AST week, I.B.M. announced that it was closing its traditional defined-benefit pension plan to new employees and instead would offer new workers a 401(k) plan.

This is just the most recent of many such announcements by major companies. In the mid-1980's, 40 percent of workers were covered by defined-benefit plans. But those plans have become less popular in recent years, and now only 20 percent of workers are covered by such plans.

As the name implies, a defined-benefit plan bases its pension payment on a formula involving years of service, final salary and other considerations. The employer effectively promises workers that it will pay them some predetermined amount when they retire.

But pension plans and companies sometimes become insolvent. Who back ups these promises? The Pension Benefit Guaranty Corporation was set up by the federal government 30 years ago to provide insurance for traditional pension plans. If an employer cannot pay the promised benefits, the pension agency steps in to cover the difference. In exchange for this insurance, the companies that offer traditional pension plans have to pay a fee to the agency.

Zvi Bodie, a professor of economics and finance at Boston University, discusses some of the problems the agency faces in an article entitled "Straight Talk about Government Pension Insurance," which will appear in the next issue of The Milken Institute Review.

The agency's biggest problem is that it faces significant potential liabilities. In 2000, it showed a net balance of assets over liabilities of $10 billion. By 2004, its financial position had deteriorated to a $23.5 billion deficit. If we add in other companies covered by the agency that face significant bankruptcy risk, the deficit could reach $96 billion.

The problem, according to Mr. Bodie, is a mismatch between the assets and liabilities of the pension plans that the agency guarantees. In a defined-benefit plan, companies promise to pay a fixed amount of money to workers when they retire. A company could be sure of having enough money available by investing in secure assets like high-grade corporate bonds.

But bonds pay relatively low rates of interest, meaning that companies would have to set aside a substantial amount of money to meet their pension obligations. They find it much more attractive to invest in assets like stocks that have a higher expected rate of return. But high expected returns go hand-in-hand with high risk, increasing the chance of a shortfall.

In 2003, General Motors' net pension expense was $2.6 billion. Their financial statements assumed a 9 percent rate of return on investments, which were primarily in stocks and other risky assets. If these funds were invested in bonds yielding about 6.75 percent, G.M. would have had to put away $4.2 billion that year, making its pension plan much more expensive.

So what is wrong with assuming a 9 percent rate of return? That is a reasonable figure for the average return on the stock market - but it is only an average. Given the historical fluctuations in the stock market, there is a reasonable chance that a stock market investment may not actually pay off enough to cover the liabilities.

That is where the pension guaranty agency comes in. Even if the stock market drops, the workers' pensions will be covered. This means that G.M. has every incentive to invest in stocks rather than bonds: it is heads they win, tails the pension agency loses.

As Mr. Bodie explains, there is a fundamental fallacy in pension accounting, which assumes that the ups and downs of the stock market will cancel out over time. This is not necessarily true.

Consider a 40-year-old worker who hopes to receive a lump-sum payment of $1,000 when she retires in 20 years. If the interest rate on 20-year bonds is 5 percent, then the company will have to set aside about $377 now, which is the present value of the $1,000 obligation at a 5 percent interest rate.

But instead of those dull bonds, the company could invest the $377 in a stock market index fund, which yields about 10 percent a year on average. After 20 years, the odds are that the company will have more than enough money to pay the $1,000, leaving itself a tidy profit, or so it seems.

The trouble with this logic is that even though the market will probably do better than bonds on average, there is still a significant risk of a shortfall, even in the long run.

To see this, consider how much the company would have to pay now to guarantee that it could cover its $1,000 obligation. The company would need to buy some sort of portfolio insurance that would pay off if the stock market investment fell below $1,000.

To provide such insurance, the company could buy a put option, a contract that gives it the right, but not the obligation, to sell the pension stock portfolio for $1,000 in 20 years. If the value of the stock portfolio ends up above that amount, there is no problem. If it falls below $1,000, the pension plan would exercise the option to make good on its promise.

How much would such an option cost today? Using standard techniques for option valuation, the price is about $125. Thus, the total cost to guarantee the $1,000 future payment turns out to be $377 plus $125, or $502.

So it is not so inexpensive to invest the pension in stocks after all. Either the employee runs some risk of not being paid the entire amount, or someone - the company or the Pension Benefit Guaranty Corporation - has to provide the put option.

The problem is that the pension agency has a difficult time charging the actuarially fair price for the insurance it offers. Companies that are close to bankruptcy cannot pay, and healthy companies find it more attractive to opt out of the program entirely and offer 401(k) plans instead.

So the financial position of the pension agency continues to deteriorate. Sooner or later, Congress will probably have to step in to fix it. The sooner it can put the program on a sound financial footing, the less it will cost the taxpayers in the long run.

Hal R. Varian is a professor of business, economics and information management at the University of California, Berkeley.