Asset pricing and nominal price illusion in China

The paper investigates whether nominal price illusion—manifested as a low-priced stock premium (LPP)—is a systematic factor in asset pricing for China’s A-share market. Classic CAPM posits market beta as the sole driver of expected returns, yet many anomalies remain unexplained, spurring multi-factor models such as Fama-French (FF3 and FF5) and others. China’s market features a high share of retail investors and observed low-price effects, suggesting behavioral influences may be important. The study’s purpose is to augment FF3 and FF5 with an LPP factor grounded in behavioral finance, and evaluate whether incorporating LPP improves model fit and pricing performance in China, thereby addressing the gap that existing models cannot fully capture high average stock returns and do not explicitly consider nominal price effects in a retail-dominated market.

The literature traces the evolution from CAPM to multi-factor models: FF3 added size (SMB) and value (HML); Carhart introduced momentum; Novy-Marx focused on profitability and sector-neutral construction; Stambaugh and Yuan proposed mispricing-based factors; FF5 added profitability (RMW) and investment (CMA). Evidence on FF models’ applicability to China is mixed: some find FF3 and FF5 work, others find limitations, with several studies noting FF5 often outperforms FF3 but investment contributes little and high average returns remain undercaptured. The low-price effect has been documented since Fritzemeier (1936). Attempts to explain it via size, value, liquidity, profitability, quality, or leverage do not fully eliminate the premium. Behavioral explanations (e.g., money illusion, catering to nominal prices) suggest investors over-prefer low nominal price stocks. Individual investors favor low-priced stocks, and firms may target trading ranges to appeal to noise traders. In China, retail dominance strengthens the low-price premium effect, especially among smaller caps. This background motivates testing LPP as an explicit pricing factor in China.

Data: Monthly data for all A-share listed firms (4,392) from CSMAR, 01/2007–12/2020, post non-tradable share reform. Variables include market return (cash dividends reinvested), risk-free rate (one-year time deposit rate), market capitalization, book value, operating profit, investment, and other firm characteristics. Outliers are filtered (e.g., long suspensions, extreme trading days, negative book-to-market). Risk-free and market rate choices follow prior China studies (Hou et al., 2019; Liu et al., 2019). Factor construction: Following Fama-French (2015), form SMB, HML, RMW, and CMA using size (S/B split at median) and characteristic sorts (typically terciles at 30%/70% thresholds for EP, OP, Inv). Compute portfolio returns and construct factor returns via long-short spreads. Extend SMB as an average across multiple SMB legs (e.g., SMB_BM, SMB_OP, SMB_INV, SMB_LPP). LPP construction: Following Luo et al. (2017) (LX method), estimate an LPP index per stock over time via cross-sectional regressions including lagged price (PRICE_{t-1}), moderators (retail ownership, institutional ownership, analyst shareholding, short-selling dummy), interactions with price, and controls with industry and year fixed effects. Then form an LPP factor analogously to FF factors as the return spread between high-LPP and low-LPP portfolios, with size neutrality: LPP = (S/F + B/F)/2 – (S/RE + B/RE)/2. Models: Estimate FF3 and FF5 baseline models; augment each with LPP to create four-factor (FF3+LPP) and six-factor (FF5+LPP) models. Conduct factor spanning regressions (each factor regressed on others) to assess redundancy. Portfolio tests: Two-way 5x5 sorts along LPP with Size, EP, OP, and Inv to examine excess return patterns across LPP quintiles. Performance and robustness: Evaluate intercept terms across sorted portfolios, compare explanatory power across models, and apply the Gibbons-Ross-Shanken (GRS) test for joint alpha significance to assess model validity and robustness.

• Descriptive factor behavior (Table 1): Mean monthly returns (%)—Rm-Rf 1.21, MKT 0.65, SMB 0.32; HML −0.13, RMW −0.01, CMA −0.08, LPP −0.23. LPP is negatively correlated with market excess returns and several factors; notably it correlates strongly with HML (0.77) and CMA (0.45). - Factor spanning (Table 2): Size (SMB), value (HML), profitability (RMW), and LPP retain significant risk premia after adjustment by other factors, while CMA appears redundant (its intercept cannot reject zero), consistent with prior findings in China. - Portfolio sorts (Table 3): In 5x5 two-way sorts with Size, EP, OP, and Inv, excess returns decrease monotonically as LPP quintiles increase, indicating a robust low-priced stock premium effect in the A-share market. - Model regressions (Table 4): LPP loads significantly and negatively in both augmented models, confirming that higher LPP is associated with lower excess returns. Reported LPP coefficients are statistically significant: approximately −0.307 (FF3+LPP) and −0.508 (FF5+LPP), both at 1% significance. Including LPP increases the models’ explanatory power relative to their baselines as stated by the authors. - Intercepts across Size–B/M and Size–Inv (Tables 5–6): Adding LPP reduces the number and magnitude of significant non-zero intercepts relative to FF3 and FF5, indicating improved fit. For example, FF3 vs. FF3+LPP shows fewer insignificant intercepts and stronger explanatory power; FF5+LPP (six-factor) outperforms FF5 across many cells. - GRS robustness (Table 7): Models with LPP generally exhibit lower GRS statistics than their baselines, indicating improved joint pricing. Examples: FF3 Size–Inv GRS falls from 1.3936** to 1.3173**; FF3 Size–PI from 1.9267*** to 1.7916***. For FF5, GRS decreases in Size–OP (1.2681** to 1.2017*) and Size–Inv (1.1617** to 1.1460*), with comparable results elsewhere. Overall, FF5 remains more applicable than FF3, and the six-factor (FF5+LPP) is the most robust. - Economic interpretation: The significant negative LPP loadings indicate that portfolios with stronger low-price premium characteristics earn lower excess returns after controlling for standard factors, consistent with the behavioral nominal price illusion mechanism in a retail-driven market.

The findings support the hypothesis that nominal price illusion, proxied by an LPP factor, captures systematic variation in returns in China’s A-share market beyond standard Fama-French factors. By showing that LPP is significant in factor spanning tests, 5x5 portfolio sorts, and regression loadings, and that including LPP reduces pricing errors and GRS statistics, the study demonstrates that LPP helps address anomalies not fully captured by FF3 or FF5 alone—particularly the persistent high average returns. The evidence aligns with China’s investor composition: a predominance of retail investors who tend to favor low nominal price stocks, amplifying the low-price premium effect. The six-factor model (FF5+LPP) yields better explanatory power and robustness than FF5, indicating that augmenting economic-based factors with a behavioral component improves pricing performance in this market. Policy-wise, recognizing the role of retail-driven preferences and nominal price perceptions can inform market development and investor education initiatives.

Using CSMAR data for 4,392 A-share firms from 2007–2020 and constructing an LPP factor via the LX approach, the study finds that LPP is an effective, systematic pricing factor with a strong negative association with excess returns. Augmenting FF3 and FF5 with LPP improves model fit; the six-factor model (FF5+LPP) performs best and passes robustness checks (GRS), while CMA appears relatively redundant in China. The results emphasize the importance of behavioral influences—especially nominal price preferences in a retail-dominated market—for asset pricing in China. Policy implications include further opening of capital markets to increase institutional participation, improve market professionalism, and reduce nominal price distortions. Future research will apply more complex tests and deepen theoretical foundations, acknowledging that no model is flawless and that continued evaluation of factor models’ advantages and limitations is necessary.

• Market- and period-specific scope: Evidence is based on China’s A-share market from 2007–2020; generalizability to other periods or markets may be limited. - Measurement choices: Risk-free rate proxied by one-year time deposit rate and market return construction reflect China-specific financial conditions during partial interest rate liberalization. - Model design: While LPP improves performance, factor correlations (e.g., with HML and CMA) may complicate interpretation, and CMA appears redundant in this setting. - Methodological constraints: The authors note that more complex tests are needed and that no model is perfect; additional robustness checks and alternative specifications could further validate results.