"There is a gap between all the money coming in to Islamic banks and the deployment of that money into real economic assets," said Sayd Farook, the global head of Islamic finance at Thomson Reuters. "A crazy amount of money has gone into their coffers and they need somewhere to invest it."
The first modern Islamic banks were founded in the 1970s, motivated by the Quran's ban on riba, which has been interpreted as any fixed payment charged for money lending. Islamic banks have focused instead on putting their money into real assets and property, and sharing any resulting profits from the performance of an asset. Muslim mortgages, for instance, are structured so that the bank buys the house and then sells it to the occupant slowly over time. Stocks are generally considered acceptable as long as the companies issuing the stock adhere to Islamic law; casinos, banks and weapons companies are forbidden.
Islamic banks have religious scholars, like Mr. DeLorenzo, review their operations on a regular basis. Yet some Islamic scholars have criticized the banks for straying too far from the spirit of the Quran into the speculative realms of Wall Street. Sometimes it is hard to tell the difference between a Western investment and a Shariah one. For instance, an Islamic bank's fixed-deposit account ties up a customer's money for a set period of time, like a certificate of deposit. Instead of offering interest, the account offers a share of the profit from its investments. The "profit rate" of a one-year deposit currently is 1.9 percent at one major Middle Eastern bank.
There is a debate among Islamic scholars about what qualifies as halal. "The industry is going through soul-searching," said Ayman A. Khaleq, a lawyer specializing in Islamic finance at the Morgan Lewis law firm in Dubai. "It's far from settled."
But these problems have not stopped the flood of deposits into banks like the Sharjah Islamic Bank, which is named for the city in the United Arab Emirates where it is based. The bank has 24 branches, some of which offer separate spaces for female and male customers. From 2006 to 2012, deposits there almost tripled to about $3 billion.
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Muhammed Ishaq, the head of the treasury division at Sharjah, said that the bank's problem was not attracting money, it was figuring out what to do with it. "It's not very easy when any financing needs to be backed by some kind of asset," Mr. Ishaq said.
Real estate has been a very popular investment in the Islamic world, but when real estate was hit hard during the 2008 financial crisis, many investors were reminded of the need for more diverse portfolios. For many banks the answer is sukuk. Like bonds, sukuk make regular payments to investors. But unlike a bond, which is a money loan, sukuk are structured as investments in hard assets that generate payments.
The amount of sukuk sold each year has grown sixfold from 2006 to 2012, to some $133 billion, according to Thomson Reuters's Islamic financial data service, Zawya. A joint venture between Dow Chemical and Saudi Arabia's national oil company sold a $2 billion sukuk this year to raise money for an oil complex. But this is falling far short of the demand from banks. "There are serious supply-side bottlenecks," said Ashar Nazim, head of Ernst & Young's Global Islamic Banking Center.
Now there are several efforts to create more supply. The Bank of London and the Middle East was founded in London with Kuwaiti money to find these new investment opportunities. "They wanted a wider range of Islamic assets that could be originated away from the Middle East," said Nigel Denison, the bank's treasurer.
(Read more: Glitzy Dubai eyes profit in setting Islamic standards)
Yavar Moini, the former head of Islamic banking at Morgan Stanley, said he was establishing an operation in Dubai that would gather assets from around the world that can be packaged into sukuk, like Fannie Mae and Freddie Mac do in the United States with mortgages. Mr. Moini said that "it's the absence of sufficient product or opportunities for Islamic investors that drives them into the conventional arena."