"Poor Millionaires" and Pensions

This morning's NYT story about the "poor millionaire" (link) gives me a chance to showcase two of my favorite equations. First this:


And then this:

That, plus a little data, is all you need for pension planning. In the top equation, "fund" means "the amount you will need to have on hand the day you quit work." To figure that, you need to know how much you will want to draw as a pension each year ("Pen"). You'll also need to know an interest rate ("r") and the number of years you expect to live ("n").

Once you know this, you can estimate how much you have to save each year to reach your goal ("Inv"), depending on how many years you have to save ("t").

For example, suppose you are a software engineer and you expect to be earning $80,000 a year when you retire at age 65. You want to keep on drawing that same sum every year in retirement. You expect to live for 20 more years. For an interest rate, throw a dart: say five percent. Then you will need to have on hand at retirement the sum of $996,976.80. To reach that sum, if you start at age 26, you'll need to put away $8,253.14, each and every year.

A few loose observations: first--if you are one of the lucky few who still has a job with a solvent pension fund, quit whining--you've got a great big balance sheet asset (here, c. $1 mill) that most people would push their grandmother in front of a truck for.

Second--for all the talk about IRAs, 401ks, blah blah, I don't think it has sunk in on us just how far you have to go by way of self-denial to get the capital fund you need. We've been able to lie to ourselves because we have been financing social security for so long on the Ponzi principle: new investors fund their predecessors. But like all Ponzi schemes, this works forever only if you have an infinitely expanding period. But with our birth rate, and Tom Tancredo standing shotgun at Ellis Island, we've pretty much played out that string.

Third--the little matter of "outliving your money." Most people think it uncool to estimate the date of their death, and to take the estimate to the bank. This is where you want a good annuity market, so you can pool the long-lived annuitants with the short. So far as I can tell, we don't really have a functioning annuity market. You can buy annuities, of course, but so far as I can tell, the interest rates are absurdly low, and the capital costs correspondingly high. So, suppose you use my previous example, except subtitute a rate of only 2 percent. Then the capital cost bumps up to $1,308,115, or about 30 percent more than my number.

Just why the market is so rotten, I cannot tell. My friend Bruce, who knows a lot about this than I do, says it is an adverse selection problem, but I don't believe it: almost any kind of insurance has some adverse selection problem, and I don't see how this one is specially insurmountable. I do recall learning way back in law school that insurance companies got burned on annuities because they underestimated longevity. Once you touch a hot stove, you never touch another, but maybe you never touch a cold stove either (but come to think of it, I also recall learning that they made out like bandits on straight life on the same principle--people payed premiums and kept their funds on account far longer than the actuaries had expected).

If you don't want to dip into your capital, God bless you, but of course you will need more money. For example, at the five percent rate, to make sure you could draw 5 percent forever without dipping into capital, you would need $1.6 million on account (at 2 percent, you'd need $4 million).


Note: Nothing here compels any particular conclusion re whether to retain social security (I am in favor) or whether to invest social security money in the general market (I'd like to give it a slow, cautious try).