I don't understand what is being used as the denominator to generate this 1/3 number in the headline. A quick search shows that the US MBS market is about $10.3 trillion in size [1] - the actual mortgage market is larger (what nostromo mentioned earlier). Putting some recent numbers [2] over the size of the MBS market would show that the Fed owns a little less than a 1/5 of all US MBS.

Also, he mentions that the Fed has been purchasing roughly $100 billion per month in MBS securities since April, but this leaves out the fact that a non-insignificant number of MBS in their holdings are either i) reaching maturity, or ii) being prepaid. The second issue is more prevalent now - with the low-rate environment that exists in the US many people are refinancing their mortgages to take advantage of lower rates, but in any case it isn't uncommon for mortgages to be paid off before their maturity date. I don't know what the net figures are, but what I'm trying to say is that purchases of MBS != growth of MBS holdings.

I seriously think this author has somehow conflated the size of the SOMA assets with the size of the MBS market - continuing growth of MBS at $100 billion for the rest of the year, leaving all else equal, will give us about $2.4 trillion of MBS over a denominator of $7.4 trillion - which would give us about 1/3.

[1]: https://www.sifma.org/resources/research/fixed-income-chart/ [2]: https://www.federalreserve.gov/releases/h41/current/