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Why somebody buy the defaulted loans from the banks, if the debtors can not pay back their debt? If I bought these loans I will cause losses myself, because nobody will pay me (or just a lower price than the original value of the loans, if these will be recovered). What is the finance logic behind this method?

On the other hand, if I can buy these loans on a lower price what I can get when its will be recovered, why the banks sell its?

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(1) Often there is some collateral behind the loan (a building, etc.) which with enough effort and time can be sold to recover at least SOME of the value of the loan. However this is not necessarily what the bank is good at or wants to do. Their business is to lend money, not make real estate deals or dispose of dubious merchandise.

(2) A smart buyer will of course pay much less for the loan than they think they can recover. But opinions differ and the residual value is hard to judge. This is a big advantage of the sale: it allows "the market" (that is many potential buyers in competition) to determine the value of the loans in some fairly objective way (the estimates of value made by the bank are ALWAYS biased upward since it is their loan and they try to put an optimistic picture on the situation. [To be a little cynical: it is in their interest to lie, to deny there is any problem, to wait a little longer, partly for accounting reasons]). As they used to say "a thing is worth what someone will willingly pay for it" and that is what the sale does: it establishes a price, removing the uncertainty.

(3) Often the regulators require the bank to sell the loan to "clean up" the bank and give it a chance to "start anew". The nonperforming loans and the hope of recovering them can be a big distraction for the bank management, which stops lending to more creditworthy enterprises. The regulators are aware of the "inaction bias" mentioned in (2) and they try to encourage the bank to face reality and move forward.

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A bank might not have the expertise in recovering defaulted loans. it might be more efficient to sell the claim to someone who specializes in recovery and knows how to doit better.

There was a nice article in the Washington Post https://www.washingtonpost.com/news/business/wp/2016/03/29/how-one-hedge-fund-made-2-billion-from-argentinas-economic-collapse/ a few years ago explaining how a hedge fund made lots of money buying bad Argentina soverein debt.

Summary: in December 2001, the Republic of Argentina defaulted on about USD 90 billion of bonds (mostly USD denominated, but some EUR and other currencies). Many bonds were sold to retirees in Europe and the like, who had no expertise in trying to recover bad debts.

Argentina said, they might have some money, but they would not pay anything, because they're the government. (No, that wasn't nice at all.)

A hedge fund that had the expertise bought some defaulted bonds (not at face value, of course), so the bond holders got some money right away. Them for over a decade, it fought the government of Argentina in U.S. courts, and eventually recovered more money than they had paid for the defaulted bonds.

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Long story short: you buy any financial asset if you see the value given the price you pay. Distressed assets give you the highest yield (with the highest risk) at lower price.

Distressed debt specialists have knowledge and sufficient experience to determine whether there's any value left on the table. Some activists aim to participate in bankruptcy and liquidation events (betting on recoveries); others focus on restructuring events aiming to either negotiate better terms for creditors or even converting into equity and effectively taking over the company.

defaulted asset [loan] is still an outstanding security up until liquidation. the asset might be technically in default after the debtor missed the payment [either coupon or principal] even if financial difficulties are temporary. The bankruptcy [liquidation] process is not yet guaranteed - at some point there still can be a chance for an asset to become performing. Therefore some participants are able to withstand such uncertainty (they'll be rewarded for that accordingly) and their investment strategy will still be solvent if the number of cases with "actual recoveries lower than expected" is below some threshold.

As for why banks sell these: 1) clean balance sheet as distressed assets have higher capital charges (rwa); 2) it might not be an area of focus; 3) get cash (with a haircut) now and avoid waiting/participating in bankruptcy events which may take years.

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