You went from having actual bonds- negative bond (aka mortgage) = "total bonds"
just having bonds=bonds.
This has likely (depending on the relative size), substantially increased your bond holdings.
Therefore, you can decrease your bonds, and increase stocks.
Now, this is to the extent that
1)It does not increase your capitulation risk
2)that it affects the riskness of your portfolio significantly.
The whole mortgage as a negative bond is one way of looking at it, but a mortgage is not in fact a negative bond. One does not rebalance the mortgage, and even with the mortgage, one can still rebalance the with FULL amount of the bonds present.
ie, if you have 100K mortage, and 100K bonds, you have ZERO net bonds to one way of looking at it..... BUT, if you have 100K morgage, 100K stocks, and 100K bonds, in a 50/50 stock bond split, and the stock market drops 50 percent, well, you can STILL rebalance with the bonds, buy buying stocks low to the tune of 25K, and selling the bonds(likely high if in a bond fund, or non ibond, as price would likely go up) high to the tune of 25K, resulting in
75K bonds, 75 K stock...... this even though, you have "zero net bonds" since 100K mortage=-100K bond. -100K+actual 100K bond= zero....
So, you still have bonds in reality. You can still rebalance.
so..... the answer is yes, it does influence my way of thinking about risk. To me, it means any given portfolio is LESS RISKY, than a portfolio with a mortgage.
By owning home, you have less need of cash flow, your minimum level you need is easier to achieve safely, therefor can take more risk. Also, house worth is usually less volatile than the stock market. A house is bond like to some extent (a zero return bond, a house can be considered about equal to an ibonds zero real return, not here, do not conflate it, I am talking about the house equity ONLY=ibond like, ie both home and current ibonds expectantly hold thier real value..... I am not talking about the mortage, the mortage is more akin to a bond with actual return by paying it off, ie a mortage =negative bond)
Home ownership affects risk qualitatively, not quantitatively that I can ascertain.
Net Worth is the big picture..... Your asset allocation is just one piece of that.
Its risk to NET WORTH, that you really care about. In the end, its net worth you can buy snickers bars, medical care, etc. with.
The money you put into your home, does not fall into a conceptual black hole.
2)Another way of looking at this is leverage.
A mortage is leverage
Leverage = risk.
No leverage = less risk.
So, by that rubric, paying off your mortage, has decreased your risk. Qualitatively, then, you can increase your stock risk.... and still have the same risk you had before to some extent at least.