A factor pricing model based on double moving average strategy

The paper addresses whether technical indicators that reflect heterogeneous investors’ trading across different term structures can improve asset pricing in China. Prior work (Fama-French five-factor; Liu et al.’s China four-factor) leaves unexplained anomalies. Behavioral finance and the heterogeneous market hypothesis imply investors have different horizons and react to information at different speeds, generating patterns in prices. Moving averages (MAs) offer a simple, widely used proxy for such behaviors and could capture short-, medium-, and long-term trading signals. The study investigates whether double moving-average (short MA crossing long MA) strategies produce excess returns in China and whether MA-derived factors can augment China’s four-factor model to better explain cross-sectional anomalies, including in different market and macroeconomic states.

The authors review evidence that technical analysis, especially moving averages, can forecast returns across markets (Brock et al., Fifield et al., Ma et al., Sun and Glabadanidis). Behavioral models (Hong and Stein; Daniel-Hirshleifer-Subrahmanyam; Barberis-Shleifer-Vishny) rationalize under/overreaction and momentum, consistent with investors with different horizons. Empirical studies show MA-based timing can outperform buy-and-hold and capture trends; weighted MAs can beat time-series momentum; MA crossovers are robust to misspecification. In China, retail dominance and heterogeneous beliefs enhance the relevance of technical signals. Prior Chinese asset-pricing work (Liu et al., PMO sentiment factor) improves anomaly explanation but may not fully capture heterogeneous term-structure behaviors. The paper positions MA-based factors as complementary to size, value, and sentiment factors.

Data: A-shares from Shanghai and Shenzhen Stock Exchanges, Jan 2000–Jun 2020 (WIND). To ensure portfolio sizes and MA lags, effective sample starts Jan 2002. Exclusions: firms listed <6 months; <120 trading days/year or <15 days/month. Unlike Liu et al. (2019), the study retains the bottom 30% by market cap. Factor construction: Start with China four factors (CH4) per Liu et al. (2019): market (Mkt), size (SMB), value (VMG, based on earnings-to-price ratio EP), and sentiment (PMO, pessimistic-minus-optimistic via turnover). Formulas (schematic): SMB is small minus big across value, neutral, growth; VMG is value minus growth across size; PMO is low-turnover minus high-turnover across size. Double moving average signals: For stock j at month t, MA_{j,t,L} is the L-month simple moving average of closing prices. Define S_{j,t,L} = MA_short / MA_long for various short/long lags. Trading rule: buy when short MA crosses up long MA; sell on cross down. Construct SCL factors (Short-term MA cross Long-term MA) as long portfolios of low S (anticipating reversal when S is very high) minus high S, value-weighted, with size splits:

1. Split universe into Small 50% and Big 50% by median outstanding shares.
2. Sort S_{j,t,L} into 30% low, 40% middle, 30% high.
3. Form six intersected portfolios (Small/Big × Low/Mid/High).
4. SCL factor is average of value-weighted (Small Low + Big Low) minus (Small High + Big High); returns realized at t+1. SCL(m,n) denotes m-month short over n-month long. Tested term structures: Short MAs of 1, 3, 6, 9, 12, 18 months crossed with long MAs of 3, 6, 9, 12, 18, 24 months (21 combinations centered on quarterly/semiannual/annual points). Filters analysis: Evaluate SCL factors with no filter, size filter (exclude bottom 30% cap), and price filter (exclude stocks with price <5 CNY). Model selection and tests: Backward stepwise spanning regressions to identify non-redundant SCL factors to add to CH4, yielding two factors: SCL(1,3) and SCL(1,12). Provide descriptive stats and correlations. Assess factor effectiveness using maximum squared Sharpe ratio Sh^2(f) per Barillas and Shanken (2016), including a bootstrap procedure (Fama and French, 2018): group 222 months into 111 pairs; randomly assign one month from each pair to in-sample and the other to out-of-sample; compute in-sample optimal weights and out-of-sample Sharpe; repeat 9,999 times. Anomaly tests and GRS: Construct 18 anomalies (e.g., E/P, B/M, C/P, ROE, volatility, 1-month max, reversal, breakout, momentum, turnover-based measures, and SCL variants). For each anomaly, decile-sort monthly and compute P10–P1 returns. Estimate time-series regressions of anomaly returns on factor models: three-factor (Mkt, SMB, VMG), four-factor (add PMO), FF5, and augmented six-factor (add SCL(1,3), SCL(1,12)). Use GRS (Gibbons-Ross-Shanken) to test joint alphas. State dependence: Partition months by GDP growth rate and Shanghai Composite Index levels: best 15%, middle 70%, worst 15%. Evaluate model performance (GRS, avg |alpha|, avg |t|, Sh^2(f)) across states. Trend dependence: Partition CSI 300 into major bear/bull regimes (2002–2005 bear, 2005–2008 bull, 2010–2014 bear, 2015.6–2020.6 bear) and repeat GRS comparisons.

• Profitability of MA strategies: SCL with 1-month short MA across long MAs of 3–24 months delivers significantly positive monthly returns. Examples (Table 1, Avg%, T): SCL(1,3) 1.173%, T=4.129; SCL(1,6) 1.144%, T=3.768; SCL(1,9) 0.965%, T=3.158; SCL(1,12) 0.920%, T=3.026; SCL(1,18) 0.912%, T=3.024; SCL(1,24) 0.901%, T=2.910. Other short MAs (3, 6, 9, 12, 18) do not show significance at 5%.
• Filters and small caps (Table 2): Unfiltered portfolios (including bottom 30% cap) have higher mean returns and Sharpe ratios than size- or price-filtered sets. Example for SCL(1,3): Avg 1.173% (no filter) vs 0.975% (size filter) vs 0.869% (price filter); Sharpe 0.277 vs 0.228 vs 0.152. Thus, small-cap inclusion strengthens MA profitability.
• Factor selection and complementarity: Stepwise spanning regressions identify SCL(1,3) and SCL(1,12) as augmentations to CH4, with these SCL factors not subsuming original factors but complementing size, value, and sentiment.
• Descriptive stats (Table 4): Average monthly returns (%, T): Mkt 0.675 (T=1.291, ns); SMB 0.916 (T=2.942); VMG 0.717 (T=2.722); PMO 0.866 (T=4.154); SCL(1,3) 1.173 (T=4.129); SCL(1,12) 0.920 (T=3.026). Sharpe ratios: PMO 0.279, SCL(1,3) 0.277, SCL(1,12) 0.203. Correlation between SCL(1,3) and SCL(1,12)=0.756; other cross-factor correlations mostly <0.5.
• Maximum squared Sharpe ratio improvements (Table 5): True-sample Sh^2(f): three-factor 0.190, four-factor 0.264, six-factor 0.323. Bootstrap out-of-sample averages: six-factor exceeds four-factor by 0.040 (T≈35.836) and exceeds three-factor by 0.095 (T≈20.301); in-sample and full-sample improvements are also significant.
• GRS anomaly tests (Table 6): Across 18 anomalies, only the six-factor model passes GRS at 5% in full sample (GRS=1.652, p=0.051). Three-factor: GRS=2.581, p=0.001; four-factor: GRS=2.049, p=0.009; FF5: GRS=2.266, p=0.003. Six-factor reduces Avg |alpha| by ~50% (0.274 vs 0.526 and 0.544) and Avg |t| to 1.017 (vs 1.370 and 1.408).
• Subsamples (Table 6): Six-factor model continues to outperform. In 2011.4–2020.6, six-factor GRS=1.457, p=0.126 (cannot reject zero alphas), while three- and four-factor models are significant.
• State dependence (Table 7): Six-factor dominates across GDP and SH-index states. In GDP middle 70%, only six-factor approaches non-rejection at 5% (GRS=1.592, p=0.072) and has higher Sh^2(f)=0.492 than three- (0.302) and four-factor (0.365). In SH-index worst 15%, six-factor p=0.102 with lower Avg |alpha| (0.757) than three-factor (0.943).
• Trend periods (Table 8): In pronounced bear/bull regimes, six-factor yields lower GRS and higher Sh^2(f) than three- and four-factor models. Example 2002–2005: GRS=0.531 (p=0.914), Sh^2(f)=0.838 vs three-factor GRS=0.998 (p=0.490), Sh^2(f)=0.747 and four-factor GRS=0.770 (p=0.531), Sh^2(f)=0.900.
• Interpretation: Short-term signals (1-month MA) carry the strongest predictive content, reflecting heterogeneous investors’ quick reactions; MA factors capture trading behavior beyond PMO sentiment and materially enhance pricing power in China.

The study demonstrates that moving-average factors reflecting heterogeneous investor horizons significantly improve the explanatory power of asset-pricing models in China. The strong performance of 1-month short MA crossovers indicates investors respond most to short-term information, consistent with behavioral theories of under/overreaction and with a retail-dominated market. Adding SCL(1,3) and SCL(1,12) to Liu et al.’s CH4 improves maximum squared Sharpe ratios, reduces joint alphas, and passes GRS tests where baseline models fail, including out-of-sample and across macro and market states. The results suggest PMO alone does not fully span noise-trading effects; MA-based trend factors capture additional dimensions of sentiment- and horizon-driven trading. Inclusively analyzing small caps is important in China, as these stocks exhibit stronger trend predictability and meaningfully affect aggregate pricing. The six-factor model remains relatively robust across GDP and market states and is especially effective during pronounced trend regimes, aligning with the notion that trend-following behavior synchronizes during such periods.

The paper establishes that double moving-average factors, particularly SCL(1,3) and SCL(1,12), capture heterogeneous investors’ trading across term structures and significantly enhance the pricing power of China’s four-factor model. 1-month short MA crossovers with longer MAs generate significant excess returns; incorporating these as factors improves maximum squared Sharpe ratios, reduces average absolute alphas by about 50%, and yields GRS non-rejection at the 5% level for a broad set of anomalies. The augmented six-factor model outperforms baseline models across subsamples and in state-dependent analyses (GDP, market regimes), with notable strength during clear market trends. Given China’s retail dominance and short-horizon trading, MA factors provide essential complementary information to value, size, and sentiment. Future work could explore additional horizon structures, alternative MA constructions (e.g., weighted/exponential), interactions with other behavioral factors, and broader robustness across asset classes and more recent periods.

• Data access: The study relies on WIND Info; data are not publicly available due to commercial confidentiality, limiting external replication.
• Market frictions: Short selling constraints in China may dampen factor effectiveness in downtrends, as observed in weaker Sh^2(f) increases during bearish regimes.
• Model scope and selection: To avoid redundancy, only two MA factors (SCL(1,3), SCL(1,12)) are included despite broader signal space; other specifications (e.g., different MA types or parameterizations) are not examined.
• State dependence: Pricing performance varies with GDP and market states; in some SH-index states (middle 70%), no model fully explains anomalies (GRS p-values near zero), indicating conditional efficacy.
• Sample design: New listings and very illiquid months are excluded, and results are specific to 2002–2020 A-share data; generalizability to other periods or markets may be limited.