Although two classes of shares on the same Chinese companies differ only in that the A-share class trade in Yuan and the B-share class in dollars, the B-shares have traded at a significant and persistent discounts to the A-shares since inception of the B-share market in the early 1990s. The persistence of the discount has been a puzzle. We find that liquidity differences between the less liquid B-shares and the A-shares do not explain the discount or changes in the discount. Moreover, discounts do not arise because the proper clientele for the B-shares are foreign investors who need higher rates of return to hold these shares because of home-country bias. The data indicate that the marginal investors who buy and sell shares in this market are generally Chinese (small) investors. The returns on the B-shares respond to the returns on the Shanghai (and not foreign) markets and the returns on the B-shares do not differ significantly from the returns on the A-shares. The evidence indicates that the various behavioral economics models such as investor sentiment or over-bidding of stocks by large volume traders are not supported by the data. The changes in the discounts of the A-shares and the B-shares fluctuate randomly.