Here's a mathematical paradox. I'm not sure if any you can help me out. A government is unable to pay back debt it owes. The government wants to pay back that debt at some point in the future but is unable to immediately pay it back. Investors believe there's a 50 percent chance they will be repaid. (For simplicity here, let's completely ignore accumulating interest) Now what normally happens in the market, if there's a loan made for 100 dollars and now it is believed there is only a 50 percent chance that loan will be repaid, then the lender that issued that loan will then sell it off to some third party investor for 50 dollars. If the borrower ends up paying it back that third party investor will end up making a big profit. Suppose the government does not want this to happen. They don't like the idea of having to pay money to people who did not lend the money in the first place. Even if the loans are completely repaid, the original lender still ends up cheated. So this is the idea the government comes up with. They will only repay a portion of the debt, based on what the current market price of that debt is going for. So for example, if lenders are trying to offload their debt for 50% of the face value, the government lets the public know they will pay back only 50% of the loan. That creates a complicating issue though, because the market price of that debt is found by multiplying together the amount of the loan that will be repaid together with the projected probability it will be repaid. This seems to create a circular feedback loop if one tries to calculate what the market price of that debt should be. Can anyone help me calculate how much the market price of that debt should be? You can use any input numbers you wish but just tell me basically how it would be calculated. Is there any way the government can pay back that debt without paying more than the discounted going market price of that debt? It might not even be government debt here. The government could be in the process of discussions to bail out loans made by big banks. But it might not make sense to guarantee the full value of that debt if most of the banks have already sold off the debt to other parties at greatly discounted rates.
Yes, the government can buy back the loans it has issued. Bonds in government debt are routinely bought sand sold on the open market. So, when Greece's government debt became junk debt equal to 1% of the debt issued, why did not the Greek government buy it all? Hence reducing the cost of their debt to 1% of the price issued. Answer: Because they are in debt. They had no money to buy any debt with. And because they had defaulted on 99% of their money, no one was willing to lend them the comparatively small amount of money they needed to make this great saving. So the problem with buying your own debt is, if you need to, no one will lend to you. Because your goal in this is to rip off lenders.
