Predicting Cross-Sectional Returns

If the market is assumed to be efficient, all securities should lie along the security market line that relates the expected rate of return to an appropriate risk measure. It is mandatory that all the securities have equal risk-adjusted returns because security prices should reflect all public information that would influence the security's risk. Therefore, it is necessary to determine whether the future distribution of risk-adjusted rates of return can be predicted (i.e., using public information, the possibility of identifying the stocks which experience below-average, risk-adjusted returns, and the stocks which experience above-average, risk-adjusted returns).

The cross-sectional returns can be predicted by examining the usefulness of alternative measures of size or quality as tools to rank stocks in terms of risk-adjusted returns. The tests for predicting cross-sectional returns are dependent on the asset-pricing model that provides the measure of risk used in the test as well as the efficiency of the market.

Price-Earnings Ratios and Returns: EMH can be tested by examining the relationship between the historical Price-Earnings (P/E) ratios for stocks and their returns. There was an opinion that low P/E stocks outperform high P/E stocks because growth companies enjoy high P/E ratios, but the market tends to overestimate the growth potential and thus overvalues the growth companies while undervaluing low-growth firms with low P/E ratios. A relationship between the historical P/E ratios and subsequent risk-adjusted market performance would serve as an evidence against the semi-strong EMH because it implies that investors can use publicly available P/E ratios to predict future abnormal returns.

For testing purposes, the stocks were divided into five P/E classes and the risk and return for portfolios of high and low P/E ratio stocks were determined. Measures of risk-adjusted performance indicated that low P/E ratio stocks experienced superior results relative to the market, whereas high P/E ratio stocks had significantly inferior results. Therefore, it was concluded that publicly available P/E ratios possess valuable information. However, these results were not consistent with semi-strong efficiency.

P/E ratios were also examined after making adjustments for firm size, industry effects, and infrequent trading. With these adjustments it was found that the risk-adjusted returns for stocks with low P/E ratios were superior to those with high P/E ratios.

Price-Earnings/Growth Rate Ratios: The Price-Earnings/Growth Rate Ratio (referred to as PEG ratio) is used as a relative valuation tool for stocks of growth companies whose P/E ratios are relatively above average. An inverse relationship was observed to exist between the PEG ratio and subsequent rates of return, i.e., stocks with relatively low PEG ratios will have above average rates of return whereas stocks with high PEG ratios experience below average rates of return. The tests used to measure the PEG ratio do not support the EMH. When a sample of stocks was examined by dividing it on the basis of a risk measure (beta), market value size and expected growth rate, the results were not consistent with the hypothesis of an inverse relationship between the PEG ratio and subsequent rates of return except for stocks with low betas and those with very low expected growth rates.

The Size Effect: An examination of the impact of size (as measured by total market value), on risk adjusted rates of return showed that small firms consistently experienced significantly larger risk-adjusted returns than larger firms; and that it was the size that influenced the risk-adjusted returns and not the P/E ratio as per the earlier studies.

Inefficiency of the markets or the incorrect estimates of the expected returns provided by the market model may give rise to abnormal returns. According to Reinganum, abnormal returns were considered to be the result of the simple one-period CAPM, which is perceived to be an inadequate description of the real-world capital markets.

When betas were computed using two different models, the Ordinary Least Squares Model and the Aggregates Coefficients Model, a substantial difference was observed in the estimated betas for smaller firms. The results demonstrated that the risk for small firms was underestimated, but at the same time, the larger betas could not explain the very large differences in rates of return. Several results imply that most of the differences in size related returns can be explained by complete measures of risk.

Since transaction costs vary inversely with price per share (because they include both the dealer's bid-ask spread and the broker's commission), their impact on the risk-return relationship of large and small firms cannot be ignored. Also, a differential in transaction costs - with frequent trading - can have significant impact on the results. These results imply that subsequent size effect studies must consider realistic transaction costs and specify the holding period assumptions (if any). If an annual rebalancing is assumed, it was found that small firms outperformed the large ones after considering risk and transaction costs.

Thus, we see that firm size seemed to influence future returns and had remained an anomaly in the efficient market literature. In an effort to explain the anomaly, several attempts were made; however, no single study was able to explain the unusual results. However, the two strongest explanations were risk measurements and the higher transaction costs.

Book Value-Market Value (BM/MV) Method: Another predictor of stock returns identified is the ratio of a firm's book value of equity to its market value. A significant positive relationship is found to exist between a firm's historical BV/MV and the future stock returns. This result does not agree with the EMH.

The joint effects of market beta, size, E/P ratio, leverage and the BV/MV ratio on the cross section average returns on the NYSE, AMEX and NASDAQ stocks provide strong evidences in support of this ratio. Both size and BV/MV ratio are significant when included together and dominate other ratios. Though leverage and E/P ratio were significant by themselves or when considered with size, they become insignificant when both size and the BV/MV ratio are considered. The influence of the behavior of stock price to size and the BV/MV ratio on earnings changes is also studied. The focus of the analysis is on the relationship of high and low BV/MV stocks and profitability (measured as ROE). Low BV/MV stocks (growth stocks) have high ROE prior to forming portfolios but lower ROE in subsequent years. On the other hand, high BV/MV stocks (value stocks) experience low ROE prior to the formation of portfolios, but high ROE after the formation. Thus, size was found to play a major role in the small-stock portfolios, while the BV/MV ratio is more important for firms with high BV/MV ratios.

Following these studies, some more studies were conducted to test (i) the relationship between beta and rates of return and (ii) the manner in which BV/MV can be used to predict rates of return. Another opinion was that the relationship between returns and the BV/MV ratio is periodic and is not significant over a longer period.