Analysis: A Look at Private Social Security Accounts

Tonight, a somewhat simplified model of what to expect as far as benefits under a partially privatized Social Security system will be demonstrated. Readers will be spared the formulas that are used, although these are standard means by which annuities are calculated and are taught in most introductory college courses in principles of financial management.

We shall use an exemplary citizen, Buster Bluerhoid, who comes of age in the era of the partially privatized system. For the purposes of this analysis, Buster stands at the door of his productive life, age 20, and faces 50 years of work before he is allowed to retire at age 70. To keep Buster's life from getting too complicated, we'll say that Buster begins his productive career making $40,000 a year, and he holds his real income constant, neither gaining nor losing anything, but staying right with whatever inflation does. Some might say that this is a really bad assumption since Buster's income growth will surely do better than just keeping up with inflation; but the assumption might not be good for the opposite reason: over the past several decades, incomes of working class people have actually lost ground in real terms. But we'll assume that Buster doesn't suffer this fate: Buster comes from a long line of inflation-matching Bluerhoids. To keep the analysis from getting off on sidetracks about nominal versus real dollars, we'll be using "constant dollar" analysis: everything is in terms of values as they stand when Buster starts his productive life. (And this assumption doesn't cause nearly as many problems as some amateurs economists in the audience might be howling that it does.)

Moving along, our protagonist, Buster, makes $40,000 a year; and the partially privatized system allows Buster to invest as much as four percent of his income that is subject to Social Security taxation in the stock and bond markets. Remember that Buster isn't really investing his money, though; instead, the U.S. government is lending Buster that four percent of income, and the government is going to retrieve that money from Buster, at an annual interest rate of three percent, at the end of his working days. Anything Buster has left, he is required to use to buy a pension annuity that will give him a monthly check for the remainder of his life.

Okay, Buster makes $40,000 per year, which we shall assume is all subject to Social Security taxation. Four percent of that is $1,600 per year, or $133.33 per month. Buster must invest this money; and he must also remember that every time he uses one of those $133.33 government vouchers, that much more is added to the loan he must repay to Uncle Sam in one lump sum at the time he retires.

First, let's see how much he'll owe the good Uncle after 50 years. According to the plan as President Bush and his people have laid it out, the government is going to charge an annual interest rate of 3%, which is what the White House is figuring it will cost the government to borrow the money to lend to Buster every month. So, we must use the financial calculator to figure out the "future value" of a loan of $133.33 per month for 50 years, considering that no payments are made on the loan through that period. The calculator spins away for a few seconds, and out comes Buster Bluerhoid's bill on retirement day:

Buster owes Uncle Sam $185,243.

Buster doesn't break a sweat, though, because he's been using those monthly $133.33 vouchers to invest in stocks and bonds. He's saying to himself, "My portfolio's gotta be worth more than that." He might be right, but before we look at his portfolio, we need to look at what it's going to cost him to buy an annuity from a private vendor.

As far as private vendors are concerned, the players in this field—which will be huge, hot, and competitive—are going to be asking themselves the following question: how much must we charge Buster right now if we have to send him a pension check every month for the rest of his life? To answer that, they must ask two more questions: how long do we expect Buster to live, and how much are we going to make off the money Buster gives us up front? Obviously, for a given amount of money Buster pays for his pension annuity, the longer Buster lives, the less they can give him in each month's check. Also, fairly obviously, the more they can earn on their own investments, the more they'll make off that money Buster paid them, so the more they'll be able to give to Buster every month.

Sounds a little complicated? Don't worry, here is some scenario help. If Buster retires at age 70, he's going to get more checks if he lives to age 90 than if he lives to age 85. That means competitive vendors will be willing to put more into each of Buster's checks if they expect him to kick off at age 85 than if they expect him to meet his Maker at age 90. As far as the vendors' expected return on their own investments, they're going to take Buster's money, and they're going to put it into stock and bond markets to profit from it. Some of the money they earn will sweeten the monthly checks for Buster, and some of the money will sweeten the bottom line.

Let's decide how long Buster is going to live. He's led a good, healthy life; he's eaten his fiber regularly; he's avoided vices like smoking, fighting, and cow tipping; and he's stayed on his meds. We'll say he lives to age 85, which means he'll get a pension check every month for 15 years.

We must also talk about what his pension annuity vendor is going to project as its earnings on investment of money people like Buster are paying them. Although this could get really complicated and controversial, what with trying to guess at what the investment markets are going to do over the 15 years they must take care of Buster, there's an easy way to look at it. Whatever the pension annuity provider, itself, makes is not very relevant; what matters is what they have to provide Buster as his cut, and that is probably going to be round about the very same three percent the government was charging Buster during his working years. Why? Well, it's because the government was borrowing money at that rate from the capital markets so Buster could do his investing, so those government bonds are the very same, pretty darned safe investment vehicle for the money the pension vendors will get from Buster. In fact, it is entirely reasonable to assume that the government is going to require the pension annuity providers to put at least some of their customers' money into those bonds. That's what the Federal Reserve System does with banks all the time right now.

So, now Buster's pension provider can work on the assumptions that it's going to be sending Buster monthly checks for 15 years, and whatever it charges Buster up front to do this, it's going to have to earn three percent per year on that money that will go to Buster, along with part of the principal, over those 15 years. As it turns out, this is a pretty easy financial calculator problem, and we'll get an answer that will tell us how much Buster will be charged per $1,000 of monthly annuity check he gets. Putting it into the calculator, we get the price Buster will be charged for his retirement pension on the day he retires:

Buster's pension will cost him $144,805 per $1,000 of monthly annuity.

So if Buster wants to get a $1,000 check every month until the day he dies, he'll have to cough up $144,805 on the day he retires; if he wants to get a $2,000 check every month until the day he dies, he'll have to cough up twice that much money; et cetera.

We're almost finished, now.

Let's say Buster figures he can make do with $1,000 per month from his private annuity plan; this amount, combined with whatever the remaining public Social Security plan is still providing, is enough to keep a frugal Bluerhoid's body and soul together.

Buster needs to have $144,805 to pay to the private pension annuity vendor. Buster needs another $185,243 to pay back Uncle Sam. Put those two numbers together, and we now know exactly how much Buster needs to have made by the day of his retirement on his investments over the past 50 years.

Buster needs to have $330,049 in his portfolio on retirement day.

So, the last question is this: what rate of return did Buster have to make on $133.33 invested every month for 50 years in order to have $330,049 at the end of the game? Truth be told, a financial calculator or a spreadsheet can do this one in a split second, but a human doing the calculation would still be cranking on it when the Lord returned. Letting a nice, handy calculator do the work, the answer comes out in a jiffy.

Buster's portfolio must earn an annualized rate of return over a 50-year life, net of transactions costs, of just under five percent.

Now, you might be saying to yourself, "Well, that's not too bad. Hasn't the stock market earned about seven percent over a very long holding period?"

Ah, yes. You might even be willing to agree with economists like Paul Krugman that the long-term rate of return will probably shift down somewhat, from seven percent to five percent, and Buster will still make it to a $1,000 per month annuity check.

Yessirree, you might want to look at it that way.

Then again, you might want to look at what's happened since George W. Bush II took office in January of 2001. Using the first trading day after Mr. Bush's inauguration in 2001 as the starting point, and working out the annualized rates of return as of this past Friday, here's what we get:

Dow Jones Industrials:  +0.60%
Standard & Poor's 500:  -2.49%
NASDAQ:                              -6.82%

So, in other words, if this kind of portfolio return is what Buster's going to face, not only does Buster not meet his five percent annualized rate of return, Buster doesn't even have enough to pay Uncle Sam back.

Oh, but surely this must be some kind of mere aberration. Even if Mr. Bush were the cause of this disastrous market, he'll be long gone, and the markets will return to their long-term trend lines.

Surely they will.

Most certainly.

No doubt about it.

Otherwise, Buster is busted. And that's such a tragic ending for a Bluerhoid, don't you think?