Case-Based Decision Theory and Investment Style Prediction
Predicting Investment Styles Using Case-Based Decision Theory
Case-Based Decision Theory measures how similar current information is to past information using distance metrics, expressed through similarity functions. In essence, it quantifies rules of thumb derived from experience. This study examines whether past experiences can be used to predict future investment styles and whether this approach is applicable to practical asset management.
Introduction
Stock performance varies depending on market conditions. In the Japanese equity market, institutional investors often classify stocks by value/growth and large-cap/small-cap categories. It is empirically known that performance differs by investment style, and if investment styles could be predicted, it would present significant opportunities for generating returns. This study focuses on Case-Based Decision Theory (CBDT) and examines whether past experiences can be used to predict future investment styles and whether this approach is applicable to practical asset management.
Relationship Between Investment Styles and Market Index Return Attributes
What is Investment Style?
Investment style refers to the fundamental concepts and methods used when making investments. When institutional investors decide on their investment policy, they categorize target stocks into several groups. Commonly used classification criteria include value (undervalued stocks) vs. growth stocks, and large-cap vs. small-cap stocks.
| Classification Criteria | Indicator |
|---|---|
| Value/Growth | PBR (Price-to-Book Ratio) |
| Large-cap/Small-cap | Log Market Capitalization |
Investment Style Trends
Analysis Conditions
| Item | Details |
|---|---|
| Value Index | |
| Growth Index | |
| Large-cap Index | |
| Small-cap Index | |
| Frequency | Monthly |
| Period | January 2000 – June 2012 |
Investment Style Trends
Analysis using spread returns shows that in the cumulative value-growth spread return trends, value was dominant in the early period, sideways in the middle, and growth slightly dominant in the later period. For large-cap/small-cap styles, small-cap was dominant early, large-cap in the middle, and small-cap again in the later period. In the short term, investment styles alternate in dominance, but long-term trends are observable. Particularly in the past, the large-cap/small-cap investment style showed more pronounced trend changes than the value/growth style.
Predictability of Investment Styles
Characteristics by Investment Style
Factor returns are used as indicators of investment style characteristics. Factor return is the slope of a regression line when performing cross-sectional regression analysis with returns as the dependent variable and factor exposures as explanatory variables. Higher values indicate greater sensitivity to factor returns.
Using BP factor instead of PBR and size factor instead of log market capitalization, analysis was conducted focusing on the large-cap/small-cap investment style across four market phases.
Factor Return Characteristics by Phase
| Factor | Characteristics |
|---|---|
| Size Factor | Positive contribution from large-cap, negative from small-cap, regardless of rising/falling phases |
| Market Sensitivity Factor | Positive contribution in rising phases, negative in falling phases |
| EP Factor/BP Factor | Positive contribution regardless of phase |
| Financial Soundness Ratio Factor | Positive contribution when large-cap stocks are dominant |
| US Stock Sensitivity Factor | Particularly positive contribution in large-cap rising phases |
It was confirmed that factor returns have distinct characteristics depending on investment style and market phase.
Persistence of Factor Returns
Correlation of Cumulative Factor Returns
Cross-sectional correlation coefficients were calculated between cumulative factor returns at month-end and cumulative factor returns ±X business days from month-end, then averaged over the long term. The long-term average correlation coefficient remains above 0.8 up to about ±7 business days. This suggests that, except during periods of significant market environment changes, market conditions persist for at least about one week on a long-term basis.
Cross-correlation Between LS Spread Returns and Factor Returns
Verification of cross-correlation between cumulative LS spread returns and each cumulative factor return showed positive lags for all factors except Size (Scale), Turnover (Turn_Over), and Non-TSE1 Flag (Non_Tpx). These factors show leading properties relative to LS spread returns.
The cross-sectional distribution of cumulative factor returns shows high correlation over a few days, and the distribution does not change much. Also, some factors were found to statistically lead LS spread returns. Considering these findings comprehensively, if cumulative factor returns can be predicted, it may be possible to predict the investment style at that point.
Existence of Factors Leading Investment Styles
To verify whether factor returns lead large-cap/small-cap spread returns, simultaneous estimation using multivariate autoregressive analysis was conducted. Results show significance up to 6 periods ahead, indicating leading properties when viewed from a factor perspective.
Factor Prediction
In the July 2008 factor return prediction example, results varied by factor—some predictions were successful while others were not.
| Factor | Prediction Result |
|---|---|
| BP/EP | Predicted rise, but actually declined |
| Market Sensitivity/Volatility/Daily Return | Correctly predicted decline |
| Large-cap/Small-cap Spread Return | Successfully predicted |
Although prediction accuracy may decrease during extreme market changes, predictions are expected to work well for certain factors.
Estimating Investment Style Probability Based on Rules of Thumb
About Case-Based Decision Theory
Case-Based Decision Theory is a collective term for decision theories that make current decisions based on past cases. While traditional finance theory generally uses expected values for prediction, CBDT assumes that if current conditions are similar to past events (similar environments), those events will occur again. By numerically evaluating the degree of similarity, the probability of an event occurring can be determined.
| Approach | Method |
|---|---|
| Traditional Finance Theory | What probability will an event occur in the future, and what average gain can be obtained (expected value) |
| Case-Based Decision Theory | If conditions are similar to past events, assume those events will recur; evaluate similarity numerically to determine probability |
Formulation
The distance function to model how similar past information is to target information based on rules of thumb is defined as follows:
is the weight, and represents the type of factor return.
The function to measure similarity using the distance function is:
The similarity function aggregates how similar information is based on distance. The style probability using this similarity function is:
The weight is determined by maximizing the likelihood function. The likelihood cross-validation method is used to find :
Optimization was performed using the quasi-Newton method.
2008 Case Study: Investment Style Probability
Suppose information from past periods when small-cap stocks were dominant has accumulated. If the prediction based on current information shows that the distance to information indicating small-cap attributes is close, it predicts a small-cap favorable market environment. The closer the distance, the stronger the conviction, so the probability increases.
When investment style probabilities were calculated monthly for 2008, many months predicted declining phases, likely due to the Lehman shock.
Simulation Using Investment Style Probability
Simulation Method
| Step | Description |
|---|---|
| ① Data Calculation | Calculate cumulative factor returns, cumulative index returns, and cumulative large-cap/small-cap spread returns for the current month at the close one business day before month-end |
| ② Estimation | Estimate each cumulative return at the following month-end using multivariate autoregressive analysis |
| ③ Style Probability Calculation | Calculate four investment style probabilities (large-cap dominant/rising, large-cap dominant/falling, small-cap dominant/rising, small-cap dominant/falling) using accumulated factor information and estimates |
| ④ Investment Decision | Use the highest probability investment style as the following month's investment style for month-end investment decisions |
| ⑤ Iteration | Analysis period: January 1992 – December 2012 (daily data). Predictions repeated monthly from the end of January 2000 |
Investment decision details are as follows:
| Prediction Result | Investment Action |
|---|---|
| Market Rising, Large-cap Dominant | Hold index |
| Market Rising, Small-cap Dominant | Buy and hold index |
| Market Falling | No position, hold cash |
Portfolio returns were calculated as time-weighted daily returns converted to monthly returns.
Results
The portfolio using investment style prediction performed well compared to large-cap index, small-cap index, and equal-weight holding. Not holding during declining phases suppressed asset value declines. Successfully predicting the major subprime decline is noteworthy. The rise comparable to the small-cap rising phase from 2004 is due to successfully predicting the small-cap rising phase.
When utilizing margin trading and short selling during predicted declining phases, even better performance was achieved.
Challenges and Summary
By applying Case-Based Decision Theory to predict equity investment styles, we demonstrated that quantifying rules of thumb makes investment style prediction possible to some extent. This approach may be applicable to other investment styles and market phases.
Future Challenges
| Challenge | Description |
|---|---|
| Rebalancing Frequency | This study examined monthly rebalancing, but investment trusts and corporate pension funds may consider annual rebalancing |
| Style Index | Various indexes exist beyond Japanese equity indexes, requiring detailed analysis considering objectives and constraints |
| Application to Value/Growth | Analysis using the same framework for value/growth investment styles, which are particularly strongly observed in Japanese markets |
| Separation of Prediction Effects | Since rising/falling phases are predicted simultaneously with large-cap/small-cap investment styles, the effect is not purely from investment style prediction alone |
References
| Literature | Content |
|---|---|
| Carl Bacon [2008] | Practical portfolio performance measurement and attribution second edition, WILEY FINANCE |
| Tsukagoshi & Eda | "Comparative Study of Logit Model and Case-Based Approach in Default Probability Estimation", Kyoto University Graduate School of Management Working Paper |
Data analysis was conducted using Nikkei Portfolio Master.