## Paying off mortgage versus investing with a twist

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Topic Author
puzzledhomeowner
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Joined: Thu Sep 15, 2016 9:16 pm

### Paying off mortgage versus investing with a twist

Hi,

Long time lurker, first time poster. I know there are lots of threads on paying off mortgage versus investing and general consensus seems to be investing is financially better in this low rate environment but if paying off mortgage make you sleep easier it may be worth it.

I have been considering both options, take a simple hypothetical scenario where mortgage is 30 year fixed with rate of 3% and amount is \$300000 and start date is today.

The mortgage payment per month comes out to \$1265.
Now, if I add extra monthly payment of \$1000, I finish the mortgage in 2030 instead of 2046.
IMHO, to make a fair comparison we cannot just count the money saved in interest with the money that would be obtained via 8% average return of the stock market. We should also consider the ability to invest the mortgage payment of \$1246 along with the extra \$1000 for 15 years.

Can someone help me do this calculation and see what the net difference is?

jjface
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Joined: Thu Mar 19, 2015 6:18 pm

### Re: Paying off mortgage versus investing with a twist

No you have to compare like with like. What are you trying to achieve? You want to know if it is better to pay the extra \$1k a month or invest it. Either way you have to pay the mortgage \$1265 so that cancels out of the equation. Put simply if you can earn 3% on the \$1k a month from the stock market you'll come out ahead (also consider taxes). However the stock market is risky and there is no guarantee you'll earn more than 3%.

Put another way if you invest the \$1265 too where are you going to live?

cherijoh
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Location: Charlotte NC

### Re: Paying off mortgage versus investing with a twist

This is not a black and white calculation - it all depends on what assumptions you are willing to make about the future.

We are in a historically low interest rate environment that would favor keeping the mortgage, but we are also at near historically high valuations for the stock market. So who knows which will turn out to be best in hindsight.

I recommend looking at things holistically. Do invest if it is going into a tax-advantage account. Don't pay down the mortgage if it means you will have too much of your net worth tied up in home equity. Do consider paying down the mortgage if your intent was to be mortgage free in 2030 but you went with a thirty year mortgage for payment flexibility.
jjface wrote:No you have to compare like with like. What are you trying to achieve? You want to know if it is better to pay the extra \$1k a month or invest it. Either way you have to pay the mortgage \$1265 so that cancels out of the equation. Put simply if you can earn 3% on the \$1k a month from the stock market you'll come out ahead (also consider taxes). However the stock market is risky and there is no guarantee you'll earn more than 3%.

Put another way if you invest the \$1265 too where are you going to live?

orca91
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### Re: Paying off mortgage versus investing with a twist

I think the OP is trying to see what the difference would be between paying the \$1265 mortgage for 30 years and investing \$1000/month all along compared to throwing the \$1000/month along with the \$1265 to pay off ASAP and then investing \$2265/month for the next 15 years of the same 30 time span. Which one wins?

It's not about where would they live. They would have a paid off home in 15 or 30 years depending on which route they take.

Topic Author
puzzledhomeowner
Posts: 13
Joined: Thu Sep 15, 2016 9:16 pm

### Re: Paying off mortgage versus investing with a twist

The Orca has summarized best what I was asking. The mortgage is done in 15 years and I would own the place.
To put it a bit differently the options can be thought of as 15 year mortgage and then investing whole mortgage payment for the next 15 years versus 30 year mortgage and investing the mortgage payment difference for 30 years.
And since this is bogleheads forum assume that my pay check is large enough and I live frugally enough that this is after tax advantaged accounts have been maximized.

orca91
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### Re: Paying off mortgage versus investing with a twist

I'm sure there are calculators out there or spreadsheets. I don't know where they are though. I've only seen this scenario played out in articles where they say what the difference would be. For me, it's not a big enough difference to invest over pay down the mortgage. After maxing out tax advantaged accounts, I pick pay down the mortgage over taxable.

I am a debt averse type though. And as others mentioned, we don't know the future. For me, paying down the mortgage is the safe bet. I'll take that.

It mainly comes down to personal preference with this subject.

physicsman
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Joined: Fri Sep 16, 2016 7:18 am

### Re: Paying off mortgage versus investing with a twist

The difference is enormous. Provided you can stomach the extra risk, it is by far favorable to your long term wealth to pay the mortgage off slowly and invest the difference.

As some ballpark numbers consider the following.

Case 1: You pay the mortgage off fast. For the first 15 years you pay 2265 per month into the mortgage and pay it off. For the next 15 years you invest that same monthly amount. If we assume 8% annual return your investment account will grow into 718,000 by the end of the 30 years.

Case 2: You pay off the mortgage slowly. For 30 years you pay 1265 per month towards the mortgage, and invest 1000 dollars a month. Again assuming about 8% compound interest, at the end your investment account is worth about 1,168,000.

Thus, in comparing the two cases we see that at the end of both you own a house, but by paying off the mortgage more slowly you are 400,000 dollars richer.

Of course the numbers here, specifically the 8% return, were rough estimates. The stock market carries risk. But over a long time horizon like 30 years it is almost certain that you will be hundreds of thousands of dollars richer by paying off your mortgage more slowly and investing the surplus.

orca91
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### Re: Paying off mortgage versus investing with a twist

How much interest was saved by paying off the mortgage in 15 years though?

That can be hundreds of thousands of dollars also to negate that difference some.

jjface
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### Re: Paying off mortgage versus investing with a twist

puzzledhomeowner wrote:The Orca has summarized best what I was asking. The mortgage is done in 15 years and I would own the place.
To put it a bit differently the options can be thought of as 15 year mortgage and then investing whole mortgage payment for the next 15 years versus 30 year mortgage and investing the mortgage payment difference for 30 years.
And since this is bogleheads forum assume that my pay check is large enough and I live frugally enough that this is after tax advantaged accounts have been maximized.
No it makes no difference. At the 15 year mark on the one hand you have a paid off house vs on the other hand a mortgage + an investment balance. If you earned greater than 3% on average you can at that time pay off the mortgage in full and have money left - investing wins. So again the mortgage payment is taken out of the equation.

Okay but then you might not want to pay off your mortgage after 15 years. What then? Then you have to compare a stream of \$1265 vs a the lump sum investment balance you'd have in the other scenario compouding at the same rate. You'll find you still come out ahead by not paying off the mortgage faster if you averaged more than 3% over the 30yrs.

I'll leave it as an exercise to run the numbers. You'll break even if you earned 3% all along. At the 15 year mark you'd have \$183k in your investment account and a mortgage balance of \$183k. If you continue at 3% you'd have the same amount if compounding \$183k for 15years vs componding \$1265 a month for 15 years.

Ignoring taxes.

rob
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### Re: Paying off mortgage versus investing with a twist

jjface wrote:Ignoring taxes.
Yeah but you cannot and when I think about this it becomes too many unknown/hard to calc things..... The 3% interest on the mortgage is somewhat less IF you can itemize - how much less depends on your tax rates and how close you are to the std deduction. Then there is the flow on effect of what you might miss in the tax system without that deduction (are you close to various cut off's). I know this is pedantic..... but if you want to make this call on pure numbers I think this stuff has to factor into the equation.
| Rob | Its a dangerous business going out your front door. - J.R.R.Tolkien

jjface
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### Re: Paying off mortgage versus investing with a twist

rob wrote:
jjface wrote:Ignoring taxes.
Yeah but you cannot and when I think about this it becomes too many unknown/hard to calc things..... The 3% interest on the mortgage is somewhat less IF you can itemize - how much less depends on your tax rates and how close you are to the std deduction. Then there is the flow on effect of what you might miss in the tax system without that deduction (are you close to various cut off's). I know this is pedantic..... but if you want to make this call on pure numbers I think this stuff has to factor into the equation.
Okay but the op hasn't provided enough info. to make a detailed tax calculation

1. Will the investments go to tax deferred or taxable?
2. Does he itemize?
3. Tax rates?
4. What investments are being considered?
5. Aca subsidy? Other tax credits? etc

If he doesn't itemize and will invest in taxable using vbinx vanguard balanced index with no tax credits or aca subsidy then he will need a little over 3% to take care of the tax on the dividends/interest. Say state tax is 7% and he is in the 15% bracket then federal will be 0% on qualified dividends (60%) and 15% on the rest. Plus 7% on the full dividend. He'll lose about 1/4% in taxes. No capital gains as he is in the 15% bracket. So he'll need 3.25% from the stock market and ignoring taxes basically holds.

orca91
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### Re: Paying off mortgage versus investing with a twist

jjface wrote:Okay but the op hasn't provided enough info. to make a detailed tax calculation

1. Will the investments go to tax deferred or taxable?.
Well they did cover that...
And since this is bogleheads forum assume that my pay check is large enough and I live frugally enough that this is after tax advantaged accounts have been maximized.
So, it's taxable investing vs. paying down the mortgage.
jjface wrote:3. Tax rates?
4. What investments are being considered?

If he doesn't itemize and will invest in taxable using vbinx vanguard balanced index with no tax credits or aca subsidy then he will need a little over 3% to take care of the tax on the dividends/interest. Say state tax is 7% and he is in the 15% bracket then federal will be 0% on qualified dividends (60%) and 15% on the rest. Plus 7% on the full dividend. He'll lose about 1/4% in taxes. No capital gains as he is in the 15% bracket. So he'll need 3.25% from the stock market and ignoring taxes basically holds.
Is someone maxing out tax advantaged accounts and owning a \$300k house in the 15% bracket? Maybe, but probably not. And, you bring up the vanguard balanced index (60/40) first and then talk about needing 3.25% from the stock market. Which are you meaning to talk about in your easy win scenario... 60/40 or 100 percent stocks?

We can all come up with a created win or lose situation here.

But as mentioned, lots of unknowns here... including the future.

I don't think it is or will be as easy as some do, to beat the mortgage rate with almost any sort of stock/bond mix of an investment.

jjface
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### Re: Paying off mortgage versus investing with a twist

That isn't the point orca. The point being that whatever return from the investments less tax must be higher than the mortgage rate taking into account any tax deductions. As simple as that - there is no twist. I was just giving an example not trying to prove anything.

orca91
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### Re: Paying off mortgage versus investing with a twist

Your example was not a very good one then, as it was all over the place.

jjface
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### Re: Paying off mortgage versus investing with a twist

orca91 wrote:Your example was not a very good one then, as it was all over the place.
Fair enough

grabiner
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Location: Columbia, MD

### Re: Paying off mortgage versus investing with a twist

puzzledhomeowner wrote:I have been considering both options, take a simple hypothetical scenario where mortgage is 30 year fixed with rate of 3% and amount is \$300000 and start date is today.

The mortgage payment per month comes out to \$1265.
Now, if I add extra monthly payment of \$1000, I finish the mortgage in 2030 instead of 2046.
IMHO, to make a fair comparison we cannot just count the money saved in interest with the money that would be obtained via 8% average return of the stock market. We should also consider the ability to invest the mortgage payment of \$1246 along with the extra \$1000 for 15 years.

Can someone help me do this calculation and see what the net difference is?
See Paying down loans versus investing on the wiki.

The extra payment you make today has a risk-free 30-year return of 3%. If you invest the money instead, you could buy a 30-year bond, and not take any more risk; if that 30-year bond yields more than 3%, you come out ahead. A 30-year zero-coupon Treasury bond yields 2.56%, which is a better deal if you aren't maxing out your IRA/401(k), as you would earn 2.56% tax-deferred and pay 2.25% or less on your mortgage in a 25% or higher tax bracket.. Right now, a 30-year municipal bond yields 2.31% (Bloomberg index), which is a better deal than a mortgage payment if you are in a 25% or higher tax bracket.

You could also take the additional risk of investing in stock, but that is no longer a fair comparison, as you increase both risk and expected return. You could also increase both risk and expected return without paying down the mortgage, by selling bonds in your IRA to buy more stock.
David Grabiner

msk
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### Re: Paying off mortgage versus investing with a twist

To simplify the quandary and perhaps better focus the mind: Would you take a million\$ loan @3% for 30 years in order to invest the million \$ in the stock market? This is similar to trading on margin, but at a low, 3% rate. There is, perhaps, always an interest rate that is low enough that investing on margin makes sense. Is there such a rate for Bogleheads? I suspect not.

onthecusp
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### Re: Paying off mortgage versus investing with a twist

I'm struggling with this decision as well, but I have a problem with the explanation provided in the wiki. It seems that there are logical problems if I look at it in the following way.

3% mortgage 10 years remaining. Cash to go to mortgage pay down or after tax investments.
By paying down my mortgage a little extra every month I am supposedly buying a series of risk free "bonds" at 3%. I immediately save the 3% on the extra payment by reducing the interest paid in subsequent months.

With these "bonds" in my portfolio I "should" move that amount of money (assuming a 50/50 stock/bond allocation) from my bond funds to stock funds to keep my overall asset allocation the same, right? I've defined my risk tolerance so keeping it the same is a goal or else I'm messing with my goals and not taking "enough" risk.

Problem 1: That does not seem right so I question the assertion that bond rates are the only fair comparison. Seems to me the comparison should be with my chosen stock / bond allocated portfolio expected return.

Problem 2: Once it is paid off I no longer have to send any money to the loan but I don't get the cash back like an expiring bond. Yes it is in the home equity; but now I'm overweight in the real estate segment. Of course I don't have to pay for rent or equivalent. I guess we are all either paying "rent" or overweight real estate. Until the loan is paid off liquidity is impacted quite a bit. I see that mentioned, but never quantified. How ever much it is worth it is on the side of not paying off vs a bond of the same interest rate.

What am I missing?

grabiner
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Location: Columbia, MD

### Re: Paying off mortgage versus investing with a twist

onthecusp wrote:I'm struggling with this decision as well, but I have a problem with the explanation provided in the wiki. It seems that there are logical problems if I look at it in the following way.

3% mortgage 10 years remaining. Cash to go to mortgage pay down or after tax investments.
By paying down my mortgage a little extra every month I am supposedly buying a series of risk free "bonds" at 3%. I immediately save the 3% on the extra payment by reducing the interest paid in subsequent months.

With these "bonds" in my portfolio I "should" move that amount of money (assuming a 50/50 stock/bond allocation) from my bond funds to stock funds to keep my overall asset allocation the same, right? I've defined my risk tolerance so keeping it the same is a goal or else I'm messing with my goals and not taking "enough" risk.

Problem 1: That does not seem right so I question the assertion that bond rates are the only fair comparison. Seems to me the comparison should be with my chosen stock / bond allocated portfolio expected return.
The amount of risk in your portfolio is not determined by your percentage asset allocation (although that is how many people view it), but by the effect of a market decline. Consider the following:

Portfolio A: \$300K house, \$200K stock, \$200K bonds, \$200K mortgage.
Portfolio B: \$300K house, \$200K stock, no bonds, no mortgage.

Either way, your net worth is \$500K, and will decline to \$400K if the stock market loses half its value. And if the bonds and mortgage have the same rate, then either portfolio also grows at the same rate; if home prices rise 2%, bonds return 3%, and stocks return 8%, your net worth will be \$522K next year. (The mortgage balance of portfolio A will decrease, but you can use bond interest to make the interest payment, and sell bonds to make the principal payment.)

Portfolio C: \$300K house, \$100K stock, \$100K bonds, no mortgage.

This is much less risky, as your net worth declines by only \$50K if the stock market loses half its value. You have a lower expected return than either A or B, but also less risk.
Problem 2: Once it is paid off I no longer have to send any money to the loan but I don't get the cash back like an expiring bond. Yes it is in the home equity; but now I'm overweight in the real estate segment.
You do get the cash back. If you pay \$1000 extra on your 3% mortgage today, then in ten years, you will have reduced your final payment by \$1344, so you will have \$1344 more to spend or invest then. If you bought a 10-year zero-coupon bond yielding 3%, you would also have \$1344 in ten years; this would be equivalent because you would owe the same \$1344 in mortgage payments.

Your weight in the real estate is independent of the mortgage. If your \$300K house loses 1/3 of its value, you will lose \$100K whether you have a mortgage or not. (This isn't as bad as losing \$100K in your portfolio, as the lower-valued house still provides you a place to live.)
Until the loan is paid off liquidity is impacted quite a bit. I see that mentioned, but never quantified.
Paying down the mortgage does decrease your liquidity, and this is a disadvantage compared to buying a bond. If you buy a bond while you have a mortgage, you can convert the bond to cash if you ever need the money. (You may lose a bit if bond prices fall.) If you use the money to pay down the mortgage, you can't get it back out of the house unless you qualify for a home-equity loan when you need the money.
David Grabiner

orca91
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### Re: Paying off mortgage versus investing with a twist

onthecusp wrote:I'm struggling with this decision as well, but I have a problem with the explanation provided in the wiki. It seems that there are logical problems if I look at it in the following way.

3% mortgage 10 years remaining. Cash to go to mortgage pay down or after tax investments.
By paying down my mortgage a little extra every month I am supposedly buying a series of risk free "bonds" at 3%. I immediately save the 3% on the extra payment by reducing the interest paid in subsequent months.

With these "bonds" in my portfolio I "should" move that amount of money (assuming a 50/50 stock/bond allocation) from my bond funds to stock funds to keep my overall asset allocation the same, right? I've defined my risk tolerance so keeping it the same is a goal or else I'm messing with my goals and not taking "enough" risk.

Problem 1: That does not seem right so I question the assertion that bond rates are the only fair comparison. Seems to me the comparison should be with my chosen stock / bond allocated portfolio expected return.

Problem 2: Once it is paid off I no longer have to send any money to the loan but I don't get the cash back like an expiring bond. Yes it is in the home equity; but now I'm overweight in the real estate segment. Of course I don't have to pay for rent or equivalent. I guess we are all either paying "rent" or overweight real estate. Until the loan is paid off liquidity is impacted quite a bit. I see that mentioned, but never quantified. How ever much it is worth it is on the side of not paying off vs a bond of the same interest rate.

What am I missing?
You're not really missing anything. You have a pretty good grasp on it.

I'm a simple guy, so I like to keep things simple.

Yes, it can be looked at like a negative bond and all, but you're simply paying off the debt you owe. You throw an extra \$100 at the mortgage and you just got 3% because you never have to pay the 3% on the \$100 again.... guaranteed return.

Most of us aren't a big business and shouldn't be mixing debts and assets in a portfolio. If you want to figure out your net worth, sure go ahead and count both. But, keep your portfolio separate from your mortgage and any other debts/loans.

Since paying down the mortgage is a guaranteed return, bonds/CDs/similar or most often used to compare. They're the closest thing to the guaranteed return you get by paying down the debt. You're welcome to use the expected return of your stock/bond portfolio, or all stocks. That's what most folks do when they say investing is better than paying down the debt. Of course, along with that comes the risk. In the example you presented, 10 years left on a 3% mortgage, how confident are you a moderate mix of stocks/bonds will easily beat 3% after taxes in that time frame?

I don't see a paid off home as overweight in real estate. Again, your home isn't part of the portfolio. A paid off home means you just paid for something you bought. Are you overweight in cars if you pay cash or pay off a car loan quickly? Yes, there's usually quite a difference in \$\$ between a home and a car, but my point is you simply paid for what you bought.

Just my take on it all. For as many Bogleheads as hang out here, there are probably as many ways to look at this topic.

Yesterdaysnews
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### Re: Paying off mortgage versus investing with a twist

I can give you my real world example -- I generally regret paying off my mortgage quickly in retrospect.

I bought a suburban McMansion in a nice neighborhood in July 2010. The price was \$1.2 M and I put \$500k down. I had \$700k jumbo loan at 4.5% for 15 years.

I had been approved for \$1M loan and could have taken it, also at 4.5%

I paid off the remaining \$700k over the next 5 years.

Had I taken out the full \$1M loan on the house at 4.5%, and invested the cash in the market instead of paying off my house quickly, I would have more money in my investment account due to the bull market.

The benefit is that I am debt-free, which is nice, and the house is valued at \$1.6M today, so not all is lost.

The problem was it was impossible to predict that this bull market would go on for so long, had I known the returns would be as nice as they have been, I would have taken the largest loan possible and invested the difference.

onthecusp
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### Re: Paying off mortgage versus investing with a twist

Been away a couple days, thanks for the thoughtful answers to my questions.
You do get the cash back. If you pay \$1000 extra on your 3% mortgage today, then in ten years, you will have reduced your final payment by \$1344, so you will have \$1344 more to spend or invest then. If you bought a 10-year zero-coupon bond yielding 3%, you would also have \$1344 in ten years; this would be equivalent because you would owe the same \$1344 in mortgage payments.
grabiner, that way of looking at it clears up my thinking a lot. Much easier to accept the bond equivalent argument.

And orca91 I understand what you say about taking that equivalent too far in an asset allocation view point. We all need housing. For me, as long as I have more house than I think we need in retirement I am looking at about a third of the value as an ongoing volatile investment even if I don't include it in my retirement planing calculations. As such it argues against my tendency towards taking higher market risks.

Right now my mortgage will be paid off in 2027, the year I turn 70 and start taking SS. So, assuming I retire before then, all of a sudden I will have much more income and far fewer expenses. That is great, but I feel like it leaves me vulnerable to a downturn in my late 60s.
I'm going to up my monthly payment enough to accelerate the payoff by about two years and also increase my taxable investments. I've only recently been able to up my taxable investments and would like to establish them a bit better. If I make good progress on that in the next year I will probably kick up my mortgage payoff to max and knock another couple of years off, match it with my expected retirement at 66.

Edited the above from "before tax" to taxable. Not sure what I was thinking when I wrote that, I am maxed out on 401k, catch-up contributions, and IRA though we do need to establish an IRA for my wife to contribute to.
Last edited by onthecusp on Mon Sep 19, 2016 9:53 am, edited 1 time in total.

finite_difference
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### Re: Paying off mortgage versus investing with a twist

Here is my strategy:

1. Pay mortgage (minimum).
2. Max out retirement accounts.
3. With leftover money, go 50/50 mortgage prepay and taxable investing.

I have not yet made it past 2, though.
The most precious gift we can offer anyone is our attention. - Thich Nhat Hanh