# Financial Cage Match: Paying down a mortgage versus investing

Photo courtesy of AnEternalGoldenBraid

This is another entry in the Financial Cage Match series, where I look at two competing financial priorities and see which one comes out on top. Here’s another entry: Paying off student loans versus investing for retirement.

WARNING: This post contains math.

So we now know that holding on to a mortgage because of the tax deduction doesn’t make financial sense. There is no place that paying \$4 to get \$1 back works.

But there is one other reason why people say that they wish to not pay down their mortgage. And for whatever reason, I tend to hear this more often:

“Why pay down my mortgage when mortgage rates are cheap and I can make more money by investing?”

Well let’s see.

### Arbitrage

So the idea is that you have money that you could use to pay down the mortgage, but instead of doing that, you instead invest that money, netting you a return. In effect, you make money with other people’s money.

This is called “arbitrage”, which is defined (by Wikipedia) as “the practice of taking advantage of a price difference between two or more markets.”

In the case of our investor/mortgage arbitrageur, the two markets are the mortgage itself and the potential investment.

Let’s see how this plays out. It’s not a stretch to say that the typical mortgage these days is 4%, so you start out with a -4% return on investment. But we’ve also heard that you can earn 8% (or even 12%) in returns by investing in the stock market.

Isn’t it true that -4% + 8% = 4%? And isn’t it true that -4% + 12% = 8%? Why am I not on board with this?

Well let’s see.

### 1. Investment results aren’t guaranteed

Your mortgage (assuming a fixed rate) will return -4%. From now until it’s paid off. To the bitter end.

On the other hand, your investments may be all over the place. Over the long term, you’re likely to return somewhere in the ballpark of 8%, but I define long term as over a decade. Possibly two. Possibly three.

So in effect you are borrowing at a fixed rate to invest at a variable rate. So at the very least, it’s not a simple equation.

### 2. You will pay capital gains tax

Capital-gains tax is the tax you pay when you sell a (non-sheltered) investment that has risen in value. For most people in the U.S., the capital gains tax rate is 15%.

So let’s see a simplified example with smaller numbers. You borrow \$10,000 at 4% and then invest it in something. (Tiddlywinks?) Let’s say that after 5 years, your investment has returned an average annual return of 8%. Bravo.

During this time, you will have paid around \$1,050 in interest on your loan, and you will have made around \$2,170 in interest on your investment. Your total benefit is \$2,170 – \$1,050 = \$1,120.

Or is it? Because you’d need to pay capital gains tax on that \$2,170. That’s \$2,170 × 15% = \$326 in taxes, so your total benefit here would be (\$2,170 – \$326) – \$1,050 = \$795.

That’s a average annual return of 1.5%. Pardon me if I snore.

(If you include the mortgage interest tax deduction, your return increases, but only to about 2%.)

And keep in mind that this is an optimal return. What would happen if your investment lost money during this time? Then you’re just paying out at a higher interest rate. Is it worth it?

### 3. You can’t live in your retirement account

While I wish no hardship on anyone, it happens.

If you have a mortgage, and you have extreme hardship, your home could get foreclosed.

And to be sure, if you don’t have a mortgage, and you have extreme hardship, your home can’t get foreclosed.

So the longer you have a mortgage, the longer you assume a certain amount of risk. Not a great risk, but a risk nonetheless.

### Be unsophisticated

Arbitrage feels like you’re getting one over on the system. Which, of course, I support, especially when it’s a system that’s designed for every one else’s benefit except for yours.

But sophistication comes at a price. And in this case, you are trading a consistent result for a more risky and (at best) a small result. The risk doesn’t match the reward.

To be sure, I’m not saying not to invest (you can do that too, and in my opinion we have to). It’s just that once you’ve figured out your investing goals and are working toward them, there isn’t a compelling reason to sit on your mortgage.

### A final note on mortgages and avoidance

A mortgage is daunting. As I say, it’s debt’s final boss character. And because it’s so big and overwhelming, it may be tempting to rationalize ways to not deal with it actively, because that way you are absolved from the responsibility. If you don’t need to do it, you’ve already succeeded!

Unfortunately, that’s not how these things work. By holding on to a mortgage for the whole duration, you are willingly paying up to 50% extra. And 50% of a mortgage is a huge amount of money!

But as daunting as it seems, a mortgage is surmountable. People do it. It just takes focus and determination, and a whole lot of patience. Don’t turn away just because it’s hard. And if you’ll excuse the double meaning, the difficult choice is ultimately the more rewarding.

And just think: if you can accomplish something like this, what else could you accomplish?

### Mike Pumphrey

I'm the founder and author of Unlikely Radical, a site to help people succeed with money, achieve their goals, and live intentionally.

I offer a free phone consultation to anyone who is interested in changing their financial narrative. Are you ready? Click here for details.

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Posted on April 14, 2016