If you have researched retirement at all (early or otherwise), you’ve probably ran across various retirement calculators online. You input how much money you have (or plan to have), your asset allocation, and it spits out some numbers. This Vanguard Retirement Nest Egg Calculator is a good example of a simple version.

Let’s try an example. If I am 40 years old and thus assume I have up to 50 years left in retirement, and I want to maintain a 4% withdrawal rate ($40,000 a year from a $1,000,000 portfolio that is 65% stocks/30% bonds/5% cash), the tool uses Monte Carlo simulations to calculate that I have an 80% chance of lasting 50 years.

There is effectively one output: the odds of not running out of money. Either you still have at least a dollar, or you don’t. In my example, I have an 80% chance of having $1 or more at age 90.

But what if you also considered the odds of running out of time? Yes, that’s a euphemism for dying. (Ever notice how many of those we have?) In another neat tool from Engaging-Data.com, Will Your Money Last If You Retire Early? adds some helpful nuance to this analysis. You input the same types of information, but now in any given year you are provided the overall odds of each of these things happening:

• Red – You are alive, but ran out of money.
• Light green – You are alive, with less money than you started with. (Kinda nervous?)
• Green – You are alive, with between 100% and 200% of what you started with. (Nice and comfy.)
• Dark green – You are alive, with over 200% of what you started with. (In hindsight, I didn’t need to save so much…)
• Grey – You are pushing up daisies. (In hindsight, maybe should’ve retired earlier…)

Here are sample results for the early retirement scenario above at 4% withdrawal rate (age 40, retirement horizon 50 years, $40k from a $1m 65/35/5 portfolio). I picked the female mortality table – if you have a male/female couple, it’s safer to pick the person likely to live longer.

There’s an angry streak of red where I’m broke. Of course, there’s a bigger streak of grey where I’m not breathing.

Here’s the same scenario, except with a lower 3% withdrawal rate ($30,000 a year from a $1,000,000 initial portfolio):

That change got rid of the red, but there is a lot of dark green. (1% makes a big difference.)

Here are sample results for a more traditional retirement scenario: (age 65, retirement horizon 25 years, $40k from a $1m 65/35/5 portfolio)

As a financially conservative person, these charts help illustrate why I prefer working with a 3% safe withdrawal rate for early retirement (50 and under) and 4% safe withdrawal rate for traditional retirement (closer to 65).

My favorite part of this tool is that it makes you take into account your mortality. It’s not all about staying above $1 in the bank, but also about maximizing your years of freedom. If you’re 40, you have a 10% chance of dying before even reaching 65. (This is why most people know someone who died shortly after retirement.) Is it better to have zero chance of broke and be 70, or 5% chance of broke and 60 with 10 more years of retirement (and 10 fewer years of work)? It is better to live a little more luxuriously for shorter time, or a little more frugally for a longer time? Playing around with all the different input variables might help you weigh the options.

Here’s another neat (and free!) portfolio analysis tool – PortfolioVisualizer.com. You can upload a custom asset allocation and get all sorts of backtest data and Monte Carlo simulation results from it. If you register for an account, it will remember your model portfolios for future use.

I created a custom portfolio “MMB Default” similar to my current portfolio asset allocation and below are selected charts that were produced. Here’s the summary:

Historical portfolio growth and annual returns. (Note that the time period shown was limited because the available data for Emerging Markets only went from 1995-2017. Apparently there are some ongoing issues with data licensing.)

Historical drawdowns during the same period. This provides a good feel of how “painful” it was to hold this portfolio. 2009 was certainly a stressful year when both our portfolio and future job prospects were being questioned.

Monte Carlo simulation of 4% withdrawal rate over a 30-year retirement period. I used my custom portfolio and had it simulate a withdrawal rate of $40,000 from a $1,000,000 portfolio (4%), adjusted annually for inflation, for a 30-year period. You can alter nearly all of these variables (withdrawal rate, inflation adjustments, period length, etc). Monte Carlo basically looks at many possible trajectories based on historical asset return characteristics. If things turn out well, you end up with a “runaway” portfolio, but if they don’t you can hit zero pretty fast.

The success rate looks at the percentage of simulated scenarios that end up with a positive value at the end of the period. At a 4% withdrawal rate for 30 years, it was 95%. At a 5% withdrawal rate for 30 years, it was only 84%. At a 5% withdrawal rate for 50 years, it was only 69%.

Here’s where I warn you that Monte Carlo simulations are not the end-all of portfolio safety. You can’t predict the next 50 years when you can barely look back 50 years. Living off a portfolio for decades involves not just a reasonable rate of withdrawal but planning as to how you could cut expenses or create additional income if conditions go sour for an extended time period. I’d rather have 90% theoretical safety and a flexible backup plan over 99% theoretical safety and no backup plan.

Portfolio Visualizer has several additional features that I may never use, but even the above is enough to make it a very interesting tool for the DIY investor. I hope they get their data source issues sorted out eventually. You can find all of my posts about portfolio tools in the Tools & Calculators category.

Investment advisory firm Research Affiliates has updated their interactive Asset Allocation tool, which now provides estimates of expected returns for more than 130 asset classes and model portfolios. There are two expected return models, “valuation-dependent” and “yield-plus-growth”. In addition, you can input your own custom asset allocation.

My initial reaction is that while the tool got new bells and whistles, it also became more confusing to navigate and harder on the eyes. Here’s a screenshot of their scatter plot showing the expected risk and return for several asset classes under their valuation-dependent model.

I created a custom portfolio “CustomMMB” using my current portfolio asset allocation and it is charted below on their risk/return map. In a separate window (not shown) you can see how each individual asset class contributes to the total expected return.

As you can see, my portfolio did not offer the maximum expected return for its risk level. The RA efficient model portfolio that did includes an exotic mix of asset classes, including Emerging Markets bonds (non-local currency), Bank Loans, US Private Equity, European Private Equity, and direct investments into US Commercial Real Estate (not through REITs). Unfortunately, I’m not even sure how to access many of those asset classes.

I appreciate that they freely share their research methodology and results, specifically covering the valuation perspective. US Equities have historically high valuations, but interest rates are also at historically lows. The next 10 years should be interesting…

Another portfolio analysis tool that lets you input your specific asset allocation is PortfolioCharts.com Safe Withdrawal Rate calculator. This Research Affiliates tool says my expected 10-year real return is only 2.4% (equates to a nominal expected return of 4.6%). The PortfolioCharts.com tool says the same personal asset allocation has a historical perpetual withdrawal rate of over 4% over a 40-year timeframe.

I just noticed that PortfolioCharts.com has updated their Withdrawal Rate Calculator. It has improved visualizations and as a personal finance geek I even found it fun. You can enter your specific asset allocation slices down to 1% and see customized results.

The Withdrawal Rates calculator shows the safe withdrawal rate for any asset allocation over a variety of retirement durations based on real-life sequence of returns. Those looking to retire early or leave money to heirs can also see the perpetual withdrawal rate that protected the original inflation-adjusted principal.

You can read about the specifics behind these improvements here. You should also read all the assumptions here. For example:

The withdrawal rate is the percentage of the original portfolio value used for one year of retirement expenses. Each year, expenses are adjusted for inflation (not for portfolio size) to maintain constant purchasing power.

Briefly, a “safe” withdrawal rate (orange) allowed a portfolio to go as low as $1 but never hit zero at the end of the timeframe. In other words, the ride could have still gotten quite hairy for a while. A “perpetual” withdrawal rate (green) never ended up less than the initial principal, even adjusted for inflation. The author Tyler recommends the perpetual WR for early retirees or for people who desire to leave an inheritance for heirs.

Here is the specific chart for my current portfolio asset allocation:

I would be quite happy with being able to confidently withdraw over 4% (+ inflation adjustments) of my portfolio for the next 40 years. The short-term drawdown paths can still be scary though. The usual caveats with using backtested data also apply.

Playing around, I noticed that the simplest way to change things up was by adding a healthy chunk (~20%) of gold instead of stocks. This seemed to significantly improve the perpetual withdrawal rates in the short-term (0 to 15 years). It’s too bad I still don’t have a firm fundamental understanding of gold. If you can’t maintain faith in it when things are scary, then you shouldn’t own it in your portfolio.