* Dollar and yen steady, holding previous day's gains
* Investors more cautious of return to risky assets
By Satomi Noguchi
TOKYO, May 12 (Reuters) - The dollar and yen were steady on Tuesday, holding most gains made the previous day as investors remained cautious about returning to risky assets with regional stocks falling after a slide in Wall Street.
The dollar had rebounded from a four-month low against a basket of currencies on Monday, after investors took profits from gains in other riskier currencies that had been lifted by optimism about the U.S. banking system.
Traders said investors may continue to lighten positions and buy back dollars and yen they used to fund investments in higher-yielding currencies such as the Australian dollar.
But hopes that the worst of the economic slump and financial crisis are over also remained strong, and that in turn provided some support to the euro and the Aussie, traders said.
"The market returned to being a little more cautious about reading economic fundamentals after optimism reigned in the past few months," said Hideaki Inoue, chief manager of forex trading at Mitsubishi UFJ Trust Bank. "The key this week will be to see how much more profit-taking will come, with eyes on economies in emerging markets which give basic support to market hopes," Inoue said.
The dollar index, a gauge for the greenback's performance against six other major currencies, was little changed from late New York trade at 82.786, above a four-month low of 82.292 touched on Monday.
The euro was steady at $1.3587 after sliding as low as $1.3557 on trading platform EBS from a seven-week peak of $1.3670 hit early the previous day.
Against the yen, the dollar edged up 0.1 percent to 97.58 yen and the euro also inched up 0.1 percent to 132.57 yen as some traders reduced yen buying positions ahead of the Tokyo fixing, when demand from Japanese importers tends to give a lift to the dollar and the euro.
Tokyo's Nikkei share average slipped 0.8 percent in early trade on Tuesday after booking a six-month closing high the previous day. (Editing by Michael Watson)