Thesis: Why Variance Risk Premium

The empirical regularity

Across stock indexes and individual stocks, the implied variance from option prices systematically exceeds the realized variance over matching forward windows. This gap, the variance risk premium, has been documented as strongly negative for the S&P 500, S&P 100, and Dow Jones indexes (large t-statistics on both raw and log forms), smaller-magnitude negative for the Nasdaq 100 and most individual stocks, and statistically distinguishable from zero across multiple decades of data.

The premium is not arbitrageable away because hedging variance risk requires either long-vol options positions (which lose money on average if you collect the premium by selling) or continuous dynamic delta-hedging that incurs friction. Both reset the risk to a different form: short-vol exposure with tail risk, or vega-and-friction exposure to dynamic-hedge slippage.

Investors are willing to pay this premium because variance shocks correlate negatively with index returns, variance risk is “insurance against market drawdowns,” and insurance commands a premium. Classical CAPM beta captures only a small portion of the empirically observed magnitude. Fama-French three-factor models leave large residuals. The premium appears to compensate exposure to a separate volatility-risk factor.

What our strategy harvests

The strategy systematically sells defined-risk volatility structures (iron condors and cash-secured puts) on instruments where the premium has been documented. We collect the option premium up front, accept the tail-risk exposure (capped by the wing widths on iron condors and by share-assignment mechanics on the wheel), and manage active positions with five exit fates.

Specifically:

5-instrument iron condor cluster (SPX, RUT, NDX, TLT, GLD): captures equity-index VRP plus cross-asset (bond, gold) VRP. The strategy harvests the structurally negative VRP across asset classes; correlation diversification reduces portfolio variance without giving up expected return.
9-name adaptive wheel basket (AAPL, MSFT, GOOGL, JNJ, KO, PG, WMT, JPM, PEP): captures single-name VRP via cash-secured puts and covered calls. Strategy adapts strike delta to the prevailing volatility regime, widens strikes per name when realized vol is elevated, and uses an XGBoost realized-vol forecaster for sizing.

What this strategy does NOT claim

Not statistical arbitrage. The premium is a real risk premium, paid for a real risk (left-tail variance shocks). Sellers earn the premium in normal regimes and pay back in stress. Sharpe is bounded; tails are real.
Not market-timing. We do not predict when vol spikes will occur. We size positions for capacity to absorb spikes and exit when current spreads breach exit triggers.
Not idiosyncratic-stock-picking. The wheel basket is selected by liquidity and structural-criteria thresholds, not by subjective conviction. The 9 names are the universe, not picks.

The capacity-versus-edge tradeoff

Single-name short-vol structures generate higher per-trade premium but carry concentrated tail risk. Index-level structures generate smaller per-trade premium but diversify cross-name idiosyncratic risk.

Our cluster mixes both:

Indexes (SPX, RUT, NDX) for diversified equity-VRP capture
ETFs (TLT, GLD) for cross-asset diversification (bond and gold vol have low correlation with equity vol over multi-year windows)
Individual names (wheel basket) for incremental premium with sector spread

The expected payoff: combined book Sharpe higher than any single instrument, with maximum drawdown bounded by halt framework + per-instrument max-loss per spread.

Why iron condor over single-side spread

The legacy strategy (SPX baseline) used put-credit spreads only. Adding the call wing converts to iron condor. Trade-offs:

Premium captured per structure: roughly doubles (both sides earn)
Defined risk per structure: wider per-structure max-loss (both wings can be in the money simultaneously, though rarely)
Trend exposure: put-side benefits from rising markets; call-side is hurt. Iron condor is delta-neutral at entry; one wing always offsets the other in trending regimes
Volatility exposure: symmetric, short vega on both sides. IV-crush after entry helps both wings

In strong trending markets (like 2018-2024 SPX), the call wing is structurally disadvantaged: spot rallies hard, calls go in the money, losses on calls partially offset gains on puts. Result: iron condor naked-mode Sharpe is below put-only naked-mode Sharpe in trending regimes (we observed exactly this in our diagnostic).

The strategy’s edge over naked-mode iron condor comes from the halt framework, exiting when market regime shifts to high-realized-vol environments where short-vol positions of any kind underperform.

Foundational pricing: Black-Scholes and Merton

Strike selection uses Black-Scholes Greeks: 16-delta short legs (one standard deviation OTM under the lognormal assumption), 5-point wings (or per-instrument-grid). The BS pricer is a fallback when OptionMetrics-published implied volatility is missing.

Black-Scholes empirically overvalues options on high-variance underlyings and undervalues low-variance, this is the published finding from BS’s own 1973 paper. That bias is itself the structural source of the volatility risk premium our strategy harvests. We do not “out-predict” the BS pricer; we systematically take the side of the trade where BS-implied premium exceeds realized variance over the holding window.

Merton’s 1973 extension covers American early-exercise (relevant for the wheel basket’s dividend-paying names) and continuous-dividend pricing. American puts on dividend-paying stocks always have positive probability of premature exercise (Merton Theorem 13). The wheel mechanic accepts assignment as a feature: when assigned shares, write covered calls until called away.

What you’ll find in the rest of the writeup

Mechanics: exact entry/exit logic, halt framework, ML stack, sizing
Results: headline OOS numbers, blotter, ledger, multiple-testing correction
Variants: basket variants, iron-condor vs put-only, halts engaged vs disengaged
Live monitoring: how to know it works, how to know it stopped
Limitations: what this strategy cannot promise
Data and Literature: data sources and reference reading

--- title: "Thesis: Why Variance Risk Premium" --- ## The empirical regularity Across stock indexes and individual stocks, the implied variance from option prices systematically exceeds the realized variance over matching forward windows. This gap, the **variance risk premium**, has been documented as strongly negative for the S&P 500, S&P 100, and Dow Jones indexes (large t-statistics on both raw and log forms), smaller-magnitude negative for the Nasdaq 100 and most individual stocks, and statistically distinguishable from zero across multiple decades of data. The premium is not arbitrageable away because hedging variance risk requires either long-vol options positions (which lose money on average if you collect the premium by selling) or continuous dynamic delta-hedging that incurs friction. Both reset the risk to a different form: short-vol exposure with tail risk, or vega-and-friction exposure to dynamic-hedge slippage. Investors are willing to pay this premium because variance shocks correlate negatively with index returns, variance risk is "insurance against market drawdowns," and insurance commands a premium. Classical CAPM beta captures only a small portion of the empirically observed magnitude. Fama-French three-factor models leave large residuals. The premium appears to compensate exposure to a separate volatility-risk factor. ## What our strategy harvests The strategy systematically sells defined-risk volatility structures (iron condors and cash-secured puts) on instruments where the premium has been documented. We collect the option premium up front, accept the tail-risk exposure (capped by the wing widths on iron condors and by share-assignment mechanics on the wheel), and manage active positions with five exit fates. Specifically: - **5-instrument iron condor cluster** (SPX, RUT, NDX, TLT, GLD): captures equity-index VRP plus cross-asset (bond, gold) VRP. The strategy harvests the structurally negative VRP across asset classes; correlation diversification reduces portfolio variance without giving up expected return. - **9-name adaptive wheel basket** (AAPL, MSFT, GOOGL, JNJ, KO, PG, WMT, JPM, PEP): captures single-name VRP via cash-secured puts and covered calls. Strategy adapts strike delta to the prevailing volatility regime, widens strikes per name when realized vol is elevated, and uses an XGBoost realized-vol forecaster for sizing. ## What this strategy does NOT claim - Not statistical arbitrage. The premium is a real risk premium, paid for a real risk (left-tail variance shocks). Sellers earn the premium in normal regimes and pay back in stress. Sharpe is bounded; tails are real. - Not market-timing. We do not predict when vol spikes will occur. We size positions for capacity to absorb spikes and exit when current spreads breach exit triggers. - Not idiosyncratic-stock-picking. The wheel basket is selected by liquidity and structural-criteria thresholds, not by subjective conviction. The 9 names are the universe, not picks. ## The capacity-versus-edge tradeoff Single-name short-vol structures generate higher per-trade premium but carry concentrated tail risk. Index-level structures generate smaller per-trade premium but diversify cross-name idiosyncratic risk. Our cluster mixes both: - Indexes (SPX, RUT, NDX) for diversified equity-VRP capture - ETFs (TLT, GLD) for cross-asset diversification (bond and gold vol have low correlation with equity vol over multi-year windows) - Individual names (wheel basket) for incremental premium with sector spread The expected payoff: combined book Sharpe higher than any single instrument, with maximum drawdown bounded by halt framework + per-instrument max-loss per spread. ## Why iron condor over single-side spread The legacy strategy (SPX baseline) used put-credit spreads only. Adding the call wing converts to iron condor. Trade-offs: - **Premium captured per structure:** roughly doubles (both sides earn) - **Defined risk per structure:** wider per-structure max-loss (both wings can be in the money simultaneously, though rarely) - **Trend exposure:** put-side benefits from rising markets; call-side is hurt. Iron condor is delta-neutral at entry; one wing always offsets the other in trending regimes - **Volatility exposure:** symmetric, short vega on both sides. IV-crush after entry helps both wings In strong trending markets (like 2018-2024 SPX), the call wing is structurally disadvantaged: spot rallies hard, calls go in the money, losses on calls partially offset gains on puts. Result: iron condor naked-mode Sharpe is below put-only naked-mode Sharpe in trending regimes (we observed exactly this in our diagnostic). The strategy's edge over naked-mode iron condor comes from the **halt framework**, exiting when market regime shifts to high-realized-vol environments where short-vol positions of any kind underperform. ## Foundational pricing: Black-Scholes and Merton Strike selection uses Black-Scholes Greeks: 16-delta short legs (one standard deviation OTM under the lognormal assumption), 5-point wings (or per-instrument-grid). The BS pricer is a fallback when OptionMetrics-published implied volatility is missing. Black-Scholes empirically *overvalues* options on high-variance underlyings and undervalues low-variance, this is the published finding from BS's own 1973 paper. That bias is itself the structural source of the volatility risk premium our strategy harvests. We do not "out-predict" the BS pricer; we systematically take the side of the trade where BS-implied premium exceeds realized variance over the holding window. Merton's 1973 extension covers American early-exercise (relevant for the wheel basket's dividend-paying names) and continuous-dividend pricing. American puts on dividend-paying stocks always have positive probability of premature exercise (Merton Theorem 13). The wheel mechanic accepts assignment as a feature: when assigned shares, write covered calls until called away. ## What you'll find in the rest of the writeup - [Mechanics](mechanics.qmd): exact entry/exit logic, halt framework, ML stack, sizing - [Results](results.qmd): headline OOS numbers, blotter, ledger, multiple-testing correction - [Variants](ablations.qmd): basket variants, iron-condor vs put-only, halts engaged vs disengaged - [Live monitoring](monitoring.qmd): how to know it works, how to know it stopped - [Limitations](limitations.qmd): what this strategy cannot promise - [Data and Literature](data_and_literature.qmd): data sources and reference reading