NEW YORK (Bloomberg) — Like an archer at the Olympics, Arch Capital has landed its target: AIG’s mortgage insurance business.

The Bermudian-based insurer said late on Monday that it would buy United Guaranty for $3.4 billion in cash and stock. The deal is set to be more than 35 per cent accretive to both its earnings per share on a run-rate basis and will also immediately lift the company’s book value per share. Investors applauded Arch’s biggest deal on record — the shares climbed as much as 5 per cent yesterday to the highest level since its initial public offering some 21 years ago.

The transaction isn’t a complete surprise. Arch has been scaling back its property-and-casualty operations and recently made a notable stride in mortgage insurance. In the second quarter, that culminated in the latter posting an 81 per cent jump in new premiums written, a figure that was driven by its reinsurance of Australian mortgages.

For AIG, the price tag is lower than the $4 billion United Guaranty was said to be valued at in a planned IPO, but the sale allows for a cleaner exit. The insurance giant will receive at least $2.2 billion up front, and can begin selling its Arch Capital shares after an initial six-month lock-up.

The proceeds will come in handy for AIG, considering it hopes to return $25 billion to shareholders by the end of next year through dividends and buy-backs. On that basis, one can assume AIG’s newest board members — John Paulson and Samuel Merksamer of Icahn Capital — were quick to give this deal the green light. Every dollar counts.