Analysis: Private Social Security Accounts: First Buster, then Bertha

This article is cross-posted at Big Brass Blog

Those of you who are regular readers of The Dark Wraith Forums know that a number of articles and comments on threads have been written about various proposals to partially privatize the Social Security system. But nothing in these extensive writings has been quite as personal as the story of Buster Bluerhoid in A Look at Private Social Security Accounts, published last month. Buster's story touched the hearts of many readers as he lived out his productive life and came to retirement facing a public pension system that had become partially privatized. As the story unfolded, Buster's fate in retirement had already been defined only to a small extent by the choices he had made during his working years. Unfortunately for Buster, much of what would constitute his financial fate upon retirement was dependent upon principles of finance, circumstances, and rules beyond his control.

To recap the prequel to the issue before us now, Buster was a man who made $40,000 in constant-dollar earnings a year throughout his entire working life. He neither gained ground on inflation, nor did he lose ground to it. He worked for 50 long years, beginning at the age of 20 and retiring at the age of 70. He chose to use the opportunity for a private Social Security account to the maximum he was allowed each month for every month of those 50 years.

Now, the way the system works is that Buster is not actually investing his own Social Security withholdings; instead, the government deducts Social Security tax as it always did in the olden days; but then, if a worker wants to have a private, personal Social Security account, the government will lend him or her up to four percent of earnings subject to Social Security taxation to invest in the stock and bond markets. This is what might be called a "credit facility," with the accumulated principal and interest due upon retirement from the money that has been invested in the markets. Keeping inflation out of the picture, the proposals floating around Washington put the interest rate the government will charge on this credit facility at three percent.

Buster is permitted to invest four percent of his monthly income every month for 50 years. That means every month Buster borrows from the government $133.33, and he puts that cash to work in a private investment portfolio. At the end of those 50 years, the portfolio gets liquidated, and the government is paid back. Whatever remains, Buster must use to buy from a private merchant a pension plan that will pay him a monthly check for the rest of his life.

Here's how the numbers worked out for Buster: at the end of his 50 years, having borrowed $133.33 every month from the United States, he owes Uncle Sam $185,243. (If that number makes your hind leg twitch, you're not alone.) Whatever remains from the portfolio liquidation, Buster must use to buy a pension annuity. The third party provider has to calculate how much it can make on what Buster is paying, and it must determine how long it will have to send him those monthly annuity checks. Assuming that the pension provider can make the same three percent in real terms at which the government is lending money to Buster, and assuming that Buster is expected to live to the ripe old age of 85, the calculations reveal that the annuity plan will cost $144,805 per $1,000 of monthly annuity Buster wants to purchase.

In other words, for Buster to get a $1,000 check from his private plan every month from his time of retirement until the time of his death, he has to pay the pension company almost $145,000. Remember, though, that Buster must first pay Uncle Sam $185,243. In total then, for Buster to get a thousand dollars a month check throughout his retirement, he must have a portfolio worth $184,243+$144,805, which comes out to $330,049. Simply put, Buster must invest $133.33 every month for 50 years and end up with just a little over three hundred grand at the end of his working life.

Finally, what annualized rate of return would Buster's portfolio have to pull to end up with this much money? Doing that calculation (for which we can thank financial calculators and spreadsheets, which make the number crunching a whole lot easier), Buster needs to make just a fraction under five percent annually in real terms.

Earning a real rate of return of five percent might not sound too hard. Historically, the stock market has been able to earn, on a well-diversified portfolio, about seven percent; and even taking into account the shift of some fundamental parameters that will affect future market performance, some mainstream economists see the long-term rate of return on a diversified stock portfolio as being somewhere right around five percent.

Well, happy days. Buster should be able to pull this off, if only by a whisker. He can pay back his $184,243 loan from the U.S. government, and he'll be able to pay a private pension annuity seller the sum of $144,805 so that he can receive a check every month for $1,000.

In the interest of full and fair disclosure, though, it should be noted before we go on that, as of last Friday, a portfolio based upon the Dow Jones Industrials has earned, since the first full day of the Administration of George W. Bush in 2001, an annualized return of a whopping 0.12%. That's right: before even taking into account how inflation has eroded purchasing power, investing in a portfolio of stocks like the Dow would have earned a little more than a tenth of a percent per year.

Investing in a broader, but still blue-chip, portfolio like the Standard & Poor's 500 would have earned an annualized rate of return of -2.88%, again, even before taking into account inflation eating away at the purchasing power of the dollars in the market. And finally, going with a widely diversified index mirroring the giant NASDAQ would have brought an annualized rate of return before inflation of -7.36%.

Still think Buster's going to have an easy time pulling off an annualized rate of return of five percent over the next 50 years?

If the neo-conservative geniuses now driving our economy have done something permanently adverse to the way stock markets appreciate investment capital, Buster won't have enough in that portfolio on the day he retires even to pay back his dear Uncle, much less have anything to go buy himself a pension annuity.

And so we must now leave Buster and get to the point of this second half of our look at private Social Security accounts.

You might be wondering what else there could possibly be, and you might also be wondering how much longer this article can go on about such a depressing topic. Not to worry: it will end shortly, but we must first give at least a brief bit of attention to Buster Bluerhoid's twin sister, Bertha Bluerhoid.

Yes, Bertha was born at the same time as Buster, and they are alike in every way, except that Bertha is a woman, which means that she and Buster are not alike in every way. For the purposes of analyzing her prospects with a private Social Security account, two differences are quite important: first, Bertha, being a woman, will probably earn less money than Buster during her life, even though she is pretty much identical to Buster in skills, job performance, and other matters that should determine her income; and second, Bertha will probably live longer than Buster. Both of these factors—as well as a couple of others—are going to work against Bertha.

Just for the sake of example, let's say Bertha has a life expectancy seven years longer than Buster; and throughout her life, she earns 10 percent less than Buster. That latter assumption means she'll make $36,000 per year. Like Buster, she'll use the maximum four percent of her income, which comes out to $120.00 every month, to invest in the stock markets, mindful that this is money she is borrowing at three percent interest from the government, and she must pay this off in one lump sum by liquidating her investment portfolio upon her retirement. Anything she has left over, she must use to buy a pension annuity that will send her a monthly check for the rest of her life.

Here's how the numbers shake out.

The good news is that, since she was borrowing less than Buster each month from the government, Bertha will owe Uncle Sam only $166,719 on the day she retires. This is the future value of a monthly loan of a hundred and twenty bucks accumulating interest at three percent annually for 50 years. So, whereas Buster owed the government about $185,000, Bertha owes the government almost $18,000 less.

Oh, but here comes the bad news: Bertha must take the proceeds that remain from her liquidated portfolio and go buy an annuity that will pay her a monthly check for the rest of her life. The calculation will work the same way it did in Buster's case: how much should be charged up front so that a check can be sent every month for what is expected to be the duration of a person's life, given that the up-front money can be invested at a real annualized rate of return of three percent?

Before seeing the price per thousand dollars of the monthly annuity benefit plan, remember that Bertha is expected to live longer than Buster. That means, if she wants the same amount of money every month, she must be charged more. (Keep in mind that this is a private system; so unless the government imposes some form of fairness on it, Buster is not going to be made to pay more so that Bertha can pay less.)

Get ready for this. For each thousand dollars of annuity Bertha wants, she must pay $193,089.

You might want to go up and see what Buster had to pay for that same $1,000 a month check he'd get in the mail for the duration of his life as a retiree.

So, to pay back her loan to the government and to have enough remaining to buy an annuity from which she'll get a grand every month until she dies, Bertha needs a total of $166,719+$193,089, which comes out to be $359,808. This is what her portfolio needs to be worth on the day she retires.

To finish off the numbers, we need to see what annualized rate of return Bertha has to make, investing $120.00 every month for 50 years, for her portfolio to hit a liquidation value of $359,808. Again, using a handy spreadsheet to do the math that would otherwise take close to an eternity, Bertha's investments need to earn an annualized rate of return for fifty years of almost five-and-a-half percent. Recall that Buster needed to pull just a little under five percent to get his thousand dollar a month pension check.

In summary, then, here are the numbers, side by side, for our two friends.

Obligation to the United States:
•  Buster owes the government $184,243
•  Bertha owes the government $166,719

Price/cost at retirement of a $1,000 per month pension annuity:
•  Buster must pay $144,805
•  Bertha must pay $193,089

Total amount needed in private Social Security investment portfolio upon retirement:
•  Buster has to have a portfolio value of $330,049
•  Bertha has to have a portfolio value of $359,808

Required, 50-year annualized rate of return on investments to reach target portfolio value:
•  For Buster, 4.89%
•  For Bertha, 5.47%

Likelihood of achieving this:
•  In Buster's case, Diddly
•  In Bertha's case, Squat




The Dark Wraith has spoken.