Portfolio Diversification Using Shape-Based Clustering

Abstract

Portfolio diversification involves lowering the correlation between portfolio assets to achieve improved risk–return exposure. It is reasonable to infer from the classic Anscombe quartet that relying on descriptive statistics, and specifically, correlation, to achieve portfolio diversification may not derive the most optimal multiperiod portfolio risk-adjusted return because stocks in a portfolio can exhibit different price trends over time, even with the same computed pairwise correlation. This research applied a shape-based time-series clustering technique of agglomerative hierarchical clustering using dynamic time-series warping as a distance measure to aggregate stocks into like-trending clusters across time as a portfolio diversification tool. Results support the use of the shape-based clustering technique for (1) portfolio allocation and rebalancing, (2) dynamic predictive portfolio construction, and (3) individual stock selection through outlier identification. The findings will be a useful addition to the existing literature in portfolio management by providing shape-based clustering as an alternative tool for portfolio construction and security selection.

TOPICS: Security analysis and valuation, portfolio construction, statistical methods

Key Findings

• ▪ Performance results indicate a clear and significant improvement in portfolio return and Sharpe performance through shaped-based cluster diversification. Even with a 50% haircut in terms of mean return performance, outperformance of shape-based cluster diversification was a compelling 730 bps, 816 bps, and 888 bps, against minimum variance portfolios, industry-diversified portfolios, and a control group of randomized portfolios, respectively. Intuitively, this is a rational result because investing in highly dissimilar trending securities across time is likely to bring about diversification benefits in portfolio management.

• ▪ Research shows time persistence of shape-based clustered assets. Rather than observing a significant decline in trend similarities over time, in approximation, 8 of 10, 8 of 10, and 7 of 10 stocks displayed similar clustering trends across the one-, two-, and three-year subperiods under investigation, respectively. Observed persistence implies usefulness for asset allocation and rebalancing in portfolio management and predictive analysis performed on such portfolio construction.

• ▪ Research finds benefits of shape-based clustering with regard to pattern recognition—the identification of outliers, or exceptional star performers and fallen angels within an industry. Another interesting find is the usefulness of identifying non-industry-related stocks within the same shape-based cluster. This allows the identification of assets that appear unrelated but have idiosyncratic risks and performance profiles that coincided during time periods under observation.