The Nominal Price Premium

Motivated by the evidence that investors tend to be overly optimistic about low-priced stocks, we examine how nominal price affects the cross section of stock returns. To circumvent the mechanical inverse relationship between price and expected return, we construct a novel way of examining the effect of nominal price on the cross section of stock returns. In the cross-section, a portfolio exploiting this strategy generates a value-weighted (equal-weighted) four-factor alpha of 85 (88) basis points per month, while raw price does not predict return robustly. Consistent with a mispricing-based explanation, the results are stronger for hard-to-arbitrage stocks and following high sentiment periods, and strategy returns are highly correlated with contemporaneous changes in sentiment. Using stock splits as an exogenous change in price level, we find that the post-split return dynamics mimic those predicted by our hypothesis. Evidence from earnings surprises and analyst price target forecasts confirms that beliefs are overly optimistic for low-priced stocks. Providing further evidence that the results reflect a belief-based rather than purely a preference-based channel, we find that the effect is distinct from other gambling related proxies that have been used in the past such as extreme returns, idiosyncratic volatility, and skewness.