DUBAI, June 29 (Reuters) - Stock markets in the Gulf look set to move sideways on Wednesday, with sentiment supported by a modestly positive global environment but many investors unwilling to take big positions before looming Eid al-Fitr holidays.

MSCI's broadest index of Asia-Pacific shares outside Japan is up more than 1 percent and Brent crude oil is 0.4 percent higher at $48.78 a barrel.

However, modest trading volumes and narrow trading ranges in Gulf bourses over the past couple of weeks suggest any major rise is unlikely, especially with Brexit still a longer-term source of uncertainty for markets.

Shares in L'azurde Company for Jewellery , a family-owned retailer, will start trading in Riyadh on Wednesday after the company sold 12.9 million shares in an initial public offer at 37.0 riyals per share.

The stock's performance may serve as an indicator for the Saudi retail sector as low oil prices and an economic slowdown squeeze disposable income.

Recent new listings in Saudi Arabia have not performed as well as in the past; Middle East Healthcare listed in late March at an IPO price of 64 riyals and after jumping on the first day, has largely moved sideways; it closed at 71.50 riyals on Tuesday.

In Dubai, Dubai Parks and Resorts , acting at the behest of Dubai's ruler Sheikh Mohammed bin Rashid al-Maktoum, has made an exception to its exclusive right to develop and operate Six Flags-branded theme parks in the Gulf Cooperation Council, in order to let Six Flags help Saudi Arabia build theme parks.

However, this may have little impact on the stock if investors believe the Saudi parks will mean little direct competition for Dubai's parks, which are due to start opening this year.

(Reporting by Andrew Torchia) ((andrew.torchia@thomsonreuters.com; +9715 6681 7277; Reuters Messaging: andrew.torchia.thomsonreuters.com@reuters.net))