Factor Research –Capital Gain Overhang | Part 1

Preface

The origins of the momentum anomaly have long been debated, with multiple competing explanations. Among them, one of the most influential behavioral interpretations attributes momentum to the Disposition Effect, a systematic bias in investor decision-making. This article focuses on the Capital Gain Overhang (CGO) factor, specifically designed to quantify this behavioral bias. Using the Taiwan equity market as a case study, we examine CGO’s predictive power as a stock selection indicator and evaluate its practical value through empirical analysis.

Capital Gain Overhang (CGO) : A Key Measure of the
Disposition Effect

A cornerstone of behavioral finance is Prospect Theory, proposed by Kahneman and Tversky (1979). The theory suggests that individuals evaluate gains and losses relative to a reference point rather than absolute wealth levels, and they experience losses more intensely than equivalent gains—a phenomenon known as loss aversion.

Building on this foundation, Shefrin and Statman (1985) introduced the concept of the Disposition Effect. Within the framework of mental accounting, investors tend to assign each stock purchase to a separate mental account, with the purchase price serving as the critical reference point for gains or losses. This bias drives two systematic behaviors: investors are prone to selling winning stocks too early to lock in gains, while holding onto losing stocks for too long to avoid realizing losses.

If such behavior is widespread, it inevitably creates predictable price pressure. To capture this effect, Grinblatt and Han (2005) proposed the Capital Gain Overhang (CGO) factor, designed to directly quantify the Disposition Effect. CGO measures the gap between the current market price and the estimated average cost basis of all shareholders. Since actual investor costs are unobservable, they introduced a turnover-based method, which approximates cost using a volume-weighted series of historical prices. Subsequent research validated this approach: Frazzini (2006) employed a completely different holding-based method using mutual fund holdings data and reached conclusions highly consistent with Grinblatt and Han. The convergence of these independent methodologies strongly indicates that the CGO effect is genuine, rather than an artifact of any specific estimation technique.

The theoretical implication is straightforward:

• When most investors hold unrealized gains (high CGO), potential selling pressure from profit-taking dampens the market’s reaction to positive news.
• Conversely, when investors hold unrealized losses (low CGO), their reluctance to realize losses provides support, muting the impact of negative news.

This asymmetric reaction creates a positive relationship between CGO and expected future returns.

Most importantly, CGO reinterprets the traditional momentum factor. Grinblatt and Han (2005) demonstrated that CGO not only predicts future returns but also subsumes the explanatory power of the conventional intermediate-term momentum factor. This suggests that the well-documented momentum anomaly may largely be a manifestation of the Disposition Effect. In other words, traditional momentum factors, based purely on past returns, may simply act as a noisy proxy for CGO.

Factor Analysis

This section presents the empirical examination of the Capital Gain Overhang (CGO) factor in Taiwan’s equity market, focusing on whether it reliably predicts future returns.

Data Source and Sample Period

The dataset is sourced from Taiwan Economic Journal (TEJ) :

• Price & Trading Data: stock price and returns.
• Market Factor Data : market risk premium, size premium, book-to-market premium, and risk-free rate
• Factor Indicators : Capital Gain Overhang (CGO), 52-week high momentum (MOM52WH)
• Sample period: Jan 2005 – June 2025
• Scope: All common stocks listed on the Taiwan Stock Exchange (TWSE) and Taipei Exchange (TPEx).

Construction of Capital Gain Overhang (CGO)

CGO is calculated following Grinblatt and Han’s (2005) turnover-based method, adapted to Taiwan’s market structure. Specifically, TEJ applies a 100-trading-day look-back window, using turnover-weighted adjusted daily prices with time decay to estimate investors’ average cost basis.

This design reflects two key assumptions:

1. Turnover weighting – high-turnover days better capture shifts in the cost base.
2. Time decay – older prices are less representative due to position turnover, consistent with investors’ mental accounting.

Descriptive Statistics

To examine the cross-sectional features of Capital Gain Overhang (CGO) in Taiwan’s stock market, we apply the portfolio-sorting method. On each trading day, all stocks are ranked by their CGO values and divided into ten equally weighted portfolios, labeled from P1 (lowest CGO) to P10 (highest CGO).

Table 1 summarizes descriptive statistics of these portfolios over the sample period (January 2005 – June 2025). The results show that average CGO values increase monotonically from P1 to P10, confirming the effectiveness of the grouping.

Table 1：descriptive statistics of CGO factor

	Min	Max	Mean	Std	Count	%
1	-0.9236	0.09118	-0.194762	0.107928	735360	10.031237
2	-0.53369	0.12821	-0.114891	0.076839	732881	9.99742
3	-0.46608	0.15705	-0.081821	0.07067	732350	9.990177
4	-0.42359	0.18262	-0.057136	0.065729	732840	9.996861
5	-0.38765	0.20536	-0.036038	0.061512	733393	10.004405
6	-0.34851	0.23364	-0.016373	0.057915	731802	9.982702
7	-0.31608	0.27171	0.003678	0.055108	732338	9.990013
8	-0.27466	0.3223	0.026796	0.053688	732727	9.99532
9	-0.22777	0.40388	0.05915	0.055491	732306	9.989577
10	-0.16402	3.2241	0.151017	0.110712	734704	10.022288

An important observation is that the extreme portfolios—P1 (largest unrealized losers) and P10 (largest unrealized winners)—exhibit significantly higher standard deviations than the middle groups. This indicates greater heterogeneity among firms at both ends of the CGO distribution.

Return Analysis

We next evaluate the predictive power of CGO for future returns by analyzing the performance of these sorted portfolios.

Table 2 and Figure 3 present the average daily returns of CGO decile portfolios across different holding horizons (1 to 100 trading days). Two key findings emerge:

1. Return predictability – Across all horizons, the highest-CGO portfolio (P10) consistently outperforms the lowest-CGO portfolio (P1). As a result, the long–short spread (P10–P1) remains positive, confirming that high-CGO stocks tend to deliver higher subsequent returns.
   
2. Evolution of return patterns –The shape of the return–CGO relationship shifts with the investment horizon.
   • For short horizons (1–40 days), the return curve shows a U-shaped distribution, where both extreme portfolios (P1 and P10) outperform the middle deciles.
   • Over longer horizons (60–100 days), the pattern transitions into a monotonically increasing relationship, providing strong empirical support for the hypothesis that higher CGO stocks deliver higher long-term expected returns.

Table 2：Average Daily Returns of CGO Factor Groups and Long-Short Hedge Portfolios

	1D	5D	10D	20D	40D	60D	100D
Top Quantile, P10	9.964	10.178	10.275	8.820	8.293	8.226	8.026
Bottom Quantile, P1	7.626	7.322	6.486	6.465	5.387	4.279	4.046
Spread, P10-P1	2.338	3.386	4.400	3.010	3.552	4.543	4.541

Figure 3：Average returns of CGO factor deciles over different holding periods

Figure 4 further illustrates cumulative performance. The high-CGO portfolio shows steadily superior cumulative returns compared to the low-CGO portfolio, with smaller drawdowns, suggesting that high-CGO firms may possess a degree of defensiveness in adverse markets. This feature enhances the factor’s ability to generate favorable risk-adjusted returns over the long run.

Figure 4 : Cumulative Return Trends by CGO Group (Top vs. Bottom Quantile)

Risk Factor Model Regression

To test whether the returns of CGO-sorted portfolios can be explained by well-known systematic risk factors, we conduct time-series regressions of monthly excess returns against several classical asset pricing models. At the beginning of each month, stocks are grouped by their end-of-month CGO values, and portfolio returns are held for one month. These returns are then regressed on the factors of four benchmark models. The primary focus of this analysis is the intercept term (alpha). A significantly positive alpha indicates the presence of abnormal returns unexplained by the included risk factors. To account for serial correlation and heteroskedasticity in financial time series, all t-statistics are adjusted using the Newey–West (1987) method.

Table 5：CGO Portfolio Factor Model Regression Alpha

Portfolio	CAPM	Fama-French 3 Factors	Fama-French 5 Factors	Fama-French 6 Factors
Bottom Quantile P1	0.0017 (0.58)	-0.0015 (-0.76)	0.0001 (0.03)	0.0034 (1.62)
Top Quantile P10	0.0106*** (5.49)	0.0082*** (5.69)	0.0090*** (5.85)	0.0077*** (5.26)
Spread P10-P1	0.0088*** (2.81)	0.0097*** (3.19)	0.0090*** (2.70)	0.0043 (1.38)

Table 5 reports the regression alphas for the lowest-CGO portfolio (P1), the highest-CGO portfolio (P10), and the long–short spread (P10–P1).Key findings are as follows:

• High-CGO portfolios show significant alpha.
  Under CAPM and Fama–French models (FF3, FF5), the highest-CGO portfolio (P10) delivers strong and statistically significant alpha, indicating that CGO captures excess returns not explained by standard factors, mainly from the long side.
  
• CGO overlaps with momentum.
  The long–short spread is significant under CAPM, FF3, and FF5, but loses significance in the FF6 model once momentum is included, consistent with Grinblatt and Han (2005) that momentum largely reflects the Disposition Effect.

Information Coefficient (IC) Analysis

To further evaluate the predictive power of CGO, we calculate the Information Coefficient (IC)—the Spearman rank correlation between CGO values and subsequent returns across different holding horizons.

Table 6：Summary of Information Coefficients (ICs) for the CGO Factor at Different Holding Periods

	1D	5D	10D	20D	40D	60D	100D
IC Mean	-0.001	0.0008	0.0065	0.0079	0.0252	0.0448	0.0635
IC Std	0.1226	0.1369	0.1389	0.1436	0.1415	0.1318	0.1144
Risk Adjusted IC	-0.008	0.0062	0.0465	0.0552	0.1781	0.3401	0.5554
IC t-value	-0.5649	0.4359	3.2661	3.8777	12.5163	23.9026	39.0314
IC p-value	0.5721	0.663	0.0011***	0.0001***	0***	0***	0***
IC Skewness	-0.1767	-0.3965	-0.4118	-0.5668	-0.9367	-1.1376	-1.1015
IC Kurtosis	1.6359	1.3835	1.1328	0.7843	1.4874	2.3776	2.7987

Table 6 reports the IC statistics. The results highlight two key insights:

1. Predictive strength grows with horizon.
   For short horizons (e.g., 1–5 days), the IC is weak and insignificant. However, as the holding period extends, IC values turn positive and steadily increase. At the 100-day horizon, the mean IC reaches 0.0635 with strong statistical significance (t = 39.03).
   
2. Strong risk-adjusted performance.
   The risk-adjusted IC (IR) rises sharply with longer horizons, reaching 0.555 at 100 days. In practice, IR values above 0.5 are considered excellent, underscoring CGO’s reliability as a medium- to long-term stock selection factor.

In sum, the IC analysis provides robust evidence that CGO is a powerful predictive signal in Taiwan’s equity market, particularly over 60–100 day horizons, where its forecasting ability is both stable and economically meaningful.

Conclusion

The empirical analysis confirms that Capital Gain Overhang (CGO) is a meaningful and robust factor in Taiwan’s equity market. Across portfolio-sorting tests, return analysis, risk factor regressions, and IC evaluation, CGO consistently shows predictive power, particularly over medium- to long-term horizons. High-CGO portfolios deliver significantly higher future returns, with evidence of positive alpha beyond standard Fama–French factors. However, its overlap with momentum suggests that CGO captures behavioral effects closely tied to the Disposition Effect.

Overall, these findings establish CGO as a reliable behavioral factor with clear economic intuition and strong statistical support. The next step is to translate these insights into Factor Strategy – CGO, where we design and backtest strategies to evaluate how CGO can enhance portfolio performance.」

👉 Continue reading to explore how CGO can be transformed from a predictive factor into actionable investment strategies.

Factor Library – Taiwan’s Factor Dataset for Quantitative Investing