The Grossman-Stiglitz Paradox

Source: http://jinsukpark.wordpress.com/2011/01/09/the-grossman-stiglitz-paradox/

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This paradox defies market efficiency, but at the same time, it contradicts market inefficiency arguments. We can clearly show this by modifying two essential assumptions of the paradox:
1. investors’ belief in market efficiency
2. information/transaction cost
 A. Belief in efficiency to market inefficiency Suppose market investors are rational, they believe the financial market is efficient (so, market prices reflect all available information). Then, they do not have any incentive to analyse information and initiate trades when the process of gathering information and making transaction is costly. Thus, they will just buy-and-hold their initial portfolios, that is, passive investment strategy is implemented all over the market. However, as time goes by, new (random) information will surely arise, but it is not going to be incorporated into the market prices since no one is willing to trade. Consequently, fundamental prices, which incorporate all relevant information, will deviate from the market prices. In other words, if all market participants truly believe the market is efficient, it will lead to market inefficiency. This is the paradox.

 B. Belief in inefficiency to market efficiency On the other hand, the opposite argument is possible. Suppose all market participants are irrational, that is, they do not believe the market is efficient. They will seek profitable opportunities and initiate market trade to exploit them. It will be strengthened if we further assume no information processing and transaction cost. However, as they intensify their efforts to search the opportunities responding the arrivals of new information, all profitable opportunities will be dried up and the market prices will eventually reach the fundamental prices (if exists). The paradox in here is that when market investors believe market inefficiency, they will drive the market into efficiency.

 C. Implications for rational investors If rational investors are truly rational, they will anticipate this paradox. Assuming rational and noise traders co-exist, the rational investors would let (or promote) noise traders fulfill their own beliefs in inefficiency. By their behaviors, market prices will remain efficient over time. The rational investors then simply can ride the market (e.g. using index funds) while paying little cost. Also, they would not spend much efforts to defy the market efficiency as the disbelief of market efficiency is essential to achieve their investment goals.
 D. The existence of fundamental prices On the other hand, whether the fundamental prices ever exist is another issue to test. It may be too volatile to be justified by ex-post dividend stream (Schiller). Or they consist of pure expectation of future cash flows, dividend payment or stock prices, which are hard to be tested by ex-post dividends.