This sounds like we have done. The "lender" is yourself, you are borrowing money against your own funds. It a Line of credit against the money in your account. So it's a matter of whether your brokerage will do a LOC on your assets there. I had a large enough account at Etrade, and they were able to do the LOC for me, at a lower than mortgage rate (2.8%-something?). You just have to have enough equity relative to the debt. And I do think they will give a lower debt/equity ratio if you are in individual stocks rather than large diversified funds.
I looked, and for Fidelity, all I could find was a margin loan at much higher rates.
The "catch" is, that rate is floating, so I can't expect it to stay that low forever. I plan to apply for a regular 30 year to lock in these historically low rates, but heard that no one wants to touch a mortgage under these conditions until the home has been owned for ~ 6 months. But it (mostly) simplified the home purchase, and that was part of the goal. Now I can deal with mortgage shopping w/o all the rush of the home buying 'experience'.
-ERD50