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An interactive companion to the paper

REBOUND

Resilience-Based Output Allocation for Nonlinear Drawdowns

Et = tanh( α · RMt − β · |DDt| )

Restore capital when resilience returns  ·  suppress it as the hole deepens  ·  bounded in [−1, 1], no leverage, no whiplash.

Sharpe ratio
0.00
vs 0.52 buy & hold
Worst drawdown
0%
vs 55.2% buy & hold
Calmar ratio
0.00
vs 0.19 buy & hold
Annual return
0%
vs 10.5% buy & hold

83% lower worst-case loss across 31.9 years & 21 markets, from one bounded equation, with no price forecast anywhere.

Start playing ↓

Part I · Why drawdowns are not volatility

A loss and its repair are not the same size

Volatility is symmetric; drawdowns are not. The path down looks nothing like the path back up, because the gain you need to recover grows faster than the loss you took. Drag the loss and watch.

…so just to break even you need a gain of +100%
That is 2.0× the size of the loss.

The climb back to break-even is gain = loss / (1 − loss). It barely moves for small losses, then runs away: 50% needs +100%, 90% needs +900%, and as the loss nears 100% the gain races to infinity. Drag the dot. This asymmetry is exactly what averaging over returns hides.

Part II · The framework, in your hands

The whole tradable core is one line. Push it around.

Exposure is a function of two things and nothing else: resilience momentum (RM) and drawdown depth (DD). Drag the white dot across the field, or move the dials. The framework never asks where the price is going.

Resilience momentum  RM →
Drawdown depth  |DD| →
−1 fully defensive +1 fully invested
α · RMt +0.00
− β · |DDt| −0.00
Et = tanh( … ) 0.00
Hold full exposure

The same pair emerges from every calibration window, a sign the parameters describe structure in the data, not a memorised sample.

Part III · The evidence, run live

Drop the rule into a crisis and watch it work

Pick a crash. The framework computes resilience momentum and drawdown from the price alone, feeds them through the one line above, and throttles exposure: suppress, confirm, commit. Compare it to buying and holding.

Wealth (log) REBOUND Buy & Hold
Exposure Et  & underlying drawdown
Onset
REBOUND worst DD·
Buy & hold worst DD·
REBOUND final wealth·
Buy & hold final wealth·
Current exposure·

Representative paths, shaped to each crisis, run through the actual REBOUND-E rule so you can watch the mechanism. The headline 31.9-year numbers up top come from the paper's real S&P 500 backtest.

Three sentences to keep

  1. Resilience is measurable: three signals with a clean statistical null, orthogonal to volatility and momentum, predictive of whether recoveries hold.
  2. Exposure can be governed, not forecast: one bounded rule cut the worst S&P 500 loss from 55% to 9% while raising return, with no price prediction anywhere.
  3. The structure is real and it travels: identical parameters from every calibration window, and improvement in all 21 markets it was never tuned for.
Read the paper ssrn.com/abstract=6560318 Contact rajiv.muttur@gmail.com

Rajiv Chaitanya Muttur
Presented at the World Finance Conference 2026 · ORCID 0009-0007-7159-5610