# 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. Apr 3 '19 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.

• Why is the bank more likely to give a lower interest rate? Is it because if you default the bank would end up with more equity when it takes the home as collateral? Apr 3 '19 at 5:18
• @Vasting: Yes. The bank has less to lose if you default as it can seize the house (which is usually posted as collateral). (Also, you're less likely to default anyway because your net worth has just gone up by \\$50 overnight.)
– user18
Apr 3 '19 at 5:19
• Could please you elaborate on why the bank is willing to offer you a lower interest rate though. I understand they can afford to, but once you have already signed the loan contract, why would they alter it in your favor? Apr 15 '19 at 5:50
• @Giskard: Banks have competitors. If Bank A from which you originally borrowed from doesn't want to refinance, then you can always go to Bank B, borrow the same amount but at a lower interest rate and repay Bank A. Now you the customer of banking services have probably been lost to Bank A and captured by Bank B. (In practice, some of both happens. Usually Bank A will refinance, but sometimes it will refuse and you'll go elsewhere.)
– user18
Apr 15 '19 at 5:58
• @Giskard: I believe most countries have laws mandating the option of early repayment, though possibly at the cost of some fee.
– user18
Apr 15 '19 at 6:17

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.

In reality, there are complications. The lasting damage to credit scores of a default, the possibility of recourse on a mortgage, losses in house value from foreclosure, and transaction costs all complicate this picture some. But the general idea still holds. Rising house prices give households with cash flow problems the ability to sell their houses rather than default. So the strategic defaulters have no reason to default and the non-strategic defaulters can sell instead of default. This lowers default risk substantially.