The Portuguese stock market provides a natural experimental area to analyse theories of optimal price per share. Its characteristics suggest that prices should be very low. Using a sample of 20 stocks from the main Portuguese Stock Index from 1999 to 2010, we observe that Portuguese corporations indeed seek extremely low prices per share through stock splits and similar actions. However, we find that low-price stocks are actually less liquid than high-price stocks. Furthermore, low-price stocks trade at lower valuation ratios. Our results do not support any of the existing theories on optimal price per share and therefore add to the nominal share price puzzle.