Comment by Tcepsa

Net worth isn't equity - mortgage + 401k. Net worth is assets - liabilities. Equity is not an asset; the house is. So is the 401k. The mortgage is a liability. So Joe's net worth is 100k (IRA) + 300k (value of house) - 200k (mortgage) = 200k positive net worth.

(Another way of thinking about equity, specifically, is it is the real estate contribution to net worth, because it is what is left when you subtract the real estate liability (mortgage) from the real estate asset (value of house). That's why you shouldn't subtract the mortgage from the equity: equity is what's left after you've already subtracted the mortgage.)

(Edit: Adjusted sign in first equation to subtract mortgage. It's probably more technically accurate to keep it as addition and consider the mortgage to be a negative value, but I believe it's more straightforward and intuitive for most people as it is now represented.)