# How does a refinance allow a mortgage to be repaid?

As long as housing prices increased, these mortgages were secure: the borrower rapidly accumulated equity in the house that could be taken out in a refinance, allowing the mortgage to be repaid.

How would this work exactly? I know that many people took out home equity loans, but I'm not exactly sure how accumulated equity would end up making liabilities easier to pay back.

• What kind of mortgages are being referred to in the text? From the context, it sounds like subprime. – Brian Romanchuk Apr 3 at 0:49

Say you buy a house for \$100. This is paid with: • A \$10 down payment (from your own cash). (This is your equity.)
• A \$90 loan from a bank at 10% annual interest. (We call this a mortgage loan or more simply a mortgage.) Notice you're paying a relatively high interest rate of 10% on your mortgage, perhaps because the bank is not very confident that you'll be able to repay the loan. Say that overnight, the value of the house rises by \$50 to \$150. Now your equity has also risen by \$50, from \$10 to \$60. You can now refinance your mortgage and ask the bank to lower the interest rate on your loan, say to 5%. You are certainly happy to do this refinancing because you'll pay a lower interest rate. And the bank might be willing to oblige because it is now more confident that you'll repay the loan.
Let's say that you have a house that you buy for $$P$$ dollars. You have a mortgage of $$M$$ dollars. There is a change in the price of housing of $$r$$ percent. Assuming no transaction costs, the home owner's equity, the value of the house after selling it and repaying the mortgage is then: $$\max[(1+r)\cdot P - M, 0]$$ because if the mortgage is worth more than the house they can default, and this option makes it so the household has equity of at least zero. There is a second reason a household might default, that they are unable to pay their mortgage. The first reason is called strategic default and the second non-strategic default. In good times, when $$r$$ is positive, the household has positive home equity and no reason for strategic default. If they are unable to make their mortgage payments (non-strategic default), they can sell their house. This allows them to pocket their home equity, protect their credit, and repay their loan.