Harvesting the index variance premium

1Motivation

This program has repeatedly found real effects that die on execution cost. A retail 0DTE iron condor was measured with a gross edge smaller than one OPRA tick; gamma-exposure signals collapsed against a VIX control; a long-straddle book lost money for three compounding reasons at once. The pattern is consistent: the mechanism is usually real and the margin over friction is usually absent.

The variance risk premium is the natural counter-case. It is among the most documented effects in the options literature, it is a selling premium rather than a directional forecast, and — critically — it is expressed in longer-dated contracts whose premium is large relative to their spread. This paper asks three questions in order: does the premium exist in our data, where does it live, and does any structure we can actually trade capture it after costs.

2Data

• Index paths. SPY and QQQ 5-minute bars, 2016-08 to 2026-08 (2,512 sessions), regular trading hours only.
• Option prices. 18,682 expired contracts across 16 underlyings, 2024-02 to 2026-08, from Alpaca's status=inactive chain. This is the binding constraint: only ~2.4 years of real option history exists.
• Implied volatility. VIX and VIX3M daily closes, 2015–2026.

The short option history is the reason for the synthetic method in §3.3. It is also why every real-option result is reported with its sample size attached.

3Method

3.1 Delta-hedged P&L, and why the unit is volatility points

An unhedged short straddle is a direction bet. To isolate the volatility P&L we hold the straddle's own delta in the underlying and rebalance on a schedule:

All results are divided by the straddle's vega, giving volatility points. This matters: a dollar figure on a large position is not an edge, and vol points are directly comparable across underlyings, tenors and position sizes. Theory gives P&L ≈ vega × (σ_implied − σ_realized).

3.2 Cost model

Charged from the first line of code, never added afterwards: an option half-spread on two legs each way, plus a share half-spread on every share the hedge trades. Option spreads are swept rather than assumed.

3.3 The synthetic extension, and its calibration

Real option history covers 17–18 independent cycles — far too few for a strategy with a fat left tail. We extend the sample without buying data by pricing the entry straddle off VIX and hedging against real SPY intraday paths. Only the entry premium is modelled; the hedge P&L and terminal payoff, the two terms that decide the trade, are measured against actual prices.

3.4 Verification of the hedging engine

Before trusting any result we tested the engine against simulated geometric Brownian motion with known realized volatility. It reproduces theory across the range:

This test resolved an apparent anomaly. A cycle spanning the March 2020 crash lost only 3.11 vol points where naive reasoning predicted ~57. The engine is correct: SPY fell 28% through the strike, gamma collapsed, and the position stopped accruing volatility losses. Trending crashes hurt short gamma far less than choppy ones — a dollar-gamma weighting effect that materially changes how this strategy's tail behaves.

4Results

4.1 The premium is concentrated in the index

Comparing 30-day ATM implied volatility to volatility realized over the following 21 sessions, per name:

The index earns +2.52 vol points; the twelve constituents average +0.38, and four are significantly negative. The +2.14 point gap is the correlation risk premium (Driessen, Maenhout & Vilkov), and it is the entire case for selling index volatility rather than single-name volatility.

4.2 The harvest, over eleven years

Both halves are positive and significant, and the independent real-option estimate (+1.39) agrees with the synthetic (+1.42). This is the first result in this program to clear an out-of-sample split.

4.3 Hedging frequency has an interior optimum

Discretisation error falls as roughly 1/√N while cost rises linearly in N, so an optimum exists; we locate it near hourly. Hedging every five minutes is worse than hourly on the real-option sample — the additional rebalancing captures microstructure noise rather than volatility.

4.4 The VIX level gates the premium

This is economically coherent rather than a fitted threshold: the variance premium is compensation for bearing volatility risk, and it is largest when that risk is most feared. It is also the only conditioning variable we tested that survived — implied correlation and the VIX term structure both failed (§5).

4.5 Cost headroom

Breakeven option half-spread is $0.41 per leg against a realistic $0.03–0.05 on a ~$31 straddle: roughly ten times headroom. Hedging costs run 0.17–0.20 vol points against a 1.42-point edge. For contrast, the retail 0DTE condor previously studied had a breakeven half-spread of $0.0018 against a $0.005 exchange minimum — underwater before any execution skill. Premium scales with √T while spreads do not, which is why the 30-day structure works where the same idea at one day does not.

5Fund simulation

Volatility points measure the edge; they do not answer whether to allocate. This section converts the same 120 cycles into a fund. Nothing about the edge changes — only sizing, compounding and reporting are added.

5.1 Sizing, and a correction

Contracts are set so that hitting the kill switch costs a fixed fraction of current equity:

This is a tail-based rule, not a notional or margin rule. Forty of 120 cycles lose and the worst is −8.9 vol points; on that shape, any rule sized off average outcomes eventually prints a full drawdown. Sharpe is invariant to the risk level, so the choice sets scale, not quality. We report everything at a 10% annualised volatility target, the scale an allocator would actually run.

5.2 The gate is the difference between matching the index and beating it

The deployed configuration — VIX ≥ 14 — returns 15.9% against the index’s 13.5%, at 10.0% volatility against 16.3%, with a −7.1% maximum drawdown against −27.9%. Calmar is 2.22 against 0.48: more than four times the return per unit of drawdown.

5.3 Calendar year returns

5.4 Why Sharpe, not CAGR, is the operative number

A 15.9% return against the index’s 13.5% is a modest headline, and read alone it understates the result. The quantity that matters is the one you can lever.

SPY runs at Sharpe 0.87. Levering it twice gives roughly 27% a year with a drawdown near 56% — a product no allocator funds and no prime broker finances. A book at Sharpe 2.14 levered twice returns 35% with a drawdown under 8%. Same leverage, entirely different instrument. Return is a function of how much risk you are permitted to take; Sharpe determines how much you are permitted.

5.5 Portfolio construction

Against SPY the strategy’s correlation is +0.425: this book carries equity beta and should be priced that way. Its asymmetry is what distinguishes it — across the nine cycles where SPY fell more than 5%, the strategy averaged −1.18% against SPY’s −9.75%.

The stronger claim is against the firm’s existing trend sleeve, where correlation is +0.074 — effectively independent. Both at a 10% volatility target:

5.6 Constraints on these figures

6Negative results

Reported in full, because they define the boundary of the positive finding.

7Robustness and limitations

• Calibration dependence. The headline scales with the assumed VIX-to-ATM gap: +4.38 at zero haircut, +1.42 at 3.0, +0.43 at 4.0. We use 3.0 because it reconciles to real option prices, but the level is an estimate, not an observation. Real option history back to 2016 would replace it with measurement.
• Tail sizing is mandatory. 40 of 120 cycles lose, averaging −2.04, worst −8.9. Any fixed-fraction sizing on this distribution eventually prints a full drawdown; sizing must be set from the tail.
• Dropping the best cycles. Mean falls +1.42 → +1.26 → +1.15 → +1.06 as the best one, two and three cycles are removed. Not concentrated in a handful of observations.
• Year dependence. 2020 contributes +5.32/cycle. Excluding it the result is thinner but the sign and out-of-sample split survive. 2018, 2019 and 2024 are flat to slightly negative.
• Modelled entry premium. Hedge P&L and payoff are measured; the entry price is not. This is the single largest methodological weakness.
• Skew is not modelled in the synthetic beyond the aggregate haircut.

8Implementation

straddlebot/vrp_trader.py — short 30-day ATM QQQ straddle, hourly delta hedge, journaled in volatility points. Deployed to paper on 2026-09-21. Design constraints carried over from prior incidents in this program:

• Hard expiry guard at 3 DTE. On 2026-09-11 a long 0DTE call was left to expire while the host slept and auto-exercised into 400 shares on margin. A short straddle expiring in the money is that failure with the sign reversed and no cap.
• Early-assignment guard on deep-ITM short calls; QQQ options are American.
• Atomic on-disk state, rebuilt from broker positions on restart. The host enters Modern Standby unpredictably; a missed hedge must degrade to a wider delta, not a corrupted position.
• VIX gate at 14, standing down if VIX is unreadable — an unreadable gate is a shut gate.
• Kill switch at −10 volatility points, the unit the edge is measured in.

9Conclusion

The index variance risk premium is present in our data, concentrated in the index rather than its constituents, and large relative to the cost of harvesting it. A delta-hedged short 30-day straddle captures +1.42 volatility points per monthly cycle net of costs across 120 cycles and two volatility regimes, with both out-of-sample halves positive and an independent real-option estimate in agreement.

It is not yet a capital decision. The entry premium is modelled rather than observed, the result depends on a calibration we estimated from 28 overlapping cycles, and the distribution has a left tail that demands conservative sizing. The recommended sequence is: raise the account's option permission, accumulate a forward paper record at one contract, and purchase option history back to 2016 to replace the calibration with measurement. On the evidence here that purchase is now justified by a specific finding rather than a hope.

10References