Towards a Unifying Theory of Math is Math and Behavioral Economics

[sol]

If you backtest it using a tool like cFIREsim, you will see that there were a handful of historical cases where a leveraged-investing-via-mortgage plan would have failed even using a 4% mortgage loan

That's not what I've found, but there could be differences in methodology.  Because the mortgage is a fixed dollar amount per month instead of being inflation adjusted, the usual SWR math doesn't quite work.  What's the lowest total 30 year return for various portfolio compositions?  This site, for example, cites the lowest 35 year rolling return (starting 1906) as 6.1% annualized.  Maybe the last five years make a big difference?

[aceyou]

Math teacher chiming in with my two cents.  The paying off the mortgage early thing is something I've put a lot of thought into. 

The general thought is that math says keep the mortgage...because math, but often behavioral theory says pay if off...because emotions.  My thought is that the math isn't as clear cut as people like boarder suggest (disclaimer: boarder is one of my favorite posters, and I respect his opinions).  But here's why I don't think it's so clear cut:

Mathematically, you have to take into account variance.  For example, investment A and B both have the same expectation, but B has higher variance, the A is mathematically the better investment. 

Paying off a mortgage lowers your long term net worth expectation(a bad thing), but it also reduces your variance(a good thing).  Boarder's strategy of keeping the mortgage gives you a higher ceiling(increased expectation), but it also gives you a lower floor due to increased variance. 

Because a person like Boarder (and most other's on this site who follow his strategy) are highly skilled individuals, I'm completely confident that they could roll with the punches if a market crash presents itself.  They are some of the last people I'd worry about.  But to be fair, a person who pays down their mortgage earlier has an easier punch to absorb if that same event happened to them. 

Disclosure:  I'm taking the middle road regarding the mortgage.  I have a 15 year note, and don't make extra payments.  I put about 70k/year towards investments, and about 14,000/year towards the mortgage(9k towards principal, 5k to interest).  So in practice, I am probably more like boarder and those who value investing over owning the home ASAP.  But I don't think my decision is as mathematically superior of a decision as boarder and others think.  Both sides make a valid case.

[brooklynguy]

This site, for example, cites the lowest 35 year rolling return (starting 1906) as 6.1% annualized.  Maybe the last five years make a big difference?

The issue is that because a mortgage loan has required scheduled principal repayments, leveraged-investing-via-mortgage could fail even if the annualized investment return over the life of the mortgage loan exceeds the mortgage loan's interest rate (in the same way that sequence of returns matters for a retiree's spending plan).  If there were no amortization, then it would be as simple as comparing the annualized investment return to the mortgage loan's interest rate (ignoring tax consequences and the like).

[boarder42]

And as @NoraLenderbee keeps missing in the above post while there may be additional security in paying off a house entirely.(which the chance this is more secure is smaller than the chance it's less secure). The act of slowly paying down a mortgage with additional principal payments is less secure than investing over this time.

"Security" is just one reason that some people have cited. There are other reasons. As I said,  there are things that people value more than the highest possible ROI. You keep going as if the only conceivable correct goal was to maximize ROI.

You've mentioned being a cafeteria Mustachian in other threads. You have a boat. Someone else has a paid-off mortgage. Neither is the most frugal option. Having a boat is no big deal, but paying off a mortgage is a terrible mistake that must be denounced in thread after thread?

Correct it should be just like owning a boat should be if there were people here asking if they should buy a boat or sell their boat.

I didn't say having a boat was no big deal I said it has no place for promotion here. Just like a mortgage. But thanks again for showing yet another example and comparison as to where that thread belongs.

It's actually much more detrimental than owning a boat the way I do or the cost of my house or my commute. But unless you do the math you never know.

So now that I think we're on the same page this is a shitty unmustachian thing to do. Do you think you could go ahead and work on moving that paydown club to the antimustachian wall of shame and comedy.

[boarder42]

This site, for example, cites the lowest 35 year rolling return (starting 1906) as 6.1% annualized.  Maybe the last five years make a big difference?

The issue is that because a mortgage loan has required scheduled principal repayments, leveraged-investing-via-mortgage could fail even if the annualized investment return over the life of the mortgage loan exceeds the mortgage loan's interest rate (in the same way that sequence of returns matters for a retiree's spending plan).  If there were no amortization, then it would be as simple as comparing the annualized investment return to the mortgage loan's interest rate (ignoring tax consequences and the like).

Correct you can find specific paydown periods where it wins. But your talking 1% or less of the time a target that's almost impossible to hit. 

I mean you're talking about having to hit the perfect storm of paydown start year and how many years it takes you to pay it off before you can start dumping in the difference. 1% is probably incredibly generous.

[aspiringnomad]

Math teacher chiming in with my two cents.  The paying off the mortgage early thing is something I've put a lot of thought into. 

The general thought is that math says keep the mortgage...because math, but often behavioral theory says pay if off...because emotions.  My thought is that the math isn't as clear cut as people like boarder suggest (disclaimer: boarder is one of my favorite posters, and I respect his opinions).  But here's why I don't think it's so clear cut:

Mathematically, you have to take into account variance.  For example, investment A and B both have the same expectation, but B has higher variance, the A is mathematically the better investment. 

Paying off a mortgage lowers your long term net worth expectation(a bad thing), but it also reduces your variance(a good thing).  Boarder's strategy of keeping the mortgage gives you a higher ceiling(increased expectation), but it also gives you a lower floor due to increased variance. 

Because a person like Boarder (and most other's on this site who follow his strategy) are highly skilled individuals, I'm completely confident that they could roll with the punches if a market crash presents itself.  They are some of the last people I'd worry about.  But to be fair, a person who pays down their mortgage earlier has an easier punch to absorb if that same event happened to them. 

Disclosure:  I'm taking the middle road regarding the mortgage.  I have a 15 year note, and don't make extra payments.  I put about 70k/year towards investments, and about 14,000/year towards the mortgage(9k towards principal, 5k to interest).  So in practice, I am probably more like boarder and those who value investing over owning the home ASAP.  But I don't think my decision is as mathematically superior of a decision as boarder and others think.  Both sides make a valid case.

I think that variance is only significant in the shorter term. Over a 30 year period, it narrows considerably going by historical data, and the expected outcomes all sit above a 4% annual return.

FWIW, I also have a 15 year mortgage at a low 2.75 rate, refinanced in late 2012. But with the benefit of hindsight and a better understanding of the math, a 30 year mortgage and plowing the difference into the market would have left me with substantially more money by this point. I lose zero sleep over it, but I’m also certainly not going to entertain something as irrational as making extra payments on the note.

You’re comparing apples to oranges if you argue that the emotional security you feel from making that suboptimal paydown choice is akin to people deciding to take a vacation or to spend anything less than the bare minimum in life. A decision about what to consume is patently different from a decision about how to pay for your consumption. If you can’t see that, you’re bringing too much emotion to the discussion.

[aceyou]

Thank you for your reply, I've been wanting to discuss this with other smart people to see if I can poke holes in my thoughts.  I'm still sticking to my theory, but I'm willing to be persuaded!

I think that variance is only significant in the shorter term. Over a 30 year period, it narrows considerably going by historical data, and the expected outcomes all sit above a 4% annual return.

The variance certainly lessens over time as you've said.  But a person truly utilizing this strategy would get a 30 year note, and after 10 years on a 30 year note, you still owe about 75% of what you did originally.  So I'd argue that while you are right, the "short term" lasts for a little while.  And the short term is what's important anyway, because in all historical cases where portfolios run into trouble, it's because a negative event occurs in the first 5-10 years.  So, the strategy to maintain the mortgage would just exacerbate an event like that. 

FWIW, I also have a 15 year mortgage at a low 2.75 rate, refinanced in late 2012. But with the benefit of hindsight and a better understanding of the math, a 30 year mortgage and plowing the difference into the market would have left me with substantially more money by this point. I lose zero sleep over it, but I’m also certainly not going to entertain something as irrational as making extra payments on the note.

Right.  You and I are basically identical with how we have handled our mortgages, including the timeframe.  And you are right that we'd have substantially more money...most times out of 10, that's what would happen.  But the key is that you said hindsight.  We know that between 2012 and 2018 we went through a period of insane market growth...this was not one of those bad periods.  Variance disappears if you have a crystal ball (hindsight).

I could use hindsight and say that if you'd have retired in 2007 using the 4% rule and a mortgage with 30 years to go, then you'd have been worse for wear.  For 5 years you'd have been depleting an already depressed stache, while making payments on a home that is severely underwater.  By the time the boom times occurred, you'd have had very little of your stache remaining.  In this case, a person who'd have retired with a smaller stache and no mortgage (aka far lower spending) would have came through in a stronger position to capitalize on the subsequent bull run.     

You’re comparing apples to oranges if you argue that the emotional security you feel from making that suboptimal paydown choice is akin to people deciding to take a vacation or to spend anything less than the bare minimum in life. A decision about what to consume is patently different from a decision about how to pay for your consumption. If you can’t see that, you’re bringing too much emotion to the discussion.

Good point and I agree, but I didn't say this...maybe someone else used this analogy in an earlier comment? :)

[boarder42]

Yes cherry picking a start year at a market peak and the top of a bubble in hindsight can achieve better results. But the odds of hitting that are miniscule.

[aspiringnomad]

Thank you for your reply, I've been wanting to discuss this with other smart people to see if I can poke holes in my thoughts.  I'm still sticking to my theory, but I'm willing to be persuaded!

I think that variance is only significant in the shorter term. Over a 30 year period, it narrows considerably going by historical data, and the expected outcomes all sit above a 4% annual return.

The variance certainly lessens over time as you've said.  But a person truly utilizing this strategy would get a 30 year note, and after 10 years on a 30 year note, you still owe about 75% of what you did originally.  So I'd argue that while you are right, the "short term" lasts for a little while.  And the short term is what's important anyway, because in all historical cases where portfolios run into trouble, it's because a negative event occurs in the first 5-10 years.  So, the strategy to maintain the mortgage would just exacerbate an event like that.

I used "short term" as shorthand, but I really meant short-to-medium term. Portfolios running into trouble due to sequence of return risk is only an issue at retirement. I would agree that the calculation changes for those retiring and relying on their portfolio to fund expenses, specifically because of that risk.

FWIW, I also have a 15 year mortgage at a low 2.75 rate, refinanced in late 2012. But with the benefit of hindsight and a better understanding of the math, a 30 year mortgage and plowing the difference into the market would have left me with substantially more money by this point. I lose zero sleep over it, but I’m also certainly not going to entertain something as irrational as making extra payments on the note.

Right.  You and I are basically identical with how we have handled our mortgages, including the timeframe.  And you are right that we'd have substantially more money...most times out of 10, that's what would happen.  But the key is that you said hindsight.  We know that between 2012 and 2018 we went through a period of insane market growth...this was not one of those bad periods.  Variance disappears if you have a crystal ball (hindsight).

I could use hindsight and say that if you'd have retired in 2007 using the 4% rule and a mortgage with 30 years to go, then you'd have been worse for wear.  For 5 years you'd have been depleting an already depressed stache, while making payments on a home that is severely underwater.  By the time the boom times occurred, you'd have had very little of your stache remaining.  In this case, a person who'd have retired with a smaller stache and no mortgage (aka far lower spending) would have came through in a stronger position to capitalize on the subsequent bull run.

I realize that hindsight from that particular time frame is not really helpful, just pointing out that events unfolded as empirical data suggested they would. It's also hard to argue that a basket of companies extracting income from all corners of the world is less safe than plowing money into an illiquid asset based in one location and subject to all the economic or catastrophic vagaries that might befall that location. I know you haven't argued that, just adding this to the broader conversation.

As you note, over the short term, anything can and has happened. But we tend to invest for the long term here, and the 30-year mortgage product available to American homeowners gives us a useful long term period to test that empirically.

You’re comparing apples to oranges if you argue that the emotional security you feel from making that suboptimal paydown choice is akin to people deciding to take a vacation or to spend anything less than the bare minimum in life. A decision about what to consume is patently different from a decision about how to pay for your consumption. If you can’t see that, you’re bringing too much emotion to the discussion.

Good point and I agree, but I didn't say this...maybe someone else used this analogy in an earlier comment? :)

Yeah, sorry. This wasn't directed at you and I should have been more clear about that.

[Cycling Stache]

what happens if you stop paying after 26 years?

If you walk away from a 30 year mortgage after 29.9 years, you get nothing.  The bank owns the house.  You own nothing.  You defaulted on a 30 year contract, and the house is the collateral.  The bank repossesses it and you're out on your ass.

Just so the thread is clear, this is incorrect.  The house is security for the loan.  If you fail to pay the loan, the bank can force the sale of the home (foreclosure) in order to satisfy the remaining amount owed on the loan.  But after that--and after whatever costs are incurred throughout the foreclosure process--the remaining equity goes to the homeowner.

I wanted to update this thread because of the flurry of new threads questioning investments decisions in light of the recent drop in the market.  If the market continues to fall, we might get some insight into how people actually handle it versus how they thought they would.  It will be interesting to see if people can "stay rational."

[boarder42]

what happens if you stop paying after 26 years?

If you walk away from a 30 year mortgage after 29.9 years, you get nothing.  The bank owns the house.  You own nothing.  You defaulted on a 30 year contract, and the house is the collateral.  The bank repossesses it and you're out on your ass.

Just so the thread is clear, this is incorrect.  The house is security for the loan.  If you fail to pay the loan, the bank can force the sale of the home (foreclosure) in order to satisfy the remaining amount owed on the loan.  But after that--and after whatever costs are incurred throughout the foreclosure process--the remaining equity goes to the homeowner.

I wanted to update this thread because of the flurry of new threads questioning investments decisions in light of the recent drop in the market.  If the market continues to fall, we might get some insight into how people actually handle it versus how they thought they would.  It will be interesting to see if people can "stay rational."

i have no issues staying rational - but i may change my AA as we further discuss the 150 year history of everything - as there appears to be a strong case for 50% or higher REIT allocation - coupled with small caps it could be a very lucrative work time cutting endeavor that allows for higher SWRs. its just a coincednce this topic was brought up b/c the paper was published very recently (4 months ago)  and now is coinciding with a pull back in the market - i likely will change nothing on my accumulation plan but may alter my post FIRE plans - as my REIT options in my 401k are too limited