I just ran a scenario on FIRECalc where you used a starting portfolio of $150,000 invested entirely in equities to amortize a 15 year, $150,000 mortgage (annual payments of $15K non-inflation adjusted at 5.75%). The success rate is 61% with a terminal value range from $-178,592 to $444,523, and an average of $66,850.
Although the transaction has a positive expected return ($66,850 non-inflation adjusted), it amounts to a compound annual return of 2.5% and has considerable volatility with a terminal value range of $600K. I imagine the monthly amortization required by most mortgages would lower the expected return. To my surprise, a 30 year mortgage resulted in only slightly higher success rate of 62%, and lower average annual expected returns of 1.7%. According to FIRECalc the same scenario (using a 30/yr mortgage and 6% interest rate) resulted in a terminal value of $-852,281 to $1,007,014, with an average of $100,680.
So unless I calculated this incorrectly (which is completely possible), holding the mortgage and investing in equities is a marginally positive NPV transaction which carries a large amount of risk.
I think I'll pay down the mortgage.