## Wednesday, March 29, 2017

### Pension Rip-off

A friend of mine who is collecting a defined-benefit pension had a complaint I’d never heard before. He is convinced he’s being ripped off because his pension benefits only go up by inflation each year, but the plan’s assets go up faster than inflation. I know this isn’t right, but it took a while to think of a good way to explain why.

Let’s start with the analogy of a mortgage. Suppose you have a 5-year mortgage with an annual interest rate of 3%. Even though your unpaid balance is supposed to go up by 3% each year, your payments stay the same for the full 5 years. Does this mean the bank is getting ripped off? Not likely. Banks know a thing or two about coming out ahead.

The truth is that your flat monthly mortgage payments are calculated to take into account the 3% interest on the declining mortgage balance. If your payments increased by 3% each year, your starting payment would be a lot lower. But banks are smart enough to know that they shouldn’t expect you to be able to keep up with ever-rising payments.

The situation with pension benefits is similar. Suppose the value of your pension starting at age 55 is \$1 million. Based on an assumed 4.1% real return, mortality tables from the Society of Actuaries, and ignoring any coordination with CPP, your CPI-indexed pension benefit would be \$5363/month. However, if you wanted your benefits to rise by 4.1% above inflation each year, your starting benefits for a \$1 million pension would be only \$3010/month.

But why would anyone want such rising benefits? By age 95, the benefits would be worth nearly 5 times more after factoring in inflation. This makes little sense. It’s better to receive more now instead of getting ever more money into old age.

The short answer to the question of whether my friend is getting ripped off is no, he isn’t. The 4.1% real return earned by the pension assets are what allow him to get a higher starting pension amount.

1. A little confused - how does \$5363/month come out to 4.1% of 1M ? and for that how does \$3010/month work out to 4.1%?
If you could clarify that would be great - thanks.

1. @GCAI: If you take \$5363/month, rising with inflation, and discount each payment by the probability of having died (that's where the mortality tables come in), and then discount each payment by 4.1% plus inflation per year, the total of all payments works out to \$1M.

If you take a stream of \$3010/month payments and increase them by inflation plus 4.1% per year, discount each payment by the probability of having died, and then discount them by inflation plus 4.1% per year, the total is \$1M.