# Pension decreasing at unexpected slow rate

1

Some additional information. I did some tests with a new, empty database with only the pension in it. With inflation set to 3% I get the following results:

Pension inflation index = 0% -- pension amount drops 3% per year

Pension inflation index = 100% -- pension remains the same in all years

Pension inflation index = 66% -- pension amount starts dropping at 1% per year (which seems correct), but the rate of change steadily diminishes such that by the 27th year it drops only 0.57% per year.

David Shannon

2

One idea that I've used:

If inflation of 3% and "degree of inflation indexation of annual benefit" of 66% (meaning a 2% COLA), then I followed these steps to tweak the 66% number until it matched the predicted behavior:

1. Use Excel to manually extrapolate pension growth at 2% rate. This will be in nominal dollars.
2. Translate these dollars back into real (inflation adjusted dollars). E.g. Year 3 inflation = 1.03*1.03*1.03. So pension in real dollars for year 3 = pension *1.02*1.02*1.02/1.03*1.03*1.03.
3. Sum pension for all years
4. Run ESPlanner with "degree of inflation indexation of annual benefit" set to different levels. Copy and paste pension results to Excel and sum pension for all years.
5. Compare ESPlanner sum with above calculations (steps 1-3)
6. After some trial and error I was able to get the delta between ESPlanner pension sum and manual calculations sum to be less than \$1K. Even though the yearly amounts were off a bit, they were minor and overall the results matched.

Hope this helps.
Brian

3

Thanks, Brian.

I believe I understand your process through step 2, which I take as a way of manually calculating what the pension figures should be in ESPlanner. Similar calculations are part of what made me post this problem.

The rest of your process seems designed to make sure that the total pension benefit over the long haul is roughly the same. I understand the idea, and I may have to fall back on it, but it's not really what I want to do. This pension also includes the provision that 50% of it goes to my wife if I die, and getting the wrong amounts year by year makes survivor planning difficult.

From your post, I take it that I am not the only one who thinks these pension numbers are off. That's encouraging, and I think I'll wait and see what the folks at ESPlanner think about it. Maybe I'm missing something and the numbers really make sense as they are, or maybe they can fix this fairly soon.

David Shannon

4

Hi, I think this is a bug. We'll check it out. It's strange because for 100 percent indexation, everything works fine. best, Larry

5

It also works perfectly for zero percent indexation -- so the edge cases are fine.

It's that damned middle ground that always causes trouble... (joking here...)

David Shannon

6

I believe these numbers are actually correct. I'm going to check with Larry on the math, but what I believe you're seeing is the effect of a conversion to todays dollars of a number that falls farther and farther behind inflation. I haven't satisfied myself completely that my interpretation is correct and I have to talk to Larry about it to make sure so stay tuned.

7

No, there IS a design flaw. The designer of this code (not me, not Larry) made the following (erroneous) assumption:

Given an inflation series inf and a percentage of inflation protection, prot:

For i = 1 to n:

((product(inf(i)) - 1) * prot) + 1 = product(((inf(i) - 1) * prot) + 1)

which is unjustified and for any non-trivial examination, false.

8

*** Ignore this post, I just saw your latest one ***

Just to be clear, my concern is not that the numbers are falling behind inflation, but that they are not falling behind inflation fast enough.

In case it helps, here's why I think the numbers are wrong.

First, here is the key assumption I am making: With inflation set at 3% and the inflation index set at 66%, the value of the pension in today's dollars from any given year to the next year should drop by about 1%.

This seems intuitively obvious, but to check my thinking I have simulated this in spreadsheets by creating an inflation index for each year (increasing at 3% per year), computing the inflated future pension values (increasing at 2% per year), and reducing the calculated future pension values to today's dollars using the inflation index. Doing so shows a value in today's dollars that declines steadily by 1% per year, as expected.

The data in my initial post shows the pension values in today's dollars from the reports. But, as you can see, while that value starts off declining year over year at about 1%, the decline slows to where it is eventually declining at only 0.5% per year.

Because in every year inflation is assumed to be 3% and the pension is assumed to inflate by only 66% of that, there seems to be no reason why the year-over-year drop in value in today's dollars would ever change.

9

Thanks for looking into this. I take your equation to mean that the program was taking 66% of the inflation index for the given year and multiplying times the original pension amount, rather than (conceptually) taking the previous year's diminished pension amount and partially inflating that.

If that's what it means, I think you've found the problem. I simulated what I take to be the program's method in a spreadsheet and it gave me almost exactly the same not-dropping-fast-enough series I saw in the report.

Thanks again. I look forward to an update, hopefully by the end of the year.

****

BTW, I've been using ESPlanner since 2005 and I retired in 2009. ESPlanner (and Larry's book and articles) completely changed the way I approached retirement planning. Finding ways to actually have more money to spend has been important, but perhaps more important has been the confidence we have in how things are going and (subject to assumptions) how things are going to go. Analysis in ESPlanner is now a regular part of our financial decision-making.

10

No, the original designer of the code got the math wrong when calculating the inflation compensation factor. In effect he was compensating too little for inflation indexing, thus allowing your pension to keep up with inflation better than it should.

Heres a simple example:

3 years of inflation = 1.03 * 1.03 * 1.03 = 1.092727

With a 50% inflation protection, the code would calculate the effect of inflation as:

((1.092727 - 1) * .5) + 1 = 1.0463635

Unfortunately this overstates the inflation protection from earlier years. Consider the first year, the inflation protection should be 1.015 and remain the same for the duration of the pension. Now consider the effect of 3 years with this interpretation of inflation protection:

1.015 * 1.015 * 1.015 = 1.045678375

Which, as you can clearly see is different from that calculated by the original design.

Best,

Dick Munroe

11

No, we're actually saying the same thing.

The first (incorrect) method applies the inflation protection factor to the current year's inflation index, understating the amount by which the pension falls behind.

The second (correct) method applies the inflation protection year by year, so that the "fall behind" from the previous years is taken into account. Your wording a little different (I talk in terms of partially inflating the previous year's pension amount, you calculate an adjusted inflation factor) but as you can clearly see:

(1.015 * 1.015 * 1.015) * OriginalAmount = ((OriginalAmount * 1.015) * 1.015) * 1.015

But as long as it's fixed, I'm happy...