The great "pay off mortage" vs "invest in stocks" debate - possible solution

[pminkler]

The main argument, as I see it, for siding on the "invest the money" argument is that over 15 or 30 years of investing in index funds, you're mostly guaranteed to sooner or later make 7-10% returns...whereas by prepaying a mortgage, you're only getting 3-5% (definitely guaranteed) returns. 

Even if you wanted to prepay the mortgage, couldn't one just invest the money until:

1.  You could sell enough stock to pay off the mortgage and...
2.  Your returns over that time are greater than the mortgage interest rate

...and be happy?  You'd also get the benefit of deducting the mortgage interest come taxes. 

What's the flip-side here?

[velocistar237]

Or never pay it off. Refinance over and over so you always have the cash to invest.

[TheGrimSqueaker]

What's the flip-side here?

Stocks sometimes go down. So can the equity in your house, if the local economy shifts and the value drops. But outstanding mortgage debt is seldom sensitive or caring enough to reduce itself in proportion to the overall economy. The mortgage debt is also a source of constant outbound cash flow every month.

[Doulos]

Say you have a fairly standard looking FIRE plan.  (cFIREsim defaults)
40k expenses
1M cool mil stash. @4%SWR

With a $200k mortgage over your head, at a great 30year 3%-4% loan; You are looking to make roughly 2-4% interest on that money.

If you look at the two situations, it undeniable that if you stick with this awesome loan you increase your risk and your reward. 
- Definitely a win financially over the long haul.

But if you look at these numbers with an eye to FIRE date instead of the long haul...
40k expenses assumes you own that house.
a $200k mortgage 30year @3.5% = $898 per month, roughly $10k per year.
So your expenses are really $50k.
That means your new Stash to keep that 4% withdraw rate you are looking for is 50k/0.04 = 1,250,000.

So the real question there is how much longer is it going to take you to get $250k in your stash?
Is that extra time worth it for the awesome long term potential increase in your stash?

Say you are paying that 50k a year now, and you are saving 50k.  To keep the match simple.
That is not a whole lot of extra time with you stash growing from 1M to 1.25M.
If you assume the reasonable 6% average return on your investments over time.  (stocks of course jump all over the place)
You are looking at 2.2 years of additional work.
Or
You just pay off that mortgage with money from your investments.  (Taxable -> real-estate net zero capital shift of your net worth.)

Each person's case would be different.
But, there is firm, reasonable, advice on this subject saying the 'right' answer is You invest that money and hold on to the mortgage.  At least until your FIRE date.
- as in, it never really makes financial sense to slowly over time make extra payments to pay down your mortgage, if you can get a 3-4% mortgage.

I hope I accurately expressed the points made by the vocal people on this issue.

[BBub]

It's a great idea, and it's not a new one.  Just keep your leverage in check because the flip side is a total wipeout if you don't.

Don't let the long term averages woo you into feeling like there's easy risk-free money to be made by combining real estate, stocks and leverage.  Looking at smoothed long term returns can be comforting, but a prudent investor, IMO, always keeps at least one eye on preventing total catastrophe.

Since you don't seem the type who is planning to go apeshit taking out jumbo mortgages to buy stocks, then I'd say if you're comfortable seeing your investments fluctuate by up to 50% while the debt remains nearly constant, year in and year out, then go for it.  If you don't have the temperament for that type of balance sheet drama, pay the mortgage off.  It's a win-win, really.  Investing will likely give you more money at the end of the 30yrs, but you'll come out ok either way.

IMO, the best logical argument to pay off the mortgage by FIRE is that it'll reduce your required cash flow.  The lower you can get your true fixed expenses, the better you are protected against sequencing risk.  If things turn south early into FIRE, it's easy to cut most expenses but may be impossible to reduce your mortgage pmt.  Depending on your SWR level and how subsequent returns shake out, having a mortgage in FIRE could negatively impact your plan in the long run.  It's not likely, but it's possible.

[MDM]

40k expenses assumes you own that house.
a $200k mortgage 30year @3.5% = $898 per month, roughly $10k per year.

That means your new Stash to keep that 4% withdraw rate you are looking for is 5040k/0.04 + $200K = 1,250,0001,200,000...[because you can] just pay off that mortgage with money from your investments [if you want].  (Taxable -> real-estate net zero capital shift of your net worth.)

See edits above.

[sol]

But if you look at these numbers with an eye to FIRE date instead of the long haul...
40k expenses assumes you own that house.
a $200k mortgage 30year @3.5% = $898 per month, roughly $10k per year.
So your expenses are really $50k.
That means your new Stash to keep that 4% withdraw rate you are looking for is 50k/0.04 = 1,250,000.

So the real question there is how much longer is it going to take you to get $250k in your stash?
Is that extra time worth it for the awesome long term potential increase in your stash?

I think this is a good point that I have already internalized but not yet seen discussed here.  My own situation closely parallels this example.

I can retire soonish if I carry the mortgage in retirement, but sooner if I pay it off instead, for precisely this reason.  Reduced expenses up front reduce total stash needed.

But the total additional profit available to me by working long enough to carry the mortgage into retirement, as pointed out here, is large.  This is effectively another OMY problem, where the next bit of profit is always greater than the last bit, so the incentive to stay on longer continues to grow. We don't usually talk about this angle of the mortgage carrying debate, but it's such a big part of my own near term decisions that it's been on my mind a lot recently.

[MDM]

I can retire soonish if I carry the mortgage in retirement, but sooner if I pay it off instead, for precisely this reason.  Reduced expenses up front reduce total stash needed.

Why? 
A good case can be made that
    stash needed = (non-mortgage expenses)/(withdrawal rate) + (current mortgage balance)
instead of
    stash needed = (expenses including mortgage payment)/(withdrawal rate)

[sol]

Sure MDM, both ways are valid.  They just produce different total stash requirements.

[brooklynguy]

I think this is a good point that I have already internalized but not yet seen discussed here.

It has been discussed not only here in the forum, but precisely in your very own "should sol pay off his mortgage early?" thread:  see Post # 57.

A good case can be made that
    stash needed = (non-mortgage expenses)/(withdrawal rate) + (current mortgage balance)
instead of
    stash needed = (expenses including mortgage payment)/(withdrawal rate)

Yes.  In fact, a good case can be made that
 
      stash needed = (non-mortgage expenses)/(withdrawal rate) + (current mortgage balance - X)

where X = the present value of the expected outperformance of your invested mortgage proceeds over your mortgage's cost.

But personally I prefer to use MDM's simpler formula and think of the built-in "X" as part of my safety margin.

[arebelspy]

You shouldn't count the mortgage as part of that spending and as a corresponding increase in WR.  "Segment" it in your mind if you have to, but take your portfolio, subtract out the amount of mortgage principal remaining.  That's your FIRE portfolio.  Now take your spending, not counting your mortgage.  That's your expenses.  Use that to calculate what your WR is.

Then keep the money invested.  It won't generate enough to pay the mortgage payment by itself (because the mortgage payment includes principal), so you "draw down" on that portion of your portfolio (and for those that don't like the idea of eating into principal--you were going to eat into the principal for the full amount by paying off the mortgage, now you're just doing it slowly) to make the mortgage payment.  That doesn't change the WR on the rest of your portfolio versus the rest of your expenses, and shouldn't push back your time to FIRE at all.

[PathtoFIRE]

ARS beat me to it, but I'll state another way, you are oversaving is you try to cover mortgage payments with your stash like everything else in FIRE.

A mortgage is time limited and a fixed and knowable expense, the opposite of everything we are trying to predict and plan for for FIRE. If you try to roll the mortgage payment into your WR, and then increase your stash accordingly, you are essentially trying to cover a time-limited expense with a reliable income stream for life, which leads to oversaving.

[brooklynguy]

A mortgage is time limited and a fixed and knowable expense, the opposite of everything we are trying to predict and plan for for FIRE. If you try to roll the mortgage payment into your WR, and then increase your stash accordingly, you are essentially trying to cover a time-limited expense with a reliable income stream for life, which leads to oversaving.

Yep.  Since this principle has now been stated at least four times in this thread, let me restate my elaboration on this principle for a second time (but in words, not a mathematical formula):

Even if you don't try to roll your mortgage balance payments into your "retirement expenses needing to be covered indefinitely by your stash" and do what MDM stated in his formula and what ARS and PathtoFIRE stated in words--namely, save enough to cover your retirement expenses, plus save an amount equal to your mortgage balance--you are still oversaving, because you don't need to save the full amount of your mortgage balance in order to cover your mortgage payments, given that your investments are going to outperform your mortgage rate (of course, this assumes that they will in fact do so, but that assumption underlies the decision not to pay off your mortgage in the first place).

[BBub]

What about sequencing risk?  Here's some fuzzy math to illustrate a hypothetical situation:

Liquid stash: $1M
FIRE exp: $40k ann
Mortgage: $50k (originally $200k, now has 5 yrs left)
Mortgage pmt: $1k

Now, for the 1st five yrs of RE, you must pull 52k/yr.  If the mkt is down significantly for multiple yrs your plan will be negatively impacted.  Even though most of the annual $12k mortgage pmt is going into home equity, the effect would essentially be the same as selling off assets and going to cash all the way down.  Keeping a mortgage in FIRE, for the first several years anyway, is kind of like forced market timing.  I'm sure some of our resident quants could more eloquently depict this scenario w/ a series of calculations. Does this logic make sense?

[arebelspy]

Yes, there are always scenarios we can make up, but the fact of the matter is if the investing rate over the time you have the mortgage is greater than the mortgage rate, you'll come out ahead. The longer the mortgage timeframe, the more likely this is the case. How far ahead you can find out with cFIREcalc sims.

[BBub]

Yes, and using your same logic, the shorter the term left on a mortgage the more risk you are taking due to the volatility of short term market returns.  So, assuming we both agreed to a standardized set of assumptions (or even ranges) about short term volatility, there must be a breakeven somewhere that it's mathematically optimal to pay off the mortgage.

[arebelspy]

Yes, and using your same logic, the shorter the term left on a mortgage the more risk you are taking due to the volatility of short term market returns.  So, assuming we both agreed to a standardized set of assumptions (or even ranges) about short term volatility, there must be a breakeven somewhere that it's mathematically optimal to pay off the mortgage.

Or rather extend it.

[BBub]

Full disclosure, I agree that keeping a mortgage & investing is optimal for many.  I have a mortgage that could have been paid off by now, but I choose to invest for the same reasons as you do.

However, I'm not convinced, like many around here that one is always better.  I think there may be some situations where paying off the mortgage is mathematically optimal.  Not just because it feels warm & fuzzy.

The factors typically used to make the case for keeping the mortgage are simply int rate vs expected returns, but there's more to it.  Where the loan is on the am schedule matters.  The fewer yrs remaining, the higher the risk.

[BBub]

Yes, and using your same logic, the shorter the term left on a mortgage the more risk you are taking due to the volatility of short term market returns.  So, assuming we both agreed to a standardized set of assumptions (or even ranges) about short term volatility, there must be a breakeven somewhere that it's mathematically optimal to pay off the mortgage.

Or rather extend it.

That won't work forever because interest rates fluctuate.

[MDM]

However, I'm not convinced, like many around here that one is always better.  I think there may be some situations where paying off the mortgage is mathematically optimal.  Not just because it feels warm & fuzzy.

I am convinced that, mathematically, investing in something with a higher return than the mortgage cost is always better.  Now, I may be wrong, but I am convinced.  The lack of any counterexamples has much to do with that.

The factors typically used to make the case for keeping the mortgage are simply int rate vs expected returns, but there's more to it.  Where the loan is on the am schedule matters.  The fewer yrs remaining, the higher the risk.

Risk, yes - in that for short periods investment returns can vary dramatically.  But for a given after tax return and a given after tax interest, that's all there is to it.  Where the loan is on the amortization schedule does not matter at all, because one is always paying the quoted interest on the remaining principal.

[BBub]

However, I'm not convinced, like many around here that one is always better.  I think there may be some situations where paying off the mortgage is mathematically optimal.  Not just because it feels warm & fuzzy.

I am convinced that, mathematically, investing in something with a higher return than the mortgage cost is always better.  Now, I may be wrong, but I am convinced.  The lack of any counterexamples has much to do with that.

I am too because it's a fact.  Are you convinced that the market returns are always positive in the short run?  Could they be negative?   If so, you could assign a probabilty of that happening and develop a risk-adjusted case for paying it off once the remaining term falls below a certain level.

The factors typically proposed to make the case for keeping the mortgage are simply int rate vs expected returns, but there's more to it.  Where the loan is on the am schedule matters.  The fewer yrs remaining, the higher the risk.

Risk, yes - in that for short periods investment returns can vary dramatically.  But for a given after tax return and a given after tax interest, that's all there is to it.  Where the loan is on the amortization schedule does not matter at all, because one is always paying the quoted interest on the remaining principal.

It absolutely does matter because of the size of the required payment relative to the outstanding balance.  It would not matter if you had an investment steadily paying a fixed rate, but assuming investments are volatile in the short term, a loan near the end of it's am schedule forcing you to pay it down exponentially faster every month could work against you.  The likelihood of it working against you increases as the outstanding term decreases.

Think about your logic.  If years remaining was of absolutely no consequence, there would be no reason for banks to even issue loans of varying maturities.

[brooklynguy]

It absolutely does matter because of the size of the required payment relative to the outstanding balance.  It would not matter if you had an investment steadily paying a fixed rate, but assuming investments are volatile in the short term, a loan near the end of it's am schedule forcing you to pay it down exponentially faster every month could work against you.  The likelihood of it working against you increases as the outstanding term decreases.

Think about your logic.  If years remaining was of absolutely no consequence, there would be no reason for banks to even issue loans of varying maturities.

I don't think anyone is arguing that the remaining life to maturity does not matter for purposes of the market returns you can expect to achieve during that period.  All that was said is that once you assume that the investment returns will outperform the mortgage rate, then as a matter of fact it is optimal to keep the mortgage.  Of course it is true that the shorter the remaining life to maturity, the higher the chances of investment returns failing to outperform the mortgage rate (assuming you are not invested in some form of guaranteed investment vehicle, like a bank CD).  But the point about extension is that in an environment where you can refinance into a new long-term mortgage at a very low rate (like right now), extending the mortgage is probably the optimal decision if you have a short remaining life to maturity.  If you later end up in a situation where you have a short remaining life to maturity at a time when prevailing mortgage rates are high, then at that point paying off the mortgage may be most likely to be optimal.

[MDM]

I am convinced that, mathematically, investing in something with a higher return than the mortgage cost is always better.  Now, I may be wrong, but I am convinced.  The lack of any counterexamples has much to do with that.

I am too because it's a fact.  Are you convinced that the market returns are always positive in the short run?  Could they be negative?   If so, you could assign a probability of that happening and develop a risk-adjusted case for paying it off once the remaining term falls below a certain level.

Seems we are very close to agreeing, perhaps differing only in the semantics of "mathematically".  I'll defer to the practicing statisticians regarding risk-adjusted cases, but would be willing to risk a bet that if the mean and median investment return are both above the interest cost, even the risk-adjusted case would say the expected outcome is "not paying off will be better."  The shorter the time period, the closer to an even bet, but the odds will always favor the investment.

Risk, yes - in that for short periods investment returns can vary dramatically.  But for a given after tax return and a given after tax interest, that's all there is to it.  Where the loan is on the amortization schedule does not matter at all, because one is always paying the quoted interest on the remaining principal.

It absolutely does matter because of the size of the required payment relative to the outstanding balance.  It would not matter if you had an investment steadily paying a fixed rate, but assuming investments are volatile in the short term, a loan near the end of it's am schedule forcing you to pay it down exponentially faster every month could work against you.  The likelihood of it working against you increases as the outstanding term decreases.

Think about your logic.  If years remaining was of absolutely no consequence, there would be no reason for banks to even issue loans of varying maturities.

Again it seems we are close to agreeing.  Pretty much the same conclusion as above regarding the statistical result:
 - When a given (i.e., assumed to be true at all times) return is higher than the interest rate it is always better to invest than pay off.
 - Assuming investment returns can fluctuate (including go negative) in the short term, but over long periods the CAGR is higher than the interest rate, the likelihood that "investing is better" increases with time.
 - Assuming investment returns can fluctuate (including go negative) in the short term, but over long periods the CAGR is higher than the interest rate, the likelihood that "investing is better" is always >50%.

Agreed?

[BBub]

Absolutely in agreement on the long term, big picture (As mentioned I haven't paid mine off despite having the means to do so).  But for that FIREE who's looking to jump ship w/ just a few yrs remaining on the mortgage, the numbers could work against him.  Looking back, multi-yr negative returns are not uncommon.  And I predict, looking forward, that the situation of an early retiree preparing to retire w/ only several yrs left on the mortgage will not be uncommon around these forums.

Long term averages are so smooth, but short term disruptions can be shockingly severe & quite common.  They have been unusually rare during the last 6 yrs, but historically the bell shaped risk/return curve has some fatass tails.

I think there could be a quantifiable scenario where if one had <X yrs left, given a generally accepted asset allocation, she'd be better served to either pay it off or refinance to a longer term to increase the probability of success.  X is a number I don't know, but it must exist.  I'll do my best try to run some calcs & post them.  If it helps out one person it'll have been a worthwhile exercise.  Especially if that person is me ;).

[MDM]

Absolutely in agreement on the long term, big picture (As mentioned I haven't paid mine off despite having the means to do so).  But for that FIREE who's looking to jump ship w/ just a few yrs remaining on the mortgage, the numbers could work against him.  Looking back, multi-yr negative returns are not uncommon.  And I predict, looking forward, that the situation of an early retiree preparing to retire w/ only several yrs left on the mortgage will not be uncommon around these forums.

Long term averages are so smooth, but short term disruptions can be shockingly severe & quite common.  They have been unusually rare during the last 6 yrs, but historically the bell shaped risk/return curve has some fatass tails.

Yes indeed.

I think there could be a quantifiable scenario where if one had <X yrs left, given a generally accepted asset allocation, she'd be better served to either pay it off or refinance to a longer term to increase the probability of success.  X is a number I don't know, but it must exist.  I'll do my best try to run some calcs & post them.  If it helps out one person it'll have been a worthwhile exercise.  Especially if that person is me ;).

Now that's an interesting problem.  Seems you'll have to specify "by how much?" or "to what value?" regarding "increase the probability of success" somewhere in the analysis.  Looking forward to what you get.

[brooklynguy]

I think there could be a quantifiable scenario where if one had <X yrs left, given a generally accepted asset allocation, she'd be better served to either pay it off or refinance to a longer term to increase the probability of success.  X is a number I don't know, but it must exist.  I'll do my best try to run some calcs & post them.  If it helps out one person it'll have been a worthwhile exercise.  Especially if that person is me ;).

Now that's an interesting problem.  Seems you'll have to specify "by how much?" or "to what value?" regarding "increase the probability of success" somewhere in the analysis.  Looking forward to what you get.

I don't understand the question being examined.  Once we've assumed that the CAGR is higher than the mortgage rate over the long term, then the answer will always be that it's better to refinance to a longer term if the same (or lower) mortgage rate is available at the time of the refinancing (assuming that any transaction costs associated with the refinancing are low enough).

Is the question really just looking for a breakeven point in the "remaining years to maturity" variable as far as the expected optimality of payoff vs. investing, assuming that refinancing/term-extension is not an option (because, for example, then-prevailing mortgage rates are prohibitively high)?

I look forward to seeing the analysis too.  BBub, are you going to look at actual historical data, or just run calculations using a given set of assumptions for all the variables?

I just ran a quick cFIREsim run (using the same methodology described here and here) to check the historical odds of coming out ahead by keeping your mortgage outstanding with only 5 years remaining until maturity on a 4% mortgage using cFIREsim's default settings for asset allocation and investment expenses, and it reported an answer of 58.57% (but that may be understating the actual "success rate" of retaining the mortgage, because, as noted in the second linked post above, in a control test using assumed fixed investment returns, cFIREsim understates the success rate of retaining a mortgage (most likely due to its built-in assumptions about the timing of portfolio withdrawals not lining up with the timing of a mortgage's monthly amortization schedule)).

EDIT:  For every $100k of mortgage that remains outstanding with a 5-year remaining life to maturity and a 4% mortgage rate, the historical median amount by which the "mortgage-retainor" came out ahead was $1,597.60, with a standard deviation of $4,955.01.  The historical arithmetic average amount by which the mortgage-retainor came out ahead was $2,254.69.  In the absolute best-case scenario, he/she came out ahead by $18,749.39.  In the absolute worst-case scenario, he/she came out behind by $9,510.38

[arebelspy]

Your analysis is spot on, BG.  There's never a time this would have made sense historically, short of market timing/a crystal ball.  Because there are more times historically you've come out ahead than behind in the market, even over a short term.

So if you were dropped into a random period and were given the choice to pay off or invest, you should invest if you want the mathematically best option, even if your payoff time is short.  You are risking it going down (you still have about 1.5-to-1 odds of it going up, versus a longer time period when the ratio gets much better), yes, but it's more likely to go up.

If you don't think we're in a random period, but that the next 5 years will be worse, okay, market time to your heart's content.  But in a random year, it's better historically, and should be better going forward (assuming the future approximates the past) to invest over paying off over today's rates, even given a short time frame (even given a year--there are more years that have earned greater than today's mortgage rates than less than today's mortgage rates).

I don't see that there's any more "math" to be done beyond what you did, for whatever time interval you want, once BBub thinks it through some more.  But I'm open to being wrong.  :)

[BBub]

Yes the market has been up more often than down regardless of the time period examined, but it's not simply binary.  "Behind" could mean -1 basis point or -50% or worse.  Applying those severe dips, weighted for the probability of them actually happening, could tilt the math in favor of payoff.

This will be a work in progress.  I dont have time to put it all together this wk, but I'll get a report put together and post for feedback.  It'll be kind of fun.  BG, I definitely plan to use actual historical data for equity returns.

[arebelspy]

Applying those severe dips, weighted for the probability of them actually happening, could tilt the math in favor of payoff.

I see where you're going, but if the more negative ones were more probable over a given time period, the average return of that time period would be negative.

That isn't the case.

[brooklynguy]

I see where you're going, but if the more negative ones were more probable over a given time period, the average return of that time period would be negative.

That isn't the case.

Yep, that my was immediate reaction too.  But if BBub is willing to do the legwork on a detailed analysis to reach that conclusion, I would be interested in seeing it.  To address this issue, I will update my post above to include stats on portfolio ending values.

[MDM]

But if BBub is willing to do the legwork on a detailed analysis

Let's hear it for volunteers!

[ShoulderThingThatGoesUp]

I try to justify buying my house in cash with closing costs and other fees, but the truth is it just made us feel better.

Also, it enables us to max out my 401k with pre-tax money, and that gets an immediate 17.6% return on otherwise post-tax value (since we are in the 15% marginal bracket, 15/85 = 0.176.)

[brooklynguy]

Also, it enables us to max out my 401k with pre-tax money, and that gets an immediate 17.6% return on otherwise post-tax value (since we are in the 15% marginal bracket, 15/85 = 0.176.)

No, purchasing your house in cash (the equivalent of having "paid off" your mortgage before you even obtained it) did not "enable" you to max out your 401(k).  The idea that carrying a mortgage necessarily disrupts your non-mortgage-related cash flow is a fallacy that trips up many people when comparing the mortgage-retention vs. mortgage-payoff options.  When doing the cost-benefit analysis of paying off the mortgage, you need to look at the situation that would otherwise exist:  if you kept (or, in your case, obtained in the first place) the mortgage and invested the proceeds, you would have a big pile of investments (which you currently do not have) that would be used to service your mortgage payments.  In other words, the obligation to make monthly mortgage payments would not interfere with your ability to max out your 401(k), because those mortgage payments would be made not from your current cash flow but from the big pile of invested mortgage proceeds (and, as Rebs pointed out above, that pile of investments does not need to generate sufficient returns to cover the mortgage payments through returns alone -- it's ok to "eat into the principal", since that is what you are effectively doing anyway (at a much faster rate) by prepaying/paying off the mortgage).

but the truth is it just made us feel better

But I don't necessarily mean to suggest that paying off (or not obtaining) a mortgage is necessarily the wrong choice -- the quoted explanation is a perfectly valid reason not to carry a mortgage, as long as you do it with your eyes open :)

[ShoulderThingThatGoesUp]

You're right, we could use some investment income to counter the mortgage payments.

I'm not to worked up about it, and I'm certainly not going to take out a HELOC to invest in stocks. We have more in our taxable accounts than we paid for the house, anyways.

[brooklynguy]

You're right, we could use some investment income to counter the mortgage payments.

I don't mean to keep harping on this, but I think it's worth clarifying further given that many people (even some of the most sophisticated FIRE planners and thinkers in the forum) keep getting tripped up by this.

It's not merely that the person choosing to carry a mortgage "could use some investment income to counter the mortgage payments"; instead, it's that using the investment income (and, importantly, the investment principal) to cover the mortgage payments is the entire point behind the strategy of investing in lieu of paying off a mortgage.

If it makes it easier, through mental accounting you can separate your investment portfolio into two buckets:  one (which represents the invested mortgage proceeds) will be dedicated purely to servicing your mortgage payments, and the other (which represents your non-mortgage-related portfolio) will be dedicated to servicing all your normal, non-mortgage-related living expenses.  This should make it easier to see that the decision to carry a mortgage should have no bearing whatsoever on one's non-mortgage-related cash flow or FIRE date (other than to speed it up, if you prefer to use the expected optimality of carrying the mortgage to speed up your FIRE date at the front-end instead of to increase your chances of portfolio success and terminal value at the back-end).*

*This is not quite true, because the decision to carrying a mortgage is relevant for various considerations like tax-impact, eligibility for means-tested government benefits, eligibility for financial aid for higher education, etc.  But in order to properly evaluate those considerations, it is first necessary to have the basic first-order understanding described above.  Then it makes sense to dig deeper into the minutia, although in my view for most people it will still make sense (from a financial optimization perspective) to carry a mortgage with rates like those available today and a sufficiently long remaining life to maturity, even after taking these kinds of considerations into account.  I think the best discussion of those types of issues is in Sol's "to pay off or not to pay off?" thread.

[brooklynguy]

This will be a work in progress.  I dont have time to put it all together this wk, but I'll get a report put together and post for feedback.  It'll be kind of fun.  BG, I definitely plan to use actual historical data for equity returns.

BBub, do you still plan to do this analysis?  I hope we didn't convince you that it would not be a worthwhile endeavor, because I would be very interested in seeing the results.

[BBub]

Yeah still on my to-do, just haven't gotten around to it.

[NoNonsenseLandlord]

I went through the analysis at length in a post a while back, but here was my situation.

$189K mortgage on a rental @ 5.5%
$1,145 payment (P&I) monthly, $13,740 annually

Put up a $189K sum, get $13,740 back.  That is 7.3% return, GUARANTEED.  And your principal is also guaranteed by RE, which you control.  You are actually only saving the 5.5%, but the actual cash flow you get is higher due to the principal part.

Find an annuity that give that return these days...  Good luck.

[brooklynguy]

Find an annuity that give that return these days...  Good luck.

For an apples-to-apples comparison, you would have to compare it to an annuity that pays out $13,740 per year only for the remaining life to maturity of your mortgage (not forever).  It's misleading to characterize paying off a 5.5% mortgage as equivalent to generating a 7.3% return; it's really equivalent to a 5.5% return (ignoring tax and other similar considerations, which generally work in favor of decreasing the "return" on paying off your mortgage).

[Cheddar Stacker]

Yeah still on my to-do, just haven't gotten around to it.

Hey Bub, I just read this thread for the first time. I'm interested as well. One thing I believe you should be considering in your thought process, if not your analysis:

Presuming you're in the last 5-10 years of paying off a mortgage, you will almost certainly have a ton of Equity in the house. A simple HELOC fixes your "sequence of returns risk" issue. You are not forced to liquidate investments with a temporarily depressed value if you can simply write a check from your HELOC to cover your mortgage. In this instance, you are likely moving principal from a lower fixed rate note to a slightly higher variable rate note, but adding 1% interest is better than cashing out an investment that just lost 20% in value. A little flexibility and foresight can go a long way.

But I'm with Rebs and Brooklyn (and any others) on this one. When I get to the last 5 years of a mortgage, I'd be more inclined to refi with a cash out and get myself a new 15 year mortgage than I would be to pay it off. That would also lower your short-term risk, and it would lock in a longer timeframe for that inflation hedge.

[gluskap]

If you're just looking at the math then yes it makes more sense to carry the mortgage since over time, stock returns have been consistently higher than most interest rates today.  But I think a lot of people ignore too much the emotional impact.  Imagine you are close to retiring now and have only 5 years or less remaining on your mortgage.  With the huge runs we've been having, a market correction in the near term is very likely.  Now you decide to keep the mortgage and we head into a bear market.  Now you have to sell off more stock to make your mortgage payments and as a result have a higher WR.  This at the beginning of your retirement is what usually causes the probability of your stache lasting to go down.  Personally I'd rather have the peace of mind of not worrying about it.  You can always reduce your other expenses if the market goes down at the beginning of your retirement but you can't choose not to pay your mortgage.  Personally I will keep the mortgage even if we could pay it off until we are ready to FIRE.  After that I think just the simplicity of having one less expense in retirement is a good enough reason to pay it off too.

[brooklynguy]

Imagine you are close to retiring now and have only 5 years or less remaining on your mortgage.  With the huge runs we've been having, a market correction in the near term is very likely.

The probable outperformance of retaining a mortgage rather than paying it off decreases as your time horizon shrinks.  The idea is that over long enough time horizons (i.e., in this context, a long remaining life to maturity), retaining a mortgage with a rate like what's available today will almost certainly turn out to be optimal.  No-one is arguing that the optimal approach for someone entering retirement today with a 5 year remaining life to maturity is to simply retain it; rather, the probably-mathematically-optimal strategy would be to refinance into a new 30 year mortgage (and carry that mortgage into retirement, and, as the new maturity date approaches, evaluate whether it makes sense to refinance again depending on then-prevailing mortgage rates, and so on).

[Bob W]

If you're older and have the cash feel free to pay off the mortgage.

If you're younger and desire to FIRE then either don't buy a house or buy a cheap house and finance. 

[NoNonsenseLandlord]

Find an annuity that give that return these days...  Good luck.

For an apples-to-apples comparison, you would have to compare it to an annuity that pays out $13,740 per year only for the remaining life to maturity of your mortgage (not forever).  It's misleading to characterize paying off a 5.5% mortgage as equivalent to generating a 7.3% return; it's really equivalent to a 5.5% return (ignoring tax and other similar considerations, which generally work in favor of decreasing the "return" on paying off your mortgage).

True, but then add in your principle return, with appreciation, when you sell the property.  Assuming you had 25 years left on the mortgage, then sold after 25 years and got 100% of your initial investment back with appreciation, it would be a hell of an annuity.  And the insurance company (you) would likely not go broke.  And the terms would not change midstream.

[brooklynguy]

True, but then add in your principle return, with appreciation, when you sell the property.  Assuming you had 25 years left on the mortgage, then sold after 25 years and got 100% of your initial investment back with appreciation, it would be a hell of an annuity.  And the insurance company (you) would likely not go broke.  And the terms would not change midstream.

Huh?  Any appreciation "capturable" upon sale of the property exists whether or not you keep the mortgage, so it is irrelevant to the cost-benefit analysis of paying off the mortgage.

[NoNonsenseLandlord]

Huh?  Any appreciation "capturable" upon sale of the property exists whether or not you keep the mortgage, so it is irrelevant to the cost-benefit analysis of paying off the mortgage.

When you compare an annuity to a mortgage payoff, you can count that in.  Maybe apples to oranges, but still a benefit to paying down a mortgage vs. making payments.

In my case, the true return was 5.5%, the interest rate.  My actual extra cash flow increase was like an over 7% return for 25 years.  Most people would jump on a 25 year, 7% annuity, getting 100% of their principle back after 25 years.  And if you are comparing to an annuity, you do not get any appreciation of your principle, let alone any of it back.

Even compared to a 100% safe bond at 5.5% is a great deal.  This is what you are doing, buying a mortgage bond.  And if you do not pay off your mortgage, you are 100% sure to make the payments...

Can you make more in the market than 5.5%?  It depends on what time period you are referring to...  And if you can predict the future.

[brooklynguy]

When you compare an annuity to a mortgage payoff, you can count that in.  Maybe apples to oranges, but still a benefit to paying down a mortgage vs. making payments.

But my point was that it's not a benefit of paying off a mortgage.  Either way (paying off the mortgage early, or carrying it to maturity), you have the same amount of equity in the property when the maturity date rolls around.

If you want to count the value of the property (i.e., you don't plan on living in it (or renting it out) forever and therefore don't want to ignore the resale value), it doesn't make sense to compare the mortgage payoff to an annuity where your lump sum payment has vanished forever.  So, again, it is misleading to characterize your "return" as being higher than the mortgage's interest rate.  The proper analysis is to examine and compare the position you would be in having paid off the mortgage vs. having not paid off the mortgage, not to make an apples-to-oranges comparison to an alternative that is not analogous.

[brooklynguy]

Yeah still on my to-do, just haven't gotten around to it.

BBub, just checking if you still plan on doing the anaylsis discussed earlier in this thread (because some discussion in the "Stop worrying about the 4% rule" sticky in Investor Alley just reminded me about it)?

[forummm]

Good discussion and thought provoking.

I think some of the discussion here is short-changing the sequence of returns risk and the effect of volatility in a draw-down phase. When in accumulation phase, volatility is our friend and makes us a lot of money beyond what we would get in a fixed return investment. That's the principle that DCA is based on. But that benefit in accumulation is a detriment in draw-down. If you take out a 30 year 6% mortgage in 2020 and FIRE the next day and invest the money in VTSAX and VTSAX provides a 6% CAGR for the period 2020-2050, you won't break even--you'll lose out to the alternative scenario where you had no mortgage (ignoring any tax costs and benefits). The volatility when the market jags down costs you more than the benefit of when the market jags up.

I don't know how much that effect is, and what the difference in expected yield and fixed mortgage rate needs to be so that you expect to come out ahead by holding a mortgage given an expected level of volatility. It would be great for someone to do the analysis.

With the current 0% CG/Div bracket and itemized deductions, that probably pushes the equation a bit towards the invest side. At least for as long as those 2 policies are in place.

[MDM]

If you take out a 30 year 6% mortgage in 2020 and FIRE the next day and invest the money in VTSAX and VTSAX provides a 6% CAGR for the period 2020-2050....

Yes - one can substitute X for 6 in both places and the conclusion would be the same.  If the market's expected return is not "some amount" (and therein lies most of the debate) above the guaranteed return of the mortgage payoff, one should pay the mortgage.  But if the market's expected return is "some amount"....