I am buying a house, and am therefore faced with the choice between a 15 year mortgage at 2.875% and a 30 year mortgage at 3.49% (as of a couple of days ago; those rates have probably changed a little by now).
The main advantage of the 15 year mortgage is that it comes with a lower interest rate and, because I’m making larger monthly payments, it keeps my money out of the stock market, which is good if the market tanks. The main advantage of the 30 year mortgage is that it allows me to keep more money in the stock market for a much longer time, which is good if the market does well.
How should I weigh those factors? Economics tells me that I will solve this problem by forecasting the return on equities over each of the next 30 years, and computing, on the basis of my forecast, which mortgage will leave me richer in the long run. No, that’s not quite right. Actually, economics tells me that I’ll make many forecasts, assign each one a probability, and thereby compute two probability distributions for my future net worth and then choose the distribution I prefer.
Now let’s get serious.
Here’s what I just did: I wrote a computer program that allows me to input my forecast of stock market returns in each of the next 30 years and then tells me which mortgage is better, and by how much.
Already, I suspect I am not the average homebuyer.
Then I ran my program multiple times, inputting a variety of assumptions. I learned that if the stock market returns 4% a year for the next 30 years, I should get the 15-year mortgage, and if it returns 6%, I should get the 30-year. What probabilities should I assign to those forecasts? I feel confident that the average homebuyer will join me in answering: “How the hell should I know?”
Of course the return on stocks will probably fluctuate, so I should consider more complicated scenarios. Maybe it will build slowly from 3% to 8%. In that case, my program tells me to get the 30 year mortgage. Or maybe it will stay around 0% for a while before jumping quickly up to 8%. In that case, I should get the 15 year. Which of those scenarios is more likely, and by how much?
But there’s not much point in worrying about that too much, because there are too many factors my program doesn’t account for. First, it does account for the fact that I can always choose to pay off my 30 year mortgage early — but it fails to account for the possibility that I might pay it off unwisely. It fails to account for the option to refinance. It accounts only imperfectly for the fact that I’m unlikely to live in this house for 30 years, and therefore won’t be able to keep a mortgage that long in any event. It fails to account for the option to invest my money in assets other than stocks and housing (though historical precedent suggests that I will never exercise that option). Has the average homebuyer written a program to account for all that?
Fortunately, economics tells me not to agonize too much about this decision, because both mortgages must be rooughly equally desirable; otherwise nobody would make the inferior choice. And why is that? Because economics tells me that, unlike me, other homebuyers are confidently doing exactly the right calculations.
Now, economics is sometimes unfairly criticized by people who point out that many homebuyers are either too uneducated or too lazy to make probabilistic forecasts, write computer programs, and account for multiple future contingencies and options. The (correct) response to this is that, in order to do economics, we don’t need to assume that all homebuyers act this way, or even that the average homebuyer acts this way, but only that the marginal homebuyer acts this way.
But what I want to know is: Who is this marginal homebuyer? Does anybody have his email address? I want to know which mortgage he recommends.