After reading the Novy-Marz and Rauh paper regarding unfunded pension liabilities you decide to compute the total obligation of the state that you live in. After some research you determine that your state's promised pension payments amount to

$ 1

billion dollars annually, and you expect this obligation to grow at

2 %

per year. You determine that the riskiness of this obligation is the same as the riskiness of the state's debt. Based on the pricing of that debt you determine that the correct discount rate for the fund's liabilities is

3 %

per annum. Currently, based on actuarial calculations using

8 %

as the discount rate, the plan is neither over nor

underfundeddashthe

value of the liabilities exactly matches the value of the assets. What is the extent of the true unfunded liability?