Bogleheads.org

Making extra principal payments is effectively the same as investing at the after-tax rate for the duration of the loan. But if the loan were to be paid off before the full duration, say through the sale of the mortgaged house, those extra payments are then equivalent to investing at the after-tax rate for the duration before the payoff.

So if we had $100k balance on a 4% mortgage loan with 20 years left, an extra $10k payment would normally be like a ~3% ~20yr bond.

But if the house is being sold in a year, wouldn't that then become a 3% 1yr bond, which seems like a really good deal.

And as the sale date approaches, the rate keeps the same with an even shorter duration, so one should pay down even more principal?

You might also view it as the same 20 year bond, but with a call option. But if you're absolutely certain that you'll be selling on or around xx/xx/xxxx, I see no harm in using that date to calculate the duration of your "investment".

Of course, if you are certain you'll be selling, liquidity may be a greater concern. Will you be buying another house before you close on the sale? There's lots of incidentals, too, like fixing little things in your house to maximize the selling price, movers, etc. But assuming adequate liquidity, this investment could certainly make sense.

Curious point. A couple corrections:
- The duration of a mortgage (an amortized loan) is much, much shorter than its maturity.
- Duration matters because it measures interest rate sensitivity. There's no way to lose principal by paying off a loan.

So it's what we've been saying all along: the guaranteed savings from paying off debt is hard to match. Liquidity is the only significant concern holding you back.

harikaried wrote:So if we had $100k balance on a 4% mortgage loan with 20 years left, an extra $10k payment would normally be like a ~3% ~20yr bond.

No, an extra $10K principal payment shifts/adjusts Net Worth using Cash to reduce Liabilities (mortgage note). By reducing Liabilities, it ALSO reduces expenses (interest).

Now the question.... what can you do with $10K to get >3% guaranteed and riskless annual return resulting from reduced debt/expenses?

FNK wrote: - The duration of a mortgage (an amortized loan) is much, much shorter than its maturity.

I'm not sure what's the terms here mean. Is the mortgage duration the time until the loan is paid off (principal = $0) and the maturity is the original schedule without prepayment, e.g., 30 years? Although maturity seems to also be defined as when a loan has all its principal and interest paid off, so wouldn't they be the same thing?

G-Money wrote:fixing little things in your house to maximize the selling price

Just a side note from my own browsing and anecdotes, it sounds like remodeling tends to speed up transactions by attracting more interested buyers, but they tend not to be a good investment in terms of money spent on materials/labor being covered with an increased sale price. So then perhaps it really makes sense to pay down the mortgage if you're looking for better returns -- although like many things, a hybrid approach with some of each might be the ideal solution.

G-Money wrote:liquidity may be a greater concern. Will you be buying another house before you close on the sale?

Assuming enough time between selling the current house and buying a new house, wouldn't one want to use the new-house-downpayment-funds to pay down the current mortgage and to save on the loan expenses/interest?

And would these extra principal payments with the home sale on the horizon factor into the bond weighting of one's asset allocation?

harikaried wrote:

G-Money wrote:liquidity may be a greater concern. Will you be buying another house before you close on the sale?

Assuming enough time between selling the current house and buying a new house, wouldn't one want to use the new-house-downpayment-funds to pay down the current mortgage and to save on the loan expenses/interest?

Yes.

harikaried wrote:And would these extra principal payments with the home sale on the horizon factor into the bond weighting of one's asset allocation?

IMO, yes. I view a mortgage as a negative bond. As you've probably seen in other threads, not everyone agrees.

G-Money wrote:

harikaried wrote:And would these extra principal payments with the home sale on the horizon factor into the bond weighting of one's asset allocation?

IMO, yes. I view a mortgage as a negative bond. As you've probably seen in other threads, not everyone agrees.

A mortgage note is a Liability to purchase an Asset. You either didn't have financial resources to purchase 100% of this Asset, or chose not to use financial resources that you had.

1. The difference between Asset (market value) less Liability is part of Net Worth. Net Worth should be considered in determining Ability and Need for risk.
2. Now, what does this Liability exclusively - only one piece of this equation - have to do with the amount of risk to take in investing (AA) other investable Assets?
3. If you feel it has something to do with it, then the Asset should also have something to do with it.

Like I said, not everyone agrees. These discussions come up regularly here. Once people pick a side, they rarely seem to be persuaded by counterarguments.

YDNAL wrote:A mortgage note is a Liability to purchase an Asset.

I only agree with the first part of this. A mortgage note is a liability. But obtaining a mortgage is a separate transaction from buying a house.
- I have a deed which gives me ownership of my house. I own the WHOLE house/asset, regardless of whether I use it as security in another transaction.
- I have a mortgage and note. It is a debt arrangement I entered into with a lender. I promised to pay money back at a certain rate over a certain period of time. That promise is secured by my house, which I pledged as collateral. I still own the whole house.

Of course, the two transactions need not be related. Say I borrow $500,000 from a friend (I have nice friends ) to purchase a $500,000 house. The loan is NOT secured by my house. From a financial standpoint, this is exactly the same as a mortgage that is secured by my house. The only difference is the risk taken on by the lender. In all instances, I own 100% of the house as soon as I get the deed. The fact that there may be debt does not change this. What I do with the debt in relation to my other investments is a financial decision, which actually has nothing to do with my ownership of the house (which does not change).

YDNAL wrote:

1. The difference between Asset (market value) less Liability is part of Net Worth. Net Worth should be considered in determining Ability and Need for risk.

Agree.

YDNAL wrote:

• Now, what does this Liability exclusively - only one piece of this equation - have to do with the amount of risk to take in investing (AA) other investable Assets?

Either you believe a mortgage (or any debt) is a negative bond, or you don't. If I have $500,000 in house, $500,000 in stocks, $500,000 in bonds (earning 2%), and $500,000 in debt (costing me 3%), then I am effectively 50% house and 50% stocks, the spread on my bonds and negative bonds is -1%. In other words, it is costing me 1%/year to maintain that amount of leverage. I could just have $500,000 in house and $500,000 in stocks, have the exact same amount of risk, and it will not cost me 1%/year (because I will no longer be levered). In that scenario, I have the ability to increase my returns (by 1%/year), with the exact same amount of risk. Because I own the whole house under either scenario, it doesn't make much difference whether I consider the house or not in this equation. The only issue is whether I can get a higher rate of return on bonds than my debt.

YDNAL wrote:

• If you feel it has something to do with it, then the Asset should also have something to do with it.

See above.

As I said, these discussions never seem to actually persuade people on either side of the issue. I suppose these discussions flesh out the various perspectives for those who are new or unfamiliar with this topic. In any event, I hope this is useful to someone.

G-Money wrote:

YDNAL wrote:

• Now, what does this Liability exclusively - only one piece of this equation - have to do with the amount of risk to take in investing (AA) other investable Assets?

Either you believe a mortgage (or any debt) is a negative bond, or you don't. If I have $500,000 in house, $500,000 in stocks, $500,000 in bonds (earning 2%), and $500,000 in debt (costing me 3%), then I am effectively 50% house and 50% stocks,....

To avoid a lenghty and unnecessary back/forth, look at the quote above.

• 1. The illustration shows $1 million Net Worth in investable (liquid) Assets.
  
  2. It also shows $0 Net Worth in real estate (hard) Assets. This person supposedly made an intelligent decision:
  a) To buy a $500K house with $500K in debt.
  b) To increase expenses (3% interest on $500K, among other things) and to impact cash flow.
  
  3. The person's Ability & Need to take risk with investable Assets and $1 million Net Worth has ZERO to do with the mortgage note.

I find it more useful to avoid mixing apples/oranges to justify decisions that should be viewed otherwise.

YDNAL wrote:1. The illustration shows $1 million Net Worth in investable (liquid) Assets.

2. It also shows $0 Net Worth in real estate (hard) Assets.

It appears you view debt as a negative house, rather than a negative bond. Therein lies the difference between our views. Not saying you're wrong, simply that I disagree (which you already knew).

G-Money wrote:

YDNAL wrote:1. The illustration shows $1 million Net Worth in investable (liquid) Assets.

2. It also shows $0 Net Worth in real estate (hard) Assets.

It appears you view debt as a negative house, rather than a negative bond. Therein lies the difference between our views. Not saying you're wrong, simply that I disagree (which you already knew).

Disagreeing is a personal liberty. That said, I've clearly stated that a mortgage note is a Liability and nothing else. You also did not include #2 in its entirety.

YDNAL wrote:2. It also shows $0 Net Worth in real estate (hard) Assets. This person supposedly made an intelligent decision:
a) To buy a $500K house with $500K in debt.
b) To increase expenses (3% interest on $500K, among other things) and to impact cash flow.

There are Generally Accepted Accounting Principles.

1. An Asset is an Asset, a Liability a Liability, Net Worth is Net Worth.
2. A personal Balance Sheet or Cash Flow Statement should be NO different that APPL's*.
3. Having "an opinion" should be of little consequence to the proper treatment of financial transactions.

* except for size and complexity.

harikaried wrote: And as the sale date approaches, the rate keeps the same with an even shorter duration, so one should pay down even more principal?

I think it makes little sense. If you prepay the mortgage entirely and the house ends up not selling, you will lose a valuable mortgage interest tax break. Getting that tax break back would involve getting another loan, but only the interest on the first $100k of home equity debt would be deductible.

IMO, you should keep things simple, and just pay off the loan at closing when the sale actually happens.

OP,

Paying off a mortgage early makes sense in some situations and doesn't in others. If you've got extra cash, is your emergency fund fully funded? Are you maxing out your tax-advantaged retirement accounts? If the answer is yes, then it might make sense to pay down the mortgage faster.

In regards to the tax deduction, keep in mind that it is a tax deduction and not a credit. If you've got $10,000 in mortgage interest and you are in the 25% bracket, you'll save $2,500 on taxes, not $10,000. Might be appealing, but is by no means the absolute golden rule. I'm in the camp that believes that anytime you're in a position to wipe out debt without sacrificing the liquidity needed for emergencies it is best to eliminate the debt, even if is a mortgage. You do not know what the house will sell for in a year or how long it will be on the market. It cannot hurt to have it paid off or have the principal significantly reduced by the time you sell.

harikaried wrote:Making extra principal payments is effectively the same as investing at the after-tax rate for the duration of the loan. But if the loan were to be paid off before the full duration, say through the sale of the mortgaged house, those extra payments are then equivalent to investing at the after-tax rate for the duration before the payoff.

So if we had $100k balance on a 4% mortgage loan with 20 years left, an extra $10k payment would normally be like a ~3% ~20yr bond.

But if the house is being sold in a year, wouldn't that then become a 3% 1yr bond, which seems like a really good deal.

And as the sale date approaches, the rate keeps the same with an even shorter duration, so one should pay down even more principal?

Everything you said makes perfect sense. If you are absolutely sure that you will sell the house and that you don't need money before the sale, then go ahead and make extra mortgage payments. Most of the comments above are saying that you can't be absolutely sure.

I'm currently in the process of purchasing a house and stumbled across the following article which advocates for not paying off the mortgage. The author argues a mortgage can make sense financially if you follow certain rules. It's a different take that made me think more about the pros/cons of paying for points or maintaining the mortgage rather than paying it off early. Be interested as to what others think about the article.

http://www.emarotta.com/using-a-mortgage-wisely/

Tatupu wrote:I'm currently in the process of purchasing a house and stumbled across the following article which advocates for not paying off the mortgage.

Long-term fixed-rate mortgages, especially at the current low rates, provide a hedge against future inflation and interest rate rises. Now, it's possible that those will remain more like current levels, but likely you will come out well anyway. It wouldn't take much of an annualized return from diversified investments over the period to beat ~3%.


Brian

Tatupu wrote:I'm currently in the process of purchasing a house and stumbled across the following article which advocates for not paying off the mortgage. The author argues a mortgage can make sense financially if you follow certain rules. It's a different take that made me think more about the pros/cons of paying for points or maintaining the mortgage rather than paying it off early. Be interested as to what others think about the article.

http://www.emarotta.com/using-a-mortgage-wisely/

This article is total trash, in my opinion. It is a mixture of basic ideas that have been reiterated here again and again and total nonsense. Among the valid points made: paying down a mortgage decreases liquidity and a guaranteed rate of return from investments needs to be compared with the interest rate after accounting for the mortgage deduction (assuming you itemize your taxes and have subtracted out the standard deduction you are passing up on).

On the other hand, this whole article is predicated on your home appreciating in value and other investments being a sure thing to return over 4% (in their example). There also seems to be a misunderstanding that when you pay principle, you are getting equity in your home, when you pay interest, you get nothing. The statement "Why pay off your mortgage when each dollar you pay only saves you sixty-six cents and you lose the other thirty-three cents to taxes?" seems to show that there is a misunderstanding here. If you have a 6% interest loan and are in a 33% marginal tax bracket that they use in this example, every extra dollar of principal you pay gives you one more dollar of equity in your home, it also saves "you" 4 cents a year and "the government" 2 cents a year in interest (in a single year, not accounting for compounding).

The idea that you save money by having a 30 year mortgage and paying more interest versus having a 15 year mortgage and paying less interest is just absurd. You aren't getting anything from the tax deduction besides a lower interest rate. This isn't free money, it is a reduction in the cost of holding a mortgage that needs to be compared to other investments.

There are valid reasons for not wanting to pay down a mortgage, this article is not particularly full of them, in my opinion.

For those following along and think better with actual numbers than theory, I worked something out so that I could better understand what's going on.

Assume you have $16k cash, $0 income, a house that will sell in a year for $200k after fees, and $100k mortgage 4% loan with $500 monthly payments.

If you just make the monthly $500 payments.. Then after selling the house for $200k, you have $112,037.08 cash on hand.

If you pay down an extra $10k principal and still make the normal monthly $500 payments.. Then after selling the house, you have $112,409.92. This is $372.84 more than the previous situation.

If instead you invested that $10k at 4% yearly interest compounded monthly.. You also gain $372.84 at the end of that year.

If instead of $0 income, we're at 25% tax bracket, the first situation would have $3,962.92 interest to deduct while the second has $3,590.08 reducing the tax owed by $990.73 and $897.52 respectfully -- a difference of $93.21. And the $10k investment's gain of $372.84 taxed at 25% is $93.21 in extra taxes.

harikaried wrote: Assume you have ... a house that will sell in a year for $200k after fees

You seem to really be missing the point that this is not a valid assumption to make. You really have no idea if, when and for how much the house will sell for until you actually put it for sale and find a buyer. Market conditions change over time.
Those changes will have a much larger financial impact than any small prepayments you might make on your loan over the next year.

Even if you prepaid the entire $200k loan now, you will save about $8,00 over the next year. Market conditions could very easily change the value by that much in a year, up or down.
These changes will happen regardless of whether you prepay your mortgage or not.

The main question is whether you value your liquidity or not. It sounds like your mind is made, and you don't, so why ask here ?

madbrain wrote:

harikaried wrote:Assume you have ... a house that will sell in a year for $200k after fees

You seem to really be missing the point that this is not a valid assumption to make.

That assumption is just to be able to make some calculations to help answer the question of if paying down the mortgage should be equivalent to something like a 4% 1yr CD, and it seems to be.

People are raising questions about liquidity, and that's a fair question. We should now also somewhat agree that it's the same question of liquidity in the two situations:

- Should I put $10k in a 4% 1yr CD if I expect to sell the house in 1 year?
- Should I pay down $10k principal on my 4% mortgage loan if I expect to sell the house in 1 year?

Basically, are you willing to tie up $10k for a year with the main difference of you being sure you'll get your money back with the CD in a year vs hoping that the house sells "on time."

madbrain wrote:Market conditions could very easily change the value by that much in a year, up or down. These changes will happen regardless of whether you prepay your mortgage or not.

Exactly. The house price might change, so might as well do something that you have control over such as getting something equivalent to a 4% 1yr CD (which is unheard of these days).

Using the previous example, if the house price drops to $100k, you would end up with $12,037.08 in the first situation and $12,409.92 in the second. Once again $372.84 ahead when paying extra principal. Similarly if the house price jumps to $300k, you have $212,037.08 and $212,409.92. Of course one would hope to be in the latter situation.

harikaried wrote: People are raising questions about liquidity, and that's a fair question. We should now also somewhat agree that it's the same question of liquidity in the two situations:

- Should I put $10k in a 4% 1yr CD if I expect to sell the house in 1 year?
- Should I pay down $10k principal on my 4% mortgage loan if I expect to sell the house in 1 year?

Basically, are you willing to tie up $10k for a year with the main difference of you being sure you'll get your money back with the CD in a year vs hoping that the house sells "on time."

Those are 2 extremely different scenarios. With the 1yr CD, you get your money back in one year for sure, regardless of whether the house sells or not.

In one year you get your CD money back and you can use that money to either pay the rent on the new place, or put the downpayment on a new place, etc.

If you move in one year, and the old place is not sold yet, you will really need that liquidity.

In any case, this is irrelevant as there are no 4% 1-year CDs.

madbrain wrote:Exactly. The house price might change, so might as well do something that you have control over such as getting something equivalent to a 4% 1yr CD (which is unheard of these days).
[/quote[

As I have demonstrated above, the 4% 1-yr CD is not equivalent to prepaying your mortgage. The CD would be a much better deal because you are guaranteed to get the principal back in time.

Using the previous example, if the house price drops to $100k, you would end up with $12,037.08 in the first situation and $12,409.92 in the second. Once again $372.84 ahead when paying extra principal. Similarly if the house price jumps to $300k, you have $212,037.08 and $212,409.92. Of course one would hope to be in the latter situation.

Or alternately, you pay off the entire mortgage, your house sits on the market for months or years for whatever reason.
Then you lose your job, so you can't extract any home equity. You are forced to let it go at fire sale price to avoid getting foreclosed.

Liquidity is not really a question of numbers, either you have it or you don't have it. Being cash-poor is not a good thing.

If you are going to prepay your mortgage in full, be extremely sure that you still have a significant ER. Don't count on extracting home equity or sales proceeds as they may not materialized.

Note that I am not at all speaking in the abstract here, but as someone who bought a new house 2 years ago, prior to having sold the old townhome.

The townhome has been sale pending for 3 times, for a total of about 5 months over the last 25 months. The first 2 buyers couldn't close their loans. After the second buyer fell through, a unit identical in size in the same complex got foreclosed. I put my unit for rent for a year to offset the costs.

I just put my townhome for sale again in June and it has been sale pending since June 20. The buyer finally got approved for their loan and PMI last week. It is supposed to close this week or early next week. I hope!
The old home is selling for $450k and the loan on it is $250k. The net proceeds (about $175k) will be applied towards the mortgage on the new home which is $620k at the time.
I will go from two homes and $870k of mortgage debt to one home and $445k of debt. And actually I will prepay it slightly more to bring it do $417k to be able to refi and get a conforming loan at 3.375% fixed.

You can bet I will be celebrating when this sale finally closes !

harikaried wrote:

FNK wrote: - The duration of a mortgage (an amortized loan) is much, much shorter than its maturity.

I'm not sure what's the terms here mean. Is the mortgage duration the time until the loan is paid off (principal = $0) and the maturity is the original schedule without prepayment, e.g., 30 years? Although maturity seems to also be defined as when a loan has all its principal and interest paid off, so wouldn't they be the same thing?

Maturity is when the debt is scheduled to be paid off, right.

Duration is time to payment averaged out across all payments (weighted by present value). For example, a bond that pays $1000 30 years from now and nothing else (a zero-coupon bond) has 30-year maturity and 30-year duration. A bond that pays $1000 in a year and $1 in 100 years has 100-year maturity and a duration of a little over 1 year. That's a ridiculous case, of course. More common terms are a bond that pays coupons and returns principal at the end. Coupons make the duration a little bit shorter than maturity. An amortized loan, such as a mortgage, pays equal installments throughout, which make duration much shorter than maturity.

So, duration is the average time you have to wait before you collect all the payments on the debt. This makes a precise measurement of how long-term the debt is, and how sensitive it is to changes of interest rates. So, duration = interest rate sensitivity. Longer duration = greater risk.

However, paying down a mortgage does not expose you to any risk, except perhaps liquidity and opportunity risk. The amount of debt does not change with interest rates, while bond prices do. So it is not accurate to compare mortgage and bond risks by comparing durations.

madbrain wrote:As I have demonstrated above, the 4% 1-yr CD is not equivalent to prepaying your mortgage. The CD would be a much better deal because you are guaranteed to get the principal back in time.

Even if the house doesn't sell in the expected 1 year, if you extend it to say 3 years or even 5 years, a 4% 5-yr CD still sounds great (assuming you can take that hit on liquidity).

madbrain wrote:If you are going to prepay your mortgage in full, be extremely sure that you still have a significant ER. Don't count on extracting home equity or sales proceeds as they may not materialized. Note that I am not at all speaking in the abstract here, but as someone who bought a new house 2 years ago, prior to having sold the old townhome. The townhome has been sale pending for 3 times, for a total of about 5 months over the last 25 months. The first 2 buyers couldn't close their loans. After the second buyer fell through, a unit identical in size in the same complex got foreclosed. I put my unit for rent for a year to offset the costs.

Thanks for the warning, and I'll keep it in mind for future home sales/purchases. At least for my current situation, I'm selling to a relative and moving from San Jose to Reno where home prices are at least half as much, and I already have funds to cover downpayment, emergency, etc., so the question is how to invest extra monthly savings.

FNK wrote:So it is not accurate to compare mortgage and bond risks by comparing durations.

I noticed as I was analyzing this more, I referred to mythical 4% 1-yr CDs more than bonds. Would that be a more accurate comparison?

harikaried wrote:Thanks for the warning, and I'll keep it in mind for future home sales/purchases. At least for my current situation, I'm selling to a relative and moving from San Jose to Reno where home prices are at least half as much, and I already have funds to cover downpayment, emergency, etc., so the question is how to invest extra monthly savings.

That sounds good, as long as you have enough emergency funds to cover your cash flow you should be fine. Just don't count your chickens before they are hatched, home value on paper can be very different from actual, and housing market conditions can change quickly, and of course you never know if a buyer can really close a transaction or not unless they are a cash buyer.

If you do choose carry 2 homes (and thus 2 mortgages) at the same time like I did, you need that much more emergency funds.

I'm happy to report that signoff on my old townhome finally happened yesterday, the proceeds should be wired into my bank by tuesday, so I will only have one house and one mortgage left finally.

Using OP numbers, if you sell the house in 1 year, then making extra $10k payment is equivalent to investing in a 4% (before tax) 1-yr CD.

If you are willing to invest in 4% 1-yr CD, then making extra payment is the right thing to do.

As others pointed out, duration of a bond is not what you think. You were talking about the term of the loan.

acegolfer wrote:As others pointed out, duration of a bond is not what you think. You were talking about the term of the loan.

Thanks for making it crystal clear. I definitely was using duration as "The time during which something continues. Synonyms: length - continuance - standing - term - period - time" and not the financial Bond duration.

It seems to take me a few looks to understand what's going on. Actually, just the other day I was explaining this post to a friend and only then did I really notice where the savings were coming from... (It seems to simple now. I guess you really do get a better understanding when you try to explain/teach things to others.)

For those following along from my detailed 12 month example:

In the case with the extra $10k principal payment and regular $500 monthly payments afterwards, the difference in amount of interest paid each month after the first month is exactly the same as the interest earned by the 4% CD each month. This is exactly the same as the additional principal in those $500 monthly payments. So this means when you sell the house, you of course get the $10k extra principal that you paid in, but additionally every month you were able to "save more" because you were paying ~$33.89 more in principal each month for a total savings of $372.84 even though you were still just making the "usual" $500 monthly payments. In other words, you prevented the bank from charging interest on a higher balance by shifting yourself ahead on the amortization schedule/table.

harikaried wrote:

FNK wrote:So it is not accurate to compare mortgage and bond risks by comparing durations.

I noticed as I was analyzing this more, I referred to mythical 4% 1-yr CDs more than bonds. Would that be a more accurate comparison?

Yes. It's less relevant that the principal in a CD does not fluctuate: if you hold a bond to maturity, you're promised the return of your principal too. On the other hand, retrieving the principal of a CD before maturity usually costs a fine and paying down a mortgage is usually irreversible.

So, both a CD and a paydown of a mortgage reduce liquidity more than a bond. A CD has a fixed maturity date, a mortgage paydown may be recovered whenever you decide to sell the house (a tad more liquidity there, although real estate is anything but liquid) or cash-out-refinance (again, more liquidity, but depends on the whims of a bank), or simply used to reduce the number of mortgage payments.

Once you understand liquidity implications, just choose the best (tax-adjusted) rate and you're good to go. Both a mortgage and a CD are usually "pre-tax". In a progressive tax regime, showing less income tends to be more advantageous.