Credit Default Swaps.
The main problem was the people writing shitty loans were not the ones incurring the risk.
A mortgage broker had an incentive to write as many loans as possible. Once they wrote the loan they would immediately sell it off essentially transferring the risk away from themselves. So far this is not, in itself, a problem. The sale should reflect the risk inherent in it which would affect the price and the return so should be self-correcting.
What they did though was bundle these loans into tranches. So, take a pile of low risk mortgages, medium risk mortgages and high risk mortgages and bundle them together. On paper, as a statistical means, you can say a given tranche would carry X-risk (i.e. a certain percentage would be expected to go bad). Knowing that, say, 10% would default still left you with 90% good ones and you can figure your overall risk and profits.
Now when riskier and riskier mortgages were made they were not wholly unaware of this but even increasing the risk from (say) 5% to 10% the things were still deemed profitable.
This became a spectacularly lucrative market. The feeling was based on two underlying assumptions:
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Property values always rise (yes a given property may depreciate but overall property values rise).
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Even if someone defaults there is the property asset standing behind it which can be sold…couple that with #1 and your risk is not bad at all.
Even here we are not in real trouble although getting there.
Now make it that not just one person can buy the risk of your mortgage but 1,000 can (any number really). Who owns it now?
Then add credit ratings agencies were beholden to the investors. Investors would “shop” the ratings agencies to get the best rating. As a result the ratings agencies eventually were ranking high risk investments as AAA. Thing is no one wanted to point out the emperor had no clothes. Everyone was making money.
As a final bit add in massive leverage as icing on the cake. Banks could borrow money from the Feds incredibly cheaply and make great returns elsewhere. They were leveraged to their eyeballs and then some.
This state of affairs cannot continue indefinitely. Sooner or later everyone realizes the property is being sold at greatly inflated prices and you have written about all the bad mortgages you can so no one really left to keep the ball rolling.
House of cards comes crashing down. Defaults skyrocket and property prices crash and no one really knows who actually needs to bear the risk they bought because it has been sliced and diced and moved around so much.
Tl;Dr version:
There is nothing wrong with writing risky mortgages in and of itself. As long as investors understand the risk it is their choice to take it on and the price/profits should reflect the reality. When you start hiding that risk and mushing it up and spreading it around till it magically does not seem risky is when the problems happen.