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Occasionally someone will question how valid my example is so I would like to get some more input about what people think and to see if there is an error in my reasoning, and if so to come up with a better simple example to explain the sequence of returns risk as it relates to paying off a mortgage or not.

Instead of hijacking that thread I am starting this new thread to discuss my example.

There is a wiki page on the sequence of returns risk and if there is a consensus about my example, or an improved version of it, then I may add a new example to that wiki page.

https://www.bogleheads.org/wiki/User:Le ... ed_example

Here is the relevant post from the prior thread;

I know it is very simplistic and sort of "back of the envelope calculation". A few comments about it;EnjoyIt wrote: ↑Tue Sep 03, 2019 8:51 amYou are assuming the $100k has to stay at $100k at the end of the loan payment. This is not what is happening. The $100k is meant to go down to $0 or slightly above it in an ideal situation.Watty wrote: ↑Tue Sep 03, 2019 8:29 amCould you give an example with some numbers to show how it is wrong?EnjoyIt wrote: ↑Tue Sep 03, 2019 8:18 amI keep seeing this thing above pop up and it is WRONG WRONG WRONG. The above assumes one will keep the $100k and pay off the mortgage from the earnings and not use up principal. This is not what any of the pay off mortgage threads talk about. I really wish people would stop posting this nonsense.Watty wrote: ↑Tue Sep 03, 2019 7:15 amIf you do not pay it off then you will have more sequence of returns risk. For example in rough numbers if you just kept a $100K mortgage and also put $100K into a separate investing account which you also pay a $500 a month mortgage out of then;

a) If you get unlucky and get a modest 10% decline in the portfolio the first year then it would be down to $90K

b) You would also need to pay the $500 a month mortgage($6,000) so your portfolio would be down to $84K

c) To break even the next year you would need to gain back the $16K and another $6,000 for the next years mortgage payments which is $22K. That would take a 25.6% return on the remaining $84K just to break even.

If you have a mortage the money to make the monthly payment needs to come from somewhere. If you just pay it out of your paycheck then in this example that would be $500 a month that you would not be able depositing into your savings.

An example is a person has $100k loan at 3% over 30 years. Payments are $421.60 a month. If for this example the person has an account holding $100k which is invested in a 3% tax-free fund (I know it doesn't exist, just an example,) by the end of the 30 year term the fund will be worth $0 and the loan will be paid off. This is where you start your argument. If returns are lower than 3% over 30 years then this was a bad decision. If returns are higher than 3% over 30 years then this was a good decision. This person would not expect to still have the $100k left over as your example suggests.

I am pretty sure you and I have gone through this at least once before yet you still keep posting your example. Now if you really want to figure out sequence of return risk then instead of creating a straw man example, plug it into fircalc and see what comes up and what is the risk of running out of money before the 30 years is up. News flash in my hypothetical example the historical chance of coming back with less than started is 0%

EDIT: The results from FIRECalc on my hypothetical example is:

Here is how your portfolio would have fared in each of the 119 cycles. The lowest and highest portfolio balance at the end of your retirement was $100,000 to $905,355, with an average at the end of $478,683.

1) It does not take into account that you would also be paying down the home equity some.

2) It does not take taxes or inflation into account.

3) A 30 year $100K mortage at 4% would have a payment of $477 so the $500 payment figure it uses is a bit high.

4) To break even the second year you would not need to bring the portfolio all the way back to $100K since you would be paying down the loan. I check an amortization schedule and a 4% 30 year loan would have a remaining balance of $96,699 after two years.

This would all through the example off some but since it is only looking at a year or two I don't think that the difference would be enough a problem in an example that I tried to keep about a paragraph long.

On the response

1) The response makes a very valid point about how going down to a zero balance would be OK after 30 years, but my example was not for 30 years so that is a modest difference over 2 years.

2) I do not use Firecalc much but when I have I have noticed that it seems to have a bug in it when it says something like, "The lowest and highest portfolio balance at the end of your retirement was $100,000 to $905,355, ...." The $100K figure seems to be in error since it seems to just uses your beginning balance in some situations. I have noticed when I have used Firecalc before.

3) I just looked at 2 years in my example. The Firecalc example used 30 years which might apply to some people but few people actually keep a 30 year mortgage for the full 30 years. As I recall the average length of time for a 30 year mortgage is more like 7 to 10 years. It would be interesting to see what Firecalc(or one of the similar web sites) says if it was run for just 1, 2 or 7 years.

If anyone can see a way to improve my example, focusing on the first year or two, I would sure like to hear any suggestions.