Academics and investment practitioners alike have documented the presence of a “value premium”, where stocks with low price-to-fundamental ratios tend to experience higher beta-adjusted returns than stocks with high price-to-fundamental ratios. While few deny that a value premium exists in equity markets, there are many theories as to why it exists. Some suggest it is a fair premium for bearing risk, while others suggest it is a result of suboptimal behavior by investors. It may simply be a product of normal pricing mistakes associated with uncertainty.

Pricing mistakes – and the resulting value effect – are bound to occur in markets characterized by uncertainty. Stocks with high price-to-fundamental ratios and are more likely to experience overvaluation errors, while stocks with low price-to-fundamental ratios are more likely to experience undervaluation errors. Furthermore, we would expect to observe this pattern of valuation mistakes even when investors are, on average, pricing stocks correctly. These systematic pricing errors can persist because there is a range of justified levels of valuation; investors cannot know for certain whether a stock is correctly priced. Indeed, a stock with a low price-to-fundamental ratio may be correctly priced to reflect either poor growth prospects or a significant non-diversifiable risk, or may be either under or overvalued.

If we consider the full universe of stocks, we can better identify where underpricing and overpricing mistakes are more likely to occur. Assume, for example, that every stock has some justified price-to-earnings (P/E) ratio that reflects the stock's growth potential and non-diversifiable risk.

We assume stocks fall into three different categories of potential growth and non-diversifiable risk, which translates into a spectrum of five levels of justified P/E ratio, from ‘very low' P/E to ‘very high' P/E. (See Table 1.) If we assume that one-third of stocks fall into each of the three categories of both growth and risk, then the distribution of justified P/Es is described by Table 2. In our example, one-third of stocks have average justified P/Es, two-ninths have low justified P/Es, and one-ninth have very low justified P/Es.

But in an environment of uncertainty, investors make pricing mistakes. Assume investors make symmetric pricing errors, where, across all levels of justified P/E, one-third of stocks are overpriced, one-third are underpriced, and one-third are correctly priced. For a given level of justified P/E, the pricing errors offset and the average observed P/E is equivalent to the justified P/E. Chart 1 illustrates how those symmetric pricing errors relate observed P/Es (y-axis) to justified P/Es (x-axis). Across all stocks within a category of justified PE, the average observed P/E reflects the justified P/E. We can now assess the distribution of P/E ratios – with valuation mistakes – that confronts investors and evaluate how the valuation mistakes stack up along the valuation spectrum.

Table 3 illustrates the distribution of observed P/Es and whether stocks within each category are correctly priced, underpriced, or overpriced. Due to the uncertainty investors face and the related valuation errors, the distribution of observed P/Es is wider than that of the justified P/Es.

More importantly, underpricing errors migrate to the low P/E side of the distribution, while overpricing errors migrate to the high P/E side of the distribution. Among stocks with below-average observed P/Es, 10% are overpriced, 30% are correctly priced, and 60% are underpriced. Similarly, among stocks with above-average observed P/Es, 10% are underpriced, 30% are correctly priced, and 60% are overpriced. Investors cannot know which stocks are mispriced, but can observe the average mispricing of stocks with high or low observed P/Es.

Some might argue that if investors perceive there is systematic underpricing of low P/E stocks, they will simply mark up the price of all low P/E stocks (and mark down high P/E stocks) to erase any underpricing. That might be true, but that would make the average observed P/E for low P/E stocks higher than what we assumed was justified. In other words, if investors correct mispricing across all low or high P/E stocks, they introduce stock-specific mispricing relative to P/Es we assume are justified. In any event, empirical evidence on the value effect is consistent with some persistent level of valuation-related mispricing. Maybe part of the hotly debated value effect is simply the normal migration of pricing errors we expect to observe in an environment of uncertainty. The challenge for investors is to understand whether those symmetric pricing mistakes represent opportunity, and, if so, how best to capture it.

This material is for your private information. The views expressed are the views of Eric Brandhorst only through the period ended January 11, 2005 and are subject to change based on market and other conditions. The opinions expressed may differ from those with different investment philosophies. The information we provide does not constitute investment advice and it should not be relied on as such. It should not be considered a solicitation to buy or an offer to sell a security. It does not take into account any investor's particular investment objectives, strategies, tax status or investment horizon. We encourage you to consult your tax or financial advisor. All material has been obtained from sources believed to be reliable, but its accuracy is not guaranteed. There is no representation nor warranty as to the current accuracy of, nor liability for, decisions based on such information. Past performance is no guarantee of future results.

Posted On: January 31, 2005