What is a variance swap and how does it differ from a volatility swap?

A variance swap is an OTC derivative that pays the difference between realized variance and a pre-agreed strike variance over a specified period. It provides pure exposure to volatility without any directional bet on the underlying.

Structure:

• Long variance swap: Profits when realized variance exceeds the strike (implied) variance.
• Short variance swap: Profits when realized variance is below the strike.

Payoff Formula:

Payoff = Notional_variance x (Realized Variance - Strike Variance)

The notional is often quoted in 'vega notional' terms for convenience:

Notional_variance = Vega Notional / (2 x Strike Vol)

Worked Example:

Ridgeline Capital enters a long variance swap on the FTSE 100:

• Vega notional: $100,000 per volatility point
• Strike variance: (18%)^2 = 0.0324 (strike vol = 18%)
• Contract period: 3 months

At expiry, realized volatility turns out to be 23%.

• Realized variance = (23%)^2 = 0.0529
• Notional_variance = $100,000 / (2 x 18) = $2,778 per variance point
• Payoff = $2,778 x (529 - 324) = $2,778 x 205 = $569,490

(Note: variance is often scaled by 10,000 for quoting convenience.)

Why Variance Instead of Volatility?

1. Replication: Variance swaps can be perfectly replicated using a portfolio of options across all strikes (weighted by 1/K^2). This makes them easier to price and hedge. Volatility swaps cannot be replicated as cleanly.

1. Convexity: Variance is the square of volatility, so long variance positions have convex payoffs. A spike from 18% to 30% vol pays much more than linear — you benefit disproportionately from tail events.

1. P&L attribution is cleaner: Daily P&L on a variance swap depends only on the squared return that day vs. the implied daily variance. No path dependency complications.

Variance vs. Volatility Swap Comparison:

Risk Warning: Short variance positions carry extreme tail risk. If vol spikes from 18% to 50%, the short side's loss is massive due to the squared relationship. This is why short variance was famously dubbed a 'picking up pennies in front of a steamroller' strategy.

Practice variance swap calculations in our CFA Level II question bank.