Citigroup Inc's spinoff of its life insurance unit, Primerica Inc
saw its shares gain more than a third in its debut on optimism that the life insurer will benefit from a rebounding economy.

The IPO's reception was also the latest glimmer of positive news for the third-largest U.S. bank, which was forced to seek various government rescues in 2008 and 2009. Citi shares closed up 3.2 percent at $4.18.

The first day rally followed investor interest that led underwriters to raise the size of the offering by 19 percent to 21.36 million shares. The shares were priced at $15 each, above the expected range of $12 to $14.

But the IPO still sold at a price-to-book value discount to Ameriprise Financial , MetLife and Prudential Financial
, which it identified in its prospectus as competitors, said IPOdesktop.com President Francis Gaskins.

The relatively low valuation, plus signs of confidence in a gradually rebounding economy, both contributed to the share's gains, analysts said.

Life insurance has been hammered by the recession like everything else has, but there has been an uptick over the past year in applications for issuance of traditional bread-and-butter life insurance, said Clark Troy, a senior analyst at Aite Group LLC. Insurers have been looking to bulk up their sales forces, and Primerica has one.

The Dow Jones U.S. Life Insurance index has more than quadrupled since March 2009 <.DJUSIL>.

Primerica shares rose much as 35 percent above their initial public offering price. They opened at $19.15 and rose as high as $20.20 Thursday afternoon.

The shares closed up 31 percent, at $19.65, on the New York Stock Exchange.

DIVIDING THE SPOILS

Citi, which accepted $45 billion worth of U.S. government bailout funds, is seeking to divest assets that are not part of its core banking business.

The bank tried to sell Primerica last year, but failed to find a buyer willing to pay a high enough price. Citi has taken nearly $1 billion in dividends out of the company since 2007 and will take another $622 million before the end of the IPO process.

Citi will take all of the proceeds from the offering and most of Primerica's existing accounts. Primerica will keep its new policies.

Primerica said in its prospectus that it would enter into co-insurance agreements with three affiliates of Citi. Those affiliates would take 80 to 90 percent of the risks and rewards of the term life insurance policies Primerica held at the end of 2009.

Despite Citi's retention of most accounts, Primerica is gaining more autonomy over its strategy, analysts said.

This will give an opportunity for Primerica management to step out of the shadow of the larger organization and assert itself, Troy said.

With a door-to-door sales force of independent contractors topping 100,000, Primerica sells life insurance to households earning between $30,000 and $100,000 annually.

Co-Chief Executives John Addison and Rick Williams told CNBC they planned to add sales people.

We're going to be a smaller, faster-growing company going forward, Williams said. When we grow the sales force, the underlying sales grow.

Citi was the sole bookrunner on the IPO. If the company and other underwriters purchase their full overallotment of 3.2 million shares, Citi's stake in Primerica will be reduced to 39 percent.

ANOTHER STEP FOR CITI'S SELL-OFF

Cutting troubled assets has been a major goal of Citi's restructuring. The IPO and a private deal with Warburg Pincus LLC should reduce Citi's GAAP assets by about $5 billion during the second quarter, the bank said in a statement.

Michael Holland, chairman of Holland & Co in New York, said that Primerica's offering was a good sign for Citi, but I wouldn't overstate the significance. It's something they had to do and they did it well.

Holland said the offering could provide some momentum for banks trying to rid themselves of non-core assets. The Primerica offering is a good way to go out there and test the marketplace, he said.

The life insurance portion of Primerica was founded in 1977, but the company has roots in American Can Co, a food packaging business. It became part of Citigroup in the 1980s.

(Reporting by Clare Baldwin and Maria Aspan; Editing by Maureen Bavdek, Richard Chang and Leslie Gevirtz)