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The insurer Arch Capital launched in 2001 just a month after the September 11 terrorist attacks to take advantage of a spike in premiums for catastrophe cover.

Twelve years later the Nasdaq-listed group again showed an opportunistic streak when it bought out of bankruptcy a chunk of the California-based mortgage insurer PMI, which had been crippled by the financial crisis.

Now Arch is expanding into the mortgage business with an agreement this month to buy United Guaranty Corp (UGC) from AIG, a $3.4bn deal that will make the Bermuda-based group the biggest private mortgage insurer in the US.

Arch, whose largest shareholders include Bill Gates’s family investment office, joins high-profile institutions and investors in trying to capitalise on the renaissance of an industry that was almost destroyed by the 2008 housing crisis.

Goldman Sachs backs Essent, founded in 2008, while Kyle Bass’s Hayman Capital Management is a big investor in another post-crisis entrant, NMI.

“The mortgage insurance industry’s history has not been stellar,” acknowledges Dinos Iordanou, Arch’s chairman and chief executive. “The space is misunderstood a bit because of the crisis. People have not really spent a lot of time and effort to understand what caused the major problems, and how they could be corrected.”

Mortgage insurance covers lenders when borrowers default. It shifts a chunk of housing market risk from banks and the US government to the hedge funds, private equity groups and conventional investment houses that invest in insurance companies.

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Fannie Mae and Freddie Mac, the US government’s mortgage guarantors, require banks to purchase the cover when homebuyers put down less than 20 per cent of the property’s value.

The market has come roaring back since the crisis, although the public sector plays a bigger role than insurance companies in providing insurance cover. Agencies such as the Federal Housing Administration (FHA) ramped up their provision during the crisis. By 2009, private sector insurers’ share of the market had shrunk to just 15 per cent, but they have since clawed back their share to 37 per cent. The state tends to provide the insurance for borrowers with low credit scores who would otherwise be unable to buy a house.

The subsector is still a relatively small part of both the wider mortgage and insurance industries. Still, it has become one of the more lucrative corners of finance as the housing market has recovered and default rates run near record lows.

The Standard & Poor’s Case-Shiller index of house prices in 20 big US cities has rebounded 40 per cent since 2012. Only 0.66 per cent of mortgage holders failed to keep up payments in July, according to S&P and Experian.

Private sector insurers wrote $71.5bn worth of the cover between April and June, according to Inside Mortgage Finance — up more than half from the same period a year ago, and the highest quarterly total since the start of 2008.

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Arch has been among the most aggressive in the sector, even before the UGC deal. It doubled volumes between the first and second quarters. After it completes the purchase of the North Carolina-based business, mortgage insurance will generate about half the group’s profits.

Arch is bulking up its presence at a time when ultra-low interest rates are squeezing the traditional businesses of property and casualty cover and reinsurance.

Pricing competition in the mainstream insurance sector has intensified as a wave of return-hungry capital has flooded in, while depressed bond yields are also hurting investment returns, the other main way insurers turn a profit.

Indeed mortgage cover is one of the few parts of the insurance industry that is flourishing in the era of cheap money — even if pricing competition has stepped up there too in recent months.

Despite the sector’s post-crisis recovery, it has come off the boil in recent months. After hitting lows of just 84 cents in August 2012, shares in the listed provider MGIC leapt to $11.64 by July last year. They have since fallen by about a third, however.

Mark Palmer, analyst at BTIG, said that as well as greater pricing competition in recent months, investors have been disappointed that the FHA has retained such a large share of the market.

The $3.4bn price tag that Arch put on UGC is lower than those mooted earlier this year, when AIG said it planned to float the business. By selling the business in one go rather than disposing of it in chunks through a listing, AIG will be helped in meeting a target to return $25bn to its shareholders over the next two years. The insurer has been under pressure from activist investors Carl Icahn and John Paulson to improve its returns.

Recent financial results from Arch show how bulking up in mortgage insurance could also bolster its returns. In the second quarter, Arch’s primary insurance business produced a combined ratio — claims and expenses as a proportion of premiums — of 99.4 per cent, meaning it only just turned a profit from selling the policies.

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The combined ratio of its mortgage insurance business was a far superior 50 per cent, making it among the most profitable of any type of underwriting.

However, returns from mortgage insurance looked similarly good before the crisis. According to industry data cited by the National Association of Insurance Commissioners, the industry-wide combined ratio ran at about 50 per cent between 1999 and 2006, before jumping to almost 250 per cent in 2008 when defaults rocketed.

Mr Iordanou acknowledges losses will rise when the economy deteriorates. He argues, however, that the risks can be managed — just as insurers deal with catastrophic events such as earthquakes and hurricanes.

Traditionally, he says, mortgage insurers have set the prices they charge on two variables: credit scores and the amount of cash put down to purchase the property. Arch says it gathers a lot more information about borrowers, such as employment details, and analyses them to determine premium levels in a more sophisticated manner.

“We didn’t make this acquisition because we can predict the future, but we can control our destiny through underwriting,” the chief executive argues. “As long as I run this company, or my colleagues here are running this company, we’re not going to make those tragic mistakes of the past.”

Shares in the Arch rallied 7 per cent in the two days after the deal was announced, suggesting that investors — at least for now — have faith he is right.

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