Stock liquidity and price‑to‑book discounts: non‑linear evidence from European‑listed firms

• Stock liquidity has a convex (non-linear) effect on the price-to-book ratio. • Illiquidity discount is pronounced for value stocks but negligible for glamour firms. • Results support accounting for liquidity in valuation models and regulatory policy. We test whether liquidity alters valuation asymmetrically across European equities in the period 2001 to 2023. Our findings reveal a convex pattern: a one‑standard‑deviation rise in illiquidity lowers the price‑to‑book ratio by 3 % in the bottom decile but becomes immaterial above the 90th percentile. Specifically, for firms with lower price/book ratios, higher trading volume acts as a mechanism that depresses even further stock pricing, suggesting a negative investor sentiment. Results imply that comparable‑multiple models, liquidity‑based regulation and distressed‑equity screens should all be conditioned on market depth.