Pension math: why the Interest Rate assumption is soooooo important.

As the debate on phony pension reform continues unabated in Springfield pundits on all sides of the issue continue talk about the IR or Interest Rate. This can be very confusing if you do not understand the basic impact changing the Interest Rate assumption has on the viability of any and all pension systems.

In pension math the IR is used for more than one thing but today we are just going to concentrate of how the IR is used in calculating pension liabilities especially the dreaded UL (Unfunded Liabilities).


In rough numbers Springfield is claiming the following for the 5 state pensions:

Total Pension Liabilities:         $160 B

Minus Assets on hand             $  65 B

Equals Unfunded Liab.          $  95 B

The only one of the three key numbers that is grounded in reality is “Assets on hand”. That is because those assets are a fact locked up in cash, bonds, stocks and some private equity all of which have tangible value and can be easily verified.

The UL (Unfunded Liability) is a simple arithmetic calculation: Total liabilities minus Assets equals UL.

So the really important number is Total Pension Liabilities. Total Pension Liabilities or AL (Actuarial Liability) is a made up or “modeled” number. That is it is calculated from a complicated algorithm that uses the IR (Interest rate) assumption to determine how much money we should have in assets today if we are to pay all the pensions, current and future, in full. Since the AL calculation is really just a modeled number it has theoretically an infinite number of possible outcomes. Unfunded Liability (UL) as we discussed above is calculated from AL minus Assets meaning how big and bad UL is, is totally dependent on the modeled Interest Rate being used to calculate AL. Since it is totally dependent on the model and IR, UL also has an infinite number of possibilities.

The key point to remember is this: you (or politicians) can make the Unfunded Liabilities be whatever you want it to be, to serve whatever purpose you may have to serve at the moment such as getting re-elected. I claim that is exactly what they are doing: playing with a low-ball modeled value of UL ($95 B) to make funding appear much better than it really is.

Currently the assumed IR is about 8% although they are beginning to lower it slightly to 7.75%. For the example I show below we will use 8% since that is close to the chosen value and will be easy to demonstrate the power of the IR assumption.

A VERY simple illustration of the power of the Interest Assumption in determining how much taxpayers owe for pensions.

This is simple because we are not going to calculate exact amounts but instead just use illustrative amounts like $4. Deal with it.

OK you are the administrator of the following pension fund.

  1. The fund only has one member, John Smith.
  2. His pension is $8 per year.
  3. You have $100 in assets.
  4. Your Interest Rate assumption is 8%.

So as pension fund administrator you take your $100 in assets and go to the local bank. The banker tells you he just happens to have a CD paying 8% (I told you this wasn’t real). So you give him your $100 and over the course of the next year he dutifully pays your fund $8 and you in turn pay John Smith’s $8 pension. With $100 in assets and an 8% IR you are 100% funded. Everything is cool.  Life is good.

The year ends and you go back to your banker thinking you will just roll over the $100 into another 8% CD. Unfortunately the banker says “Things are tougher this year I can’t do 8% I can only do 4%”. Oops. Everything is not cool. Life sucks.

Because if you only get 4% then you will have to dig into your $100 assets for $4 to fund the rest of the $8 you owe John Smith. Then your assets will be down to $96 from $100.

So at the end of year 2, your assets are $96 and your assumed interest rate is still 8% therefore you still need $100 in assets to get the $8 pension. Since you only have $96 your unfunded is now $4 and you funded ratio is down to 96% from 100%.

Since by law you need to project costs and benefits going forward 30 years you seek reassurance for your 8% IR assumption by going to the banker and see what he thinks he can do on interest rates going forward 30 years. That way you could tell your Board of Trustees not to worry, over the long term everything will work out. You will get 8% on average.

The banker, wanting to keep you as a customer hems and haws but says yes he thinks you can/maybe/probably get 8% per year average over the next 30 years. Problem solved, you can go to your board of trustees and say everything is OK.

But suddenly another banker shows up and his name is Moodys. Moodys says no you probably will not get 8% going forward more likely you will get 4%. If you IR assumption is 4% then your Actuarial Liability is $200 because it takes 4% of $200 to get the $8 you have promised your retiree.

Your banker says you are 96% Funded

Moodys says you are 48% Funded.

Your banker says you have $4 Unfunded Liability.

Moodys says you have $104 Unfunded Liability.

The answer is nobody knows who is right but certainly Moodys has at least as much if not more credibility than your banker does in determining the funded ratio.

Since two credible parties have very divergent opinions of the future funding requirements of your pension system doesn’t it make sense to also plan for the option put forward by the party with no political motives?

Pension math and common sense say “yes”.