How would you have done if your Social Security money had been invested in the market? Actually, pretty well.

Over the past several weeks we've heard a number of people – Sen. Obama and the AFL-CIO come to mind, though there were others – point to current stock market conditions as seemingly proof positive that Social Security personal accounts would have been a disaster. Sen. Obama recently said,

"If my opponent had his way, the millions of Floridians who rely on it would've had their Social Security tied up in the stock market this week. Millions would've watched as the market tumbled and their nest egg disappeared before their eyes."

Presumably this is a rhetorical question, since no one seems to actually be trying to answer it. Here's an attempt at doing so.

To begin with, it's worth noting that had President Bush's proposed Social Security plan been passed, personal accounts would not have been established until 2009-2011, meaning that no one would actually have money in the market yet.

Moreover, under Bush's plan and some others, personal accounts would automatically be shifted to a "life cycle" portfolio as of age 55, which would automatically move the account from stocks to bonds as retirement neared. So even had accounts been established, most near-retirees would have very little of their money in stocks.

In any case, though, I've simulated how current retirees would fare had accounts been established throughout their working lifetimes, to give a feel for how accounts would have performed under circumstances similar to those today. I've assumed a fairly generic personal account plan: individuals would invest 4 percentage points of their wages – around 1/3^rd of the total payroll tax – in a personal account holding a life cycle portfolio. The portfolio would hold 85 percent stocks through age 30, falling to 15 percent stocks by age 60. The stock element is assumed to be an S&P 500 index fund while the bond portion is long-term government bonds. Administrative costs would equal 0.3 percent of assets annually.

To keep Social Security's finances roughly equal, account holders would give up traditional benefits equal to their account contributions compounded at the government bond interest rate. This "shadow account" effectively compensates the trust fund for lost earnings. In simple terms, a worker's total Social Security benefits would increase if the personal account's average return exceeded the average return on government bonds, because the payment from their own account would exceed the benefit reduction due to the "shadow account."

Annual earnings are simulated by applying the SSA actuaries 'medium scaled earner' factors to the average wage projected by the Social Security trustees from 2008 onwards. (In effect, future earners are being modeled, but we use stock/bond returns from 1964 through September 2008.)

So how would it all have turned out? The end balance on our model worker's personal account would equal approximately $161,500. Using a single life, CPI-indexed annuity formula from the federal Thrift Savings Plan, this would translate into an annual personal account payment of $10,330. The "shadow account" balance (again, account contributions compounded at the government bond rate) would equal approximately $122,380, which annuitized would produce an annual offset to traditional benefits of $7,830. Netted out, the personal account would increase annual benefits by a total of $2,500.

Measured against a base benefit of a medium earning retiring in 2008 of $15,730, a worker retiring in 2008 would increase his total Social Security benefits by approximately 16 percent by virtue of holding a personal account.

Now, this is not precisely an answer to Sen. Obama's question, "How would you be feeling about the prospects for your retirement?" Personal account holders retiring today would no doubt be disappointed that their account values have fallen, even if by holding an account their total benefits increased relative to remaining entirely in the current program. That's just human nature. At the same time, however, to the degree there is a quantitative answer to how the person should be feeling, it's "around 16 percent better off than had they not participated in a personal account."