Before revision:  By relying on the theory of progressive enlargement of filtrations, we explicitly show that arbitrage profits can never be realized strictly before an honest time, while classical arbitrage opportunities can be realized exactly at a honest time and stronger arbitrages of the first kind always exist after an honest time  .
After revision:  By relying on the theory of progressive enlargement of filtrations, we explicitly show that arbitrage profits can never be realized strictly before an honest time, while classical arbitrage opportunities can be realized exactly at a honest time and stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time .