Fannie Mae posted a modest increase in new business activity in June, hitting its strongest month so far in 2005, while Freddie Mac may be losing some of the gains it has made in building its share of the conventional conforming market. Fannie Mae’s $48.79 billion in new business for June was up 7.7 percent from the previous month, according to company data released late last week. That gave Fannie a total of $139.39 billion… [One data table included]