Drawdown-Speed clustering for portfolio insurance

This thesis investigates whether return correlation is the appropriate notion of similarity for constructing the risky portfolio of Constant Proportion Portfolio Insurance (CPPI) strategies. While traditional clustering approaches group financial assets according to return co-movements, CPPI exposure is governed by the cushion, the distance between portfolio value and the protection floor. This suggests that the relevant information for portfolio insurance may lie less in average return correlation and more in the dynamics through which downside losses propagate over time. To address this issue, the thesis proposes a hierarchical clustering framework based on Drawdown Speed (DDS), defined as the first finite difference of the drawdown process. DDS is not interpreted as a continuous-time derivative, but as a discrete time measure of the local propagation rate of drawdowns. Assets are clustered according to the correlation of their DDS trajectories, transformed into a Euclidean distance, and grouped using Ward’s hierarchical clustering; one representative medoid is selected from each cluster to construct a parsimonious risky basket. DDS is compared against three further representations: return correlation, downside return correlation, and the correlation of drawdown levels. All four share the same universe, distance transformation, linkage, cardinality and weighting, so that any difference is attributable to the representation alone. The empirical analysis uses a survivorship-bias-free, point-in-time universe of S&P 500 constituents from the Norgate Data database, including currently listed and delisted securities. A rolling out-of-sample design with five-year training windows and one-year holding periods produces thirty-one disjoint evaluation years from 1995 to 2025, spanning different market regimes. The resulting baskets are evaluated within a CPPI framework over a grid of cardinality, multiplier, floor, accrual and rebalancing settings. The evidence produces a division rather than a ranking. Against return correlation, DDS baskets sustain a higher average cushion, spend fewer monitoring dates close to the protection floor and, at intermediate cardinalities, earn more, while return correlation delivers a shallower drawdown of the insured portfolio and a less severe single-period contraction of the cushion when a common shock arrives. The comparison with downside-return correlation narrows the claim, while the correlation of drawdown levels operates as a negative control and performs worse than random selection from the same universe. Overall, the thesis shows that the effectiveness of clustering for portfolio insurance depends not only on the clustering algorithm, but also on the notion of similarity used to represent asset behaviour, and that the representation should be chosen to match the state variable of the allocation rule downstream.