Do Shariah compliant shares perform better?

During the global financial crisis many experts pointed out that Shariah compliant shares had performed much better than those which were not. However, once the world emerged from the crisis, the Shariah All-World index has consistently underperformed its conventional counterpart. A conventional investor who is selecting shares from the complete universe of shares will, on average, outperform a Shariah compliant investor who selects shares only from the Shariah compliant subset of the universe. The conventional investor is always free to buy high quality Shariah compliant shares, but the Shariah compliant investor can never buy high quality non-Shariah compliant shares. This is simply a fact of life to be accepted.