(For a Reuters live blog on U.S., UK and European stock markets, click LIVE/ or type LIVE/ in a news window) March 30 (Reuters) - European shares inched toward all-time highs on Tuesday on hopes of a strong economic recovery, while investors looked past concerns over a U.S. hedge fund default that hit banking stocks a day earlier. The pan-European STOXX 600 index rose 0.5% by 0813 GMT, trading less than a percent below its record high, with bank stocks leading the gains. Swiss lender Credit Suisse inched up 0.8% after its near 14% slide in the previous session as it warned of “highly significant and material” losses after the fund, named by sources as Archegos Capital, defaulted on margin calls. The German DAX rose 0.6% to scale new record peak, boosted by automakers and a 1.7% rise in Deutsche Bank . Spanish mobile phone mast operator Cellnex rose about 1.5% after it launched a 7 billion euro ($8.23 billion) capital raise. (Reporting by Sruthi Shankar in Bengaluru; Editing by Shailesh Kuber)