Mr. Math and paying off your mortgage

[Scortius]

We are flexible, so we can be evil and time the market.

I'd like to see what happens if, on any down month in the market I invest, and any up month in the market I decide to prepay.

This would work horribly.  Just wait for a bull run like we're having now, you'll be putting all your money into your house while the market soars up and up. Strategies like these are no better than your average Las Vegas gambler's favorite "system".

By work horribly you mean, work no worse than the worse of the other two systems being proposed... with possible upside.

Yes and no, but I caution you against trying something like this.  Yes, it won't do any worse than the worst of the two options.  No, it doesn't really have potential upside.  Rather, if you look at my example, it's actually more likely to ensure that you end up closer to the worst of the two scenarios.  Yes, you may grab a bunch of stock during a correction, but then you'll be paying money into your house when the market continues its upward trajectory.  On the other hand, if there's a long-term recession, you'll be putting more money on average into the market and not into your more stable mortgage payment.

If you want the best of both worlds, you're probably better off picking an allocation of the two options that works best for you and sticking to it.  This is no different than choosing a specified portfolio allocation of US stock, international stock, and bonds and sticking to that.  Market timing ends up putting you on the wrong side of the curve more often than not.

Personally, if your horizon is long enough, the analysis seems to show that over all historical 30 years periods, investing is better.  If your horizon is shorter, then you may want to consider a more balanced approach, depending on your ability to handle market volatility.

[Seradoc]

We are flexible, so we can be evil and time the market.

I'd like to see what happens if, on any down month in the market I invest, and any up month in the market I decide to prepay.

This would work horribly.  Just wait for a bull run like we're having now, you'll be putting all your money into your house while the market soars up and up. Strategies like these are no better than your average Las Vegas gambler's favorite "system".

By work horribly you mean, work no worse than the worse of the other two systems being proposed... with possible upside.

Yes and no, but I caution you against trying something like this.  Yes, it won't do any worse than the worst of the two options.  No, it doesn't really have potential upside.  Rather, if you look at my example, it's actually more likely to ensure that you end up closer to the worst of the two scenarios.  Yes, you may grab a bunch of stock during a correction, but then you'll be paying money into your house when the market continues its upward trajectory.  On the other hand, if there's a long-term recession, you'll be putting more money on average into the market and not into your more stable mortgage payment.

If you want the best of both worlds, you're probably better off picking an allocation of the two options that works best for you and sticking to it.  This is no different than choosing a specified portfolio allocation of US stock, international stock, and bonds and sticking to that.  Market timing ends up putting you on the wrong side of the curve more often than not.

Personally, if your horizon is long enough, the analysis seems to show that over all historical 30 years periods, investing is better.  If your horizon is shorter, then you may want to consider a more balanced approach, depending on your ability to handle market volatility.

It's cool and all.  I just would like to see it plugged into the model and how it all shakes out.

[boarder42]

We are flexible, so we can be evil and time the market.

I'd like to see what happens if, on any down month in the market I invest, and any up month in the market I decide to prepay.

You'll come out way behind what you would have just investing for 30 years.

[uwp]

I don't understand how we have multiples of these threads (and I still love to read through them!).

The math is always very clear. 

Yes, there are situations were it might not work out, or you have some special circumstances, or you hate debt, or whatever (and I don't think the Invest "side" argues against people making personal choices). 

But the math doesn't really change.  Historically speaking, Invest wins. 

[mr_orange]

For completeness and to hopefully dampen all of the new threads seeking to prove what is not capable of being proved I will point you all to the CAPM resources I was able to find easily online:

http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-CAPM.pdf
https://en.wikipedia.org/wiki/Capital_asset_pricing_model

CAPM has problems in the real world, but does a pretty good job of demonstrating that none of this discussion can be had in isolation.  All of the numbers cited in this thread would need to be combined with the numbers from the rest of each person's portfolios to have any meaningful discussion of the topic.  Each person will have a different Markowitz efficient frontier similar to this:

https://en.wikipedia.org/wiki/Capital_asset_pricing_model#/media/File:Markowitz_frontier.jpg

that is defined by their own situation.  It has been over a decade since I studied this stuff so it is a bit hazy, but the short answer is everyone's situation is different. 

[maizefolk]

We are flexible, so we can be evil and time the market.

I'd like to see what happens if, on any down month in the market I invest, and any up month in the market I decide to prepay.

You'd get a result that is about midway between the "pay down your mortgage" curve and the "invest in the stock market curve" because a little more than half the time you'd be putting extra money in the market and a little less than half the time you wouldn't be. Although to be clear we're discussing a simulation where you pay down the mortgage if the market was up the previous month, and and you invest in the stock market if the the market was down the previous month, right?

[Tyson]

Paying down the mortgage gets me 4% return, investing in the market gets me almost 10% return, if I'm OK with volatility.  I'm OK with volatility. 

[mizzourah2006]

The one thing that would be interesting to look at is tax consequences of needing more money in early retirement to pay on the mortgage. If you need XX/yr without a mortgage and XX + $15k with the mortgage, that's $15k less you can fit into your roth conversion ladder. Obviously this is only important to someone at the retirement phase, but could have implications on a 30 year mortgage for many, especially if they continue to refi @ 4% and put the equity into investments.

Brooklyn has done that math. And it just doesn't come out ahead.  I'm sure he'll share links to his posts about it.

I don't recall having done any modeling on this question for specific scenarios using specific tax rates, but the related point that I regularly (and possibly excessively) harp on is that retaining a mortgage loan does not necessitate having extra taxable income to cover the required mortgage payments on a dollar-for-dollar basis.  Ordinarily if you choose to retain your mortgage loan instead of paying it off you wouldn't need an extra $15k of annual taxable income unless the annual required mortgage payments were some large multiple of $15k. My most recent post on that point was this one.

For example if my spending in early retirement was $50k/yr without a mortgage and $65k/yr with a mortgage. I understand you don't need 25x the mortgage to make the mortgage payment, but you still need to come up with the extra income to make the monthly payments. For example, pulling an extra $15k from your taxable investments. While it is not taxable in and of itself assuming you are in the 15% bracket it does add to your income, which could lessen the bucket you have for your Roth conversion ladder each year.

[brooklynguy]

I understand you don't need 25x the mortgage to make the mortgage payment, but you still need to come up with the extra income to make the monthly payments.

No, you don't need extra income [edit: that is, not in the full amount of the required mortgage payments, or anywhere close to that amount] because you have the invested funds that you could have used to pay off the mortgage loan to use as your source of funds for the mortgage payments.  As long as those investments generate most of their returns through capital appreciation (as stock index funds do), you will accrue relatively little income as a result of holding them (which is why I objected to Virtus' use of the completely unrealistic assumption that unrealized capital gains will incur taxes).  And as you sell those investments to fund the mortgage payments, only the capital gains (and not the return of investment principal) will represent taxable income, which should be a relatively small portion of the investment sale proceeds in the early years of a leveraged-investing-via-mortgage strategy (when your cost basis in the investments is still relatively high).

[Khan]

We are flexible, so we can be evil and time the market.

I'd like to see what happens if, on any down month in the market I invest, and any up month in the market I decide to prepay.

You come out poorly from this system because >2/3 of the time the market is going up, that is, it only goes down about ~1/3 of the time. I'm not sure how months relate to yearly data, maybe one of the others here has that in their excel file or whatnot, but:

The market had 134 positive years and 55 negative years (the market was up 71% of the time)

http://basehitinvesting.com/the-stock-market-a-look-at-the-last-200-years/

Also:

Nearly 7% of all market trading days have seen new all-time highs since 1950.
....
The average returns following an all-time high one, three and five years out into the future have been similar to the average gains over this entire period.

http://awealthofcommonsense.com/2016/11/dont-be-afraid-of-all-time-highs-in-the-stock-market/

[boarder42]

The one thing that would be interesting to look at is tax consequences of needing more money in early retirement to pay on the mortgage. If you need XX/yr without a mortgage and XX + $15k with the mortgage, that's $15k less you can fit into your roth conversion ladder. Obviously this is only important to someone at the retirement phase, but could have implications on a 30 year mortgage for many, especially if they continue to refi @ 4% and put the equity into investments.

Brooklyn has done that math. And it just doesn't come out ahead.  I'm sure he'll share links to his posts about it.

I don't recall having done any modeling on this question for specific scenarios using specific tax rates, but the related point that I regularly (and possibly excessively) harp on is that retaining a mortgage loan does not necessitate having extra taxable income to cover the required mortgage payments on a dollar-for-dollar basis.  Ordinarily if you choose to retain your mortgage loan instead of paying it off you wouldn't need an extra $15k of annual taxable income unless the annual required mortgage payments were some large multiple of $15k. My most recent post on that point was this one.

For example if my spending in early retirement was $50k/yr without a mortgage and $65k/yr with a mortgage. I understand you don't need 25x the mortgage to make the mortgage payment, but you still need to come up with the extra income to make the monthly payments. For example, pulling an extra $15k from your taxable investments. While it is not taxable in and of itself assuming you are in the 15% bracket it does add to your income, which could lessen the bucket you have for your Roth conversion ladder each year.

We have a very expensive mortgage for this place at 1535 a month. And we spend alot relative to mustachians. We plan for spending including mortgage up to the top of the 15% bracket. 

You're missing deductions. In your example the youd have at least 8k in personal exemption with no kids and 12600 in standard. So you'd have 20k in deductions.  Roth contribution plus so little of the taxable actually being income is what makes it work and the only years you have to be really careful are the 5 year bridge.

[mizzourah2006]

The one thing that would be interesting to look at is tax consequences of needing more money in early retirement to pay on the mortgage. If you need XX/yr without a mortgage and XX + $15k with the mortgage, that's $15k less you can fit into your roth conversion ladder. Obviously this is only important to someone at the retirement phase, but could have implications on a 30 year mortgage for many, especially if they continue to refi @ 4% and put the equity into investments.

Brooklyn has done that math. And it just doesn't come out ahead.  I'm sure he'll share links to his posts about it.

I don't recall having done any modeling on this question for specific scenarios using specific tax rates, but the related point that I regularly (and possibly excessively) harp on is that retaining a mortgage loan does not necessitate having extra taxable income to cover the required mortgage payments on a dollar-for-dollar basis.  Ordinarily if you choose to retain your mortgage loan instead of paying it off you wouldn't need an extra $15k of annual taxable income unless the annual required mortgage payments were some large multiple of $15k. My most recent post on that point was this one.

For example if my spending in early retirement was $50k/yr without a mortgage and $65k/yr with a mortgage. I understand you don't need 25x the mortgage to make the mortgage payment, but you still need to come up with the extra income to make the monthly payments. For example, pulling an extra $15k from your taxable investments. While it is not taxable in and of itself assuming you are in the 15% bracket it does add to your income, which could lessen the bucket you have for your Roth conversion ladder each year.

We have a very expensive mortgage for this place at 1535 a month. And we spend alot relative to mustachians. We plan for spending including mortgage up to the top of the 15% bracket. 

You're missing deductions. In your example the youd have at least 8k in personal exemption with no kids and 12600 in standard. So you'd have 20k in deductions.  Roth contribution plus so little of the taxable actually being income is what makes it work and the only years you have to be really careful are the 5 year bridge.

True, I was just asking the question. I'm on the keep the mortgage side, just trying to think of potential concerns in early retirement. In that situation your are at around $20k/yr in conversions that can fit into the 15% tax bracket instead of $35k/yr. One other thing (at least at this point) is the impact it could have on ACA help. Just a quick look at the Kaiser institute calculator shows an extra $140/month for healthcare coverage with an AGI of $60k vs $75k for a family of 3.

[boarder42]

The one thing that would be interesting to look at is tax consequences of needing more money in early retirement to pay on the mortgage. If you need XX/yr without a mortgage and XX + $15k with the mortgage, that's $15k less you can fit into your roth conversion ladder. Obviously this is only important to someone at the retirement phase, but could have implications on a 30 year mortgage for many, especially if they continue to refi @ 4% and put the equity into investments.

Brooklyn has done that math. And it just doesn't come out ahead.  I'm sure he'll share links to his posts about it.

I don't recall having done any modeling on this question for specific scenarios using specific tax rates, but the related point that I regularly (and possibly excessively) harp on is that retaining a mortgage loan does not necessitate having extra taxable income to cover the required mortgage payments on a dollar-for-dollar basis.  Ordinarily if you choose to retain your mortgage loan instead of paying it off you wouldn't need an extra $15k of annual taxable income unless the annual required mortgage payments were some large multiple of $15k. My most recent post on that point was this one.

For example if my spending in early retirement was $50k/yr without a mortgage and $65k/yr with a mortgage. I understand you don't need 25x the mortgage to make the mortgage payment, but you still need to come up with the extra income to make the monthly payments. For example, pulling an extra $15k from your taxable investments. While it is not taxable in and of itself assuming you are in the 15% bracket it does add to your income, which could lessen the bucket you have for your Roth conversion ladder each year.

We have a very expensive mortgage for this place at 1535 a month. And we spend alot relative to mustachians. We plan for spending including mortgage up to the top of the 15% bracket. 

You're missing deductions. In your example the youd have at least 8k in personal exemption with no kids and 12600 in standard. So you'd have 20k in deductions.  Roth contribution plus so little of the taxable actually being income is what makes it work and the only years you have to be really careful are the 5 year bridge.

True, I was just asking the question. I'm on the keep the mortgage side, just trying to think of potential concerns in early retirement. In that situation your are at around $20k/yr in conversions that can fit into the 15% tax bracket instead of $35k/yr. One other thing (at least at this point) is the impact it could have on ACA help. Just a quick look at the Kaiser institute calculator shows an extra $140/month for healthcare coverage with an AGI of $60k vs $75k for a family of 3.

yeah there is a math game with the ACA as well.  but i fully expect that to be 100% different by the time i reach FIRE in 4-7 years.  selling tradelines has greatly decreased my working time if its still around in 4 years.  holy cow its alot of free money.

[rantk81]

Oooh I had to research what "selling tradelines" is.... Sounds like an easy way to make a little bit extra on the side... but damn it sounds risky. Don't think I'll be doing that.

[AdrianC]

Paying down the mortgage gets me 4% return, investing in the market gets me almost 10% return, if I'm OK with volatility.  I'm OK with volatility.

It's a no-brainer...unless...could there be any flaw in this thinking?

[boarder42]

Paying down the mortgage gets me 4% return, investing in the market gets me almost 10% return, if I'm OK with volatility.  I'm OK with volatility.

It's a no-brainer...unless...could there be any flaw in this thinking?

 just total market collapse.  in which case most everyones FIRE plans fail as well. so i dont think its relevant IMO.  we're here to FIRE paying of my house makes that take longer and increases the chances i run out of money in RE. if there is a total market collapse i lose my FIRE plans anyways so who cares if i own my home.  i likely would have to rethink how the entire financial world works and start over regardless of if my house was paid off. so i'll maximize my returns based on what we know historically to be true, and not bet on total FIRE failure by paying down my home

[Prairie Stash]

I get a sense that some of the hyper enthusiasm is fueled by folks who have taken both large loans and significant market risk and want to feel good about their choices.  Personally, i always held a lot of market risk via a very high savings rate and aggressive investing.  However i also always bought way less home than i could afford.  This meant that my home loan was relatively small relative to my net worth, which is my personal philosophy. 

In every single case a smaller loan is better. Bigger loans (relative to locale) mean bigger taxes, more utilities and more repairs.

Having a smaller house trumps the whole debate; it cuts living expenses down. However, you can still cue up the folks who will justify their large loans as a hedge, an investment, or something else. Few people will admit to buying an over sized property though; but I think controlling housing costs is the biggest factor in NW (I can't think of any larger expense I have than housing; taxes, utilities, repairs).

Once we assume people buy moderate houses then, and only then, is it appropriate to debate mortgage vs. invest. I chose mortgage, cause I'm CDN, I skip the whole interest deduction and loans run 5 year lengths which increase volatility a lot. However I also have a HELOC to invest (live off) after the next downturn; its my security blanket to compensate for the downturns.

How does it work for Americans when you need to pull $30K/year even in downturns from the investments? My HELOC smooth's out the withdrawals so I can delay 5 years (pay the interest with the HELOC too). Does the timing of withdrawals matter? After 5 years I would be in trouble, but in a market crash that lasted 5 years I would also be destroyed selling off. Do y'all keep 3 years cash on hand to avoid the downturn sell off risk?

[boarder42]

I get a sense that some of the hyper enthusiasm is fueled by folks who have taken both large loans and significant market risk and want to feel good about their choices.  Personally, i always held a lot of market risk via a very high savings rate and aggressive investing.  However i also always bought way less home than i could afford.  This meant that my home loan was relatively small relative to my net worth, which is my personal philosophy. 

In every single case a smaller loan is better. Bigger loans (relative to locale) mean bigger taxes, more utilities and more repairs.

Having a smaller house trumps the whole debate; it cuts living expenses down. However, you can still cue up the folks who will justify their large loans as a hedge, an investment, or something else. Few people will admit to buying an over sized property though; but I think controlling housing costs is the biggest factor in NW (I can't think of any larger expense I have than housing; taxes, utilities, repairs).

Once we assume people buy moderate houses then, and only then, is it appropriate to debate mortgage vs. invest. I chose mortgage, cause I'm CDN, I skip the whole interest deduction and loans run 5 year lengths which increase volatility a lot. However I also have a HELOC to invest (live off) after the next downturn; its my security blanket to compensate for the downturns.

How does it work for Americans when you need to pull $30K/year even in downturns from the investments? My HELOC smooth's out the withdrawals so I can delay 5 years (pay the interest with the HELOC too). Does the timing of withdrawals matter? After 5 years I would be in trouble, but in a market crash that lasted 5 years I would also be destroyed selling off. Do y'all keep 3 years cash on hand to avoid the downturn sell off risk?

Yes owning a smaller house is more mustachian,
mowing your lawn is more mustachian
not paying down your mortgage in the US today is more mustachian. 


this "fear" of downturn sell off risk is highly overstated here.  you started pumping money into the market years before you have to sell it off.  would some of the later investments be sold at a loss in a downturn yes.  but all historical modeling shows you're safer in the long term by having a mortgage when you're FIREd and the only real risk will present it self in the first 5 years or so.  When your not far removed from the work force and could go back part time to make up the gap if you had to.  also adjusting your withdrawal by as little as 10% down in the event  of a down turn while keeping a mortgage creates a scenario in which you likely never run out of money barring the hyper inflation that even the mortgage couldnt offset in 1966, but did a much better job offsetting than having a paid off house.

[boarder42]

i also am not looking to feel good about my choice but to show others they should make the same choice and feel better about it than the feeling they get paying down their mortgage.  in general this forum fits the following

1. US based
2. FIREing at 40 or less
3. using Equities and some version of the 4% rule to primarily fund their FIRE.

so in general they should be keeping their mortgages b/c it presents less risk to FIRE over the long run and expedites FIRE.  Now if you understand all of this and you still choose to pay it down awesome.  Just like some here get satisfaction out of not mowing their own lawn.  but it shouldnt be applauded as a good thing.  it should be looked at the same way as eating out or paying for lawn service.  less than ideal but with an understanding of the tradeoff you're making for whatever personal reason you chose to come up with. 

do i own a larger house yes.  But when my wife and i made the decision to move to the house we looked at the math and it added 2 years to our FIRE date.  but we determined the house was worth it for our enhanced quality of life to be lake front. 

Far too many in these forums gloss over payoff vs invest as equal options when one is far superior and cuts years off a FIRE time line. As long as that choice is evaluated and the math is understood, more power to ya.  but more often than not it is not correctly understood and people make the wrong arguements to try to make the math look good for paying down their mortgage but its highly unlikely this can ever be accomplished with today's rates and historic returns.

[EscapeVelocity2020]

I would also add, most of these 'I can prove that paying off the mortgage beats investing' threads rely on some cherry-picked example of paying off the mortgage during a period of negative market returns then investing the extra for the up-swing.  Like investing in lottery tickets can be a great return on investment for that "1-in-a-billion" winner, for the vast majority, you are better off if you stick to the historically successful strategy of not wasting your money on a long-shot. 

[boarder42]

I would also add, most of these 'I can prove that paying off the mortgage beats investing' threads rely on some cherry-picked example of paying off the mortgage during a period of negative market returns then investing the extra for the up-swing.  Like investing in lottery tickets can be a great return on investment for that "1-in-a-billion" winner, for the vast majority, you are better off if you stick to the historically successful strategy of not wasting your money on a long-shot.

thats a good analogy. i'm gonna use that.

[boarder42]

I would also add, most of these 'I can prove that paying off the mortgage beats investing' threads rely on some cherry-picked example of paying off the mortgage during a period of negative market returns then investing the extra for the up-swing.  Like investing in lottery tickets can be a great return on investment for that "1-in-a-billion" winner, for the vast majority, you are better off if you stick to the historically successful strategy of not wasting your money on a long-shot.

This is inaccurate because the lottery has a negative expected return. Both investing and early mortgage pay-off have positive expected returns (with investing there needs to be a sufficient time horizon). Also this thread does not claim "paying off the mortgage beats investing" it accurately claims that paying off the mortgage early has less risk than investing. My analysis did not cherry-pick data it considered all rolling 30-year periods between 1870 and 1873.

how does it accurately claim it has less risk.  i havent seen evidence that there is inherently less risk.  you've shown there is more risk historically b/c in your data and even with the incorrect taxing and inflation applied improperly in very rare circumstances did the mortgage paydown come out ahead.  so you're betting on smaller probability which is higher risk.  You're betting on green in the risk game while we're betting on black and red.

[BFGirl]

i also am not looking to feel good about my choice but to show others they should make the same choice and feel better about it than the feeling they get paying down their mortgage.  in general this forum fits the following

1. US based
2. FIREing at 40 or less
3. using Equities and some version of the 4% rule to primarily fund their FIRE.

I'd like to know where you get your empirical data for the make up of this forum.  I don't meet 2 of the 3 criteria that you state above.  If your advice to not pay off your mortgage is dependent on the above assumptions, then you need to start stating that when you are giving advice or you are misleading people.

[brooklynguy]

This is inaccurate because the lottery has a negative expected return. Both investing and early mortgage pay-off have positive expected returns (with investing there needs to be a sufficient time horizon). Also this thread does not claim "paying off the mortgage beats investing" it accurately claims that paying off the mortgage early has less risk than investing. My analysis did not cherry-pick data it considered all rolling 30-year periods between 1870 and 1873.

how does it accurately claim it has less risk.  i havent seen evidence that there is inherently less risk.  you've shown there is more risk historically b/c in your data and even with the incorrect taxing and inflation applied improperly in very rare circumstances did the mortgage paydown come out ahead.  so you're betting on smaller probability which is higher risk.  You're betting on green in the risk game while we're betting on black and red.

Virtus tends to focus on a single risk -- namely, the risk that one's capital allocation strategy's actual return will underperform its expected return, which is unquestionably greater in a leveraged-investing-via-mortgage strategy (at least one that uses stocks as its investment vehicle) than in a mortgage-payoff strategy (which is precisely the reason why the former's expected return is higher than the latter's).  But, as has been pointed out to Virtus before, by doing this Virtus is ignoring the broad array of other, arguably more significant, risks faced by aspiring and actual early retirees, many of which are mitigated by a leveraged-investing-via-mortgage strategy.

[maizefolk]

Virtus tends to focus on a single risk -- namely, the risk that one's capital allocation strategy's actual return will underperform its expected return, which is unquestionably greater in a leveraged-investing-via-mortgage strategy (at least one that uses stocks as its investment vehicle) than in a mortgage-payoff strategy (which is precisely the reason why the former's expected return is higher than the latter's).  But, as has been pointed out to Virtus before, by doing this Virtus is ignoring the broad array of other, arguably more significant, risks faced by aspiring and actual early retirees, many of which are mitigated by a leveraged-investing-via-mortgage strategy.

"the risk that one's capital allocation strategy's actual return will underperform its expected return" That's an interesting way of defining it, and I think it gets at some of the emotional biases that come into play when assessing risk.

Imagine a hypothetical scenario where I roll a 6 sided die and based on the number that comes up someone pays me some amount of money.

Scenario A: If I roll 2-6 I receive $12k, but if I roll a 1 I receive nothing.  The expected value of rolling the die is $10k, and odds that the actual return will underperform its expected return are ~17%.

Scenario B: If I roll 1-5 I receive $12k, if I roll a six I receive $24k. The expected value of rolling the die is $14k, but the odds that the actual return will underperform the expected return are 5/6 or ~83%.

By the definition of risk above, scenario A is less "risky" than scenario B.

[EscapeVelocity2020]

This is inaccurate because the lottery has a negative expected return. Both investing and early mortgage pay-off have positive expected returns (with investing there needs to be a sufficient time horizon). Also this thread does not claim "paying off the mortgage beats investing" it accurately claims that paying off the mortgage early has less risk than investing. My analysis did not cherry-pick data it considered all rolling 30-year periods between 1870 and 1873.

how does it accurately claim it has less risk.  i havent seen evidence that there is inherently less risk.  you've shown there is more risk historically b/c in your data and even with the incorrect taxing and inflation applied improperly in very rare circumstances did the mortgage paydown come out ahead.  so you're betting on smaller probability which is higher risk.  You're betting on green in the risk game while we're betting on black and red.

Virtus tends to focus on a single risk -- namely, the risk that one's capital allocation strategy's actual return will underperform its expected return, which is unquestionably greater in a leveraged-investing-via-mortgage strategy (at least one that uses stocks as its investment vehicle) than in a mortgage-payoff strategy (which is precisely the reason why the former's expected return is higher than the latter's).  But, as has been pointed out to Virtus before, by doing this Virtus is ignoring the broad array of other, arguably more significant, risks faced by aspiring and actual early retirees, many of which are mitigated by a leveraged-investing-via-mortgage strategy.

As always BG, your comment is excellent, but probably too nuanced to be grasped fully.  And I can understand PS and Vitus taking umbrage at my 'lottery analogy', being maybe a bit heavy handed, but easier to understand. 

So, from what BG said, investing in t-bills (or a fixed, low rate mortgage (because a high rate mortgage is dumb if you can refinance at any time and lower your payments - which is a 'yuge' feature of this 15 or 30 year inflation hedge btw)) is actually 'riskier' over extended periods because the expected return becomes more definitely below the more volatile equity return.  Over sufficiently long periods, you become like the lottery participant - paying a penalty to enjoy the ride you've been taken on.

But, just to head off the next rebuttal, sure 100% US equities could under-perform historically low yielding bonds for 30 years.  Maybe even diversifying into a distribution of mostly large cap, with a dose of mid and small cap domestic equities, add some developed world and sprinkled with REITs and Emerging Markets...  maybe even that magic formula underperforms bonds.  You are still in good shape as long as inflation stays at 2% or increases (since your mortgage is a fixed debt).  Or maybe Vitus and PS really are betting on the zombie apocalypse (which they think is more likely than winning the lottery)? 

[EscapeVelocity2020]

I'll support you, 100%, in the comment that 90/10 AA should not be criticized.  And I'm sorry that it was somewhat insulting to be compared to survivalists on the internet, but there is certainly a guns, gold, and ammo element out there.  I've appreciated your work Vitus, but history is what it is, investing in certainty is less profitable than be willing to accept some volatility (misunderstood as risk) over long (and maybe even longer expected, if we are optimistic) periods.

Also, I'm just one of those 'experienced veterans' that want to help the next generation not repeat some of my inexperience and failures.  I bought my first house in 2001.  I think it was a 6%/30 year rate.  We had our first child, and both of us were working because my job was insecure.  We actually did prepay the (very low at the time) mortgage with the double income, thinking it would be great to pay off our house so one of us could retire early.  Holy crab-cakes if only we had been investing that money in the stock market instead.

To conclude my story, we sold our first (not entirely paid off) home at a profit (that was hobbled by realtor fees and paying back some home office tax deductions).  But throughout the years on our second home, I've enjoyed the flexibility in tax deductions and refinancing to lower rates (and investing all that extra non-pre paid, lower payment moolah).  By paying off a mortgage early, with money that could be invested in anything that you think could out perform your 'refinancable' low fixed interest, well - you must just have to think that the future for investing is gonna really suck for your lifetime, you're not going to have tax deductions above the standard deduction, that inflation is going to stay low for the duration of the loan, etc., etc..

[FIPurpose]

Is there a reason we can't use industry standard markers for risk-adjusted returns?

The VTSAX Sharpe ratio is about .9 - Meaning that the fund is somewhat risky.

It has a lifetime earning of about 10% on average.
We're comparing a 4% risk-free rate.

6% / 10.7 (the standard deviation of VTSAX) = .56

This turns the the return into a fairly risky investment.

Or with the Sortino Ratio where VTSAX is typically 1.6 is instead changed to about 1.

It's not an impossible bet, in fact you have a pretty good chance of winning. But it puts the risk of this deal somewhere around a developed international stock. If you include international stocks in your portfolio, you have a good chance of coming out ahead. If you believe in investing over paying off your mortgage, but think international funds are too risky, I think there is some collision.

[MDM]

Is there a reason we can't use industry standard markers for risk-adjusted returns?

Maybe because the main complaint is [the Sharpe] ratio relies on the notions that risk equals volatility and that volatility is bad?

The validity of those notions is part of the debate here.

[boarder42]

Is there a reason we can't use industry standard markers for risk-adjusted returns?

Maybe because the main complaint is [the Sharpe] ratio relies on the notions that risk equals volatility and that volatility is bad?

The validity of those notions is part of the debate here.

correct volatility does not equal risk.  if you understand the market can be volatile and you're somewhat flexible in your FIRE plans you can have plans in place that reduce or eliminate volatility risk based on what the markets have done historically. 

As to the 90/10 comment above a 90/10 AA is better than a 100/0 with a paid off house making up 10% of your total assets.  you have more risk in your paid off home it is not liquid even with a HELOC and if the plan is to HELOC to get equity out in bad times why not just take the better path of having your mortgage still opened.  when you historically test 90/10 vs 100/0 - 90/10 has a distint advantage in greatly decreasing downside volatility while still maintaining almost the same returns.  the amount of extra income gained at the cost of higher downside volatiliy is something everyone needs to evaluate themselves but for me it isnt there.  on the flip side a paid off home increase the chances of FIRE failure and losing everything later into FIRE when its less likely you can get a PT job in your field or are less physically able to perform some labor jobs that could supplement the rough patch. More over historically bonds have averaged higher returns than the current mortgage rates so if one were to pay down their house in 7 years at todays rates and if/when bonds recover back to the norm you can no longer secure a mortgage at the past rate you paid off and that money is sunk in a fixed asset and the amazing leverage you could have had is gone.

there is higher risk having a paid off house at today's rates than having invested capital if you plan for equities to fund your FIRE and i personally dont think its a matter of opinion. 

[maizefolk]

I don't want to be in the position of arguing in favor of bonds. But the feature bond investments have that a partially paid off mortgage does not is that one ends up rebalancing in and out of them. In the average scenario over the long term this doesn't increase yields over either 100% stocks or buying 10% bonds and 90% bonds and never rebalancing. But it does increase yield over the average of the returns of the two asset classes weighted by your initial percent allocation to each.

In addition, the conventional wisdom, right or wrong, is that you want few bonds early in the accumulation phase and that the time to have them be more of your portfolio (if ever) is right before FIRE. Paying off your mortgage right away and then investing in the stock market produces the opposite profile where a lot of your savings are going towards "bond-like" assets early in the accumulation phase, and once your house is paid off you start increasing your allocation to stocks and keep increasing it until FIRE.

If someone was proposing a model where they'd keep 10% of their net work in home equity and rebalance into more home equity as the stock and/or bond portion of their portfolio rose, and out of home equity when the value of their home portfolio fell, that would be interesting. Depending on what portion of your asset allocation you set to "home equity" your expected return would be a little to a lot lower than a stock portfolio, but you would reduce volatility and get some diversification/rebalancing bonus above the weighted average of the returns for different asset classes. However:

A) mortgages don't really allow for rebalancing (maybe you could get close with a HELOC? That's a whole separate debate (boarder also touched on this issue directly above)).
B) As your portfolio grew towards FIRE and the value of your home was less than 10% of your total net worth, would you have to start buying additional homes to keep up with your preferred asset allocation? Or worse, have to buy a bigger house? (I suspect the actual solution would be to fill the gap between home value and the percent of your portfolio that should be allocated to home equity with bonds.)
C) Since deciding on asset flows depends on total equity in the home, we'd need to historical data on housing prices in different markets to backtest it. And that data just doesn't exist over the timeframes being used for the simulations.
D) Most critically: As far as I can tell, no one is actually proposing this strategy.

Speaking of datasets:
Virtus, I had a couple of questions about your latest simulation, if you don't mind. Are you using data from an index of different types of bonds? Or are you using the shiller data on the returns of 10 year government bonds from 1871-present? What marginal income tax rate, if any, are you assuming for taxes on bond coupons? Is this the result of your simulation without inflation or with inflation corrections to market yields?

[brooklynguy]

there is higher risk having a paid off house at today's rates than having invested capital if you plan for equities to fund your FIRE and i personally dont think its a matter of opinion.

It depends on how you define "risk."  We tend to use that word loosely, without precisely defining what it means, which is the reason everyone always ends up talking past each other in these debates.  If "risk" means "exposure to an adverse possibility," we should be clear about which specific adverse possibility or possibilities we are referring to, or, alternatively, that we are broadly referring to the entire universe of conceivable adverse possibilities.

Virtus is, without question, correct that as between leveraged-stock-investing-via-mortgage and mortgage-payoff, the former exposes you to each of the following possibilities, none of which are present in the latter:  the possibility of underperforming the expected return, the possibility of underperforming the worst-case possible outcome of the other strategy, and the possibility of loss of capital.  Leveraged-stock-investing-via-mortgage is therefore riskier in each of these specific respects.

However, there is a panoply of other risks that are (or should be) material to the decision-maker, and that therefore should also be accounted for in the analysis, including, not least of which for the aspiring early retiree, the risk of having to work longer than necessarily before achieving self-declared financial independence.  I agree with you that, on balance, when all relevant risks are taken into consideration, paying off "fixed-rate non-callable government-favoured low-interest tax-deductible long-term possibly-non-recourse debt secured by an instrument on which creators are generally slow to foreclose" (as Cathy aptly described today's available mortgage debt in the post cited in the one I linked to above) is risker than retaining such debt and investing the proceeds in the stock market.

[runewell]

This is inaccurate because the lottery has a negative expected return. Both investing and early mortgage pay-off have positive expected returns (with investing there needs to be a sufficient time horizon).

This is inaccurate because investing has a positive expected return regardless of the time horizon.

[FIPurpose]

Is there a reason we can't use industry standard markers for risk-adjusted returns?

Maybe because the main complaint is [the Sharpe] ratio relies on the notions that risk equals volatility and that volatility is bad?

The validity of those notions is part of the debate here.

And the Sortino ratio that describes downside volatility?

[AdrianC]

Paying down the mortgage gets me 4% return, investing in the market gets me almost 10% return, if I'm OK with volatility.  I'm OK with volatility.

It's a no-brainer...unless...could there be any flaw in this thinking?

 just total market collapse.  in which case most everyones FIRE plans fail as well. so i dont think its relevant IMO.  we're here to FIRE paying of my house makes that take longer and increases the chances i run out of money in RE. if there is a total market collapse i lose my FIRE plans anyways so who cares if i own my home.  i likely would have to rethink how the entire financial world works and start over regardless of if my house was paid off. so i'll maximize my returns based on what we know historically to be true, and not bet on total FIRE failure by paying down my home

Well, there are alternative scenarios between a net 6% return on the borrowed money (maximum optimism) and "total market collapse" (maximum pessimism). I think other posters have made the case well in this and concurrent threads. There is a real chance that stock market returns will be below 4% for the time period an investor has.

This doesn't preclude getting to FI, of course. Most of us get to FI by earning a lot and saving a huge part of it. Investment returns are just icing on the cake in many cases (was in mine).

[maizefolk]

A) mortgages don't really allow for rebalancing (maybe you could get close with a HELOC? That's a whole separate debate (boarder also touched on this issue directly above)).

A)You could re-balance using future cash in flows. Frank would then split his $1,500 per month to keep his net worth lets say 80% equities and 20% house equity (Or whatever ratio he decided).

Thanks for the answers on methodology, Virtus. I've singled out one point from the above as the most interesting to think about (although a little off topic).

Say you have a target asset ratio of 20% home equity, 80% broad stock market index. You start out with 20% in equity in your primary residence (let's say the house is worth $250,000 which is high for where I live, but low for a lot of coastal mustachians) and $200k invested in the stock market. The stock market is growing at 8%/year and your house is appreciating at 4%/year (just a little above inflation). After 1 year (assuming no new investment), your house is worth $260,000 and your equity has grown to $60,000. Meanwhile the value of your stocks has grown to $216k which is now ~78% of your total portfolio of $276. Great. To get back to a 80/20 split, you need to invest an extra $24,000 in your stocks (brings the total to $240k), plus 4x how ever much money you'd have paid off on your mortgage even making minimum payments (so another ~$14k assuming this is the first year of a 30 year mortgage at 4%). Net result: first $38k of extra money goes into the stock market, then 4:1 split between buying stocks and paying down the mortgage for any extra money.

If it's a bad year for stocks though, and they close 8% lower at the end of the year, now your home equity is still $60k, but your stock portfolio needs $56k of new cash to come back up to where it should be plus 14k to make up for mortgage pay down. Net result: first $70k of extra money goes into the stock market, then 4:1 split between buying stocks and paying down the mortgage for any extra money.

I guess my point is just that, if your goal is maintain a fixed ratio of home equity to stock investments, that in an average year one would end up putting a lot more of their surplus cash into the stock market than into prepaying the mortgage. And in a down year for the stock market it is very easy to end up in a situation where it'd take an awful lot of new investment to rebalance your portfolio without being able to pull money out of your home equity the way you can pull it out of a bond fund. Doesn't mean the approach isn't valid. Just that there are some logistical hurdles to implementing it in practice, and the end result probably wouldn't look a lot like paying off the mortgage as quickly as possible.

[maizefolk]

Well, there are alternative scenarios between a net 6% return on the borrowed money (maximum optimism) and "total market collapse" (maximum pessimism). I think other posters have made the case well in this and concurrent threads. There is a real chance that stock market returns will be below 4% for the time period an investor has.

A lot of the discussion about predicting future stock market returns tends to focus on "real" returns. And there are indeed some folks predicting real returns in the 4-5% over the next couple of decades.

For comparing against the mortgage one has to use nominal returns. Even assuming zero risk of increased inflation going forward, 4% nominal returns would imply something like 1.5% real returns.

This doesn't preclude getting to FI, of course. Most of us get to FI by earning a lot and saving a huge part of it. Investment returns are just icing on the cake in many cases (was in mine).

Investment returns may not have been important in you getting to FIRE. They're pretty essential to most in remaining FIRE. At 1.5% real returns, a 25x annual expenses stash would be exhausted in 31-32 years.

[Dicey]

I'll support you, 100%, in the comment that 90/10 AA should not be criticized.  And I'm sorry that it was somewhat insulting to be compared to survivalists on the internet, but there is certainly a guns, gold, and ammo element out there.  I've appreciated your work Vitus, but history is what it is, investing in certainty is less profitable than be willing to accept some volatility (misunderstood as risk) over long (and maybe even longer expected, if we are optimistic) periods.

Also, I'm just one of those 'experienced veterans' that want to help the next generation not repeat some of my inexperience and failures.  I bought my first house in 2001.  I think it was a 6%/30 year rate.  We had our first child, and both of us were working because my job was insecure.  We actually did prepay the (very low at the time) mortgage with the double income, thinking it would be great to pay off our house so one of us could retire early.  Holy crab-cakes if only we had been investing that money in the stock market instead.

To conclude my story, we sold our first (not entirely paid off) home at a profit (that was hobbled by realtor fees and paying back some home office tax deductions).  But throughout the years on our second home, I've enjoyed the flexibility in tax deductions and refinancing to lower rates (and investing all that extra non-pre paid, lower payment moolah).  By paying off a mortgage early, with money that could be invested in anything that you think could out perform your 'refinancable' low fixed interest, well - you must just have to think that the future for investing is gonna really suck for your lifetime, you're not going to have tax deductions above the standard deduction, that inflation is going to stay low for the duration of the loan, etc., etc..

Thanks for the real-life example, EV2020. Your post deserves a huge bump, so BUMP!

[FIreDrill]

Well, there are alternative scenarios between a net 6% return on the borrowed money (maximum optimism) and "total market collapse" (maximum pessimism). I think other posters have made the case well in this and concurrent threads. There is a real chance that stock market returns will be below 4% for the time period an investor has.

This doesn't preclude getting to FI, of course. Most of us get to FI by earning a lot and saving a huge part of it. Investment returns are just icing on the cake in many cases (was in mine).

Well the average 30 year returns on the S&P 500 are around 9.6%.  Though you are looking at net so I'm assuming you are looking at inflation adjusted returns?  In that case the average would be around 6.7% inflation adjusted.  This doesn't take into account taxes but assuming you are not selling off the funds then you are only looking at being taxed on dividends which would be minimal.

Maybe you should pull a Dave Ramsey and assume 12% return on the maximum optimist side. :)

You never know, we could go through a massive bull market over the next 30 years.  Many times in the past people have predicted the market to "slow down" and it usually just adjusts and grows.  New technology gets invented and we continue to progress at an amazing rate.  I honestly think the next 30 years will result in some amazing changes.

[FIreDrill]

Well, there are alternative scenarios between a net 6% return on the borrowed money (maximum optimism) and "total market collapse" (maximum pessimism). I think other posters have made the case well in this and concurrent threads. There is a real chance that stock market returns will be below 4% for the time period an investor has.

A lot of the discussion about predicting future stock market returns tends to focus on "real" returns. And there are indeed some folks predicting real returns in the 4-5% over the next couple of decades.

For comparing against the mortgage one has to use nominal returns. Even assuming zero risk of increased inflation going forward, 4% nominal returns would imply something like 1.5% real returns.

This doesn't preclude getting to FI, of course. Most of us get to FI by earning a lot and saving a huge part of it. Investment returns are just icing on the cake in many cases (was in mine).

Investment returns may not have been important in you getting to FIRE. They're pretty essential to most in remaining FIRE. At 1.5% real returns, a 25x annual expenses stash would be exhausted in 31-32 years.

I think this is very fundamental and particularly important to remember.

Retiring at 30 with 25X annual spending saved relies upon positive market (or something) real returns to avoid running out of funds.  It is not a bad bet to make, but various folks think differently.  The typical Bogleheads poster would perhaps argue that the 30 year old is taking a big gamble that they may end up living on SS in old age.  That said, many of them will die with millions unspent.  Different choices.

This is where resilience and backup plans come in.  I dont buy the arguement that a sufficient backup plan is a statement like 'the markets always go up, so we are ok (source: backtesting)' or 'a crash is like the zombie apocalypse, so we are all hosed, anyway, hence  i need no plan (source: your favorite ostrich) '.  At least it is not enough for me.  My plan is to retire with a more conservative portfolio and well above 50X.  However, when i originally set my wealth goal, my minimum was at about 25x level.  I did not chose to stop then, so i am not very mustachian, i admit.  Those who do want to stop at the earliest possible moment likely should bet on leverage.  That epic thread about market_timer on bogleheads is a cautionary tale however.

These discussions have always fascinated me.  Some people look at a 30yr old trying to retire at 4% withdrawal rate and say they are taking a huge risk.  Although,  I'd argue there is risk if they continue working.  If they FIRE, they are taking on risk in a theoretical situation where market returns do not keep up with their spending.  On the other hand, if the continue working they are taking a guaranteed risk that they will lose that amount of time doing something they really don't want to do.

So FIRE and OMY syndrome really boil down to two different types of risk.

FIRE= theoretical risk
OMY= guaranteed risk

I am also looking at this assuming the imaginary 30yr really want's to quit and peruse other things.  If you love your job and would hate leave, that's a totally different scenario.

[Tyson]

Why not just save up 30x expenses and pay off your mortgage as part of FIRE?  Seems like it solves all the risk that's being discussed here.

[FIreDrill]

Why not just save up 30x expenses and pay off your mortgage as part of FIRE?  Seems like it solves all the risk that's being discussed here.

But then I'd have to work longer.... lol

[Tyson]

Why not just save up 30x expenses and pay off your mortgage as part of FIRE?  Seems like it solves all the risk that's being discussed here.

But then I'd have to work longer.... lol

Well, then people can make that call, between "work as little as possible" vs. "be as safe as possible".

[FIreDrill]

Why not just save up 30x expenses and pay off your mortgage as part of FIRE?  Seems like it solves all the risk that's being discussed here.

But then I'd have to work longer.... lol

Well, then people can make that call, between "work as little as possible" vs. "be as safe as possible".

I guess my point is you are not getting rid of risk by working longer.  You are negating a financial risk by taking on a guaranteed risk of losing a certain amount of time.

Whether it's worth it will be different for every individual situation.

[brooklynguy]

Why not just save up 30x expenses and pay off your mortgage as part of FIRE?  Seems like it solves all the risk that's being discussed here.

No, it removes some risks at the cost of leaving you more exposed to other risks, chief among them, in my view as it pertains to my own situation, the risk that you end up delaying retirement longer than necessary.  I'm also much more worried about the long-term impact of inflation on my retirement plan (which leveraged-investing-via-mortgage does a good job of protecting against) than I am about hitting a bad patch of market returns early in the sequence (which leveraged-investing-via-mortgage heightens your exposure to).

[boarder42]

Why not just save up 30x expenses and pay off your mortgage as part of FIRE?  Seems like it solves all the risk that's being discussed here.

But then I'd have to work longer.... lol

Well, then people can make that call, between "work as little as possible" vs. "be as safe as possible".

to be as safe as possible one must take the worst year of inflation and assume that happens forever.  then they must save up to cover all of their expected expenses plus inflation at the longest life a human has ever lived in cash ... then one would be dead before they got their and would not have retired at all.

[Tyson]

I'm just pointing out that "pay off the mortgage or invest in stocks" is not necessarily an either-or choice.  You could do both.

Optimal?  Depends on what 'optimal' means to you.  If it means 'retire as soon as possible', then it's not optimal. If it means 'have the least risk of running out of $$ and losing your home', then it is. 

[boarder42]

I'm just pointing out that "pay off the mortgage or invest in stocks" is not necessarily an either-or choice.  You could do both.

Optimal?  Depends on what 'optimal' means to you.  If it means 'retire as soon as possible', then it's not optimal. If it means 'have the least risk of running out of $$ and losing your home', then it is.

no b/c you can invest vs pay down your mortgage and satisfy both of those thats the common misconception being discussed here.

[AdrianC]

This doesn't preclude getting to FI, of course. Most of us get to FI by earning a lot and saving a huge part of it. Investment returns are just icing on the cake in many cases (was in mine).

Investment returns may not have been important in you getting to FIRE. They're pretty essential to most in remaining FIRE. At 1.5% real returns, a 25x annual expenses stash would be exhausted in 31-32 years.

Oh sure, we need a positive real return. But lasting 30 years is the basic 4% rule.

I think a lumpy 4% real return is a reasonable number for planning purposes. Say 5-6% nominal. 4% mortgage, 1-2% advantage using leverage. Yeah, it's worth a gamble for the folks 10 or 15 years away from FIRE. It's not the slam dunk that some posters make out, though. Not from here.

[boarder42]

This doesn't preclude getting to FI, of course. Most of us get to FI by earning a lot and saving a huge part of it. Investment returns are just icing on the cake in many cases (was in mine).

Investment returns may not have been important in you getting to FIRE. They're pretty essential to most in remaining FIRE. At 1.5% real returns, a 25x annual expenses stash would be exhausted in 31-32 years.

Oh sure, we need a positive real return. But lasting 30 years is the basic 4% rule.

I think a lumpy 4% real return is a reasonable number for planning purposes. Say 5-6% nominal. 4% mortgage, 1-2% advantage using leverage. Yeah, it's worth a gamble for the folks 10 or 15 years away from FIRE. It's not the slam dunk that some posters make out, though. Not from here.

its single handedly one of the easiest things you can choose to do to increase FIRE safety and decrease time to FIRE.  mowing your lawn = effort, making lunch = effort, moving closer to work= effort, hang drying clothes = effort, choosing to put money in vanguard vs a home = negligible mouse clicks.