Freddie Mac’s total mortgage portfolio declined at an annualized rate of 10% in December compared to 6.9% in November.

The steeper decline comes amid much discussion about how to pull the influence of Freddie and Fannie Mae out of the mortgage finance market, making room for private capital. The government-sponsored enterprise ended the year with a total mortgage portfolio valued at $2.08 trillion.

Freddie’s single-family loan purchase and guarantee volume hit $23 billion in December, making up 76% of the entire portfolio. That is down 14% from November when the guarantee volume hit $27 billion, representing 71% of the portfolio.

The company completed 5,591 loan modifications in December, down from 6,886 in November. The December tally brought the total for the year to 109,174 completed loan modifications.

Fannie’s current aggregate unpaid principal balance on its mortgage-related investments portfolio fell to $653.3 billion in December from about $663.23 billion in November.

The GSE’s seriously delinquent rate on single-family homes remained mostly unchanged, edging up from 3.57% in November to 3.58% in December. In addition, the multifamily delinquency rate declined from to 0.22% in December from 0.28% the prior month.

Write to Kerri Panchuk.