Guide

Variance swaps explained

Harbor Capital wanted pure exposure to whether the S&P 500 would realize more volatility than the options market priced over the next three months — without running an intraday gamma scalping book or guessing VIX futures roll dynamics. Buying ATM straddles gave convexity but embedded skew and path dependence; selling weeklies was the wrong sign. The desk entered a variance swap as variance receiver: if annualized realized variance over the observation window exceeded the agreed strike (quoted in vol terms, e.g. 18.5%), Harbor would receive the difference times notional; if realized came in lower, Harbor paid. When March delivered a two-week 12% drawdown followed by a sharp rebound, realized variance printed 24.1% vs an 18.5% strike — a clean $2.8M payout on $10M variance notional with no delta hedge on Harbor's side. The dealer on the other leg dynamically replicated the payoff with an OTM options strip.

A variance swap is an OTC forward on realized variance of an underlying over a fixed window. Unlike listed options, the payoff is linear in variance (not volatility), sampling uses log returns at defined fixings, and the counterparty (usually a bank) handles replication and gamma risk. This guide covers contract anatomy, payer vs receiver economics, strike quoting and vega notional, replication intuition, vol swaps vs variance swaps, dispersion applications, the Harbor Capital overlay refactor, a technique decision table vs VIX products and option straddles, pitfalls, and a production checklist — building on options Greeks, volatility skew, and variance risk premium foundations.

Contract anatomy

Standard equity index variance swaps specify:

Underlying — e.g. SPX, single-stock name, or cross-asset index.
Observation window — start and end dates; daily (or intraday) fixings of the official close or VWAP.
Realized variance — sum of squared log returns, annualized. Industry conventions differ on business-day vs calendar-day annualization and whether dividends are included in the return series.
Strike — quoted as annualized volatility K (e.g. 20%); the variance strike is K².
Notional — often defined in “vega notional” or variance notional; determines dollars per vol point at expiry.
Payoff at maturity (variance receiver perspective):

Payoff = Notional × (Realized Variance − Strike Variance)

Example: Notional $50,000 per vol point, strike 18%, realized vol 22%
  → Variance gap = 22² − 18² = 484 − 324 = 160 (in vol² units, scaled by convention)
  → Cash ≈ f(notional, annualization factor) — confirm ISDA / dealer term sheet

Always read the term sheet: some dealers quote payoff per 1% vol move squared, others use vega notional where P&L ≈ vega notional × (realized vol − strike vol). Rounding, cap/floor, and disruption events (market halts, index reconstitution) belong in the legal schedule.

Payer vs receiver

Leg	Bet	Profits when	Typical user
Variance receiver (long variance)	Realized > strike	Choppy, high-vol paths	Hedge funds pre-event, vol funds
Variance payer (short variance)	Realized < strike	Quiet, low-vol grind	Banks warehousing customer flow, yield seekers

The receiver is structurally long gamma and long vega relative to a delta-neutral book — but without managing the hedge yourself. The payer is the opposite and must replicate dynamically.

Realized variance: sampling matters

Realized variance is not the same as closing implied vol on the last day. It accumulates from discrete returns:

σ²_realized ≈ (Annualization factor) × Σ [ ln(S_i / S_{i−1}) ]²

Design choices that move P&L:

Fixing source — official index close vs 15-minute VWAP; flash crashes and auction prints can swing final realized.
Business-day annualization — 252 is standard for US equities; calendar 365 changes the scale.
Overnight vs intraday — some contracts include only close-to-close; others add open-to-close segments.
Disruption adjustments — trading halts may skip a day or interpolate; read the 2008 ISDA equity derivatives definitions updates.

Forecast realized vol with GARCH or historical estimators, but remember variance swaps pay on the actual sampled series, not your model's annualized forecast.

Replication: why dealers quote strikes

Dealers do not warehouse unhedged variance risk indefinitely. At inception they approximate the variance swap payoff by holding a portfolio of OTM calls and puts across strikes — the classical replication result linking integrated option prices to expected quadratic variation (Carr-Madan style replication). Intuition:

OTM options are sensitive to tail moves; a strip weighted by 1/K² mimics squared return exposure.
At inception, forward-start replication sets the fair variance strike where receiver and payer are zero PV.
As spot moves, the dealer rebalances the strip — this is where their gamma scalping P&L lives (see gamma hedging).
Skew and discrete monitoring mean replication is imperfect; dealers embed a vol-of-vol and convexity charge in the strike.

Fair strike is typically above ATM implied vol because OTM puts trade rich on equity indices ( skew lifts integrated variance). That wedge is related to the variance risk premium: on average, implied variance exceeds realized — variance payers earn a premium for bearing gap and replication risk.

Volatility swaps vs variance swaps

A volatility swap pays on realized volatility (not variance). Because vol is the square root of variance, the payoff is concave in variance — replication needs forward-start vol options or a convexity adjustment. Variance swaps are more liquid in equity indices; vol swaps appear in FX and commodities. Traders convert mentally: for small moves, vol diff ≈ variance diff / (2 × strike vol).

Trading and portfolio use cases

Pure vol direction — receiver before earnings season if you believe realized will beat index implied; payer if you expect a quiet grind.
Dispersion trades — receive index variance, pay single-stock variance (or the reverse) to bet on correlation: index realized vol often underperforms weighted single-name realized when correlation spikes.
Skew and correlation hedges — complement static option overlays; variance strike embeds skew, so compare to replicating with straddles.
Fund mandate hedges — long-only equity funds buy variance receivers as crash insurance without daily delta management.
Relative value vs VIX futures — VIX futures embed roll yield and convexity; variance swaps are a different term structure on SPX realized.

Capital efficiency depends on CSA terms: variance swaps are OTC, require ISDA, initial margin under SIMM for many counterparties, and lack the transparency of listed options.

Harbor Capital dispersion overlay refactor

Problem: equity sleeve held 40 large-cap tech names; index-level short-gamma covered-call program capped upside but left correlation risk unhedged. When the index fell, single-name realized vols spiked while index realized lagged (correlation up, index vol muted).

Entered 3-month SPX variance receiver ($8M vega notional) at 19.2% strike.
Partially funded by paying variance on a basket of five highest-beta names (dispersion leg) — net position long correlation break.
Documented fixing calendar and disruption clauses with two dealers for mark-to-market comparability.
Daily MTM from dealer runs; internal model cross-check using replicated strip and 20-day rolling realized.
Rolled quarterly; capped total variance notional at 5% of sleeve NAV.

Q1 outcome: index realized 21.4% vs 19.2% strike; basket realized 28.7% on paid legs — net P&L positive after funding, outperforming an equivalent VIX call spread by 140 bps after roll costs (that quarter's path favored realized over VIX term structure).

Technique decision table

Approach	Exposure	Best when	Watch out for
Variance swap receiver	Long realized vs strike	Clean vol-of-index view, no hedge desk	OTC CSA, strike vs model fair
ATM straddle + gamma scalp	Long gamma, path-dependent	Need strike-specific convexity	Hedge costs, theta, skew embedded in one strike
VIX futures / options	Forward vol, roll exposure	Liquid listed expression	Roll yield, VIX-SPX basis
Variance payer	Short realized vs strike	Earn VRP, warehouse capacity	Tail events, replication gaps
Dispersion package	Correlation view	Index vs single-name vol wedge	Basket fixing mismatches
GARCH / vol forecast only	No trade	Research and sizing	Not a hedge by itself

Common pitfalls

Confusing vol and variance strike — 20% vol strike is 400 variance units, not 20.
Ignoring convention sheets — 252 vs 365 annualization shifts breakeven by several vol points on short tenors.
Marking to one dealer — fair value and strikes differ; get two-way quotes.
Assuming VIX proxy — VIX is 30-day model vol; your swap may be 3-month close-to-close realized.
Short tenor noise — 2-week variance is dominated by one gap day; size down.
Correlation trades without basket detail — dispersion P&L dies on fixing mismatches and beta drift.
No disruption plan — halts and special dividends move realized; legal language matters.
Counterparty concentration — OTC exposes you to dealer credit; diversify or clear where available.

Production checklist

Confirm underlying, fixing source, observation dates, and annualization factor.
Translate strike quote (vol vs variance units) and notional into dollar P&L per vol point.
Compare dealer strike to internal replication fair value and skew-adjusted model.
Document ISDA, CSA margin, and disruption fallback language.
Model breakeven realized vol vs current implied and historical percentiles.
For dispersion, align basket weights with fixings and corporate actions.
Set MTM process: dealer runs, independent cross-check, dispute resolution.
Stress with 2008-style and 2020-style realized paths on the same tenor.
Cap variance notional as % of NAV; report alongside options gamma and vega.
Plan roll calendar before expiry; avoid forced negotiation in illiquid weeks.

Key takeaways

Variance swaps are forwards on realized variance — linear in vol², not a single listed option.
Receivers profit when realized exceeds strike; dealers replicate with OTM strips and bear gamma risk.
Sampling conventions (fixings, annualization) define the bet as much as the strike level.
Skew and vol-of-vol embed in fair strike — related to the variance risk premium payers harvest on average.
Harbor Capital used index receiver plus single-name payer legs to express a correlation view without intraday stock hedging.