# Unfunded personal pension liabilities

When I read Gordon Pye’s article (“When Should Retirees Retrench?” (2008)) I had an “ah ha” moment: the PMT formula can be turned into a risk metric.

Though Pye covers the same basic ground as all other PMT advocates (of which there are many) Pye’s paper is interesting because of a very slight change in perspective. Instead of starting with the results of the PMT calculation and then telling retirees to use that number, he starts with the amount of money a retiree needs to maintain their lifestyle and then uses PMT to tell them whether they are okay or need to make cuts to their lifestyle.

This rule determines whether a retrenchment is required at any time, and if so how much.

This change in perspective continues throughout his paper: when the PMT math tells us we can withdraw more money, Pye (unlike most PMT advocates) tell us to ** not** do that. He worries that if we increase our withdrawals this year, we might need to cut them next year. And cutting our standard of living is always painful. For him, the PMT result is a red flag, not a schedule of withdrawals to be adhered to.

With this slightly changed mindset we can think of PMT as generating a warning signal. When our spending is below the number PMT calculates we are (relatively) “safe”. When our spending is above the number PMT generates we are (relatively) “risky”.

In Waring & Siegel’s “The Only Spending Rule Article You’ll Ever Need” they are more explicit about this mindset.

In fact, the payment will vary

preciselyproportionally to the change in the asset value (for a given discount rate). Think about the last time you bought a car on time payments: the $40,000 car that you considered had a payment exactly twice that of the $20,000 car. Principal and payment are two sides of the same coin.

By using PMT you are exposing yourself to 100% of the risk of the underlying assets. If your portfolio is composed of a risk-free asset then your PMT-derived-income will also be risk-free. If your portfolio is composed of risky assets then your PMT-derived-income will expose that risk directly to you.

The standard deviation of the portfolio’s investment strategy is also (for a constant discount rate) the standard deviation of consumption.

With this new perspective on PMT, we can think of withdrawals that are *under* the PMT number as building up a “rainy day fund” and withdrawals that are above the PMT as eating into the “rainy day fund”.

Let’s take a look at how this might look in practice; here’s a sequence which eventually fails for a retiree.

- The portfolio is 100% S&P 500.
- The retirement starts in 1966.
- Withdrawals start at $40,000 a year and are then inflation-adjusted.
- 4% discount rate for PMT
- 30 year period for PMT
- All numbers below are real, not nominal.

In this scenario, the retiree will run out of money in the 23rd year of retirement.

investment risk translates directly into consumption risk

In the first year of retirement, the PMT formula says we can withdraw $55,606; we actually withdraw $40,000. We can think of that extra $15,606 as going into a “rainy day fund”.

In the second year of retirement — after adjusting for our first withdrawal and market returns — PMT says we can take out $48,888; we still withdraw our constant $40,000. Our rainy day fund increases by $8,888 up to $24,494.

Since we’re using the 1966 sequence of returns, we know that means things will eventually take a turn for the worse. Our withdrawal rate isn’t sustainable. After 8 years we stop contributing to our rainy day fund and start withdrawing from it.

Now let’s look at this hypothetical rainy day fund for a 1980 retiree, which is a successful scenario for the 4% constant dollar withdrawal rate.

We end up with a ridiculously huge portfolio.

Why would you ever want to use this concept of tracking your Rainy Day Fund? Why not just use the PMT numbers directly?

Most people don’t like it when their income changes every year. People are willing to make ** small** changes to their lifestyle in response to the market but very few people are willing or able to make changes commensurate with the size of market events.

If the stock market drops 50% next year, how easy would it be for you to cut your standard of living by 50%? Have your kids transfer to a community college, move to a new house, sell a car…we’re talking about dramatic lifestyle changes in the span of just 2–3 months.

Waring & Siegel’s answer to this is: Well, if you can’t tolerate changes in the withdrawals, then the assets in your portfolio are too risky. Use less risky assets.

Consumption volatility directly follows from investment and discount rate volatility, and is what risk is

There is a lot of truth to that. But I’m not convinced how realistic it is to put into practice for most people. With a portfolio that is 50% bonds you are still exposed to a 21% drop in nominal portfolio value (in 1931) and 23% drop in inflation-adjust portfolio value (in 1974). That’s a dramatic consumption volatility for a portfolio that is 50% bonds.

Even if we reduce our equity holdings, so we are holding 80% bonds, we are still subject to an 8% nominal income drop and a 19% inflation-adjusted income drop.

Except, as we know from all the safe withdrawal research, by holding so few bonds we’ve exposed ourselves to quite a lot of longevity risk.

So it doesn’t seem straightforward to simply say “if you can’t tolerate income volatility, change your asset allocation.”

But people ** definitely** want stable incomes. One survey I saw (unfortunately I can’t find the source) showed that 80% of respondents preferred a stable retirement income stream over a more volatile one.

And income smoothing is more than just a “nice to have”. It is one of the fundamental models of modern economics via Modigliani and Brumberg’s life-cycle model. Instead of matching our consumption perfectly to our current circumstances we try to smooth it out over our lifetime.

Buying a house is the best example of this. Very few people pay cash for a house. Instead we borrow from our future income stream to buy a house today, instead of 15 or 20 years from now.

Yes, this introduces some risk. Houses get foreclosed.

I find it hard to swallow Waring & Siegel’s suggestion to stop doing consumption smoothing after a lifetime of doing it.

We shouldn’t avoid risk, we should manage it. And that might mean ignoring (or dampening) the income changes called for by PMT.

By smoothing our income adjustments we’ve introduced the Rainy Day Fund.

Now is time to introduce another concept: our retirement portfolio and the withdrawals from it are really our own personal pension plan. We think of pensions as magical creatures but they aren’t. Whether your employer contributes 8% to a pension plan or 8% to your defined-contribution plan…it is exactly equivalent. The only difference is whether the money is managed by you or someone else. No money is created or destroyed either way.

Think of yourself as the manager of your own personal pension plan.

You know all those news articles you’ve read about underfunded pension plans? Income smoothing means your own personal pension plan can now become one of those “underfunded pensions”.

The Rainy Day Fund is a measure of how over-funded or under-funded your personal pension is.

Even with smoothing, the true underlying, unsmoothed risk is realized whenever there is a long period of disappointing returns

The Pension Benefit Guaranty Corporation is a U.S. Government Agency that protects the pensions of 40 million Americans. But it doesn’t protect our personal pension. We want income smoothing. But we’re afraid of accumulating too much risk. The Rainy Day Fund gives us a tool to manage our risk. By smoothing our income, we’ve borrowed from our future self. We’re in debt to yourself. The Rainy Day Fund shows us that debt.

Here’s a 1966 retiree. This time she’s using VPW (with a 50-year withdrawal horizon). But she’s added Ken Steiner’s income smoothing adjustments.

In the very second year of retirement, we already need to start smoothing. We took out $52,168 last year. Plain PMT tells us to cut that to $46,160; after applying income smoothing we instead take out $48,576. Our Rainy Day Fund is now $2,166 in debt.

Over the next 16 years our Rainy Day Fund will continue to go further into debt. Eventually the economy improves. We start paying back the debt on our Rainy Day Fund. But even after 30 years our Rainy Day Fund is still $40,000 in debt.

How much debt is too much for the Rainy Day Fund? When should you worry about it? What kinds of corrective actions could you take? Are there good or bad ways to manage that debt? Are there ways to build a better or worse income smoothing algorithm?