What Is Variance Swaps?

A comprehensive look at variance swaps, financial derivatives that deal with squared returns, and their sensitivity to extreme market movements.

Variance swaps are sophisticated financial derivatives that allow investors to speculate on or hedge against the future variability of an asset’s returns. Unlike volatility swaps that deal with the standard deviation of returns, variance swaps instead focus on the variance (the squared returns), making them more sensitive to extreme movements in the underlying asset’s price.

What Are Variance Swaps?

Variance swaps are over-the-counter (OTC) contracts that provide a payoff based on the difference between the realized variance of the returns of an underlying asset and a pre-agreed strike variance. These financial instruments are utilized by traders to gain direct exposure to the volatility of an asset without owning the asset itself.

Key Formula

The payoff of a variance swap at maturity can be expressed as:

$$ \text{Payoff} = N \times (\sigma_{\text{realized}}^2 - K_{\text{variance}}) $$

Where:

• \( N \) is the notional amount
• \( \sigma_{\text{realized}}^2 \) is the realized variance of the asset’s return over the life of the swap
• \( K_{\text{variance}} \) is the strike variance agreed upon at the inception of the swap

Squared Returns and Sensitivity

Definition and Calculation

Variance focuses on the average of the squared deviations from the mean return, which makes it more sensitive to extreme values:

$$ \sigma^2 = \frac{1}{n} \sum_{i=1}^n (R_i - \bar{R})^2 $$

Implications of Squared Returns

• A single large deviation from the mean has a larger impact on variance than on volatility (standard deviation).
• Variance swaps, therefore, are particularly useful for traders concerned with the intensity and frequency of large price swings.

Applications of Variance Swaps

Hedging

Investors can use variance swaps to hedge against volatility risk in their portfolios. By taking a position in a variance swap, they can mitigate the impact of unexpected market movements.

Speculation

Traders speculative about future market volatility can use variance swaps to capitalize on their predictions. Higher future volatility than expected leads to profits on a long variance swap, while lower volatility results in losses.

Historical Context

Variance swaps have grown in popularity as a financial instrument since the early 2000s, particularly after the dot-com bubble and the 2008 financial crisis, which highlighted the need for better management of volatility and extreme market behavior.

Example

Consider an investor who enters a variance swap with the following details:

• Notional amount, \( N \) = $1,000,000
• Realized variance, \( \sigma_{\text{realized}}^2 \) = 0.25
• Strike variance, \( K_{\text{variance}} \) = 0.20

The payoff can be calculated as:

$$ \text{Payoff} = 1,000,000 \times (0.25 - 0.20) = \$50,000 $$

Therefore, the investor gains $50,000 if the realized variance exceeds the strike variance.

Related Terms

• Volatility Swaps: Contracts providing payoffs based on the standard deviation of returns, as opposed to variance swaps which are based on squared returns.
• Delta Hedging: An options strategy that aims to hedge the price risk associated with the underlying asset.

FAQs

What is the main difference between a variance swap and a volatility swap?

The primary difference lies in their respective payoffs: variance swaps focus on the variance (squared returns of an asset), whereas volatility swaps focus on the standard deviation.

Why are variance swaps more sensitive to large price movements?

Variance measures squared deviations from the mean, thus extreme values (high or low) are amplified due to the squaring process, making variance more sensitive to large price movements compared to standard deviation.

References

1. “Options, Futures, and Other Derivatives” by John C. Hull.
2. “The Concept of Variance Swaps in the Financial Market” – Journal of Derivatives & Hedge Funds.
3. “Practical Guide to Trading Variance Swaps” – Investopedia.

Summary

Variance swaps are pivotal financial instruments for hedging and speculating on market volatility. Their focus on squared returns makes them particularly sensitive to extreme market movements, offering distinct advantages and applications compared to other volatility-related derivatives. Understanding their mechanics and applications can significantly enhance risk management and trading strategies in volatile markets.