By Karin Strohecker, Daniel Bases and David Randall

LONDON/NEW YORK, July 20 A few investors are racing to establish funds for Iran following last week's nuclear deal with world powers, and many others are tapping into multinationals already present in the $400 billion economy.

The agreement has made some seek a foothold in Tehran's $100 billion stock market even before sanctions are lifted, although others are taking a more cautious approach.

Classified as an upper-middle income country, with a population of 78 million and annual output higher than that of Thailand or the United Arab Emirates, Iran is set to be the biggest economy to rejoin the global trading and financial system since the break-up of the Soviet Union over 20 years ago.

Brokerage Renaissance Capital predicts $1 billion will flow into Iran in the first year after sanctions end, although that is not likely to happen for months and may not occur in one go.

London-based boutique First Frontier Capital Ltd. is in the process of setting up a sanctions-compliant fund dedicated to Iran, hoping to allow investors to take a position in Tehran's bourse before sanctions are lifted.

"This is a market where everyone is totally underweight and there will obviously be a lot of money going in, hot money at first but then also others," said First Frontier's co-CEO, Richard Adley, who plans to launch the fund in the next couple of months and aims to have 100 million euros invested by year-end.

"And then there is a big valuation gap there, Iran has a lot of catching up to do when you look at other frontier or emerging markets," said Adley, who estimates valuations at a very cheap five to six times earnings.

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