Life After Full-time Work Blog

Getting into the meat of it: how to calculate it, different points on the risk spectrum, and numerical examples

 

See the end of this post for another message.

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The subject last time was your Personal Funded Ratio, the ratio of how much you have to how much you need, typically used in the context of retirement. The concept is almost childishly simple: do you have more than enough (a PFR higher than 100%) or not enough (a PFR lower than 100%)? What’s less simple than the interpretation is how you actually calculate the number, and more specifically, how you calculate the denominator, meaning how much you need to retire on.

So yes, this post is a bit on the technical side.

Let’s start with retirement right now. At the end we’ll see that it’s only a small conceptual adjustment to deal with retirement in the future.

What I’ll take as known is your age, sex and health, and how much each year is your target income (before income tax). Those are all “today” items.

What’s not known is what happens in the future, specifically your future lifespan, future inflation and your future investment return. Those three together make financial actions for retirement the nastiest, hardest problem in finance, according to Bill Sharpe, the celebrated 1990 Nobel Prize winner in Economic Sciences.

Let’s simplify the unknowns slightly by combining the last two, and calling them your unknown future “real” return on your assets (that is, your investment return each year minus that year’s inflation).

Already we can reach one important conclusion: your PFR is unknown, until your lifespan and your future real returns are known. In other words, you’ll know exactly what your current PFR is, once you’ve passed away! The easiest way to look at your PFR today, then, is to make assumptions about your lifespan and your future real return; and then, whatever PFR results from those assumptions, it’s essentially an estimated PFR.  So, we can make what we think of as our “best estimates,” and then we have a “best estimate PFR.” Or we can use (as a safety margin) safer estimates (meaning: a longer than expected lifespan, and a lower than expected real return) and calculate the resulting safer estimates of our PFR.

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Let’s look first at longevity as a separate unknown.

There are many longevity tables (for those who are in at least average health – for those in below-average health, consult your doctor if you really want an estimate of your future life expectancy). I use longevityillustrator.org. As examples of numbers in this table, the average expected future lifespan for a non-smoking 65-year-old male in average health is 21 years, for a female 23 years, and for their joint-and-last-survivor mode (meaning: while at least one is likely to be alive, or, to the second death) is 27 years. Let’s say we’re planning for the couple: we’d use 27 years as the planning horizon for our best estimate. (And yes, you’d be right if you think there’s a small safety margin already built in there, because after the first death the amount of income required by the survivor will almost certainly fall, relative to what the couple needed together.)

If you want an explicit safety margin, you might consider what’s technically called the 25^th percentile estimate, meaning the horizon that only 25% of similar couples will survive to. The table says it’s 31 years. Clearly the amount required to fund 31 years of income will be higher than what’s needed for 27 years.

Or if you want a bigger safety margin, you might use the 10^th percentile, meaning the horizon that only 10% of similar couples will survive to. The table says it’s 34 years.  And again, that will require even higher assets to fund.

You can see how using the 25^th and 10^th percentile joint-and-last-survivor lifespans build in safety margins (without actually achieving total certainty: that would require planning to the end of the longevity table, which I can’t actually find on the website; I think it’s at least age 105.)

The amount of assets you’ll need is called a “present value of an annuity” (an annuity being a stream of income, and the present value being the amount you need today in order to generate the stream).

Let’s use the notation P(50%L), P(25%L), P(10%L) and P(0%L) for the present values that use the 50^th (or “expected”), 25^th, 10^th and 0^th (or, end of table) percentile lifespans. There’s nothing new in these notations: they’re simply ways of condensing a large number of explanatory words.

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We can look similarly at the real investment return as a separate unknown.

Let’s skip the technical side of how you might come up with hypothetical future real returns that are reasonable, and what their probabilities are. Go to an investment professional for that. There’s the added complication that the degree of uncertainty about the real return changes as the planning horizon changes. That’s another reason for skipping the technical side. But once you have assumed some distribution for the future, we can use similar notations for the present values of the resulting annuities.

P(50%R), P(25%R), P(10%R) and P(0%R) would be our notations for the annuities based on the 50^th percentile projected real return, the 25^th percentile (so, a lower return, hence a higher present value), the 10^th percentile (even lower return, even higher present value) and the 0^th percentile (whatever you can actually lock in with certainty over the relevant period).

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Obviously P(50%L, 50%R) would then be the notation for the present value of the annuity that provides a real income stream that’s based on the best estimate (or “expected”) return over the period, for whatever that best estimate longevity horizon happens to be.

That’s a combination of the L (lifespan) and R (real return) probabilities.

How do you combine the two 25% probabilities? Fortunately, there’s a comfortingly simple answer.

Notice that the L and R probability distributions are independent of each other. Your return depends exclusively on your investments, and not at all on your age. Similarly, your lifespan depends exclusively on your age and health, and not at all on what you’re invested in. So it’s easy to combine the inputs.

For example, P(25%L, 25%R) denotes a 75% (or ¾) chance of financial success with the longevity table (meaning you won’t run out of income before death – a strange definition of success, when you’re saying you won’t live that long!), and a 75% (or ¾) chance of financial success with your real investment returns (meaning you’ll earn at least that much).

So, the chance that both will be successful is ¾ x ¾, or 9/16. The chance that both fail is ¼ x ¼, or 1/16. And the remaining 6/16 is the chance that one fails and one succeeds. Half of those 6/16 will result in aggregate success, half in aggregate failure.  Add those 3/16 halves to your 9/16 and 1/16, and voila, the aggregate chance of overall success is 9/16 + 3/16, or 12/16, or ¾. And the aggregate chance of failure is similarly ¼. Lo and behold, using the individual input estimates for 25%L and 25%R will combine to give you the estimate for the combined (25%L, 25%R) annuity.

And so we can calculate P(25%L, 25%R) [and similarly P(50%L, 50%R) and (P10%L, 10%R)] without having to do all the sets of inputs for L and R separately. Whew!

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That’s the payout, or “decumulation” phase. The “accumulation” or saving phase is very similar, and adds no new concepts.

All we need to do is to add future savings (typically called “contributions”) to the retirement account, and accumulate them until the proposed retirement age; and we’ll calculate the present value of the required annuity at that retirement age.

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Let me show you some numbers, just to make the ideas crystallize. They’re not meant to reflect any particular situation, or even to be in any way close to realistic. I just need numbers, and I’ve made these ones up.

Let’s consider a couple, male and female, both currently aged 40. And they’re planning to retire at age 65. Their current combined annual earnings are $150,000. They have saved $200,000 in their combined retirement savings accounts so far, and plan to contribute $10,000 a year together (which includes their employers’ contributions) in the future (or 6.7% of their combined pay). They’re hoping for a combined $30,000 a year from their (equivalent of) Social Security, from age 65 (that’s what a friend told them). They have a home currently worth $750,000. It has a mortgage, but since it will be paid off before age 65, they’ll ignore the mortgage, since all these projections are as at age 65.

They don’t have a target retirement income, but friends say that everyone suggests they should initially target 70% of their current income.  So they’ll input $105,000 a year (in real terms, that is, adjusted for future inflation).

Their best estimate planning horizon (therefore with a 50% chance of failure) is (from the table I mentioned) 27 years. They also want to calculate their 25% and 10% personal funded ratios, so they’ll use 31 years and 34 years for those projections.

How about their investments? As before, I won’t go into the details of how they’ll invest and what their expected real returns and uncertainty measures are. I’ll just disclose the numbers they’ll be using in their projections.

For their best estimate, they’re using 3.5% real per annum up to retirement (they’ll be mostly in equities until then) and 1.0% real per annum after retirement (with a much more conservative portfolio, because that’s what everyone seems to suggest they should do).

The results (from this obviously totally artificial set of circumstances)?

Ther best estimate (that is, 50%L, 50%R) of how much they’ll need at age 65 for their projected “desired” or “target” annual retirement income of $105,000 is $1,777,805. And the best estimate of what they’ll have is $2,641,398. That’s 135% of the target. “Good news!” is their first reaction (plus the fact that they now actually have a number. They had no idea whether the projected best estimate funded ratio would be 50%, 150%, 250% or whatever).

More detail: their projected income is projected to be funded to the extent of 29% from Social Security, 19% from their current retirement savings, 16% from future savings, and 71% from their home.  Whoops, they hadn’t realized that they’d have to somehow monetize their home (which they consider not just as shelter but as an emotional support) to get to their projected income.

For their (25%L, 25%R) or 25^th percentile (safety) projection, they use 31 years as their planning horizon and 1.6% real for their pre-retirement annual investment return. Now their target is projected to be 91% funded. And even that PFR requires 40% support from monetizing their home. Very, very sobering.

Their (10%L, 10%R) PFR would be even lower, obviously. They don’t even bother to calculate it. Enough bad news already.

With sinking hearts, they decide to next project what happens if they work to age 70.

Now their 50%L is 22 years, their 25%L is 26 years, their 50%R is again 3.5% before retirement and 1% after, and their 25%R is 1.8% before retirement and 1% after. And their friends suggest using $40,000 for their (equivalent of) Social Security estimate, starting at 70.

Never mind their best estimate (that is, 50%L, 50%R inputs). They realize that a 50% failure possibility is unacceptable.

Their (25%L, 25%R) or 25^th percentile (safety) projected funded ratio rises to 121%. Oh, thank goodness, more than 100%! It shows 38% from Social Security, 14% from their current savings, 16% from their future savings, and still a whopping 53% from monetizing their home.

But these calculations, these orders of magnitude, have now started to become understandable. And, as a result, here’s what they’re starting to think:

• Let’s reconsider the target post-retirement income. After all, with their mortgage payments and their retirement contributions, their lifestyle doesn’t even closely reflect 70% of their current income. Maybe that’s far too high a target. Let’s start keeping track of our lifestyle, and maybe in a year’s time re-do these calculations with a more accurate lifestyle input. Surely that will result in much higher projected personal funded ratios at both 65 and 70. So maybe we won’t have to work to 70 after all. (And when our mortgage is paid off, we can direct those payments to increase our retirement savings, which will make the outcome even better than currently projected.)
• Let’s get more accurate estimates as well for our (equivalent of) Social Security, while we’re at it. Getting estimates from friends isn’t good enough.
• Maybe we should save more. That 6.7% (which includes what our employers contribute) isn’t very high. It’s time to take this aspect seriously right now (in addition to increasing our savings after the mortgage is paid off).
• Perhaps if all of that could get our (25%L, 25%R) estimated personal funded ratio at age 70 above 100% without including our home, that would give working to 70 a new meaning and purpose: the ability to exclude our beloved home from our planned retirement assets, so that we can age in it, as we currently hope to do, or at worst downsize if we need to monetize part of it.

All in all, a meaningful, informative and easily understood exercise, with a big influence on their future attitudes. Thank goodness they did this at age 40, when there’s still a lot of time to change the projected outcomes.

And, as they make projections over the years, they’ll naturally start to consider other approaches. For example, divide their spending into “needs” (what they consider they could absolutely never cut back on) and “wants” (their desires, capable of being trimmed – no matter with how much sadness – if all of them turn out to be unaffordable). If their future projections of personal funded ratios turn out to be consistently above 100% when needs alone are considered, but below 100% when both needs and wants are considered, perhaps they may want to take more investment risk post-retirement (since, after all, their planning horizon then is still over 20 years). Or, if they gradually become more risk-averse, perhaps they’ll buy a guaranteed joint-and-last-survivor annuity from an insurance company, inflation-proofed, to lock in their needs, and use the balance of their assets to finance whatever they can of their wants.

Lots to think about. But at least knowing their PFRs gives them a base for planning their financial future.

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Added message:

I got to know Steve Vernon many years ago at the Stanford Center on Longevity. He has launched an illustrated series of comic-book-like pieces to accompany his website on retirement planning. I highly recommend anything Steve does!

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Takeaway

You can calculate different probability points in your PFR distribution by using independent probability estimates regarding longevity and real investment returns. While most people will want a financial expert to help with these calculations, it requires no expertise at all to get a deep understanding of the lifestyle implications.   

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