Last week, in this forum, Lou Paulson argued that the pension debate in California should be more concerned with math and less with politics. I completely agree, which is why I was perplexed after reading his op-ed.

Among other things, he argues that California’s state and local governments should not fully fund pension plans for their employees. When he actually uses math or data to justify his arguments, his conclusions are largely incorrect or misleading.

For instance, Mr. Paulson is wrong when he simply equates funding a pension to paying a mortgage. He says that in both cases, “[the borrowers] finance the large amount, and pay it off over 30 years.” But because pension plans must generate sufficient investment returns on their assets to fill the gap between those assets and the total benefits promised to employees, funding a pension is inherently more complex than simply paying down a mortgage.

Let’s say Dave borrows $100,000 to buy a house. Over 30 years, he pays down the $100,000 principal plus interest on his mortgage. Assuming that he makes his payments on schedule, he continues to reduce his liability.

But things become more complex whenever he fails to make his required mortgage payment in full or borrows against his home. That’s when his liability grows.

That is how governments fund pensions today. A pension liability equals the amount of assets the fund needs to have today to fully cover its larger, future obligation. The liability grows as employees continue to work and earn benefits, as more employees join the system, and whenever their benefit levels increase. These add-ons are akin to borrowing against a house year after year and incurring additional debt.

Paulson then misinterprets the funding ratio when he says, “[CalPERS is] already sitting on 70 percent of the money it will need over the coming 30 years. Should it have 100 percent? Of course not.”

Of course not? Pension funding plans are structured with the goal of constantly being 100% funded because the investment returns they earn help sustain the plans themselves. As the Academic Academy of Actuaries says, “Actuarial funding methods generally are designed with a target of 100% funding—not 80%.”

A simple interest example makes this point. A pension plan is expected to pay $325,000 after 30 years. It starts with $100,000 in assets, generates 7.5% in investment returns every year, and ends with $325,000. But if it only starts with $70,000 in assets, it must generate 12.1% in investment returns every year to end with $325,000.

And those calculations assume that the liability remains constant over that 30 period.

But as the liability increases, the pension fund requires additional asset contributions from employers and/or employees to ensure there are sufficient assets to invest and earn sufficient returns.

Just last month, CalPERS announced that annual rates for state, school, and local government employers statewide will increase by 50% in 2015. Similarly, the state teachers’ pension fund, CalSTRS, says that its fund will be depleted by 2044 without an additional $4.5 billion in annual contributions.

A pension plan is not supposed to contain just enough assets to “cut checks” to those next in line to receive them. Being fully funded is what allows the pension fund to realize the full returns intended. When a plan is only partially funded, every dollar not invested results in missed investment returns the plan was supposed to realize.

In discussing CalPERS’s investment performance, Paulson errs again. He conflates expected investment returns and discount rates. While governments do generally set their investment discount rates equal to their expected rates of return, they are actually distinct figures that differ in nature.

The pension fund’s rate of return on its investments is an asset-side metric that describes how much more valuable the investments are now than they were previously. On the other hand, the pension fund’s discount rate is a liability-side figure that determines the current value of the pension liability, or how much funding it needs to have today to cover its future obligations.

Using a lower discount rate to calculate the value of the liability results in a larger liability, meaning the fund would require higher annual contributions. But it would also have less risk of underestimating its liability and being unable to fulfill its future obligations.

Thus economists who advocate for a discount rate lower than the current 7.5% do so not based on the expected level of investment returns, but rather the amount of risk a government can assume when setting aside funds for benefits it is legally obliged to pay.

Using math shows us that when governments underfund pension plans, annual required contributions to the fund necessarily rise, straining budgets that are unable to absorb the annual growth levels over extended periods.

California’s fiscal health is a function of the state’s commitment to securing its pension systems. The math is already at work.