Your forgetting about the return you could be getting. If your mortgage is 6% and your making 7% then keeping a mortgage is a good idea. The other option is to get a 7 year interest only loan with zero or 3% down and walk away if you get under water. With 1+ million in the bank you can trash your credit ratting with little issue so let your bank take the risks.
PS: One great option is to get US gov bonds that get ~2% over inflation for 10+ years which makes them really safe. (https://www.bernstein.com/public/story.aspx?cid=466&nid=...) Ok, you are still taking a currency risk if your living outside the US but that's fairly safe.
Edit: Think of the first 1 million as 40k inflation adjusted every year for the rest of your life and only take risks when you need to until you have more money to live off of than you need. Risk is something you don't want and buying a house is risk.
With the interest only loan, wouldn't you need to make sure that you had non-recourse debt, or that the property was bought with a business entity that protected your 2 million in case of default? Are most mortgages (I'm specifically thinking in the U.S.) non-recourse in the sense that the property is the only collateral? Or is there still a way for the bank to come after your personal assets? I'd want to be 100% sure of the answers to these questions before betting on being able to walk away if the house loses value.
Most private mortgages in the USA use the house as the only collateral, however if you put less than 20% down most banks require some form of PMI to reduce their risk. This is a large part of why the housing bust has hit banks so hard, also many of the company's selling PMI went bust so the coverage became worthless.
If you invest and get 7% interest, after taxes you may get 1-2%. If you have to get 12%+ things look a lot different. Also, investing is risky, debt anchors you and keeps you from trying new things. At that point, you're gambling your house away. That behaviour is exactly what caused the Great Depression.
Government bonds are a terrible investment strategy. You may barely hold out against inflation (the next 5 years I vey much doubt that will happen) but there's better vehicles. The stock market, for all that it's fallen, historically speaking has never had any 10 year windows that it's shrunk. It will rebound.
If you're going to get a mortgage, it should be a 15yr, fixed-rate.
If your interest is tax deductible then you are only paying taxes on the 1% that's above the interest.
Government bonds are a hedge, I would still have lot's of stocks, but the goal is to avoid needing to sell stock when the market is down. Normal bonds have higher interest rate until inflation hits or the company goes bankrupt at which point you might not get your principle back.
Owning your home ties you to that location and selling property can be a major issue. If you are living off your savings then having a single investment with 30% of you money tied down is a huge risk. If your single and there is a 20% chance you will move in the next 10 years buying a house is a bad investment but feel free to run the numbers in your area including: tax, the high cost of buying and selling, the loss of liquidity, maintenance costs, appliances etc.
1+ million in the bank you can trash your credit ratting with little issue so let your bank take the risks
Actually, with $1 million in the bank, if you walk away from the mortgage, you bet your ass the bank will come after you to collect on what they can't get from the value of the home. It's going to be hard to declare bankruptcy when you have that kind of cash lying around.
PS: One great option is to get US gov bonds that get ~2% over inflation for 10+ years which makes them really safe. (https://www.bernstein.com/public/story.aspx?cid=466&nid=...) Ok, you are still taking a currency risk if your living outside the US but that's fairly safe.
Edit: Think of the first 1 million as 40k inflation adjusted every year for the rest of your life and only take risks when you need to until you have more money to live off of than you need. Risk is something you don't want and buying a house is risk.