ROE shows how profitable a business is for the owner/stockholder. The denominator is simply shareholders' equity.
ROIC and ROA show the OVERALL profitability of the business because the denominator INCLUDES DEBT in addition to equity.
ROE and ROA will differ widely in businesses that employ a lot of leverage.
Banks for instance earn a very low return on assets because they simply earn a small spread (ex: borrow at 1%, lend at 4%). The best banks in the US earn 3% ROA. But these banks have the majority of their capital structure in depositors' money (i.e. low-interest bearing debt) and this leverage magnifies their returns. So a bank earning 3% ROA could easily earn 25% ROE.
