Radian Group Inc. (RDN) swung to a profit of $137.1 million, or $1.03 per share, in the second quarter after the company recorded gains from changes in the fair value of derivatives and other financial instruments, the Philadelphia-based mortgage insurer said Tuesday. That is up dramatically from last year when the firm reported a $475.1 million, or $4.31 per share, loss on the value of derivatives that swung in a negative direction, eating into profits. The company’s provision for losses tied to mortgage insurance claims also plummeted to $270 million in 2Q, down from $414 million in the first quarter and $427.6 million a year ago. Radian saw provisions for losses on mortgage claims go down as delinquent loans continued to improve with age and overall composition. Total mortgage insurance loss reserves hit $3.3 billion in June, down from $3.7 billion a year earlier, showing more confidence in the mortgages Radian insures, according to the company’s report. Radian believes the number of claims paid out already has reached its peak and will continue leveling off. “As we face an uncertain U.S. economy and housing market, we believe that Radian’s risk-to-capital ratio of 19.8 to 1 and the financial flexibility of our holding company cash position provide a competitive advantage for our mortgage insurance business,” said Chief Executive Officer S.A. Ibrahim. Rob Haines, an analyst with CreditSights, said earlier in the year that under normal circumstances, a mortgage insurer is at the high-end in terms of risk when the risk-capital ratio hits 15-to-1: a level most of the nation’s mortgage insurers have already surpassed. Radian’s confidence stems from its ability to remain only slightly above the ideal ratio, while other carriers have moved far beyond it — even hitting the 25-to-1 range. More positive news came out of Radian’s second-quarter report with delinquencies on loans insured by the carrier falling  5% between 1Q and 2Q, making it the sixth consecutive quarterly decline on delinquent loans. The earnings report boosted the company’s stock price as much as 20% Tuesday morning, with the insurer surpassing analyst estimates of a loss in the quarter. Write to Kerri Panchuk.