# Connecting Funded Ratios and Success Rates

I think the Funding Ratio is a pretty great tool for retirement planning. It can easily take into account your entire balance sheet — things like pensions, Social Security, and downsizing your house. It can easily handle different amounts of spending every year. And, with a bit of arithmetic re-arrangement, it can also be used to guide your savings before retirement. But it does have some downsides and one of them is that the resulting number isn’t exactly intuitive.

You have a Funded Ratio of 0.9. Does that mean “monitor and see”? Or “start panicking”? Does a Funded Ratio of 1.2 mean “you should have retired 3 years ago”? Or does it mean “eh, there’s still a chance it could all explode”?

And, to complicate the question — how much does all of that depend on your current age and the discount rate you are using? If you have a Funded Ratio of 1.3 at age 50 is that the same as a Funded Ratio of 1.3 at age 60? People disagree about what discount rate to use when calculating the Funded Ratio. How big of a difference does it make?

One way we can get a better understanding of this is to figure out the link between Funded Ratios and Failure Rates via backtesting. What we want to do is pretty simple. If someone is 65 years old, with a Funded Ratio of 1.0, and retired that moment…what’s their probability of failure?

Except we want to know the answer for all possible ages and Funded Ratios. Which, it turns out, takes my computer a little while to chug through. But it does result in some pretty looking charts!

Before I start interpreting that chart: what are the assumptions underlying it? We assume the couple lives until age 97. That’s the 95th percentile for a male/female couple according to the Society of Actuaries. We assume a 60/40 portfolio of US equities and US intermediate-term Treasuries, rebalanced annually. We assume a discount rate based on historical global asset class returns. That means 5% for stocks and 1.8% for bonds, for a weighted average of 3.72%.

Back to that chart: All of the light colored dots mean “no failures”. We can clear things up a bit by redoing the chart but only showing failures.

Some initial takeaways:

The color of the dots is keyed to the failure rate…but that doesn’t tell us much. We’re looking at a three-dimensional plot (the colors are the third-dimension) in two-dimensional space, which never works well. If we take slices of the data we can make some two-dimensional plots that are a bit easier to understand.

With a Funded Ratio of 1.0, we’re still generally looking at a 30–40% chance of failure. Which is almost certainly too high for anyone. With a Funded Ratio of 1.2, a 40-year old (super early retiree) only has a 5% chance of failure. At age 60, that same Funded Ratio has a 10% chance of failure. And by age 70 it has over 15% chance of failure.

We can follow this change over time by looking at the Funded Ratio required to maintain a constant 5% chance of failure over time.

Or, if you prefer, a 0% chance of failure over time.

If you’re using a Funded Ratio to guide your retirement, then you’ll want it to follow one of these curves. And if it isn’t…then you’ll want to make adjustments.

We can also slice things by age. For a person who retires at age 60, what level of Funded Ratio corresponds to what failure rate?

If you actually run a linear regression on the above curves it turns out that most of them have a slope pretty close to -1. In other words, increasing your Funded Ratio by 0.1 decreases your probability of failure by (approximately) 0.1 as well. Take the age 50 one as an example. A Funded Ratio of 0.8 has a probability of failure of 0.62. A Funded Ratio of 0.9 has a probability of failure of 0.54. A Funded Ratio of 1.0 has a probability of failure of 0.36. A Funded Ratio of 1.1 has a probability of failure of 0.20. It’s not perfect but it seems like a pretty good rule of thumb.

Everything we’ve done so far is based on a discount rate of average historical returns. Another common choice is the TIPS real yield. Currently the real yield of 30-year TIPS is 0.54%. It should be obvious that using a (much) lower discount rate means that lower Funded Ratios are much safer. But how much safer?

Let’s look at a Funded Ratio of 1.0 using our two different discount rates.

Somewhat surprisingly, even with a low discount rate of 0.54%, the failure rate is uncomfortably high for people actually in retirement. So even with a low discount rate, we need our Funded Ratio to increase during retirement to maintain our margin of safety.

With our new, lower discount rate what kind of Funded Ratio do we need to maintain over time to keep our probability of failure at 0%?

Even well into our 50s, a 0.8 Funded Ratio appears perfectly safe with this low discount rate. But we also need to ensure that our Funded Ratio increases over time during retirement, peaking around 1.2.

It should be clear that there’s a fairly direct relationship between discount rate and Funded Ratio. If you pick a higher discount rate, then you need a higher Funded Ratio in order to maintain safety. But it isn’t especially linear. With a discount rate of 0.54% a Funded Ratio of 1.2 is safe. With a substantially higher discount rate of 3.7% a Funded Ratio of 1.5 is safe. Increasing the discount rate by 6.8x only increased the safe Funded Ratio by 0.8x.

That suggests that we aren’t overly sensitive to the exact discount rate we pick. I think the biggest surprise to me from all of the above is the impact that age on all of this. Of course, that might be a result of using a constant asset allocation (60/40). Maybe I’ll try the same thing with glidepaths and if that changes anything.

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