NEW YORK(Reuters) - American International Group’s bid to take back $15.7 billion in risky mortgage bonds may inject fresh confidence in a market where investors had started to question a nearly two-year rally.AIG said it made the offer to the Federal Reserve Bank of New York for the residential mortgage-backed securities it gave up at the height of the financial crisis. The Fed on Friday confirmed it received AIG’s offer for the bonds, held in Maiden Lane II, an entity formed in late 2008 as part of AIG’s bailout.For more than a year, the insurer has been preparing the offer on the bonds, whose values have soared despite rising foreclosures on the underlying loans. An index of top-rated subprime securities has rallied more than 50 percent since the depths of that market in April 2009, according to Amherst Securities Group.The New York Fed would make a profit of about $1.5 billion on the portfolio, AIG said.“It shows you how far we have come from the fall of 2008,” said Jesse Litvak, a managing director at Jefferies & Co. in Stamford, Connecticut.“I also think that this is far from being final, and I imagine a lot of others are scrambling to see what the value of this portfolio could really be worth.”