The use of pricing frontier to analyze cross-sectional equity values and returns

The purposes of this study are to provide a theory of security pricing frontier for capital market research and to test the efficient market hypothesis. The pricing frontier can be used to construct the measure of the relative price level of securities, which is called the pricing score. In previous studies, the simple ratios such as price to book ratio and price to earning ratio are used to find the abnormal stock returns, which are called anomalies. Because these ratios are not fully justified by risk and cash flow factors, their corresponding anomalies may be explained by some risk or cash flow factors. The pricing frontier model explicitly includes risk and cash flow factors. The pricing scores that were calculated from the frontier model for different stocks should be close to each other if the stock market is of a strong form of efficiency. If the stock market is not efficient, the pricing score should give the relative divergence of stock prices from fundamental values, which implies that the pricing scores can be used to know whether the stock is under-valued or over-valued. If the stock market is in the weaker form of efficiency, the trading strategy based on the pricing scores cannot provide any abnormal returns. We used data of the stocks traded on New York Stock Exchange and American Stock Exchange in our empirical test. The empirical results of four different methods, econometric stochastic frontier model, ordinary least square model (OLS), data envelopment analysis (DEA) models and artificial neural networks, reject the efficient market hypothesis. They also strongly support our theory that the pricing scores have the power to predict stock returns if some stocks are over/under priced.