Thanks for the math work Clarkfan, my numbers are pretty well aligned.

To nerd out on the #s I ran the math assuming you couldn’t get a 0% down $1mn mortgage. With 20% down and investing $800k in stocks at 10%, 7.5% mortgage rate (P&I only payment of $5,594/mo) and no tax considerations I get $14.0mn portfolio value in 30 years putting 20% down on the house and $11.5mn for paying cash for the house and investing $5,594/mo in the market. **Edit- if you have a 30 year timeline for retirement it may make sense to carry the mortgage, but most people here are shooting for much faster than that, which makes the narrower range of returns distribution of the no mortgage portfolio pretty attractive. **

In your example, there is a $2.5 million benefit to holding the mortgage. $2.5 million is real money. Why is it smart to walk away from that? Especially since you have to take large uncompensated risk to do so?

And disagree with the part in bold. You can carry a mortgage in retirement no problem. I do, and so do lots of people here. The key number is have liquid assets equal to 25 times expenses (or whatever number you decide). While no mortgage lowers your expenses, it lowers your liquid assets too.

I've run the numbers a bunch of times for myself and won't do it again here, but I recommend modifying your calculations to match most people's choices (and the title of this thread): Namely, once you have a mortgage, do you pay extra each month, or do you invest the surplus?

So, instead of the no mortgage option being investing $6,000/month for 30 years, a more realistic scenario for most people would be making the mortgage payment of $6K/month, plus putting say, an extra $2000/month towards the mortgage. The option of holding a mortgage would be simply investing the extra $2000 month for 30 years.

What happens of course, is the person paying extra eventually retires the mortgage. Let's say around year 15-ish. At that point, they can invest the full $8000/month (the original $6K payment plus the $2K extra) and the mortgage holder continues to invest $2000/month. But thanks to the power of compounding the mortgage holder is so far ahead at year 15 that by the end of the 30 year period, the mortgage holder will still has a substantially higher final portfolio value.

By all means, run the numbers yourself and plug your own assumptions. I did a deep dive into this years ago (when interest rates were lower it should be noted) and paying down the mortgage never penciled out in any scenario I looked at. To be clear, there are specific situations where it is important to lower income. Qualifying for ACA subsidies for example. Those are special cases and not the general result.

One final thought. One thing we didn't talk about but needs to be considered is the effect of inflation. If we assume a modest 3.5% inflation rate, by the end of year 15 our $6000 payment will be the equivalent of $3500 today. In other words, by paying extra we're using fully valued dollars today to save smaller valued dollars in the future. The payment is becoming easier and easier to make over time, which means there is less and less practical benefit to paying it off early.