A 15-Year Mortgage Costs $409,112 More Than You Think

Yeah, $409,112 more.

And a 20-year mortgage is $265,103 more expensive than you thought.

Specifically, a 15-year mortgage ends up costing you around $400k more than a 30-year mortgage, while the 20-year loan is $265k more expensive than the 30.

Since people tend to opt for the shorter loan duration under the impression doing so saves them money, it’s safe to say 15-year and 20-year mortgages are much, much more costly than you might have believed.

Which leads to the conclusion: Given today’s interest rates, taking a 15-year or 20-year mortgage rather than a 30-year mortgage on your home purchase is the financial equivalent of chaining yourself to the tread of an M1 Abrams tank.

Bad things, man.

Those are the takeaways drawn from a nasty bit of spreadsheet work I did to try to nail down the real financial differences among 30-year (30Y), 20-year (20Y) and 15-year (15Y) mortgages.

A 30-Year Mortgage Can Save You Hundreds of Thousands
A 30Y Mortgage Saves Hundreds of Thousands

Here’s why I bothered. Most calculators, articles and other resources that purport to outline the economics of these three popular mortgage types miss some pretty important stuff.

Either they ignore opportunity costs outright, or they don’t tax-effect interest and returns, or they don’t account for home price appreciation, or they get halfway through the analysis and then sort of throw their hands up in surrender at the bazillion inputs and assumptions that go into analyses like this. And then they conclude: Do what feels right. Or something equally unhelpful.

Not at Libre!

I’ll get to the calculations that yielded the above results in a minute. But I’ll first mention the obvious. The specific numbers would be different for each unique mortgage because of those bazillion factors that influence the results.

And, yes, there are more assumptions baked into the numbers than there are foul-tasting bits of rind baked into your aunt’s fruitcake.

So, yes, if you change some of the assumptions and you change some of the inputs and you carry the calculations out a little differently, you’ll get different results.

But most reasonable alternative inputs and computations will still lead you to exactly the same general conclusion: Don’t be fooled or misled by mamarrachos telling you they “saved tens (or hundreds) of thousands of dollars by getting a 15-year mortgage instead of a traditional 30.”

They didn’t. They should ask for a Mulligan.

Curb Appeal

I recently spewed some econ knowledge your way about debt repayment. In that post I mentioned that I’d discuss the mistake people make when they arrive at the conclusion that a 15Y or 20Y mortgage will save them lots of money relative to the 30Y.

In that same post, I characterized 15Y and 20Y products as “suboptimal.” But I really should amend my earlier characterization of 15Y and 20Y mortgages as “suboptimal.” They are not. They are ludicrous.

“Ludicrous (loo’ du krus): so foolish, unreasonable, or out of place as to be amusing; ridiculous.” —New Oxford American Dictionary

They’ve gone to plaid.

They’re a travesty.

They’re so bad for personal finances that it pains me to write this – because I’m sure someone reading their daily Libre will have taken a 15Y or 20Y mortgage on the belief and counsel from others that the product would be better for their wealth.

Those people were deceived.

Staging

Here’s the “conventional” logic usually invoked to argue in favor of 15Y and 20Y mortgages:

1) By taking a shorter-term mortgage, you pay down principal much more rapidly. As a corollary, your total interest charges over the course of the loan are much lower.

AND

2) By taking a shorter-term loan, you can obtain a lower interest rate. As a result, every dollar borrowed is a little cheaper than with longer loans.

SO

3) Combined, these factors make it seem like a slam-dunk. Yeah, your monthly payment’s a little higher than with the 30Y product. But man-oh-man those interest savings…We’s goin’ be rich!

So far so good. I can more or less agree with the conclusion that 15Y and 20Y mortgages save you lots of interest expense. (In my analysis, the 15Y results in about $130k less in interest expense relative to the 30Y. So that side of the equation is unambiguously right.)

But you can’t stop the analysis there. You’ve got to do the whole other half of the study to get the full picture.

It’s opportunity cost, Luchadores, and it’s a beast.

By taking a 15Y or 20Y mortgage rather than the 30Y, your monthly payments are higher. For the 15Y product, they’re way more than you’d pay with the 30Y. And that makes perfect sense. You’re borrowing the same amount of money either way; you’re just paying it back twice as fast with the 15Y.

The trouble is that the savings in interest charges garnered by taking on the shorter-term loans don’t even come close to compensating you for the opportunity cost associated with those higher/faster payments.

This is especially true when the period of analysis approaches the average amount of time homeowners own a house in the U.S. (Which is close to 15 years, depending on how the data are sliced.)

Inspection

How’d I go about my calculations to get those eye-catching numbers I dangled above? Pretty slowly, as it turns out. This was kind of a tedious analysis. So I’ve developed an appreciation for why people get roped into these shorter-term mortgages. Running all the numbers for something like this makes you want to claw out your brains.

I’ve also developed an appreciation for why, when you scour the web for reasoned discussion on this topic, there are lots of competing conclusions – all of which initially seem reasonable – but which are often predicated on only superficial analysis.

You’ve got to dig in to reveal the Truth. You’ve got to use amortization tables, tax-effected payments and rates of return, historical statistics… a whole Titanic-load of data.

And an iceberg-sized helping of assumptions.

And a fancy computer to run all the numbers.

And maybe advanced degrees in quantum physics to get it more or less kinda right.

At the highest level, here’s how I structured the analysis. I asked: What is the overall financial result for a homebuyer who finances a primary residence purchase with a 30Y v. 20Y v. 15Y mortgage?

  • I assumed three identical hypothetical homebuyers, each of whom selects an identical and rationally-budgeted home to purchase.
  • I then assumed one finances the purchase with the 15Y mortgage, one with the 20Y, and one with the 30Y.
  • I finally assumed that each buyer has monthly cash income sufficient to service the monthly payment on the 15Y mortgage (since the 15Y mortgage has the highest monthly payment). In my analysis, the tax-effected monthly payment for the 15Y mortgage is $2,044, meaning each buyer has $2,044 in income each month that isn’t needed for other living expenses and can be directed to a mortgage payment if need be.
  • For the 15Y buyer, this last assumption means he spends all his monthly free cash on the mortgage during the first 15 years of the analysis. The 20Y and 30Y buyers, who have lower monthly payments, invest the excess cash available to them each month in U.S. stocks.
  • Once the 15Y buyer’s mortgage payments end, he invests the full amount of monthly free income in U.S. stocks. (The same is true for the 20Y buyer.)

Accordingly, over each month and year of the analysis, all three homebuyers have the same amount of cash at their discretion to pay their mortgage and/or invest in stocks. The proportions of funds placed into equities or spent on the mortgage simply differ year by year on the basis of the mortgage payment each is servicing.

With this setup established, I ran the numbers and then took “snapshots” of the financial results for the three homebuyers at 5-year intervals following the home purchase (i.e., at years 5, 10, 15, 20, 25 and 30). At the time of each “snapshot,” I assumed the home would be sold, yielding the homebuyer cash equivalent to the sum of his home equity and gains from the sale.

I then compared the overall financial position of the buyers by summing together their cash from real estate and the value of their portfolio of stocks.

Here’s a table summarizing the results.

Base Case Results
Base Case Results

And here’s a table that translates those results into direct comparisons among the three buyers’ financial positions.

Base Case Comparison
Base Case Comparison

You can see some of the assumptions listed underneath the meat of the tables.

And so let’s address the analysis’ inputs now. Here’s a high-level overview of the inputs and assumptions:

Data Inputs
Data Inputs

The home price used is $400k because the average U.S. home sales price in 2016 reached around $380k, and I wanted to start with a nice round number for the analysis. So I rounded up.

The traditional 20% down payment was used to avoid private mortgage insurance issues.

The nominal mortgage rates reflect what’s shown on Bankrate as of August 2016.

The tax-effected mortgage rate reflects the impact of income tax deductions allowed on mortgage interest payments. This tax-effected rate implies a household federal marginal tax bracket of 25%, qualification for income tax deduction itemization, and a state income tax rate of 8%. The 25% marginal bracket is probably right for most buyers of $400,000 homes. A calculator for this conversion is available from Bankrate.

Ok. That’s the first batch of inputs and assumptions. Those more or less give us the lay of the land: How much house we’re dealing with, the three mortgage products we’ll compare, etc.

They’re kind of our “initial statics.”

Now we gotta get dynamic. I also used/assumed the following inputs.

Average annual real home price appreciation is 2.8%. This reflects the observed average annual real residential real estate appreciation in the U.S. over the last 30 years.

At the time of the home’s sale, a 3% commission would be paid and zero capital gains taxes would be owed.

Average annual real returns on equities are 8.4%. This reflects the observed average annual real returns to the S&P 500 over the last 30 years.

Since the equities investment would be made in a taxable account, annual dividend income would be taxed at 15%. Depending on the statistics looked at, up to about 50% of total returns derive from dividends. So I assumed roughly half of returns would be taxed at 15%, leaving a 7% annual effective tax rate on the 8.4% returns. Tax-effected annual real returns are therefore 7.81%.*

I’ll relax the home price appreciation and equities returns assumptions for comparison purposes later because they do matter. But maybe not as much as you’d expect.

For the excess cash available to the 30Y and 20Y mortgage-holders to invest in equities, I used tax-effected excess cash to account for the beneficial tax implications of carrying higher mortgage interest on the 30Y and 20Y mortgages.**

Comparables

That’s painful to read. And you’re probably taking issue with a few of the inputs or assumptions by now.

That’s cool.

So let’s monkey with the couple of assumptions that you probably don’t like. First, let’s change the rate of stock returns. The 8.4% makes a lot for sense for a lot of reasons. After all, it’s the observed average over the last 30 years. Since we’re looking forward (up to) 30 years, it’s a pretty great starting point.

But let’s chop it down by ¼ to 6.3%. Here are the results if we do that:

Low Equities Returns Case
Low Equities Returns Case

Ok. Now let’s keep the lower equities assumption and increase the rate of real estate appreciation by 50% from 2.8% to 4.2%:

Low Equities & High Real Estate Returns Case
Low Equities & High Real Estate Returns Case

All right. Now let’s keep the real estate return at 4.2% and put equity returns back to 8.4%:

High Real Estate Returns Case
High Real Estate Returns Case

No surprises: the main sensitivity in the results is associated with the rate of stock returns. But the sensitivity isn’t really that “elastic.” Reducing stock returns by 25% really only makes a minor directional impact in the earlier years.

Our results make intuitive sense because the stocks investments are the “opportunity cost” alternative. The bigger the delta between the equity returns and the cost of the mortgage, the better the leveraging effect.

But we also see that we need a fairly big delta between the tax-effected interest rate on the mortgage and the tax-effected returns on the stocks investment in order to benefit from the free cash flow using the 30Y mortgage.*** It’s not good enough to simply say, “Hell, FL, this conclusion is obvious because the returns on stocks are so much better than returns on residential housing.”

That’s because there’s a big “distortion” brought on by something we’ll call the scaling effect. Since the mortgage rate applies to an initially very large sum, while the stocks investment starts small and needs time to grow, you need a fairly big wedge in rate differential to get good overall incremental returns from this sort of leveraging, and the 30Y accordingly needs around 5 years to “pay” for itself as a result.

Offer

  1. The 30Y mortgage makes (much) better financial sense for most homebuyers than 20Y or 15Y alternatives.
  1. The 30Y mortgage is most powerful as a lever for wealth accumulation when it’s held for the full term.
  1. Although 15Y and 20Y mortgages look like superior options for 5-year holding periods, I’d argue that, if there’s a high degree of likelihood the house will be sold in fewer than 7 years, a 7/1 ARM or an interest-only loan is much better than either the 15Y or 20Y. The 15Y and 20Y products aren’t much worse than 30Y for 10-year holding periods; but they’re not really better. In part, you can think of their shortfall relative to the 30Y for a 10-year holding period in terms of “option value.” If you’re not sure whether you’ll keep the house for 10 years plus, the 30Y mortgage makes the option of keeping it longer much cheaper, which makes the 30Y more valuable. (This is particularly true given today’s low interest rates, which are almost sure to be higher 10 years from now, making refinancing later a bad bet.)
  1. The 15Y and 20Y mortgages probably only make any (tiny) amount of sense for people who are able to perfectly accurately foresee that future equities returns will be far below their historical averages during the period of their mortgage terms. Which is pretty much nobody.

Negotiations

You hear this kind of stuff: “I prefer paying down my mortgage faster than needed (as opposed to investing the difference) because that prepayment is a risk-free return equal to the saved interest expense (say 3.5%). But with investing there’s risk associated with the higher prospective gains.”

My response: Ok, I get that. But here’s the thing. If your investing horizon is 10 years or 15 years or 20 years or 30 years (i.e., the horizons we’re dealing with in mortgages), then the risk of negative or substandard returns from equities is very low. We’ve discussed this concept elsewhere on FinanciaLibre, but the headline is this: If you’re passively invested for a very long period in stocks, you’re likely to get excellent returns that approximate the long-run averages.

Nevertheless, there is a real argument for timing risk or sequence risk.

Consider this. Over a 30-year period, equities markets could generate the 8.4% real return rate and still leave your mortgage-levered portfolio’s total return in the dust. Because there’s a possible timing problem. That real return can be comprised of over-the-top returns in the early years of your investing program and crap performance later on.

In that event, equity market returns over the period would be much higher than total returns in your portfolio because of the small scale of your holdings during the good years, and the large scale of holdings during the bad.

There’s no way around this issue with equity investing. But note:

1) this sequence risk applies equally to all volatile investments, so it’s not really peculiar to the mortgage analysis, and you wouldn’t let this concern stop you from making “normal” investments in equities;

2) volatility is really more of an issue when the portfolio is being drawn from rather than contributed to;

3) the problem can more or less be accounted for when we reduce the assumed returns from 8.4% to 6.3% (i.e., you’re not likely to get a worse result than 25% below the long-run average just because of sequence risk over a long horizon, so the 30Y is still most likely beneficial even directly accounting for this issue); and

4) that’s just the downside risk (i.e., it could also just as easily go the other way and work to your great advantage).

Let me explain point 4. There’s also upside “risk” that the sequencing scenario reverses. Poor equity returns could all be concentrated early when your stock holdings are small, and crazy equity returns could all occur later when your nut is big and buoyant and beautiful. You can’t know how it’ll go beforehand. So the smart money sticks with returns’ central tendencies.

You also hear: “I like the discipline of a 15Y or 20Y mortgage payment. It forces me to save.”

Yeah, well, buck up, cowboy. If you really don’t have the constitution to invest the free cash associated with the 30Y mortgage, you should be demoted from cowboy to rodeo clown. And rodeo clowns are rarely, if ever, lionized as great financial geniuses. They’re mainly gored and laughed at. Don’t be gored and laughed at.

But, if you are a clown, there are plenty of ways to make investing automated via regular deductions from accounts, etc. I won’t get into the particulars here. But the programs that take care of that kind of thing are good behavioral economics “choice architecture” in action.

Closing

I know this is a long and kinda technical post.

But I feel like the mortgage selection topic is important and relevant for lots of people, and I feel like there aren’t great resources out there that do a complete job of getting into this mortgage mess. So I hope this helps.

Note, though: When I took a mortgage on our house (a 30Y, as it turns out), I didn’t do any of this analysis. I went with intuition. But it was what we’ll call “informed intuition”; I suspected the results of a laborious analysis would, at least directionally, be what we found here.

And so, really, I hope the way this post will be helpful is by providing some girding for solid intuition about the big levers involved in a decision like this. Oh, and I guess I hope it’ll also help you streamline the mortgage decision when you buy a home. You know, so you just go with the 30Y and stop worrying about it.

Luchadores, I’d love to know your thoughts: Good, Bad and Ugly. If you’d like the spreadsheets I used in the analysis, subscribe to the newsletter (on the righthand sidebar, under “Get Libre”) and I’ll send them along so you can manipulate the numbers.

(*Note: I assumed zero equity trading costs, and I assumed no equities would be sold once purchased. This zero trading cost assumption is not material here because of the large sums invested and because of my use of the midpoint convention for investment returns, which can be interpreted to suggest very few total transactions. Separately, quants will say: “FL, you underestimated taxes due from equities investments by using the real return rate of 8.4% and tax-effecting that, when you should have tax-effected the nominal return and then deducted CPI to get the real tax-effected return.” True. But I also probably over-estimated the returns due to dividends, which is the only taxable component of returns in this analysis. Doing that overstates the tax impact. Together, the factors probably wash; and there’d be no real impact either way.)

(**Note: The use of tax-effected mortgage rates does not substantially impact the results of this analysis. Although the tax-effecting impact serves to improve the performance of the 30Y relative to 20Y and 15Y mortgages, the ability for a homeowner to claim itemized deductions including the mortgage deduction is not necessary for the 30Y to provide superior financial outcomes. Quantitatively, you can see the scope of the impact on inputs by looking at the “Data Inputs” table and comparing the “Free Cash” and “Tax-Effected Free Cash” rows; using these non-tax-effected payments does not result in any directional differences in the conclusions but simply “tightens” the deltas among the three mortgage types.)

(***Note: One sensitivity not addressed that could impact the analysis is the differential in mortgage rates among 30Y, 20Y and 15Y products. Were the rate differentials different, the results of the analysis would change. A large enough differential could cause 15Y and 20Y products to be better than 30Y. But these rates tend to more or less move in lockstep so the rates’ differences don’t fluctuate that much, and rates of all three products have been pretty steady for a while now. Plus, “today’s” rates are used since they’re what current homebuyers are dealing with.)

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