Before revision: We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability  if the market admits statistical arbitrage opportunities which we term \rho-arbitrage for a risk measure \rho.
After revision: We show that coherent risk measures are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term \rho-arbitrage for a risk measure \rho.