What Determines the Stock Price and the Informative Efficiency: The Omitted Information Frequency Observed

證券價格及其訊息性之決定因素：被遺漏的資訊觀察頻率

10.30163/BR.200606.0003

陳立偉(Li-Wei Chen)；楊清溪(Chinghsi Yang)

充分統計量 ； 資訊觀察頻率 ； 價格訊息性 ； 資訊效率 ； 理性預期均衡 ； Sufficient Statistic ； Observational Frequency of Information ； Price Informativeness ； Informationally Efficiency ； Rational Expectations Equilibrium

文大商管學報

11卷1期（2006 / 06 / 01）

29 - 59

英文

先前股票市場交易模型中假設每位投資人僅觀察一種訊息藉以推測股票真值並據以進行交易，以追求個別效用或利潤極大，因此得出均衡股價為市場中所有私人訊息之平均，且論斷市場價格為所有私人訊息之充分統計量。 本文首先指出市場中各種資訊被投資人觀察之頻率（次數）並非齊一，應將模型假設為各種資訊各有不同之被觀察頻率。本文假設投資人之絕對風險厭惡係數為常數，各自追求預期效用極大，市場結清均衡。主要發現有： 第一，競爭均衡價格與理性預期均衡價格相同，為市場中各種私人訊息值按照各種訊息精確度及被觀察頻率之乘積加權平均，因此股價不僅反應訊息值，同時也反應各種資訊之被觀察頻率及精確度。完全訊息均衡則為前者在假設各種資訊觀察頻率為齊一下之特例。 第二，當資訊觀察頻率為齊一時，均衡價格為各種訊息之充分統計量。但實際上，投資人間存在資訊不對稱，各種資訊之被觀察頻率並非齊一，故均衡價格難以成為市場中各種訊息之充分統計量，因此投資人除了觀察市場價格之外，仍有搜尋其他私有資訊之動機。Grossman(1976)因假設資訊觀察頻率齊一而產生之結論中，僅為一個不符實際之特例。

This paper investigates the determination of the price system of the stock market. Different from previous studies, we emphasize the concept of the ”observational frequency” of information. This paper allows each informed investor to observe more than one kind of information. There are I kinds of information x1, x2,...x(subscript I) available in a competitive stock market. Since there exists information asymmetry among investors, the market information are respectively observed f1, f2,..., f(subscript I) times by N constant risk-averse traders to form a more precise estimate for the expected value of the risky asset, v, to buy the shares to maximize their own expected utility, and then to determine the stock market equilibrium simultaneously. Our main findings are as follows. First, we propose that the equilibrium price, trading quantity, and the expected utility of investors depend not only on realized value of the information but also on the observational frequencies and the precisions of the market information. The competitive equilibrium price is equal to the rational expectations equilibrium price, which aggregates all the market information according to their observational frequencies and the precisions of the market information. Second, the fully-informed economy equilibrium is a special case of the competitive equilibrium (or the rational expectations equilibrium) only when the observational frequencies of all the market information are just equal and it serves as a sufficient statistic for all the market information about the intrinsic value of the risky asset. Finally, we prove that the heterogeneity in the observational frequency of information is impossibility for informationally efficiency. Since the observational frequencies among the market information are not uniform, the equilibrium price still aggregates the market information but will not break down as the case described by Grossman (1976).

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