Doesn't the arbitrage play require you to match your 30 year, 3.6% mortgage (which seems a bit high these days) against similar risk, fixed income assets (like Bonds, CDs, etc) in your "investment portolio"?
No.
You match the 30 year mortgage term with the same 30 year period of investment portfolio returns.
The risk in the mortgage is, as we keep saying, failing to make the monthly payments. Even if your "investment portfolio" is no more than the initial mortgage amount, you've got more than enough time to let the long-term compounding investment returns cover the monthly mortgage payment.
I would say that there is no doubt that a reasonable investment portfolio is going to return much more than a 2.5% mortgage over the next 30 years.