Matt Frost noted that there were “strange reproductive politics implicit in the comments” on the foreclosure email post. This is fascinating, from a commenter: “I finally lost my sympathy when they decided to have a baby without their financial situation being resolved.”

You know who else was born at a moment where the parents didn’t have access to stable housing? Jesus. But I’ll stick to the maths.

I suppose that comment hinges on what you mean by financial situation being resolved. If it means waiting to have a baby until, say, all your student loans are paid off, sorry to tell you but on behalf on my generation the piping will probably have gone dry by the time the last of those are paid off. I assume it means that life, moving to new jobs, starting new careers, etc. should be put on hold until underwater mortgages start to clear. How long is that going to take?

Let’s assume that there’s an option value in being above water in your mortgage, if only because you can sell it without having to go into your pocket for additional payments. You’d have to do that for the massive transaction and closing costs in the exercise we are about to do, so we’ll assume that’s even.

I’m also fascinated by this post at calculated risk. They reproduce this graph:

Noting: “Strategic default on the part of the owner occupier becomes more likely at such high levels of negative equity….The default rate increases sharply for homeowners with more than 20% negative equity.”

This got me thinking: what does the payment schedule look like for someone who is 20% negative equity? How long will you be underwater, given reasonable market conditions?

Let’s take a reasonable suggestion of market conditions. This, as everything that is at the rortybomb blog, is not to be taken as financial advice. Let’s say inflation is 2% in the near future. According to Shiller’s data, the real gain to housing is .26% compounded annually. (Huge thanks to Richard Serlin for thoughtful help with me thinking through these examples.) So let’s say the nominal value of your home increasing year to year is 2.26%.

Let’s also say your mortgage is 30 years, and that the interest rate on it is 6%. As a reminder, LTV means Loan-To-Value, or the ratio with the mortgage amount divided by the property amount. Many people bought at the top of the bubble so when prices crashed, their mortgage turned out to be a lot higher than what the property is worth.

One key to remember is that, as always with mortgages, the first mortgage payment you make is almost all interest, and the last mortgage payment you make is almost all principal. I am going to assume that this mortgage is three years into the payment cycle when we calculate the LTV.

## Example One: Average

Here’s a chart (*click to enlarge*) that takes this example and graphs the LTV versus the years it takes for a mortgage to become above water, to have the principal of the mortgage equal the house value through growth of the value of the property and paying off the principal (R code available if interested):

So if you are 10% underwater, it will take around 29 months, or around 2 and a half years, until you own a small piece of your home. If you are 30%, it will take around 76 months, or around 6 and a half years. For those with an LTV of 120, they have 54 months – they will pay for the first small piece of their home around August 2014.

## Example Two: Interval

Now that’s an average case scenario. Let’s plot it again with a good case and a bad case, to give us an interval. How best to do it? I’m going to assume a 4% yearly nominal growth for the good case scenario – split that between inflation and property value growth however you’d like. For the worst case, I am going to assume the nominal value of the house decreases 2% for 2 years, and then goes back to increasing 2.25% year after year. Here is that graph (*click to enlarge*):

The higher line is the bad case scenario – keeping LTV the same, it means more time until you are above water. Here the range is 20 to 54 months for an LTV of 110 and 55 to 97 months for an LTV of 130. For an LTV of 120, where the defaults accelerate, looking out you’d see an interval of 39 to 77 months, or a timeframe between April, 2013 and June, 2016, when you can be above water. How’s that for uncertainty?

As you can see, the marginal effect of principal increases never really decreases – it’s always equally bad to add more principal, and equally good to remove some, in terms of getting above water. This is why mortgage modifications that add principal are *terrible*, which I’ll discuss in the next post.

*Edit: Original code accidently added one to the value of months for all LTV; changed in text and charts. Sorry, I blame the lack of sunlight and too much time at a screen.*