# Do I Have Enough Money To Retire?

Out intern is such a goody goody…Uncertainty Around InflationA quick refresher — inflation is the tendency for stuff (everything from the price of a latte to the rent you pay your landlord) to increase in price over time.

In retirement simulations, inflation is usually modeled as a drag on the portfolio return.

For example, if Randy’s portfolio earned 6% in nominal terms (nominal = before inflation) and inflation was 3% during that year, his inflation adjusted return would be 6%-3%=3%.

Inflation just stole half of the return!Stepping away from our chat with Randy for one second, let’s get a sense of how inflation drives retirement uncertainty.

The following plot shows that just varying our inflation assumption (and not changing investment returns at all), we get a significant variation in outcomes.

And while 2% may seem like a reasonable estimate for future inflation, the other values are within the realm of possibility as well (for example, Japan experienced deflation for decades and the U.

S.

experienced double digit inflation throughout the 1970s and severe deflation during the Great Depression).

Inflation can cause significant variation in wealth outcomesDigression over, let’s get back to our client, Randy.

Unfortunately, he now wants us to model how his inflation adjusted wealth changes in retirement.

Randy expects to get some money from Social Security each year so he estimates that he will only need to fund spending of \$28,000 from his portfolio each year to maintain his current lifestyle.

This \$28,000 is an inflation adjusted value — meaning that if inflation were 1% for the year, then next year Randy would need \$28,280 in nominal terms.

Annual Portfolio Withdrawal (Inflation Adjusted): \$28,000Expected Age at Death: 85So we jump on our laptops and start coding.

We decide to model inflation as a normally distributed variable with an expected value of 2% and a standard deviation of 1%.

Also, we ignore the correlation between inflation and investment returns in order to simplify the analysis.

After some number crunching we come up with the following chart:Inflation is quite the dragOur intern explains it to Randy, “Mr.

Randy, our median estimate of your wealth at age 85… when we expect you to umm… pass away is \$81,000.

So in our median scenario, you did have enough money.

We also included the no inflation case (the red line) to show you how our estimate of inflation negatively impacts your wealth.

”“However, in 40% of the simulations that we ran (and we ran 5,000 btw), you ran out of money!.If your portfolio runs dry, you would have only Social Security to live on for the rest of your days…”And he continues “I also made you this histogram to better visualize your wealth outcomes.

” (Our intern is such a showoff)That’s a lot of observations to the left of the red line (which denotes \$0)Uncertainty Around Living Expenses and Age of DeathNow Randy wants to know what are some things he absolutely must avoid if he wants to stay in the black throughout his retirement.

Our intern pipes up again (sigh…) and says, “There is no guarantee that you will be able to maintain an inflation adjusted spending level of \$28,000 throughout your entire retirement.

You could get hit with unforeseen medical expenses, higher taxes, etc.

So we should take a look at how our projections change if you end up spending more.

”“Mr.

Randy, we simulated what would happen if you spent \$38,000 in retirement (instead of \$28,000).

Just like before we ran 5,000 simulations.

Now you end up running out of money (besides Social Security) in 76% of the simulations we ran!.Previously you ran out in just 40%.

If Randy overspends, he is in big trouble“And if you end up living longer than expected by 5 years (passing away at age 90 instead), you end up running out of money in 56% of the simulations that we ran for you, up significantly from only 40% previously (when we assumed you would pass away at age 85).

Living 5 years longer than expected depletes poor Randy’s portfolioConclusionFinally Randy is satisfied.

Very worried but satisfied.

He looks at us and says.

“I learned something today.

You can run thousands of simulations for me (which already have their own variance due to investment returns and inflation), yet a slight tweak of the assumptions and everything changes again!.So it’s like variance stacked on top of even more variance!.So much uncertainty…We have no idea what he is talking about but our intern shows Randy the following chart.

High level breakdown of the sources of variance (a.

k.

a.

uncertainty)“Mr.

Randy, we can split the variance into two parts: the known and unknown.

The known sources of variation, which we explored in detail earlier, come from volatility in investment returns, inflation, age of death, spending etc.

Each of these sources of variation stack on top of each other and compound each other.

But there are also the ‘unknown unknowns’ — things that contribute hidden variation that we are unable to model because either we just don’t know about it or what we know is wrong.

”Randy says he needs a few days to digest all the findings but sets up a meeting with our intern in a week to go over next steps.

Seems like our intern has stolen our client.

We resolve to think harder before hiring any more interns in the future (we originally only hired him because his latte art is incredible).

Source: 10-Year Capital Market Return Assumptions, BNY Mellon.