Optimal Hedging of Leveraged ETF Positions (Convexity Protection)

A multi-tranche hedging engine on Tesla's 2× leveraged ETF (TSLL) — short the LETF, long ATM calls, short OTM puts (a collar) — harvesting structural volatility decay with maximum drawdown capped ex ante by a closed-form, model-free bound. The bound is fixed before the data run; the realized equity path never breached it.

Approach & findings

• Each tranche's worst-case loss is an exact no-arbitrage limit — L = C + K_c − S₀ (call-only) or L − P_p (collar) — valid continuously rather than only at expiry, via no-arbitrage bounds on American options.
• Settlement-based accounting keys the risk budget to checkpoint equity instead of daily marks (removing procyclicality); a cycle ceiling converts equity peaks into checkpoints, yielding the closed-form guarantee MaxDD ≤ (d + g)/(1 + g) = 15.0% at the headline configuration, and a one-parameter risk limit x with bound 2x/(1 + x).
• Verification: the bound was never breached in-sample, out-of-sample, or across seven risk-limit configurations — 960 trading days each; realized drawdowns used 75–96% of their guaranteed envelopes, so the bound is informative, not vacuous.
• Collar (frictionless): +15.69% CAGR, Sharpe 0.899, −12.29% MaxDD (Calmar 1.28) vs. −81.1% MaxDD for the unhedged short. With approximate borrow fees, call-only earns +13.42% at −15.44% MaxDD; the borrow cost is measured and added to the bound, so it remains a theorem.
• A cost gate deploys capital only when the net floor cost is ≤ 15% of protected notional (removing it cuts CAGR from 14.0% to 4.9%); selling rich TSLL crash insurance (median ~10% of spot) cuts the net floor cost by roughly a third.
• Data: full TSLA/TSLL option-chain history 2020–2026 (1M+ daily option prices) built via a Bloomberg BDH + OpenFIGI pipeline, with spot/OHLCV via yfinance.

Results

Guaranteed MaxDD bound (ex ante)

15.0%

Bound breaches (960 days)

0

CAGR / Sharpe (collar)

+15.69% / 0.90

Unhedged-short MaxDD

−81.1%