Nov 30 (Reuters) - Credit Suisse's planned $2.4 billion fundraising to help pay for a major overhaul faced mounting market headwinds on Wednesday, with the cost of insuring exposure to its debt hitting a record high, while the bank's shares and bonds tumbled.

The rights issue is part of the Swiss bank's broader capital raising worth 4 billion francs, which got shareholder approval last week, to help fund Credit Suisse's recovery from the biggest crisis in its 166-year history.

"Investor confidence has not been restored yet," said Joost Beaumont, head of bank research at ABN Amro.

Credit Suisse declined to comment on the market moves.

Five-year credit default swaps on Credit Suisse, the cost of insuring against a default on its debt by the Swiss bank, rose to around 446 basis points (bps) from 409 bps at the open, S&P Global Market Intelligence data showed.

This level compares with 57 bps at the start of the year and is not far off levels for Italian bailed-out bank Monte dei Paschi di Siena at 466 bps.

CDS for other European lenders such as Commerzbank, Santander or Swiss peer UBS are between 69-81 bps.

After opening higher, Credit Suisse's shares tumbled 2% to a new record low, marking their ninth straight session in the red. The stock has lost more than 66% since the start of the year.

Credit Suisse rights for its 2.24 billion Swiss francs ($2.4 billion) share issue were down 8%, having reversed initial gains. This came on top of a 30% tumble on Tuesday.

Holders of the rights to subscribe to new shares have time until 8 December to exercise them but investor response has been so far lukewarm.

Credit Suisse bonds also weakened, with additional tier 1 dollar bonds down over 4 cents and many sinking below the levels seen during a sell off in the bank's shares and bonds in early October, Tradeweb data showed.

Switzerland's second-largest bank last week flagged that it was on course for a pre-tax loss of up to 1.5 billion Swiss francs in the fourth quarter, and revealed that wealthy clients had made hefty withdrawals.

Battered by a series of scandals and mounting losses, Credit Suisse last month embarked on a turnaround plan.

"The bonds had a little rebound when the strategic review was announced, but it is still a difficult story, with question marks on the execution of the strategic review," Beaumont said.

The euro-denominated bond issued by Credit Suisse's holding company in mid November at a record coupon of 7.75% also fell. It is quoted at a below par price of 98.5 cents, which suggests investors require a discount to buy the bond.

The bond's price was as high as 103 cents on 22 November.

($1 = 0.9501 Swiss francs) (Reporting by Chiara Elisei and Danilo Masoni; Editing by Karin Strohecker, Jane Merriman and Alexander Smith)