On the maximum drawdown during speculative bubbles

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On the maximum drawdown during speculative bubbles

Giulia Rotundo
Mauro Navarra
Published on 7/27/2006
Equities
Risk management
Market timing

This paper investigates risk measures based on drawdown and maximum drawdown during the rising phase of speculative bubbles that end in large endogenous crashes. Building on prior work that identifies such bubbles via log-periodic power laws (LPPL), the authors analyze the duration and size of drawdowns (consecutive price declines) in 17 historical bubble episodes across global stock indices. They define pure drawdown (DD) as the cumulative loss from a local peak to the next local minimum, and measure drawdown duration as the number of days in that decline. The study finds that drawdown duration during bubble rising phases follows a power law distribution with an exponent close to 1, indicating a heavy-tailed behavior. Using the generalized Pareto distribution (GPD), they fit the cumulative probability of drawdown size conditioned on duration, revealing that bubble phases exhibit lower scale parameters (β) and higher shape parameters (ξ) compared to the entire time series, with non-overlapping confidence intervals. The expected maximum drawdown (E[M]) and the worst-case drawdown (D̄) are also computed, showing that bubble rising phases have narrower ranges and lower values than the full datasets, though some overlap exists for indices with severe internal drops. The authors argue that incorporating drawdown duration into risk measures provides a more nuanced view of market risk during bubbles, as long sequences of declines can trigger investor withdrawal. The results suggest that risk profiles during speculative bubbles are distinct from normal periods, offering potential for embedding these measures into predictive frameworks for crash timing. This work contributes to quantitative finance by emphasizing the role of time in drawdown risk and providing empirical benchmarks for bubble-specific risk assessment.

Highlights

  • 1Analyzes drawdown and maximum drawdown during the rising phase of speculative bubbles, focusing on endogenous crashes identified by log-periodic power laws (LPPL).
  • 2Introduces drawdown duration as a key risk measure, complementing traditional size-based measures like VaR and CVaR.
  • 3Compares risk profiles of bubble rising phases versus entire time series using GPD fitting and empirical distributions.
  • 4Provides empirical evidence that drawdown duration follows a power law with exponent near 1 during bubbles.
  • 5Shows that risk measures based on drawdown size and duration can discriminate bubble periods from normal market conditions.

Methods

  • M
    Log-periodic power law (LPPL) fitting to identify speculative bubble periods and crash times.
  • M
    Drawdown and maximum drawdown definitions: pure drawdown (DD), epsilon-drawdown (εDD), and maximum drawdown (M and D̄).
  • M
    Generalized Pareto distribution (GPD) fitting to cumulative drawdown probabilities conditioned on duration.
  • M
    Empirical estimation of expected maximum drawdown E[M] using duration-conditioned maxima.

Results

  • R
    Power law exponent for drawdown duration during bubble rising phases ranges from 0.46 to 1.7, with mean ≈1; for entire series, mean ≈0.94.
  • R
    GPD parameters for bubble rising phases: β=0.0089, ξ=0.4273; for entire series: β=0.0153, ξ=0.3012, with non-overlapping confidence intervals.
  • R
    Expected maximum drawdown E[M] for bubble rising phases: 0.01–0.08; for entire series: 0.05–0.13, with partial overlap.
  • R
    Maximum drawdown D̄ for bubble rising phases: 0.04–0.17; for entire series: 0.08–0.35.
  • R
    Drawdown risk profiles during bubbles are lower and distinct from those of entire time series, enabling potential predictive use.
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