Persistent fractional Brownian motion at H = 0.8 appears frightening: its 90th-percentile maximum drawdown is 8.01x the Brownian benchmark. Most of that multiple comes from the annualisation convention. At T = 750 days, the self-similar dispersion factor T^(H-1/2) is 7.29. Divide by it and the residual falls to 1.10x. Landolfi performs the same division and gives the result in his abstract, describing a failure of square-root-of-time calibration rather than intrinsic danger. Anyone who misses that decomposition may walk away believing in an 8x effect that the paper does not support.

The larger practical problem is uncertainty about drift. With a reported Sharpe of 1 estimated over three years, the Sharpe standard error is about 0.71 under Lo's conservative annual-frequency form, which Landolfi uses.

Rebuilding the drawdown model

Rej, Seager and Bouchaud modelled strategy P&L as drifted Brownian motion with unit annual volatility. Under that normalisation, drift equals the Sharpe. They then derived closed-form densities for the depth and length of the drawdown in progress.

Landolfi reconstructs the model by Monte Carlo, using 250 trading days a year and 20,000 paths. The numerical check lands almost exactly on the published results. Integrating the exact RSB densities produces a 5% length of 2.144, compared with their fitted 2.140, and a 5% depth of 1.498, compared with 1.500.

RSB reported two quantities. Landolfi expands the set to four: maximum drawdown, maximum loss measured from the starting level instead of the running peak, final negative time, and longest recovery time. For the Gaussian row at Sharpe 1 over three years, median and 90th-percentile drawdown are 1.16 / 1.88 annual volatilities. Max loss is 0.31 / 1.09. Final negative time is 0.42 / 2.37 years under water, while longest recovery is 0.86 / 1.82 years.

His decision panel gives slightly different values for the same cell: 1.16 to 1.89 for drawdown, 0.31 to 1.10 for max loss, 0.42 to 2.37 for final negative time, and 0.85 to 1.80 for recovery. A manager selects the assumed Sharpe and elapsed horizon. The number on the right marks the point beyond which the pain is meant to look unusual.

The later simulations relax the Gaussian assumption. Daily returns follow AR(1)-GARCH(1,1), with normal-inverse-Gaussian innovations, across 16,000 paths per cell and 750 days. The archetype panel covers assumed Sharpes of 0.5, 1.0, 1.5 and 2.0 over three years. In the headline style table, the process Sharpe remains fixed across archetypes, at 1, leaving return shape as the changing input.

There is no fund data anywhere in the paper. Parameters for the archetypes are taken from the literature. Landolfi supports that choice by citing Valeyre on the limited data available for identifying richer specifications without overfitting.

Depth separates from duration

The short-volatility archetype has NIG asymmetry -0.7 and GARCH alpha 0.12, with realised daily skew -1.85 and excess kurtosis 11.3. Its 90th-percentile maximum drawdown rises from the Gaussian 1.88 to 2.48. Max loss moves from 1.09 to 1.41. The duration measures head in the other direction, with final negative time at 0.94x the Gaussian and longest recovery at 0.86x. Landolfi's phrase is that it falls hard but climbs back quickly.

Trend produces the reverse pattern. Final negative time reaches 2.61 years versus 2.37, and longest recovery reaches 1.96 versus 1.82. Depth changes little at 1.97 (1.05x). The +1.74 skew might suggest shallower drawdowns, yet excess kurtosis of 7.8 and volatility clustering consume that benefit. Market-neutral remains within about 7% of Gaussian across all four measures, a restrained endorsement of the RSB table for symmetric books.

For a short-vol manager, the Gaussian table underestimates depth by about a third while overstating recovery time. The error matters. Sharpe uncertainty matters more.

Unknown drift dominates

Marginalising over Lo's Sharpe standard error shifts every measure in the same direction. The 90th-percentile max loss reaches 1.62 (1.48x Gaussian). Longest recovery becomes 2.36 (1.30x), final negative time 3.00 (1.27x), and max drawdown 2.32 (1.23x). This exceeds every style effect in the study and widens all four measures together.

Landolfi gets there by drawing an effective Sharpe for each path from a normal distribution centred on the reported value. He deliberately leaves the normal untruncated. At a reported Sharpe of 0.5 over three years, it assigns about one chance in five to a genuinely negative true Sharpe. He treats that as an honest uncertainty penalty rather than a modelling artefact.

For the S = 1 cells, his choice is persuasive. The plausible range runs roughly from 0.3 to 1.7, so truncation would have little effect. In the low-Sharpe cells, however, the 90th percentile includes paths with no edge at all. A near-worst outcome for a strategy known to possess an edge answers another question. The distinction depends on how much confidence you place in the Sharpe estimate and the selection process behind it.

Long memory, broken annualisation?

Using the convention managers usually quote, with identical daily mean and daily volatility across Hurst exponents, fBm at H = 0.8 produces a 90th-percentile maximum drawdown of 8.01x the Brownian benchmark. Max loss reaches 13.13x. Duration barely changes on the same row: final negative time is 1.26x and right-censored at the horizon, while longest recovery is 1.65x. The apparent explosion lies in depth. Both depth figures should be divided by T^(H-1/2) = 7.29.

The maximum-drawdown residual is 1.10.

Across H from 0.4 to 0.8, the residual stays within 1.03 to 1.10. Equalising terminal dispersion reverses the direction. Persistence then reduces depth to 0.72x, 0.50x and 0.31x at H = 0.6, 0.7 and 0.8. Anti-persistence at H = 0.4 lifts it to 1.36x. Given the same terminal spread, a persistent path trends more smoothly and reverses less, while the zig-zagging path creates deeper holes before arriving at the same endpoint.

The full row still contains a genuine effect. Max loss retains a residual of 1.80x at H = 0.8. Landolfi reports this directly: persistence makes the worst single excursion below the starting level more severe than scaling alone would predict. The share of paths still under water at three years rises from 4% at H = 0.5 to 33% at H = 0.7 and 40% at H = 0.8. His explanation is that the effective horizon Sharpe S·T^(1-H)/sqrt(250) declines as H increases.

Persistent fBm tops the ranking in his synthesis table. At H = 0.65, it records 2.83x for max drawdown and 4.00x for max loss relative to the Gaussian, far beyond the 5-50% distortions attributed to skew, tails, clustering and Sharpe uncertainty. Yet the same caption says the magnitude is driven predominantly by dispersion scaling rather than shape. Landolfi supplies that warning himself.

The fBm engine receives a clearly bounded validation. For driftless paths at H = 0.5, simulated positive-time fractions {0.024, 0.147, 0.503, 0.856, 0.976} match the arcsine values {0.024, 0.146, 0.500, 0.854, 0.976}, agreeing to three decimals. An independent exact-Cholesky generator recovers the depth multipliers: 1.98 versus 2.03 at H = 0.6, then 4.00 versus 4.08 at H = 0.7. Between n = 250 and n = 4000, the Kolmogorov-Smirnov distance from the continuous arcsine law contracts from 0.037 to 0.010. Landolfi claims no closed form for drawdown-with-drift distributions under fBm, and none is validated.

Why the cells are stress axes

We would treat these cells as stress axes rather than trading triggers. Landolfi gives stronger operational advice: a live observation beyond a cell is, in his words, the evidence-based trigger to revise the Sharpe downward or to cut. He limits the stress-axis interpretation to the Hurst exponent. We disagree with him on that point.

All three limitations in the conclusion bear directly on the tables. The archetypes are stylised rather than fitted. The stationary Gaussian fBm model cannot combine long memory with fat tails, skew or clustering. And the long-memory results cover a single three-year horizon. Final negative time and longest recovery are right-censored there, making those 90th percentiles lower bounds, as Landolfi flags.

One worked example also deserves checking before the panel reaches a live monitor. It says that a maximum drawdown of about 1.05 times annual volatility is already a one-in-ten event at Sharpe 2 over two years. Landolfi's own panel shows 1.15. The discrepancy is small, but it appears in the paper's one worked decision rule.

His non-parametric recommendation is the one we would retain: apply a stationary block bootstrap to realised daily P&L, using blocks long enough to preserve autocorrelation and volatility clustering. The gap from the parametric fit then measures the estimate's fragility. We are running that test on our own series instead of selecting an archetype off the shelf.

The correction history also deserves credit. In the first release, innovations were standardised to exact in-sample mean and variance. That choice silently converted the process into a Brownian bridge and understated drawdown depth. Readers identified the problem, Landolfi corrected it and thanked them in a footnote. Every figure reported above comes from the corrected construction. A simulator that pins terminal P&L will bias drawdown quantiles in the direction a manager can least afford.