David R. Henderson  

McArdle on 15-Year Mortgages

PRINT
Does Paying More to Hire Ameri... A few notes on utilitarianism...

Megan McArdle has a good post on why it can make sense to switch from a 30-year to a 15-year mortgage. I agree with most of her reasoning. Her point that I think is most important for most people, based on my observations of lots of people over many years, is that a 15-year mortgage, compared to a 30-year mortgage, is a way to make yourself save. For her and her husband, as for my wife and me, this doesn't apply because we have greater than usual discipline in saving.

I want to point out one misleading statement, though, not one that's wrong, but one that's misleading. I also want to point out one factor that goes in favor of a 30-year mortgage.

The misleading statement:

Over the life of your loan, you'll save 65 percent of your total interest costs. On a 30-year loan at current rates, you'll pay almost $300,000 in interest costs on a $350,000 loan, versus about $100,000 on a 15-year loan. The benefit comes from two things: shortening the payment term, and lowering your interest costs. I don't know about you, but I could find something to do with an extra $200,000.

If by "lowering your interest costs," she means simply that you get a lower interest rate by switching to 15 years, then I have no objection. Her reasoning is accurate. But the "shortening the payment term" part is misleading. It's accurate. But it's misleading. To separate out the effects, assume that the interest rates on a 15-year and a 30-year mortgage are equal. Then, the reason you're paying so much less interest is entirely due to a shorter term. Why do I say she's misleading? Because it ignores the whole point of borrowing and the whole point of interest. Interest is the price for current command of resources. You have fewer resources currently if you pay the loan off faster. I can't judge, nor can Megan, which is better for you. But we can say that it's misleading to add up interest costs, undiscounted, over a long period. It treats a $1,000 payment on interest in the 15th year as equal to a $1,000 payment of interest in the first year. In other words, ironically, it ignores why interest exists. And that's what she did to get her $300K vs. $100K comparison. The interest payments on the 30-year loan should be discounted back to today, as should the interest payments on a 15-year loan. Indeed, of course, if you use the same interest rate you're paying to discount interest plus principal on each mortgage, you'll get that the present value of each is exactly $350K. I'm not saying that that's the right interest rate to use to discount those payments. The right interest rate will depend on your investment alternatives. If you use a higher interest rate than the one on the mortgage you're paying, because your investment alternatives are really good, then the present value of payments on the 30-year mortgage will exceed the present value of payments on the 15-year mortgage. That suggests going with the 30-year, all other things equal. And, of course, vice-versa.

The factor that goes in favor of a 30-year mortgage over a 15-year is the threat of higher inflation. Megan writes:

Interest rates are going to have to go up sometime soonish. Mortgage rates are not at their all time lows (more's the pity). But they're still very low, and by refinancing now, you can lock in 3 percent or so. As inflation rises, this will ultimately mean that your mortgage loan is practically free. But this state of affairs cannot last forever; the Federal Reserve will eventually be pulling back on credit, and you will not be able to get such a good deal. Why not lock it in now?

But that argues for locking in a low rate. It doesn't argue for switching from a 30-year to a 15-year mortgage. True, you'll probably get a lower rate by switching. But that's separate from the issue of inflation. If you expect higher inflation in the future and you expect that inflation to stay at that higher level, that argues for the 30-year mortgage over the 15-year mortgage because the 30-year mortgage leaves more principal for inflation to whittle away. Other than a handful of gold coins, I have few good inflation hedges. My fixed-interest-rate loan is one of them. The more slowly I pay it off, the longer I keep my inflation hedge.


Comments and Sharing


CATEGORIES: Finance



COMMENTS (25 to date)
Bryan writes:

"we’d been paying a substantial extra sum on the principal every month."

Full stop.

More than taking out a 15-year mortgage, this is what would result in "every financial analyst I know is mentally screaming in anguish."

Paying down principle on a loan with a low-rate made even lower through tax deductions makes little sense. Your return is probably 2%, which is easily bested in stocks.

OTOH, converting to a 15-year makes even less sense if you are already paying extra on your 30-year mortgage. Why not simply make the 15-year mortgage payments and keep the 30-year so that should a time come when you need the extra dough you have it?

I realize there are some mitigating factors here (interest rates, stock risk, etc.), but overall, this makes advice seems to make little actual sense in this particular case.

What am I missing.

Nick writes:

The best approach is to try to match the duration of your assets with your liabilities. So if you think you are going to sell your home in 5 years, get a 5/1 or 7/1 ARM. If you are buying your first home and hope to be there forever, get a 30-yr fixed. If you are moving up or refinancing with school age kids, and expect to move to Florida as soon as they graduate, a 15 year makes a lot of sense.

This is only slightly complicated by the optionality in 30-year fixed loans, which means that you are never "stuck" with a long term liability should you desire (have to) sell the asset (house). But you pay a lot for that optionality, say 75bps at current rates over a 15 year, and over 1% versus a 7/1 ARM. That is like an additional 20-25% in interest cost (the part you don't get back when you eventually sell the house/leave it to your heirs).

Of course, liquidity should be probably the primary consideration but if you can afford the monthly payments on a variety of loan types then you really should be thinking about how long you are going to live in your home so you don't overpay for the prepay option and don't risk overstaying past when you no longer get the benefits of a fixed rate or the inherent leverage.

Kevin Erdmann writes:

There are two financial assets here. The homeowner is long the house. The house will be generally hedged against inflation over time. But higher real rates will lower the nominal value of the home, all else equal.
If the homeowner is short a mortgage, both real and inflation premiums will have the same effect on the mortgage. If rates go up, the mortgage will be paid back advantageously over time. But, if the homeowner sells the house, the mortgage will have to be paid off at full value, so further gains from interest rate changes would be lost.

So the home does provide some inflation protected tion, but there could be a catastrophic loss for a leveraged homeowner if real rates rise and they have to sell. Home prices are probably below intrinsic value now, so this risk is probably lower now than it would be if rates were low while credit markets were more functional.

Kevin Erdmann writes:

There are two financial assets here. The homeowner is long the house. The house will be generally hedged against inflation over time. But higher real rates will lower the nominal value of the home, all else equal.
If the homeowner is short a mortgage, both real and inflation premiums will have the same effect on the mortgage. If rates go up, the mortgage will be paid back advantageously over time. But, if the homeowner sells the house, the mortgage will have to be paid off at full value, so further gains from interest rate changes would be lost.

So the home does provide some inflation protected tion, but there could be a catastrophic loss for a leveraged homeowner if real rates rise and they have to sell. Home prices are probably below intrinsic value now, so this risk is probably lower now than it would be if rates were low while credit markets were more functional.

Craig Richardson writes:

David,

I agree with your post about the point of interest.

However, what I think many economists miss in advocating for 30 year mortgages comes from their model of perfect rationality that lack an emotional component to money, and assumptions of always being employed. They miss the positive feeling of being debt free, and the psychological drain of having a large debt overhang... even if the accounting shows us to be better off if we hold onto debt and make our deductions.

Putting aside the tax advantages, the feeling of being debt-free has numerous daily benefits that give many people a lot of utility, not measured by simple dollars and cents on the tax return. For example, it takes the stress off of knowing that even under a long unemployment spell, one can not be foreclosed upon. The financial crisis really warmed people up to this idea, and made them realize that a 30 year mortgage can encourage excessive debt, and take too much for granted.

David R. Henderson writes:

@Craig Richardson,
However, what I think many economists miss in advocating for 30 year mortgages comes from their model of perfect rationality that lack an emotional component to money, and assumptions of always being employed. They miss the positive feeling of being debt free, and the psychological drain of having a large debt overhang... even if the accounting shows us to be better off if we hold onto debt and make our deductions.
Fair enough. I thought Megan handled that part pretty well, though. I just didn’t see the need to repeat it at length. My shorthand was the point about self-control, which already challenges the “perfectly rational” assumption. As my former colleague Richard Thaler once put it in a seminar at the University of Rochester B-School, “if you talk about self-control, exactly who is the self that is controlling and what is that self controlling?"

David N writes:

I hate advice that essentially says, "Do this because you lack self-control." Forced savings? Sure, into a depreciating, illiquid asset.

At certain times a steep yield curve can make 15-year mortgages attractive. But the yield curve has been flat for a long time now. If bond rates were at historic highs you'd want to buy the 30 year, right? So with mortgage rates near historic lows you want to short the 30 year, i.e. take a mortgage.

A 30 year gives you the option to prepay if that return makes more sense than a liquid portfolio return. If your mortgage rate is less that 4% I think you should pretend you have a 15-year mortgage and invest that extra money in equities that pay qualified dividends with a comparable yield.

Charlie writes:

@Bryan,

Very few people have a 30 year fixed-rate loan with a 2% tax-adjusted rate. And equities are not an appropriate comparison. Most people hold some bonds in their portfolios. Does it make sense to borrow money, only to turn around and lend it at a lower rate? Once all tax-advantaged accounts are maximized, prepaying a mortgage is typically a better choice than investing in a taxable accounts, barring a need for liquidity.

As to your second claim about switching to a 15 year loan, this is why people should have emergency funds. As Nick mentioned, that optionality is expensive. 75 to 100 bps on a large balance.

Nick has it correct. Match the duration of your assets and liabilities. I am currently 1 year into a 5/5 ARM and I expect to move in 3 years. Many people would probably be better off in 5/5 ARMs, since they don't stay in one home for very long, and this provides the flexibility of a 30 year amortization to boot.

LD Bottorff writes:

If mortgage rates were rational, they would reflect the risk that the bank takes by offering the borrower a longer term. That should make the 15 year mortgage rate lower - the bank is taking less risk and charges accordingly. Conversely, the borrower is living with a more difficult cash flow for 15 years, risking that the higher payments may put the family budget in a bind. My observation is that those who take the risk generally get the reward. Those who think they are getting something by letting someone else take the risk are usually paying someone else to take the risk.

Marty R writes:

David,

I think that you have the discount rate decision reversed. For instance, at today's mortgage rates (4.27% for 30 year and 3.27% for 15 year) a 5.79% interest rate makes the present value of the stream of net payments, 15 year minus 30 year, equal to zero. A higher discount rate gives a positive PV; a lower a negative. (In reality the calculation should be done on a after tax basis with principal payments at 100% and interest rates at 100% less the tax shield, all discounted at the after tax rates. But the principle of the higher discount rate favoring the cost stream spread out over the longer term still applies.

David N writes:

Marty R,

I think we agree that the greater the spread between 30 and 15 the more the 15 makes sense. 5.79% is pushing it these days, I admit, but I'd probably still do it. Back in 2013 when the 30/15 spread was 0.75% the required discount rate was just 4.5%.

Mark V Anderson writes:

My wife and I recently finished off paying off our (30 year) mortgage. I talked to my wife about taking out a home equity loan, because we would definitely come out ahead economically. There is no way that investments in the stock market won't make more than we pay in interest over the long term.

We are not doing this just because my wife hates the idea of adding on debt when we don't need to. I respect that emotional reaction, but it bugs me when supposedly numerate financial advisors suggest that paying off the mortgage quickly makes financial sense. It only makes sense if one is shaky on liquidity or if you will just spend the extra money. But the advisors rarely make this clear. I suspect they usually don't understand it themselves.

David R. Henderson writes:

@Marty,
A higher discount rate gives a positive PV; a lower a negative.
Wrong. Both high and low discount rates give positive PVs. But the lower the discount rate, all else equal, the higher the PV.

David R. Henderson writes:

@Mark V Anderson,
There is no way that investments in the stock market won't make more than we pay in interest over the long term.
The probability is very high but you can’t say “no way.” If the stock market fell by 50% and then rose by 6% a year for a lot of years, it would take a lot of time to work your way back.
Re the home equity loan, in the early 2000s, when we had a lot of equity in my house, I went to the bank that had the mortgage and asked for the highest credit line I could get. The loan officer asked me what I planned to do with the money. I answered, “Nothing.” I wanted it for emergencies, my daughter’s college, etc. I got a $250K line of credit, which I still have, and which I have used occasionally and then paid off. Right now it’s paid off. In a few weeks, with some work we’re having done on our house, it won’t be.

David N writes:

You know what else drops like a rock then rises 6% a year? Real Estate.

David R. Henderson writes:

@David N,
You know what else drops like a rock then rises 6% a year? Real Estate.
Sometimes true, but irrelevant. Recall that both Megan and I are discussing how to finance a house, not whether to buy a house. As long as you hold large equity in a house, or, alternatively, if you are the kind of person who absolutely will not default, even if underwater on the mortgage, the drop in house prices is irrelevant to your choice between 15-year and 30-year mortgages.

Hazel Meade writes:

In my experience, mortgage rates on 30 year loans ARE typically higher than 15 year loans though.

For a 15 year loan right now you're paying a minimum 3%.
For a 30 year loan that number is more like 3.8% or higher.

Also, your return on other investments is risky. Paying off your mortage instead gives you a *guarenteed* 3% return. You might get an average 6-7% return from a mutual fund, but the stock market is at a high right now, so this may be a good point to get out of stocks and put money into paying off a mortgage.

Megan McArdle writes:

We got 125 bp off of our rate by switching to a 15 year. I agree that it wouldn't make sense to do if the rates were at, or even near, par; then I'd just prepay a bit every month.

Troy writes:

The analysis between 15/30yr is not accurately presenting the real cost difference between the two loans.

For instance, for a $200K loan the marginal cost of extending into a 30yr loan is nearly 20%!

The payment difference between a 15-year $200K loan (4% rate= $1,479/month) and a 30yr $200K loan (4.5% rate=$1,013/month) is $466 per month.

$466/mo*12 months= $5,592 lower cash payments in year one from having a 30yr loan (versus 15yr).

However, total interest payments from the 30yr loan are $8,934 in year-one, versus $7,812 for the 15yr loan. $8,934-7,812=$1,122

As such, the actual financing cost of deferring principal payments in a 30yr mortgage (versus the 15yr) is 20.1% ($1,122 interest/$5,592 principal)

Finch writes:

> the drop in house prices is irrelevant to your
> choice between 15-year and 30-year mortgages.

I don't think this is true, though I'm having a little trouble reasoning it out. To the extent that there are various downside protections for borrowers like the ability to stop paying your mortgage, live in the house for free for a few years, and then go get another one, it seems like you would get maximum value out of them by keeping your LTV as high as possible as long as possible. The implicit strategic default option is more valuable when it is closer to in-the-money.

So that's a mechanism for price volatility to come into your decision.

David R. Henderson writes:

@Finch,
To the extent that there are various downside protections for borrowers like the ability to stop paying your mortgage, live in the house for free for a few years, and then go get another one, it seems like you would get maximum value out of them by keeping your LTV as high as possible as long as possible. The implicit strategic default option is more valuable when it is closer to in-the-money.
All true. That’s what I was getting, but perhaps I was a little brief, when I wrote, in the comment above:
As long as you hold large equity in a house, or, alternatively, if you are the kind of person who absolutely will not default, even if underwater on the mortgage, the drop in house prices is irrelevant to your choice between 15-year and 30-year mortgages.
@Megan,
Thanks. BTW, I would have made your same choice.

jb writes:

@bryan

What you're missing (speaking only for myself of course) is the sense of joy I feel at the prospect of having no debt. Within parameters that I have not calculated, I would rather have zero debt and some money in the bank, vs a good chunk of debt, and even more money in the bank.

Even acknowledging I'd be financially better off in the second case, I would be emotionally worse off. I hate being in debt. The idea of having no debt at all at ~55 years of age fills me with happiness. The idea that I might have to hold onto some job until I'm 70 so I can pay that mortgage every month makes me twitch with anxiety and a sense of entrapment.

And there's another angle to this - I build a great deal of emotional satisfaction by staying ahead of the game. I show up to meetings/events/appointments early. I pay off my debt early. I overpay most of my bills (just a little) so I can see that credit balance on my next bill. I know it's not rational, but I feel like a miserable failure when I'm not exceeding my obligations.

[minor edit made to comment by permission of commenter--Econlib Ed.]

David N writes:

I think the right way to think about 15 vs. 30 is to calculate the NPV of: (a) the compounded return on the monthly cash available for investment (the 15 payment minus the 30 payment), and (b) the difference in the remaining principals after N years. Then, solve for the discount rate so NPV = 0.

I ran the solution for N = 15 years. At the 4.27%/3.27% rates quoted above, the discount rate is 6.78%. That's a tough hurdle now, but it's not historically tough. And the NPV is not that sensitive to the discount rate. If you change the discount rate to 4% your NPV is only -$75 per $1,000 borrowed.

Dan King writes:

So I've gone all in with deflation. I refinanced my mortgage at 2.875% with a 3/1 ARM. I think inflation (along with interest rates) will remain low, and I'm not willing to pay the premium to insure myself against the risk.

Besides, the ARM is capped at 6%, which is lower than the 6.75% I was paying before I refinanced. So I can't really lose with this.

The theory is if you can afford to insure yourself, you should always do so.

AS writes:

@jb, "What you're missing (speaking only for myself of course) is the sense of joy I feel at the prospect of having no debt."

That's great if it works for you but that shouldn't necessarily be the default advice for everyone else. IMO we should train people to be more rational, not less rational. Emotional impulsive decisions have caused much ruin in the world. The more you emphasize irrational components in decision making, and give false validation to them, the more irrationality spreads like a plague.

Comments for this entry have been closed
Return to top