10 Correlations, Hierarchies, Networks and Clustering
259
• Reference [5] investigates several network and hierarchy based active portfolio
optimizations, and find their out-of-sample performance competitive with respect
to conventional ones.
• Reference [82] presents the performance of seven portfolios created using clustering analysis techniques to sort out assets into categories and then applying classical
optimization inside every cluster to select best assets inside each asset category.
• Reference [51] applies a hierarchical clustering to a set of government bond factors
(investment styles such as carry, momentum, slope, convexity, reversal, real rate
vs. growth), and finds that most factors benefit from a positive carry.
• References [35, 84, 85, 117, 120, 121] leverage hierarchical clustering to build
diversified portfolios that outperform out-of-sample by refining the risk parity and
the equal risk contribution methods to take into account the hierarchical correlations of assets.
• Reference [65] compares the Hierarchical Risk Parity (HRP) from [85] to more
traditional risk-based portfolios such as inverse volatility weighted, minimum variance and maximum diversification portfolios. The main takeaway from the study
is that results strongly depend on the estimation of the covariance matrix. If
estimates are crude, then inverse volatility weighted portfolios outperform the ones
obtained from the other methods as less sensitive to the covariance misspecification. HRP stands in between this simple yet robust method and the optimizationbased ones. Rebalancing frequency of the portfolios also impacts the relative
performance of the different methods, HRP being superior at minimizing outof-sample portfolio variance with longer rebalancing horizons. Note that the study
only considers the HRP [85] to represent the class of machine learning-based portfolios whereas other methods are available in the literature such as the Hierarchical
Clustering based Asset Allocation (HCAA) [120] and the Hierarchical Equal Risk
Contribution (HERC) [121]. Note also that the empirical results described in the
paper were obtained for portfolios of 10 assets only. HRP, and related methods,
would benefit from larger portfolios, since not inverting the covariance matrix.
10.6.2 Trading Strategies
• In [115], they suggest that tracking the merging, splitting, birth, and death of the
clusters in time could be the basis for pairs-like reversal trading strategies but with
pairs corresponding to clusters.
• One can build a simple mean-reversion statistical arbitrage strategy whereby one
assumes that stocks in a given industry move together, cross-sectionally demeans
stock returns within said industry, shorts stocks with positive residual returns and
goes long stocks with negative residual returns [68].
• Earnings per share forecasts prepared on the basis of statistically grouped data
(clusters) outperform forecasts made on data grouped on traditional industrial
criteria as well as forecasts prepared by mechanical extrapolation techniques [44].
259
• Reference [5] investigates several network and hierarchy based active portfolio
optimizations, and find their out-of-sample performance competitive with respect
to conventional ones.
• Reference [82] presents the performance of seven portfolios created using clustering analysis techniques to sort out assets into categories and then applying classical
optimization inside every cluster to select best assets inside each asset category.
• Reference [51] applies a hierarchical clustering to a set of government bond factors
(investment styles such as carry, momentum, slope, convexity, reversal, real rate
vs. growth), and finds that most factors benefit from a positive carry.
• References [35, 84, 85, 117, 120, 121] leverage hierarchical clustering to build
diversified portfolios that outperform out-of-sample by refining the risk parity and
the equal risk contribution methods to take into account the hierarchical correlations of assets.
• Reference [65] compares the Hierarchical Risk Parity (HRP) from [85] to more
traditional risk-based portfolios such as inverse volatility weighted, minimum variance and maximum diversification portfolios. The main takeaway from the study
is that results strongly depend on the estimation of the covariance matrix. If
estimates are crude, then inverse volatility weighted portfolios outperform the ones
obtained from the other methods as less sensitive to the covariance misspecification. HRP stands in between this simple yet robust method and the optimizationbased ones. Rebalancing frequency of the portfolios also impacts the relative
performance of the different methods, HRP being superior at minimizing outof-sample portfolio variance with longer rebalancing horizons. Note that the study
only considers the HRP [85] to represent the class of machine learning-based portfolios whereas other methods are available in the literature such as the Hierarchical
Clustering based Asset Allocation (HCAA) [120] and the Hierarchical Equal Risk
Contribution (HERC) [121]. Note also that the empirical results described in the
paper were obtained for portfolios of 10 assets only. HRP, and related methods,
would benefit from larger portfolios, since not inverting the covariance matrix.
10.6.2 Trading Strategies
• In [115], they suggest that tracking the merging, splitting, birth, and death of the
clusters in time could be the basis for pairs-like reversal trading strategies but with
pairs corresponding to clusters.
• One can build a simple mean-reversion statistical arbitrage strategy whereby one
assumes that stocks in a given industry move together, cross-sectionally demeans
stock returns within said industry, shorts stocks with positive residual returns and
goes long stocks with negative residual returns [68].
• Earnings per share forecasts prepared on the basis of statistically grouped data
(clusters) outperform forecasts made on data grouped on traditional industrial
criteria as well as forecasts prepared by mechanical extrapolation techniques [44].