I wanted to do another yearly update post. This time I’ll refresh the worst times to retire in history with data from 2013 which adds another year in the retirement story of the 5 ‘unluckiest’ retirees in history. See here for last year’s update.

As I said in last year’s update:

The worst time to retire since 1929 turns out not to be the Great Depression, as most people would believe. In fact, the worst time to retire in history was 1966, followed by 1965, then by the Great Depression year of 1929. The SWR (safe withdrawal rate) of 4.39% for a 70% stock 30% bond portfolio is solely determined by the retirement results of the 1966 retiree. Of course, we care about the present not the past. How are the year 2000 and the year 2008 retiree doing compared to those who retired during these worst of times? The table below (click for a larger image) shows the year by year progress for 5 retirees; the 1929 retiree, the 1965 retiree, the 1966 retiree, the 2000 retiree, and the year 2008 retiree. It uses a starting portfolio value of $1M, with a 70% stock 30% bond portfolio, which yielded a max SWR of 4.39%.

Here is the updated table with 2013 data.

Worst times to retire in history 2013 update CWR vs years

After 14 years, the year 2000 retiree is doing pretty well compared to history. It may not seem that way. The year 2000 retiree’s portfolio is down to $787K and the $61K yearly withdrawal is now 7.7% of the portfolio. CWR is defined here. But that is way better than the 1929, 1965, or 1966 retiree, all of whose portfolios survived a 30 year retirement. The year 2008 retiree is doing even better. After 6 years, despite the financial crisis, portfolio value is back to where it started and so is the current withdrawal rate. This is a much better situation than any of the other 4 example retirees.

In short, both our ‘unlucky’ modern retirees, 2000 and 2008, are doing just fine. With respect to history they are in a better position than the three worst retirement periods in history (1929, 1965, 1966). The 4% SWR rule looks to be just fine for yet another year.

P.S. I only discuss the worst retirement periods in history and the worst current periods, 2000 and 2008. This means that any other starting year in retirement has better results than that shown here. For example, the 2001 retiree would be better off than the 2000 retiree.


Higher Safe Withdrawal Rates from a 100% Bond Portfolio?

October 5, 2013

Is it possible to achieve higher safe withdrawal rates, compared to a stock/bond portfolio, from a 100% bond portfolio? With bond prices at historical highs? That’s what I wanted to find out. I started thinking in this direction after my look at bottoms up retirement planning and calculating what low real rates are actually needed to achieve retirement success. This is mainly because what really kills SWRs in risky portfolios is negative withdrawals early in retirement and inflation as I discussed in my ‘Insist on 1966′ post. So I thought it would be useful to look at what the lowest risk retirement model is and what are the SWRs (safe withdrawal rates) from such a model. Then we can compare all other models, using riskier assets, to this minimum risk model and decide on the tradeoffs. The results are rather surprising.

I’ve always been somewhat surprised just how low the recommended SWRs are. The 4% SWR rule for a 30 year retirement that has proven to work historically for even the worst retirement periods has a worst case 30 yr period return of about 7%. That’s a 4% withdrawal rate from 7% returns! Pretty low when you think about it. Basically, because of negative returns, particularly early in retirement, what they call sequence of return risk, SWRs are much lower than the worst case portfolio returns. But it gets even more interesting. Lets look at what the SWR would be for a portfolio if you could get guaranteed 0% real return. Then lets compare those  ‘ideal’ SWRs to those from risky portfolios. In the table below I show such a comparison. BTW, the 0% real return SWRs are simply 1/retirement period.

Zero risk retirement model vs sotck bonds models oct 2013

The two highlighted SWRs are the most commonly recommended asset allocations in retirement; 60/40 stock bond allocations or 70/30 stock bond allocations for a 30 year retirement period. As the table shows you don’t get much of a benefit in SWR from risky portfolios until you go beyond a 25 year retirement period. At the same time I think it would be surprising to many investors that you could have an SWR of 3.33% for a 30 yr retirement period with a 0% real return. At this point you should be asking, ‘great, but where in the world can you get a guaranteed 0% real return?”. Turns out we can get pretty darn close with a laddered bond portfolio of US Inflation Protected Bonds (TIPS). TIPS offer a guaranteed return of principal and inflation protection of that principal which takes the two biggest retirement risks off the table from the start.  And beyond zero real returns, so far over their history, US TIPS have offered positive real returns over the entire term structure. The next thing to I tool a look at is what SWRs are achievable with a portfolio of US TIPS at today’s prices?

To calculate the SWRs for a laddered portfolio of bonds, in this case US TIPS, takes a little doing. I started with prices and data on the available US TIPS from the WSJ quote page. I used prices at the end of day on Sept 23, 2013. Download those into an excel spreadsheet and build a model for various time periods with a target of having equal payouts for each year of retirement, basically keeping real standard of living the same, just like the traditional SWR models. Fortunately, you can use the solver function in excel to do the hard work for you. The results are shown in the table below and you can access my spreadsheet here and play with the model for yourself.

SWRS for 100% TIPS priced as of Sep 23 2013

So, for retirement periods of 20, 25, and 30 years, you get higher SWRs from a 100% US TIPS portfolio than from a 60/40 stock bond portfolio! Let that sink in for a minute. And that is with the  historically low real rates offered today. This again shows just how detrimental negative returns are for retirement portfolios and is what keeps SWRs for risky portfolios so low. And if you, like many others, think future returns and SWRs will be lower than the past then these numbers should be even more compelling. At the minimum these super safe SWRs should be used as a benchmark when considering riskier asset allocations.

What about the downsides? Of course there are always downsides or drawbacks to any approach. For me, the biggest one of a 100% US TIPS portfolio is that there not as much upside as there is with a risky portfolio. If you hold the bonds to maturity the indicated SWR is all you get. No adjusting SWRs higher if markets perform well. If real rates only go higher from here the bonds also need to be held to maturity in order to protect principal. On the other hand, if/when markets experience another major/correction crash, real rates will undoubtedly go much lower, the TIPS could be sold with nice capital gains, and you could then implement a risky 60/40 portfolio at much lower valuations. So there is the potential for some upside. The other downsides are that the portfolio is a bit harder to implement that just buying ETFs for stocks and bonds, and TIPS do bring up some tax complications for investors. None of these are insurmountable and if people are interested I can provide some more info in the comments to this post.

In exchange for potentially less upside in total wealth you get, most importantly, a much higher probability that your portfolio will last throughout your retirement period. No worrying about stock market fluctuations and the like. In other words, greater piece of mind. Of course, it doesn’t have to be all or nothing. A TIPS portfolio such as this can be used as a base for a retirement portfolio and combined with risk assets (mainly stocks), to provide upside for the investor. Or you could even add other bonds to the TIPS ladder for some bond upside. For the investor who wants to take even more risk off the table a TIPS portfolio can be combined with a deferred income annuity to take longevity risk complete off the table.

In short, its very possible to build a retirement portfolio out of 100% US TIPS that has higher safe withdrawal rates than those provided by riskier portfolios. This can be a great option for conservative retirees or those who do not want to take any stock market risk.

Big upside from flexible spending in retirement

September 26, 2013

Back in 2010 I posted on an alternative retirement withdrawal approach that allows for higher safe withdrawal rates (SWR). Back then I didn’t have a detailed model of this approach to provide much more insight. Now I do. Its very worthwhile revisiting this strategy and discuss the great benefits it can have to retirement plans. This alternative approach relies on having some flexibility, on the downside, in retirement spending. Lets take a look in detail on how this works, its benefits, and how you can apply it to your retirement plans.

This alternative withdrawal method is called the floor-ceiling model (FCM) and it was pioneered by William Bengen, the man behind the concept of SWR in the first place. Basically, the method calls for spending a fixed percentage of your portfolio each year subject to certain limits. Applying a fixed percentage to each year’s portfolio value can and will cause dramatic fluctuations in spending. That’s where the limits come in. This is quite different from the traditional SWR strategy where your SWR percentage is applied once at the beginning of your retirement and all subsequent withdrawals are simply adjusted for inflation. The FCM method just applies a limit to how much of a decrease you are willing to endure to real spending in any given year. As it turns out there is no need for an upper limit. Having this flexibility to adjust spending during bad years increases the SWRs. The chart below is from my original post.

FCM SWRs Sept 2013

As you can see from the table, having downside flexibility in spending allows higher SWRs while also providing upside spending possibilities in years where the portfolio does well. In Bengen’s original model in addition to the FCM method he added alternative assets classes, e.g. small cap stocks, in calculating his SWRs. I wanted to recreate his approach but isolate the impact of purely applying the FCM method to the traditional portfolio allocations of the SP500 and 10yr government bonds for various allocations to stocks and bonds. The table below shows the SWRs for various asset allocations for the traditional SWR method.

SWRs for traditional SWR method sept 2013

And here are the SWRs for the various asset allocations for the FCM method with a -10% limit to inflation adjusted spending.

SWRs for FCM SWR method sept 2013

As the tables above show the FCM method allows approximately 10% higher SWRs in retirement. The downside being that on average you end up with less wealth after the 30 year retirement period. I think most retirees would trade a guaranteed 10% per year higher spending rate for the possibility of higher end wealth. I would. But that’s not all. To see the true impact of the FCM method vs the traditional SWR model lets look at the detailed spending by year for the worst case and the best case retiree in the historical record. The table below compares the tradition versus the FCM method for the 1966 retiree (the worst case) and the 1975 retiree (the best case) for a 70% stock, 30% bond allocation. For the FCM method I highlighted years in which spending decreased from the previous year.

SWR traditional vs FCM for 1966 and 1975 retirees sept 2013

For the worst case retiree, 1966, the higher FCM SWR of 4.84% came at a small cost. In two years spending would have gone down and overall total dollars withdrawn over the 30 years would have been slightly less. $3.37M vs $3.38M. For the best case retiree, the FCM not only had a higher SWR of 4.84% but provided huge upside in spending $422K of spending in year 30 vs $163K in spending for the traditional method. In addition total lifetime spending was 2.5 times higher with the FCM method. The downside was more volatility to that spending as you can see from the highlighted cells. A worthy trade off? I think so.

In short, allowing for some flexibility in spending into your retirement model can have some huge benefits with little downside.


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