For the past three decades, finance has claimed a growing share of the U.S. stock market, profits and the overall economy.

But the role of finance -- the businesses of borrowing, lending, investing and all the middlemen in between -- may be ebbing, a shift that would redefine the U.S. economy. "The role of finance in the economy is going to come down significantly in the coming years," says Carlos Asilis, chief investment officer at Glovista Investments, a New Jersey money manager. "From a societal standpoint, we got carried...