# The 4% rule means you let the market determine how much risk you are taking with your retirement.

Over on RiversHedge, the recent post “A hidden variable” made me think about something from a slightly different perspective.

even though consumption smoothing (e.g., the 4% rule’s method) is considered to be an expression of risk aversion in the macro-econ lit, a 4% constant inflation-adjusted spend is actually quite risk-seeking due to the compounding effects of errors

The point he is making here is that when you perform consumption smoothing, the amount you withdraw every year stays constant. Which feels like one kind of safety. But in reality, your dynamically-evaluated “risk of ruin” changes every year, which means you are actually **increasing** another kind of risk**.**

Here’s a simple example of what he’s talking about:

- Imagine you retire at the start of 2018. Go to Firecalc and use the defaults: $30,000 a year from a $750,000 portfolio over 30 years. It has a 5% chance of failure. Your plan looks pretty good, right? Pull the trigger on retirement!
- Now it is 1 year later. Your portfolio is now at $691,830. You need to withdraw $30,654 (after adjusting for CPI). And it only needs to last 29 years now. Go plug those numbers into Firecalc and you’ll see that you now have a 12% chance of failure.

You wouldn’t have retired with a 12% chance of failure. You would have considered it far too risky. But here you are, on a retirement trajectory that now has a 12% chance of failure.

## Letting the market determine our risk-level

This has a lot of similarities to arguments in favor of rebalancing. Why do we rebalance? If we don’t rebalance, then an extended bull run will mean we end up with 80% or 90% equities. If we decided that our risk tolerance required a 60/40 portfolio, it would be weird to *let the market determine our exposure to equity risk*.

And so we rebalance back to 60/40 because we’re in charge of our risk exposure, not the market.

When we don’t adjust our withdrawals in retirement, then we are doing the same thing: we are *letting the market determine our exposure to risk of ruin*.

If we wouldn’t spend a 30-year retirement with a 12% chance of failure, why are we okay spending a 29-year retirement with a 12% chance of failure?

Yet, how many retirees — even ones who run hundreds of simulations before they retire — continue to monitor their risk of ruin after they retire?

When we don’t adjust our withdrawals in retirement, then we are doing the same thing: we are

letting the market determine our exposure to risk of ruin.

There are two ways to visualise how much risk we are exposing ourselves to when are in the middle of executing a retirement plan: Milevsky’s *risk quotient* and Suarez, Suarez, and Waltz’s *Perfect Withdrawal Amount*. Let’s take a look at both in turn.

## Risk Quotient

In “A Gentle Introduction to the Calculus of Sustainable Income”, Moshe Milevsky produces an analytical solution (i.e. without relying on simulations or backtesting) to calculating the risk of ruin.

I actually wrote about this a few years ago but after reading the post on RiversHedge I realised I wanted to more clearly & explicitly lay out something I hadn’t really done before.

We can re-calculate this metric every year to see how our retirement is going. If assume 4% constant withdrawals for someone who retired in 1955, then the chart of annual *risk quotient *will look like:

See what I meant about “letting the market decide our risk exposure”? It is all over the place. We’re not making any conscious decisions about how much risk we are exposed to. We aren’t managing our risk exposure. Maybe we’re suddenly taking too much — or too little — risk…but we never explicitly make that decision.

For a 1955-retiree the *risk quotient* is volatile but never exceeds the starting value. You could argue that taking “too little risk” is something you can live with. But we can easily find ourselves taking *too much risk* as well.

Here’s a 1940-retiree. Notice how the *risk quotient* hits **double** the starting value **two times** in the retirement.

And this 1940 cohort is a perfect example of what RiversHedge mentioned:

a 4% constant inflation-adjusted spend is actually quite risk-seeking

The risk isn’t controlled and we spent a decade of our retirement taking on too much risk.

## How much risk does a 4% constant withdrawal scheme actually expose you to?

Instead of a few examples, we can perform a slightly broader analysis of every retirement cohort. For each retirement cohort, let’s calculate the average *risk quotient* of their entire 30-year retirement. And then chart all of the cohorts.

*(Note: because risk quotient is calculated analytically — not with a laborious simulation — it ideal for using in these kind of broad back tests that cover thousands of retirement years.)*

We can see that there are quite a few retirements where the *average* is extremely high. **This hardly looks like the strategy that a risk-averse person would take, does it?**

This is really just an variation of the same argument I made in “The Myopia of Failure Rates”. Even if a retirement starts out looking safe & low-risk it can quickly become risky. All you have to do is read about real world retirees in 2008 and see how it plays out in reality.

What we’re looking for is tools that help us diagnose that reality — so we’re not relying on gut feels — and tools that help us react to that reality.

## Perfect Withdrawal Amount

The second tool we can turn to is the *Perfect Withdrawal Amount.*

When I originally wrote about the *Perfect Withdrawal Amount* I was less impressed with it. But I’ve come around to a more favorable opinion over time. The *risk quotient* above only tells us that we’re in trouble, it doesn’t directly tell us what to do about it. The *Perfect Withdrawal Amount *not only tells us we’re in trouble but gives a way to figure out what to do about it.

Let’s go back to the Firecalc example we started with and use some numbers from the spreadsheet at at the end of my post on “The Perfect Withdrawal Amount”.

We start with $750,000; withdrawing $30,000; and we have 30 years to go. We choose some parameters for our *Perfect Withdrawal Amount* engine and it spits out a result: $30,000 out of $750,000 is the 7.5th percentile rate.

Instead of letting the market determine our exposure to risk of ruin **we want to maintain a constant risk exposure**. That means every year we re-run our *Perfect Withdrawal Amount* engine see what the new, current 7.5th percentile rate is and then use that for our withdrawals.

To continue our example, recall that in the second year our portfolio has fallen to $691,830 and we have 29 years left. What’s the new 7.5th percentile amount?

$28,373.

In other words, in order to maintain a constant risk of ruin we need to withdraw not $30,654 but instead $28,373. That difference, 8%, is small but not trivial.

Going back to the RiversHedge post, that 8% is the “compounding errors”. We can ignore 8% for now but — if the market continues to move against us — 8% could turn into 10%, then 20%, then 30% and more.

## Risk of Ruin vs. Risk of Lifestyle Adjustments

Of course, there’s never only one risk facing us. We’ve always known that we can avoid risk of ruin by adopting some sort of variable withdrawal strategy. So does *risk quotient *or the *Perfect Withdrawal Amount* add anything new to our tool belt? I think it does.

By using the *Perfect Withdrawal Amount* we are able to be very explicit about the trade-off we are making between the two main risks a withdrawal plan faces: risk of ruin & risk of non-smooth consumption.

From the example above we know:

- If we want a constant exposure to risk of ruin, then we should withdraw $28,373.
- If, on the other hand, we want a constant exposure to non-smooth consumption, then we should withdraw $30,654.

But there are also a multitude of points in between. In reality, we are going to compromise between the two extremes. Maybe we accept a *little bit* more risk of ruin in order to maintain our smooth consumption for the next 12 months (maybe we *really* want to attend our granddaughter’s college graduation and so we’ll postpone any bigger cuts to spending until next year). Maybe we just take a simple average of the two — a kind of Solomic compromise — and decide to withdraw $29,513. Or maybe we decide in the end that we’re not comfortable increasing our risk of ruin just 12 months into retirement.

But whatever we do, *we’ve made a conscious choice*. We didn’t let the market decide for us.