A Valuation Study of Stock Market Seasonality and the Size Effect

Existing studies on market seasonality and the size effect are largely based on realized returns. This paper investigates seasonal variations and size-related differences in crossstock valuation distribution. We use three stock valuation measures, two derived from structural models and one from book/market ratio. We find that the average valuation level is the highest in mid summer and the lowest in mid December. Furthermore, the valuation dispersion (or, kurtosis) across stocks increases towards year end and reverses direction after the turn of the year, suggesting increased movements in both the underand over-valuation directions. Among size groups, small-cap stocks exhibit the sharpest decline in valuation from June to December and the highest rise from December to January. For most months, small-cap stocks have the lowest valuation among all size groups and show the widest cross-stock valuation dispersion, meaning they are also the hardest to value. Overall, large stocks enjoy the highest valuation uniformity and are the least subject to valuation seasonality. One of the salient facts in finance is the documented seasonality in stock returns. Specifically, recent losers tend to experience fortune reversals in January (hence, the January effect), whereas recent winners tend to continue and expand their fortunes in December (hence, the December effect). Most studies on stock market seasonality have relied on return differences across calendar times. In this paper, we analyze seasonality from a different perspective: cross-sectional valuation movements from one calendar time to another. Using alternative valuation measures, we investigate how the cross-stock valuation distributions shift from month to month. Our goal is to study whether such month-to-month variations exhibit any systematic patterns. If seasonal patterns exist, we then want to see whether they can shed new light on the documented January and December effects. This approach offers unique insights into the seasonality effects by allowing us to gauge the relative and absolute valuation characteristics of stocks in various months of the year. At the same time, given the documented seasonal return patterns, our study allows us to evaluate alternative valuation measures, with the understanding that a good stock valuation metric must be able to demonstrate in advance certain seasonal dynamics and predict such return patterns. That is, which valuation measure best anticipates the return seasonality? The fact that beaten-down stocks, especially small firms, experience return reversals in January has long been a puzzling phenomenon. There are several proposed explanations, including ”window-dressing” by institutional investors (Lakonishok, Shleifer, Thaler, and Vishny [1991]) and the tax-loss selling hypothesis (Grinblatt and Moskowitz [2004]). The window-dressing hypothesis contends that institutional investors sell losers and buy winners to prepare for year-end reporting. Such buying and selling create positive price pressure on winners and downward pressure on losers before the turn of the year. As the selling by institutions stops at year end, prices for beaten-down stocks rebound in January, producing large returns for last year’s losers. The tax-loss selling hypothesis asserts that it is the individual investors faced with capital gains taxation who sell poorperforming stocks to reduce their taxes. To achieve such tax reduction, an investor must sell the losing stocks before year end as capital losses can be used to offset gains only upon realization. Both hypotheses predict that losers as of late fall will likely continue going lower in December, but will have high returns in January. The window-dressing hypothesis also suggests that strong performers by late fall shall continue going strong in December, which may be a key reason behind the December effect. The purpose of this paper is to identify and understand what valuation picture is behind the return seasonality. Such an exercise does not only help deepen our understanding of the seasonality phenomenon, but also shed new light on the development of stock valuation models. Specifically, we implement three valuation measures. The first measure is based on the dynamic stock valuation model developed by Bakshi and Chen [2005] and extended by Dong [2000], (“BCD model”). We refer to the percentage deviation by the market price from a stock’s model valuation as the BCD mispricing. The second measure is the value/price (V/P) ratio, where “value” is determined using the residual-income model as implemented in Lee, Myers and Swaminathan [1999]. The last measure is the book/market (B/M) ratio, which is a traditional valuation metric. Our results are briefly summarized below: