### Aaagh!

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.

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.

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#### 76 Responses to “Aaagh!”

1. 1 1 Mike H

If you have the option to refinance at any time with no exit fees, you take the mortgage with the lower interest rate, no? Are these variable-rate mortgages or fixed rate?

I have good news for you. I’m paying 6.05%, and that’s after negotiating a discount with my bank after threatening to refinance. Don’t feel too bad, whatever choice you make. Enjoy the schadenfreude.

2. 2 2 Biopolitical

The marginal homebuyer is also the marginal mortgage lender and the marginal stock market investor and the marginal entrepreneur and the marginal liquidity seeker etc. She has a good grasp of the world. The key is finding how your particular tastes and circumstances differ from hers.

3. 3 3 Nick

I’d advise against trying to predict stock market returns (especially since you should predict what returns YOU will receive – cognitive biasese and fees will likely reduce your returns vs the index)

Try and match the tenor of your loan to your propsed holding period (liability matching). This is the more conservative approach!

4. 4 4 Steve Landsburg

Mike H:

If you have the option to refinance at any time with no exit fees, you take the mortgage with the lower interest rate, no?

Really? Would you prefer to borrow one dollar at 0% or a million dollars at 1%?

Although the two loans are for the same amount, the 15-year loan gets paid off faster, which means that after, say, a year, the outstanding loan is smaller. So you still have the tradeoff between lower-interest-rate and bigger-loan-at-a-higher-but-still-really-good-interest-rate.

Edited to Add: To make the same point another way: With the 15 year loan, my monthly payment is (say) \$1000 higher. That’s \$1000 that I don’t get to put in the stock market each month, which is a downside if the market’s doing well. It’s that downside that I have to weigh against the upside of a lower interest rate.

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5. 5 5 Steve Landsburg

Biopolitical:

I can’t forecast stock market returns but I can forecast with considerable confidence that you win “best comment” for this post.

6. 6 6 Ken B

So Steve, I thought you bought the EMH? Flip a coin?

7. 7 7 David Pinto

Why not pay cash for the house, and put all the money you would pay for the mortgage into the stock market?

8. 8 8 David P

Could you split your loan and borrow x% at 30 years and 1-x% at the 15 years? IE if you think that there’s a 75% chance of the stock market doing well in the next 15 years borrow 75% at 3.49% and 25% at 2.875%

9. 9 9 Mark Skousen

The best advice I ever got was from an old real estate guru Jack Miller: “How do you make a million? Borrow a million dollars and pay it off.” Your regularly monthly mortgage payments is the best investment you will make, much more dependable return than the stock market at this point. If you can comfortably make monthly payments with the 15-year mortgage, go with that one.

10. 10 10 Gavin

How big is the difference between scenario A (stock market 4% for 30 years) and scenario B (stock market 6% for 15 years) given the other basic assumptions you were making?

11. 11 11 nobody.really

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.

The purpose of words is to convey ideas. When the ideas are grasped, the words may be forgotten.

But where can I find a man who has forgotten words? He is the one I would like to talk to.

Zhūangzi (c. 369 BC – c. 286 BC)

12. 12 12 Gavin

Do the scenarios take into account tax deductions and possible changes in tax law?

13. 13 13 Steve Landsburg

Gavin:

Do the scenarios take into account tax deductions and possible changes in tax law?

Nope! I just spent an hour implementing my program on my iPhone, before you reminded me that I should have worried about tax consequences first.

14. 14 14 Steve Landsburg

David Pinto:

Why not pay cash for the house, and put all the money you would pay for the mortgage into the stock market?

I seriously considered this. The downside is that paying cash for the house necessitates withdrawals from mutual funds, which trigger capital gains liabilities. I haven’t done the math, but I’m pretty sure this is a mistake.

15. 15 15 Steve Landsburg

Gavin:

How big is the difference between scenario A (stock market 4% for 30 years) and scenario B (stock market 6% for 15 years) given the other basic assumptions you were making?

According to my program, which is oversimplified in many ways (and also only approximate because it assumes, for example, annual compounding instead of continuous compounding, etc):

Under Scenario A (4% for 30 years), the 15 year is better (by about \$21,000 if I sell the house in 15 years or \$24,000 if I sell in 30).

Under Scenario B (6% for 30 years), the 30 year is better (by about \$24,000 if I sell the house in 15 years or \$145,000 if I sell in 30).

16. 16 16 Zachary Shrier

6% total annual returns for the U.S. stock market is not a particularly high bar. Recall that the current dividend yield of the S&P 500 is 2% and inflation will likely run at least 2% over the long-term. With just 2% real earnings growth, and no change in P/E multiples, you get to 6% nominal total returns. You can do it, Steve!!!

17. 17 17 desconhecido

Whether or not taking the money out of mutual funds to lower the mortgaged amount depends very much on the future tax rate for LT capital gains. Current max rate is 15%. There is a strong possibility that at the end of 2012, the maximum LT capital gains tax rate will revert to what it was before the so-called Bush tax cuts. That is a 33% increase (15% to 20%). Add in the proposed limitation of itemized deductions and the Obama-care surtax and you see a 67% increase in the tax rate (15% to 25%). If Obama gets the Buffet rule through, the rate may rise to 30% or more. That’s an increase of at least 100%.

18. 18 18 desconhecido

Boy, I wish that I had a 6% mortgage; it would make an investment decision much easier for me.

I have quite a bit of money which I wish to invest in something very safe. That’s a good thing to do, I believe. I think everyone with the means should have a significant portion of investments in a very safe vehicle. But, in today’s market, with LT treasuries yielding less than 3% (with a significant interest rate risk attached), it’s tough to find a safe investment with a reasonable return. But, if your mortgage is 6%, it seems pretty clear that making an additional principal payment would be a safe investment with a reasonable rate of return. I think a may refinance from my current 3% mortgage to a 6% mortgage so I can take advantage of this.

19. 19 19 Tal F

You should reconsider taking those capital gains (so long as they’re long-term capital gains). Rates are historically quite low and I haven’t heard any major politicians propose to lower them further, only raise them, so in all likelihood now is a good time to trigger those capital gains (even if only by shuffling around between similar mutual funds). Plus, if your new investments end up losing money, they can offset ordinary income (taxed at a much higher rate) up to \$3000/year.

As for your mortgage, the most important factor in this decision is really how long you intend to stay in your new house. Given how low rates are right now, most of the value of the 30 year is the ability to have a sizable loan out at just 3.5% 15 years from now, when interest rates will likely be much higher. Of course, if you do not intend to stay in this house for 15+ years, you will not get this benefit.

20. 20 20 Yancey Ward

Sounds like to me that you should just flip a coin.

21. 21 21 Ken

Steven,

A new house?! What happened to your plan to bury your house? I was looking forward to seeing how that project turned out.

22. 22 22 Ken

Steven,

Also, can you make your program source available? In what language is it?

23. 23 23 TravisA
24. 24 24 J.R.

1. A key aspect of a 30 year mortgage is that it gives you some protection against massive inflation. This seems likely to happen sooner than 30 years from now.

2. Is it plausible that today’s mortgage rates are partly artificially low due to actions by the Fed which are short term? If so, the long term mortgage has more advantages.

25. 25 25 Andy

Are you starting with a stock market investment equal to the size of the mortgage? And then just investing more each month with the 30 year mortgage while keeping the original investment with the 15 year?

26. 26 26 Steve Landsburg

Ken:

Also, can you make your program source available? In what language is it?

I’m a little hesitant to post the program source, since the program itself is so very rudimentary (not even accounting, for example, for tax consequences, let alone refinancing options, etc.). But what the hell…..here it is.

The language is Mathematica. Explanation of variables: x is the return on equity in years 0-5, y is the return on equity in years 5-10, z,u,v,t are returns on equity in years 10-15, 15-20, 20-25, and 25-30. After loading the program, type, for example, “try[3,4,5,5,5,5]” to see what happens if (x,y,z,u,v,t)=(3,4,5,5,5,5). The output tells you which mortgage is better if you plan to keep the house for 15 years (and how much richer you’ll be after 15 years if you follow the advice) and ditto for 30 years.

f15[p_,x_]:=(p-34256.6)(1+x/100)
g15[p_,x_]:=f15[f15[f15[f15[f15[p,x],x],x],x],x]
f30[p_,x_]:=(p-22442.3)(1+x/100)
g30[p_,x_]:=f30[f30[f30[f30[f30[p,x],x],x],x],x]
mort15yrs15[p_,x_,y_,z_]:=g15[g15[g15[p,x],y],z]
mort30yrs15[p_,x_,y_,z_]:=g30[g30[g30[p,x],y],z]
mort15yrs30[p_,x_,y_,z_,u_,v_,t_]:=mort15yrs15[p,x,y,z]((1+u/100)^5)((1+v/100)^5)((1+t/100)^5)
mort30yrs30[p_,x_,y_,z_,u_,v_,t_]:=mort30yrs15[mort30yrs15[p,x,y,z],u,v,t]
after15[x_,y_,z_,u_,v_,t_]:=mort30yrs15[0,x,y,z]-mort15yrs15[0,x,y,z]-267685
after30[x_,y_,z_,u_,v_,t_]:=mort30yrs30[0,x,y,z,u,v,t]-mort15yrs30[0,x,y,z,u,v,t]
test1[x_,y_,z_,u_,v_,t_]:=Print["Assumed interest rate pattern: ", x,",",y,",",z,",",u,",",v,",",t]
p1[tt_]:=Print["If paying off after 15 years, 30-year is better by ", tt]
p2[tt_]:=Print["If paying off after 15 years, 15 year is better by ", tt]
p3[tt_]:=Print["If paying off after 30 years, 30 year is better by ", tt]
p4[tt_]:=Print["If paying off after 30 years, 15 year is better by ", tt]
test2[x_,y_,z_,u_,v_,t_]:=If[after15[x,y,z,u,v,t]>0, p1[after15[x,y,z,u,v,t]],p2[-after15[x,y,z,u,v,t]]]
test3[x_,y_,z_,u_,v_,t_]:=If[after30[x,y,z,u,v,t]>0, p3[after30[x,y,z,u,v,t]],p4[-after30[x,y,z,u,v,t]]]
try[x_,y_,z_,u_,v_,t_]:={test1[x,y,z,u,v,t];test2[x,y,z,u,v,t];test3[x,y,z,u,v,t];}

27. 27 27 AMTbuff

I’m with J.R. Today’s rates are massively subsidized by the Fed. Inflation is bound to cut loose some time before the 15-year mark. Then your remaining balance will be payable in cheap dollars. Maximizing your loan term maximizes this benefit.

Consider it a partial offset to the losses you will incur when the Chinese stop lending and our economy collapses.

28. 28 28 Bill

Steven:

I have a tangential question. Have you ever seen any research (or discussion for that matter) regarding the deadweight cost associated with third party fees and transaction taxes of home purchase?

I recently bought a home and I couldn’t help but constantly try to work the deadweight cost of all of the optional, “yet nearly forced” insurances, the taxes, third party (in theory expert or information fees) and such and how that impacts housing prices.

Bill

29. 29 29 Person of Choler

Don’t forget maintenance, insurance, property taxes … and their various ups and downs.

30. 30 30 Jacob

You can now put your model on steroids and add in correlation between home value and the stock market. That’s when it gets really interesting.

On a slightly more serious note, I’d add in your risk preferences. Higher required payment also means lower after debt/after tax cash flow. If your cash flower to diminish, a high debt payment is more likely place you and your household under a greater level of stress than you would otherwise have with the 30. So, risk appetite and cash flow fluctuation’s impact on your utility must also be taken into account!

31. 31 31 iceman

#1 (& #4) – another way to put it is the 15-yr loan has a shorter duration so you *should* pay a lower rate (with a positively-sloped yield curve).
And yes (#30) for many people cashflow contraints are a real issue; they may (rationally) choose to enjoy themselves by *consuming* more now with the extra cashflow, financed by borrowing longer term via the lowest-cost vehicle at their disposal. I’ve known people who were enticed by the lower 15-yr rate and ended up miserable.
In that sense the 30-yr gives you the option to make larger payments if you choose, for which you pay a (currently modest) yield premium.

#3 – on matching: to me your expected holding period can affect your choice of a traditional fixed-rate vs. a hybrid ARM (e.g. floats for 5 or 10 years and then locks in to a fixed 30-yr schedule for the remaining term).
However the underlying asset itself presumably has a longer useful life than the holding period.

#9 et al – on your house being a “safe investment” – I think people can mislead themselves on this; the risk is your personal credit risk, which we may tend to underestimate for ourselves.
E.g. if you lose your job and default on your mortgage (more likely with the 15-yr?) you could lose the equity you’ve “invested” via past principal payments.
I also recall someone once writing about how a house, unlike a stock certificate, doesn’t just “sit there”, it provides valuable services as a primary residence which you receive in lieu of the CF from an income property.

32. 32 32 Zazooba

You will probably move or pay off your mortgage for other reasons before 15 years. So, take the one with the lower rate.

You can’t worry about what the stock market will do, but you can minimize your interest payments.

33. 33 33 Mike H

To make the same point another way: With the 15 year loan, my monthly payment is (say) \$1000 higher. That’s \$1000 that I don’t get to put in the stock market each month, which is a downside if the market’s doing well

true enough. But if you can refinance at any time at no cost, I think you only need to worry about stock market returns this year, not in 2020.

And, again assuming no transaction costs, when the extra 1000 goes to pay off your loan, you can always redraw the 1000 to invest in the stock market whenever you want to, eg by getting a margin lending facility secured against the extra equity you’ll have in your house. Done properly, that’s equivalent to getting a longer-term mortgage and investing the money directly. However, if you take the lower interest mortgage now, you’ll have more to invest this way in 2020.

I think my point stands.

34. 34 34 Mike H

Who is this marginal homebuyer? Does anybody have his email address? I want to know which mortgage he recommends

I think, based on the fact that you are finding it hard to choose between these mortgages, you can contact the marginal homebuyer via the contact link at the top of this page.

35. 35 35 Steve Landsburg

Mike H:

But if you can refinance at any time at no cost, I think you only need to worry about stock market returns this year, not in 2020.

I believe you’re quite mistaken.

when the extra 1000 goes to pay off your loan, you can always redraw the 1000 to invest in the stock market whenever you want to, eg by getting a margin lending facility secured against the extra equity you’ll have in your house.

Sure, but I will have to borrow this 1000 at some future interest rate, as opposed to locking in today’s low rates. My opportunity to borrow that 1000 at today’s rate will be gone and unrecoverable.

36. 36 36 Phil King

You can attempt to weigh certain economic probabilities and predict the future all you want. You can guess when inflation will strike, but why would you want to?

Instead I would think about how the banks came up with those rates. They did all that work for you. They likely came up with a rate after running thousands of equity, interest rate, housing, etc scenarios.

So, assuming the banks’ models are well calibrated – the rates should roughly return the same.

The 15 year has more costs associated with it because they’ll need to generate 2 loans for each 30 year they produce. The 30 year essentially gives you a more valuable prepayment option.

Your model will never be accurate enough to capture enough to make a better decision than flipping a coin.

37. 37 37 Steve Landsburg

Phil King: I’d be entirely convinced by your argument except for the fact that I think the banks are probably responding to all sorts of artificial incentives set up by regulators and by the Fed’s willingness to purchase some assets but not others at prices that have little to do with their true economic value.

38. 38 38 Mike H

Sure, but I will have to borrow this 1000 at some future interest rate, as opposed to locking in today’s low rates. My opportunity to borrow that 1000 at today’s rate will be gone and unrecoverable

true, true. This may be good or bad, of course.

When I had to choose between a fixed-rate mortgage and a variable-rate mortgage, I reasoned like this.

* The fixed-rate means the bank accepts interest-rate risk, the variable rate means I accept it.
* The bank hires top-notch economists full-time to carefully analyse interest rate futures. I have neither the time nor knowledge to out-guess them. Therefore I should trust the bank’s evaluation of the value of that risk, above my own.
* The bank will surely charge me a premium if I effectively buy interest rate insurance via a fixed-rate mortgage
* Therefore, the variable-rate mortgage will be a better deal.

It turned out I was right. (The fixed rate would have switched back to a variable rate by now.) Of course, it made it easier for me that the lower-interest option was the one that gave me more flexibility. The existence of consumer power probably helped bring the price down further. Maybe.

Perhaps you can figure out the better deal by assuming the bank has the numbers right? They’ve told you two weighted averages of their best guesses of future interest rates, modified by the premiums they charge for risk and for whether or not they have you trapped, and perhaps other factors. Assuming they are right, what premiums have they charged on each product? And therefore, what’s the best option for you?

Perhaps you can also fit an IS or IS/LM or some other model to historical data and deduce stock market returns too, given the bank’s told you what interest rates are expected in future.

39. 39 39 Cos

>> 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. <<

Other homebuyers have different interests than yours. You want to maximize your long term expected value, and to you, all else *is* equal, apparently. But other homebuyers have other priorities.

Some intend to keep the house for a long time and really want to get it over with. Their priority is to get the shortest mortgage term for which they can afford the monthly payment. Many more, though, I'm pretty sure, prioritize a lower monthly payment, even if it means losing more money in the long run. It's a lower risk of forcing them into a bad situation. A smaller obligation broadens their options each month about what to do with their money. And of course there are the people who either know or suspect that they're only going to keep the house for a few years, and are just looking for the choice that will force them to pay the smallest total amount in interest in the first ~20-30 payments or so – which is probably the 30 year mortgage, even though it has a higher interest rate.

40. 40 40 David

Cos seems to have the more interesting answer so far.

Another thought — how about diversification of your investment? Either variable or fixed is OK today if you can refinance easily and cheaply. I would suggest keeping your home debt in balance with your market asset value of the home and invest with the idea of keeping your market investments well diversisfied.

41. 41 41 Steve Landsburg

Mike H:

Re #38:

* The fixed-rate means the bank accepts interest-rate risk, the variable rate means I accept it.
……
* Therefore, the variable-rate mortgage will be a better deal.

This is the same sort of reasoning that led me to choose a fixed rate rather than a variable rate for my electric bill, but this case differs in a couple of ways.

First (and most interesting but perhaps least important) is that the mortgage is for a fixed amount, whereas I get to continuously choose how much power I will consume, so the nature of the risk for the electric company is not the same as the nature of the risk for the bank. If you think hard enough about this, you’ll see, I think, that this makes the reasoning even more compelling in the electric case, though it remains compelling in the mortgage case.

Second, as Cos eloquently observes in #39, everyone’s goals are different, but as you’ve pointed out, that’s still enormous progress — we take it as a starting point that the two mortgages are equally good for the bank and then we can narrow the problem down to my *idiosyncratic* concerns, as opposed to enumerating *all* my concerns.

The question remains whether regulatory considerations — together with the willingness of various governmental and quasi-governmental agencies to purchase some kinds of mortgage assets and not others — are distorting the fundamentals enough to make this kind of reasoning untenable.

42. 42 42 ColoComment

I don’t understand why you’re factoring in a possible refinance opportunity. Do you really think that mortgage rates will ever drop enough below ~2.8% to 3.5% to warrant refinancing, given the usual costs of doing so? Or am I missing something very obvious (which may very well be the case!)?

43. 43 43 Keshav Srinivasan

Steve, are you saying that government intervention in the market could make the indifference principle no longer apply? How could it do this? How could it make one choice more desirable for some and less desirable for others?

44. 44 44 Brian

Why don’t you apply comparative advantage.

Hire an accountant who has done most of these calculations and who has a good reputation. Stop writing programs to do this work which is already done for you, and start writing another sequel to Armchair – i’ve finished reading the revised edition. Each re-read is a joy, as I’m able to pick up a nugget of wisdom to use in class from each time i read it. And I’m assuming royalties from the book are in part going to pay for the mortgage.

45. 45 45 kenneth preston

To go from theoretical to practical, I run Monte Carlo simulations at firecalc. If you have something between 30minutes and 3 days to kill, that’s where to find your comparative answers. Mortgage news daily has several blogs from MBS traders for short term rate futures. The idea that banks are calculating odds in their rates shows dreadful misunderstanding of the market forces behind mortgages, and some time at MND should be interesting
by itself. Good luck!

46. 46 46 Jon Shea

What are you using to program financial models on your iPhone?

47. 47 47 Andy B

SL: I think there is a key element in your fixed rate electricity and fixed rate mortgage comparison that you are missing. In both instances you have purchased an option. In both instances I would expect the seller of those options to price them so that on average they will make money. So in both cases you own an option that is not expected to be in the money, or at least sufficiently so to offset what you paid for it. Outliers happen for sure, but this is not the expected outcome.

So the relevant question is does the fact that I can alter my consumption of electricity somehow change the expected outcome? I wouldn’t think so. The fact that you can alter your usage is the expected outcome. If the electric company has done a good job thinking this through then they’ll expect you to do alter your consumption in a way that is predictable given certain environmental, economic and other conditions, run lots of simulations on all of that and derive an expected outcome of what the average adverse cost to them is of giving you this option and incorporate that into their price.

This is the same as the mortgage. And because you can elect the timing of when you pay the money back you can vary the amount you consume over the full contractual term of the mortgage.

This is all not to say in either case they have priced all of this correctly and that you can’t pick them off. But as I understand it that wasn’t your argument. Simply having the ability to alter your usage is a purchased option. You should have paid for that privilege more than you are expected to benefit from it.

48. 48 48 Barry Zuckerkorn

“Here’s what I just did: I wrote a computer program”

The computer program was already completed in the 1980s. MS Excel or equivalent will do all of the calcs that you need.

I would focus more on the assumptions of the model than on writing code.

49. 49 49 iceman

Yes to #43 – I was going to ask why the marginal buyer simply hiring an advisor with a sophisticated model isn’t a nice market solution?

But now I’m getting worried – it took dozens of toothpastes, but now only two flavors of mortgages, before we’re ready to surrender to Leviathan?

It seems to me that over just about any holding period that would make owning a home worthwhile (e.g. given the risks and costs of real estate transactions), one can be sufficiently confident that stocks provide a higher expected return than mortgage rates to choose to minimize the debt payment (borrow longer-term).

50. 50 50 Peter Tennenbaum

Pay cash for your house. Surely, at this point in your storied career, you have accumulated SOME savings. If it isn’t enough to buy the “house of your dreams”, then settle for something more modest. Moreover, think of the PSYCHOLOGICAL advantage of not having to worry about mortgage payments. Does economic theory take THIS factor into account? Who can put a price on peace of mind? It might even have productive “spillover” effects: some interesting new work, an invention or ten, etc.

Indeed, why borrow money for ANYTHING, especially if your are in a relatively high income bracket (compared to, for example, 85% of Americans)? Further, given that it’s an “academic question”–albeit using up extremely valuable computing time[!]–it appears that you have substantial leisure to “ponder”. Perhaps another answer to YOUR question would be to jettison the dilemma and devote, instead, more time to making more money–enough to render this (practical) issue “moot”.

Or did you run up some gambling debts… earlier in life… when sensibility was in “scarce supply”…

51. 51 51 Steve Landsburg

Peter Tennenbaum: The primary argument against paying cash is that it necessitates selling stocks, which in turn triggers a capital gains tax liability.

52. 52 52 Steve Landsburg

Jon Shea: I am using an app called SophitimaCalc, which I like very much.

53. 53 53 Steve Landsburg

ColoComment: Well, rates *could* of course drop to, say, half a percent. But I am in fact excluding refinance opportunities from the calculation.

54. 54 54 Steve Landsburg

Brian (#44): Your comment is, of course, a great classroom lesson in and of itself. I think the inference we can draw is either that I am not fully rational, or that I enjoy doing mindless calculations, or both.

55. 55 55 Ken P

To flesh out my earlier comment, now that I’m not at work: firecalc is a online free retirement calculator that runs your numbers through past market data to generate return forecasts based on actual histories. My 30 minutes or 3 days remark was based on 30 minutes to fill in all the info, but if you’re like me, that’ll. Lead to 3 days of tinkering with the results. Seeing 100 lines laying out all the historical results is intuitive, and you can factor for portfolio, inflation,what have you.

MND is a site tuned to mortgage professionals. It is very informative to read what the pros say to the pros. For practical purposes, it’s handy to see the influencing factors on MBSs when deciding to float or lock a rate.

56. 56 56 Mike H

The question remains whether regulatory considerations — together with the willingness of various governmental and quasi-governmental agencies to purchase some kinds of mortgage assets and not others — are distorting the fundamentals enough to make this kind of reasoning untenable.

I can see how regulatory considerations might have an effect, eg if the bank was given some government handout or charged some extra tax for their short-term or long-term mortgage.

If not, I’m not sure how acts by profit-non-maximising entities mess up the argument. The bank is still trying to maximise its profit from its transaction with you, irrespective of these other things.

If there are regulatory considerations applying on your side (uneven taxes/incentives etc) that also messes up the argument, but at least you can account for them.

You ignore the possibility of other forms of market failure. Paul Krugman has stated once, to my knowledge, that a liquidity trap is “kind of” a market failure (my paraphrase) – people would really prefer to freely spend in a roaring economy, but they don’t. If the bank is operating irrationally, this would also mess up the argument.

Maybe #44 is the way to go :-)

57. 57 57 Mike H

Alternatively, you could argue like this.

* If I were not a marginal consumer of mortgage products, I would see one option as preferable to the other.
* However, both products seem equally good and bad to me.
* Therefore, I am the marginal consumer.
* Therefore, the choice doesn’t matter greatly to me in rational expectation.
* Therefore, I will toss a coin and be done with it.

58. 58 58 Phil King

I still stand by the fact that they’re equally priced and that there isn’t regulatory incentives tipping the scale significantly. Reason being that regulatory considerations rarely stretch out past 15 years and if they do I doubt 15 is considered other than 30. For an insurance company capital requirements on a 30 year bond would be somewhat higher than 15 but that reflects the underlying incremental risk. Banks have slighter capital requirements and probably get credit for hedging it away.

My first post was more from a theoretical pricing standpoint, which I believe still holds. The other consideration you might consider is this. Figure out why you would prefer one over the other. Then figure out who else would. If you think you’re relatively more likely to default at 15 years, take that. If you’re more like to default at 30, take that. That way you can receive subsidization from your insurance pool.

That said, it gets back to the same place really. Instead of trying to predict rates and scenarios and weight them, you’re myopically trying to assign yourself a risk class and say you have an advantage over that class. I think this is less hard, but still a fool’s game.

Flip that coin.

59. 59 59 Greg Finley

Isn’t the capital gains tax a non-issue? You’ll presumably sell those stocks at some point and have to pay the tax. Unless you are talking short vs long term or waiting until you retire and are in a lower tax bracket.

60. 60 60 Steve Landsburg

Greg Finley: the longer you can delay paying the capital gains tax, the more time you have to earn interest on the funds that are eventually taxed away.

Steve,
to get a better idea of prospective stock market returns, you may want to correlate or 10 or 20 year stock market returns with valuation levels according to Shiller’s P/E 10 or maybe Hussman’s P/Peak E.

http://www.crestmontresearch.com/pdfs/Stock%20Matrix%20Tax%20Exempt%20Real3%2011×17.pdf

http://www.econ.yale.edu/~shiller/data.htm

It’s been a while since I ran the numbers, but the total return at these levels should be around 5% over 20 years assuming that valuations return to normal historical levels, 6% if they don’t.
That said, it is virtually certain that valuations will go below normal historical valuations at some point during the next 10 years, and portfolio performance between now and then will be negative.

62. 62 62 Ken B

Re 44 and 54. This reminds me of Ken’s comment on the toothpaste thread. Is it possible Steve feels a *responsibility* to do this, and would feel *guilty* if he just said, oh a good accountant will figure it out? I am suggesting this, a presumably cluturally inculcated emotional response, as a mechanism to explain the irrational behaviour. Like the way some of us eat to much because we finsih everything on our plate because were taught about starving children in India.

63. 63 63 Al V.

Reminds me of the story of a friend of mine (an accountant). When TS’s father died in 1990, his mother received the payout on a large life insurance policy. She wanted to use the proceeds to pay off her mortgage, which was taken out in 1970. TS pointed out that bank deposit rates in 1990 were higher than the interest rate she was paying for her mortgage. By paying off the mortgate, she would be hurting herself from an interest arbitrage perspective, and of course losing the (relatively small on a mortgate with 10 years remaining) tax benefits.

Steve, you can’t ignore the tax component of your question. I would take out the 30 year loan. In all likelyhood, interest rates will be higher in the future, so the longer you stretch out the loan, the longer you will benefit from rate arbitrage. And with the mortgage interest tax deduction, your rate arbitrage is subsidized.

64. 64 64 Andy

RE #41. The bank can use interest rate swaps to swap between fixed and floating as it pleases. Presumable it will hedge any interest rate risk the moment you take out a mortgage in either cases and just make money from the spread on what they can borrow at vs. where you borrow from them, as well as other fees of course.

65. 65 65 Neil

You cannot systematically outguess the market. The difference (you should care about) between the 15 and 30 year rates is largely determined by lender perceived average default risk. It is higher for 30 year borrowers for a variety of reasons. Since you know your default risk better than the lender, you should take the 15 if your default risk is less than average and the 30 if it is higher. I’m guessing you should take the 15.

66. 66 66 Ken B

@Neil: that (65) looks like a great answer, but I confess I do not understand it. Why the difference?

Neil,
I believe that is incorrect. The difference between the 15 and the 30 year interest rate is most likely mainly due to the fact that current low inflation and interest rates are expected to go up at some point in the future.

68. 68 68 Neil

Of course some of the rate difference reflects those factors, but does Steve have inside knowledge of them? I think not. He does have inside knowledge of his default risk.

69. 69 69 Ken B

@Advo: I think Neil is syaing that all those consideration fall under the aegis of the EMH, as I speculated earlier. The market has expectations about inflation, but Steve cannot outguess them. Neil is suggesting that there IS an area where SL can outfox the EMH: default risk. That’s an interesting idea.

70. 70 70 Seth

I like the cash flow flexibility of the longer-term mortgage. If I feel I like have good investment opportunities I can sink my money there. If I feel like I don’t, I can pay extra on the mortgage.

71. 71 71 AMTbuff

The question remains whether regulatory considerations — together with the willingness of various governmental and quasi-governmental agencies to purchase some kinds of mortgage assets and not others — are distorting the fundamentals enough to make this kind of reasoning untenable.

I maintain that the Fed has driven long-term rates far below market-clearing levels. If the Fed stopped buying long-term debt today the 30-year rate would soar. Sooner or later they will stop, as Herb Stein would say.

Take a lesson from George Soros: When the government is fighting the market, take the side of the market. It’s almost like getting free money. Choose the 30-year fixed loan to maximize your take.

Today’s mortgage rates are NOT market rates. You can take that to the bank.

72. 72 72 Phil King

I already mentioned the default risk above, and I still think SL cannot outfox them in this manner. It’s not his level of default risk that matters, it’s his risk comparable to the group he is in, in the two different cases.

Yes, he can try to outfox it thinking he has a better idea of his default risk than others. But chances are his insurance pool is made up of a lot of people who think they have a better idea. In a pool of many borrowers who think they are certain not to default, some still do. No reason it couldn’t be SL.

Also re 64 – yes the actual bank doesn’t take on the interest rate risk because it gets hedged away, but someone somewhere is accepting that and the cost of the banks insurance – ie the cost to hedge – ultimately would have to reflect the interest rate risk.

73. 73 73 Fonzy Shazam

I think you all are significantly over complicating this question. The decision is whether to pay for the house right now or over time, and if over time, over how long. What is at issue is Steve’s personal discount rate versus the market’s borrowing rate. Steve’s discount rate should factor in his desire to consume versus invest now then consume later versus some mixture including his forecast for investment return. To add a little more complication one could factor in a probabilistic factor for interest-payment deductibility, effective tax rates, et al. blah, blah, blah… Look, estimate a discount rate that effectively does all that (pick a number between 5 and 10). Okay, now build a stream of cash flows that represent the loan amortization. Discount that back at the discount rate. Repeat the process for various terms of loans. Find the highest present value among them and we’re done. Credit is cheap right now. I find it hard to justify paying cash now when borrowing is so easily (i.e., painlessly) available. I’ve ignored any factors for debt aversion as well as other considerations for personal peccadillos, idiosyncrasities, etc. Short of the esoteric we have our solution.

74. 74 74 Kirk Taylor

2. This may be of no use to you if you make too much money, but, you should liquidate assets to the extent that your taxable income, including the gains, remains in the 15% tax bracket. This will result in 0% tax on the gains. Use the money for down payment on the house, or, immediately reinvest in the same stocks and mutual funds – there is no wash sale rules for gains.
3. You should do 2. every year whether buying a house or not (current Cap Gains rates assumed.)

75. 75 75 Kirk Taylor

Above comment by me also assumes no enormous broker fees involved…

76. 76 76 Rahul

Prof Landsburg,

My two cents as a former student of yours (currently a small business owner): Comparing a residential mortgage to a stock market investment may be an apples to oranges comparison. The former is a liability, producing no revenues, let alone cashflows, wheras the latter is an investment in a going concern with revenues & expenses, and the hope of either dividends or capital appreciation (or both) based on present value of future earnings.

One model may be to view yourself as a corporation, with income, expenses, assets and liabilities. Based on your confidence in the consistency of future earnings, as well as your liquidity cushion and asset base, you can choose what level of indebtedness you are comfortable with (possibly taking black swan type scenarios into account with their probabilities – death/injury/worldwide economic collapse etc).

Given that information, a 30 year mortgage allows you to have lower monthly payments (maximising your cashflow), and you can prepay/reamortize any time. If you want to pay off your loan quicker, a bigger downpayment reduces your risk substantially more than a reduced amortization, which increases the strain on your cashflow. This may be a plan to reduce the downside risk to both your balance sheet and your income statement.

As far as the opportunity cost of the borrowed/invested money, here is an alternative opinion: due to our tax structure, the dividend yield on most publicly traded stocks is negligible. With almost all the gains coming from capital gains, you are at the mercy of market timing and investor sentiment. However, if you instead invest the money in a small local business or investment property (e.g. a small retail center, or apartment building), you have far more predictable returns (at the cost of lower liquidity, admittedly).

You can payoff your house at the earliest possible date, and refinance it or use a line of credit to generate a down payment as soon as you find an investment property with a yield differential that makes it worth while – e.g. if you can refinance at 3.5%, a deal with a cashflow of 10-15% may be worth doing with the refinanced dollars. If interests rates rise, so will the corresponding yields on the commercial real estate you purchase, so you will be hedged.

Now you have a more predictable cashflow, and a more secure balance sheet (admittedly with an less liquid investment on your hands that might need some babysitting from time to time – the yield differential assumably being something that compensates accordingly).