Stock price indices are used extensively by investors, brokers and portfolio managers as a general indicator of the stock market conditions. They are also used extensively in finance theory notably in operationalizing the popular Capital Asset Pricing Model (CAPM). In recent years, the indices published by the Bombay Stock Exchange (BSE) - the Sensitive Index (Sensex) of 30 scrips in Bombay and the 100 share National Index (Natex) - have become extremely popular with academics and practitioners alike. Anecdotal evidence suggests that the Sensex is by far the more popular index among brokers and lay investors while the Natex is the index of choice among mutual funds, professional investors, foreign investment agencies and academics. This paper studies the two BSE indices and their inter-relationship. The analysis in this paper indicates: 1. The Natex is a sluggish index which responds too slowly to market conditions. Changes which are reflected in the Sensex on any day are completely reflected in the Natex only by the next day. 2 Sensex is more volatile than Natex, but this difference is accounted for by two factors - (a) the autocorrelation of the Natex which conceals the true volatility of Natex, and (b) a higher beta of Sensex relative to Sensex. Therefore, the excess volatility of Sensex is not a matter of serious concern. In many applications, however, the higher beta of Sensex is worrisome, but it is easy to correct for it. The conclusion, therefore, is that those who follow the Natex because of its greater comprehensiveness and theoretical appeal may be mistaken. The Sensex needs to be taken more seriously as a sound market index. The observed deficiencies of the Natex raise several disturbing questions for finance theorists and researchers. Is the market for the less well traded securities in the market inefficient? Do the scrips constituting the Sensex lead the other scrips? If so, can this relationship be used to make extra normal returns? Does the Bombay market lead other exchanges which are also represented in the Natex? These issues call for further research.