Another thread on mortgage payoff vs not

[FIPurpose]

Ok I don't mean to make this into another thread on debating which comes out with more money. But I had a thought experiment: If the most perilous time in retirement are the first 10 years, then does the increased cashflow requirements of a mortgage hurt or help your retirement?

Assumptions:
30 year retirement
you are withdrawing all your income from your investments

To do this I used the standard 40000k spending with 1MM 75/25 portfolio to represent the paid off mortgage scenario

The other was assuming that we started our retirement 15 years into a 240k mortgage with 15 years left to go. So I adjusted the portfolio with 1.16MM (the remaining amount of the mortgage) and added non-inflation adjusted spending per year of 14k for the first 15 years retirement.

What were the results? (These are ending portfolio values listed in today's dollars)

                      Paid off Mortgage | Not Paid off | Difference
Success Rate                92.11%  |  92.98%      |  <1%
Median Port.                 1.33MM  |  1.5MM       |  ~11%
Std Dev.                       1.66MM  |  1.8MM       |  ~8%
Avg.                             1.88MM  |  2MM          |    6%


While I expected not paying off the mortgage to result in better numbers, the numbers actually aren't that much better. I'd actually go so far as to say they are negligible.

While not paying off the mortgage after retirement results in higher average, adjusting for the risk of the decision they come out with similar ratios:

Median / Std Deviation: 0.8 vs .833   (not paying mortgage has a slightly better risk adjusted median)
Avg.    / Std Deviation: 1.13 vs 1.11  (paying off the mortgage was slightly better risk adjusted average)


Conclusions:

It seems that the advantage of not paying off your mortgage is mostly nullified by the increased sequence of returns risk. On a risk adjusted return basis both decisions seem to provide an equal return.

Both portfolios failed around the 70's high inflation period. The tail end of a mortgage was not enough to prevent portfolio failure.

Perhaps both decisions are equally valid. There are some Mustachians that are allured by the increased portfolio potential and value they provide through the increased risk taking. Others prefer to stop trying to win and want the lowered sequence of returns risk.

If you are not withdrawing from your portfolio, and therefor not subject to sequence of return risks, then this post is not about you. Keep your mortgage.

[kenmoremmm]

(grabs popcorn...)

[moof]

Not stated is your assumed interest rate on the mortgage.  Somewhere around a ~5-6% interest rate tips the scales from being better to wait to being better to pay it off ASAP.  In the middle it basically stops mattering.  There are also a lot of tax and withdrawal strategy implications that are often too individualized to wrap up in a single statement

My digging for my own scenario with a 3% interest rate on what will be about 140k remaining for about the last 6 years of my 15 year mortgage showed a small improvement in success rate, or a small increase in my safe withdrawal rate.  It amounted to the equivalent of getting to retire roughly 2 months earlier as another metric.  Not huge, but I'll take it and not look back.

I completely sympathize with those who find it re-assuring to have your house paid off.  Having a home base with no strings attached gives much better flexibility to shut down expenses if some sort of calamity happens such as losing a job or getting an illness that prevents working before being FIRE.

[FIPurpose]

Not stated is your assumed interest rate on the mortgage.  Somewhere around a ~5-6% interest rate tips the scales from being better to wait to being better to pay it off ASAP.  In the middle it basically stops mattering.  There are also a lot of tax and withdrawal strategy implications that are often too individualized to wrap up in a single statement

My digging for my own scenario with a 3% interest rate on what will be about 140k remaining for about the last 6 years of my 15 year mortgage showed a small improvement in success rate, or a small increase in my safe withdrawal rate.  It amounted to the equivalent of getting to retire roughly 2 months earlier as another metric.  Not huge, but I'll take it and not look back.

I completely sympathize with those who find it re-assuring to have your house paid off.  Having a home base with no strings attached gives much better flexibility to shut down expenses if some sort of calamity happens such as losing a job or getting an illness that prevents working before being FIRE.

For the mortgage payments I assumed about a 4% mortgage. I did some rounding of numbers. So to look at different scenarios with a bit more precise numbers:

(with a 30 year mortgage and 15 years remaining, principal + interest only)

3% - 147k left, annual payment - $12,150

                      Paid off Mortgage | Not Paid off
Success Rate                92.11%  |  92.98%     
Median Port.                 1.33MM  |  1.5MM     
Std Dev.                       1.66MM  |  1.8MM     
Avg.                             1.88MM  |  2.06MM         

4% - 155k left, annual payment - $13,750

                      Paid off Mortgage | Not Paid off
Success Rate                92.11%  |  92.98%     
Median Port.                 1.33MM  |  1.48MM       
Std Dev.                       1.66MM  |  1.796MM     
Avg.                             1.88MM  |  2.02MM         

5% - 163k left, annual payment - $15,500

                      Paid off Mortgage | Not Paid off
Success Rate                92.11%  |  91.23%     
Median Port.                 1.45MM  |  1.45MM     
Std Dev.                       1.66MM  |  1.79MM     
Avg.                             1.88MM  |  1.98MM     

6% - 170k left, annual payment - $17,300

                      Paid off Mortgage | Not Paid off
Success Rate                92.11%  |  90.35%
Median Port.                 1.33MM  |  1.41MM
Std Dev.                       1.66MM  |  1.78MM
Avg.                             1.88MM  |  1.93MM

So the scale for these back tests shows that it does the scale tips around 5-6% but what is the return on risk?

                      Paid off mortgage |    3%    |     4%    |    5%    |    6%    |
coefficient var.         .88                   .87           .89        .9            .92


For comparison the vanguard total bond fund 15 return/ std dev is .76 and the total market fund is 1.3.

At least in my eyes, when people are looking at fire calcs, they far too often look at the final number or the small fluctuations in survivability rate. Here the variation on a risk basis isn't all that different. It's all within an extremely tight window.

If you change the portfolio from 75/25 to 90/10 the back test reduces the 6% mortgage down to .88 coefficient. This decision doesn't seem to change the numbers much if at all. For people about to FIRE, a reduction in risk for the same outcome seems to be a reasonable decision.

[moof]

More power to you fellah.

[Telecaster]

For comparison the vanguard total bond fund 15 return/ std dev is .76 and the total market fund is 1.3.

At least in my eyes, when people are looking at fire calcs, they far too often look at the final number or the small fluctuations in survivability rate. Here the variation on a risk basis isn't all that different. It's all within an extremely tight window.

If you change the portfolio from 75/25 to 90/10 the back test reduces the 6% mortgage down to .88 coefficient. This decision doesn't seem to change the numbers much if at all. For people about to FIRE, a reduction in risk for the same outcome seems to be a reasonable decision.

This statement is going to be controversial, but I don't think return/std dev is a useful metric.  A lot of people, smart ones even, use it but it doesn't give much actionable information, IMO.   Stocks are volatile, but they are mostly volatile in an upwards direction.   That increases the standard deviation and lowers the risk adjusted return...but if your portfolio value is steadily increasing in value, how is your risk also increasing?   

The thing we're all concerned about is the SOS risk, which is to say downward, not upward, volatility early in the retirement years.  The Success Rate metric tells us that.   In the 4% mortgage scenario, the Success Rate is virtually identical for either POYM or DPOYM.   So the risk we care about most (or at least I care about most) is the same either way.  In words, you are not really reducing "risk."   You are reducing an arbitrary measure of risk, but I don't care about arbitrary metrics.   

On the flip side, the final DPOYM value is higher by a non-trivial amount.    POYM reduces upside, with no discernible protection from SOS risk.   

[FIPurpose]

For comparison the vanguard total bond fund 15 return/ std dev is .76 and the total market fund is 1.3.

At least in my eyes, when people are looking at fire calcs, they far too often look at the final number or the small fluctuations in survivability rate. Here the variation on a risk basis isn't all that different. It's all within an extremely tight window.

If you change the portfolio from 75/25 to 90/10 the back test reduces the 6% mortgage down to .88 coefficient. This decision doesn't seem to change the numbers much if at all. For people about to FIRE, a reduction in risk for the same outcome seems to be a reasonable decision.

This statement is going to be controversial, but I don't think return/std dev is a useful metric.  A lot of people, smart ones even, use it but it doesn't give much actionable information, IMO.   Stocks are volatile, but they are mostly volatile in an upwards direction.   That increases the standard deviation and lowers the risk adjusted return...but if your portfolio value is steadily increasing in value, how is your risk also increasing?   

The thing we're all concerned about is the SOS risk, which is to say downward, not upward, volatility early in the retirement years.  The Success Rate metric tells us that.   In the 4% mortgage scenario, the Success Rate is virtually identical for either POYM or DPOYM.   So the risk we care about most (or at least I care about most) is the same either way.  In words, you are not really reducing "risk."   You are reducing an arbitrary measure of risk, but I don't care about arbitrary metrics.   

On the flip side, the final DPOYM value is higher by a non-trivial amount.    POYM reduces upside, with no discernible protection from SOS risk.

I'll agree that risk is only one number. Though I think this post does say something about the large number of people on this forum who think that people who pay off their mortgage are taking on additional risk or somehow making the mathematically worse decision.

You can look at the median/ std. dev. and you would see a similar pattern. The two choices don't deviate much. While stocks generally move in an upward direction (Over a 10-20 year cycle) In retirement, it's the 1-year returns that matter. Comparing the general trend of the stock market to a withdraw strategy is folly. The way to measure that is through volatility. You can have a stock market that rises 200% in a 10 year time frame and still have a retirement failure.

Either way, a mortgage that only makes up about 10% of your portfolio isn't going to steer the ship much one way or the other. It's not detrimental, it's not obviously riskier nor going to save your portfolio from inflation. The increased volatility in stocks during the withdraw phase negates most of the additional returns that the market would provide over that same period. Both decisions to me seem to be about a wash towards portfolio survival.

I would suggest some of what Portfolio Charts writes on this topic: https://portfoliocharts.com/2019/07/23/how-to-study-portfolios-when-the-data-is-full-of-bubbles/ We have to be careful on how we view "average" portfolio results. Stock bubbles can skew certain "ending portfolio" averages higher than we should reasonably expect our real life to play out. (How many people hit their FIRE number and retire at the bottom of a stock cycle?)

[Telecaster]

I'll agree that risk is only one number. Though I think this post does say something about the large number of people on this forum who think that people who pay off their mortgage are taking on additional risk or somehow making the mathematically worse decision.

Didn't your post show it is mathematically worse?  The failure rate is virtually identical, yet the POYM final portfolio value is lower by a non-trivial number of dollars.   Like fund a scholarship or buy an airplane amount of dollars.  Given that up for no benefit I think falls into the "worse" category. 

[FIPurpose]

I'll agree that risk is only one number. Though I think this post does say something about the large number of people on this forum who think that people who pay off their mortgage are taking on additional risk or somehow making the mathematically worse decision.

Didn't your post show it is mathematically worse?  The failure rate is virtually identical, yet the POYM final portfolio value is lower by a non-trivial number of dollars.   Like fund a scholarship or buy an airplane amount of dollars.  Given that up for no benefit I think falls into the "worse" category.

For the 5% scenario paying off the mortgage, the the average value represents a CAGR of 2.13%, for keeping the mortgage: 1.79% The portfolio growth difference is 0.34% CAGR.

I tried my best to figure out what the p value is between paying off the mortgage or not (with the 5% interest scenario). I got p=0.65. Someone can  double check my work on that, but in other words, the difference between the 2 is not statistically significant between each other.