Variance vs volatility
In finance, variance is the average of squared deviations from the mean return. Volatility is its square root (the standard deviation). Variance and volatility are related but behave differently mathematically. Variance swaps are settled on realised variance — not volatility — because variance is easier to replicate theoretically (a static portfolio of options across all strikes replicates variance exposure). A variance swap typically quotes its strike as a volatility number (e.g. 20%) but settles on variance (20% squared = 400 "vols squared"), with the payoff expressed per unit of vols squared.
Replication and the volatility surface
Variance swaps can be theoretically replicated by a continuous strip of options at all strikes (weighted inversely by the square of the strike). In practice, only a finite set of liquid strikes exists, and the tails of the distribution matter enormously — very low strike puts (which capture crash scenarios) are expensive and drive up the fair value. This means variance swaps embed a large weight on tail events and trade at a premium to at-the-money volatility. The gap between the variance swap rate (higher) and ATM implied vol is called the volatility convexity or the skew premium.
The variance risk premium
Empirically, implied variance (from variance swap strikes) has consistently exceeded realised variance over most market periods. This variance risk premium (VRP) averages 2–5 volatility points for equity indices — meaning that systematically selling variance swaps (being short volatility) has historically generated a positive risk premium, similar to selling insurance. The risk is concentrated in crash periods: when volatility spikes (2008, March 2020), variance swap losses are convex — a spike from 20% to 80% vol causes variance losses proportional to 80² − 20² = 6400 − 400 = 6000 vol points, not just 60 points. This convexity is the defining characteristic of variance swap payoffs.
“A variance swap does something elegant and dangerous in equal measure: it makes volatility directly tradeable. You are no longer predicting direction. You are predicting the size of moves.”
What this means for you
Variance swaps are exclusively institutional instruments. Their relevance to sophisticated investors is in understanding the volatility risk premium and its systemic implications. Many institutional volatility strategies (risk premia funds, volatility-targeting allocations) implicitly sell volatility and embed variance-like convexity in their risk profiles. In periods of low volatility and compressed VIX, these strategies appear low-risk; in volatility spikes, they exhibit the convex loss profile of short variance. This is why the February 2018 "Volmageddon" — triggered by inverse volatility ETPs facing convex losses — caused a sharp, seemingly inexplicable market dislocation. Understanding variance convexity demystifies such events.