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Variance Swap 101 Print E-mail
21/01/2007
Peter S. Allen, Head of European Equity and Credit Derivatives Strategy at JPMorgan, answers this week's 101 on Variance Swaps


1. What is a variance swap?

A variance swap is a contract which gives an investor direct exposure to the volatility of an underlying asset such as an index or stock. Buying a variance swap is like being long volatility at a pre-agreed level. The pre-agreed level is called the strike of the swap – not to be confused with the strike of an option.

If, over the life of the swap, the realised volatility of the underlying asset is higher than the strike, then the long variance swap position is in profit (and the short has an equivalent loss). Conversely, if the realised volatility is lower than the strike, then the long variance swap position makes a loss and the short makes a profit.

The most liquid variance swap maturities are generally from 1 month to 2 years, although some indices and more liquid stocks have variance swaps trading out to 3 or even 5 years and beyond.

2. What are the advantages, the expected returns and risks of investing in variance swaps?

Variance swaps allow investors to take direct exposure to volatility without the cost and complexity of managing and delta-hedging vanilla option positions – the payoff from a variance swap is based purely on the level of volatility. This makes variance swaps an effective way of exploiting a volatility view, hedging or diversifying an investment portfolio.

The size of a variance swap trade is usually expressed in terms of vega notional, or the average profit/loss for a 1% move in volatility. Typically, the vega notional for index variance swaps is around €100,000 – 200,000, and around €50,000 for variance swaps on single stocks.

Formally, the p/l of a long variance swap position at maturity is given by



By convention, volatility is scaled by a factor of 100, so that a strike of 17 represents a volatility of 17%.

For example, on 2 January 2006, the strike of a one-year variance swap on the Euro Stoxx 50 index was 17. Suppose an investor sells this variance swap with a vega notional of €100,000. Subsequent realised volatility during 2006 was 14.5%. Overall profit works out to be €231,618 or 2.3 vegas, slightly less than the expected 2.5 vegas due to the convex nature of the payout (see section 4).

Risks
Variance swaps expose investors to the level of volatility. At maturity, variance swaps will lose money if realised volatility turns out to be lower than the strike (for the long), or higher than the strike (for the short). If the position is unwound or marked-to-market before maturity, then the investor is also exposed to changes in implied volatility, as reflected in changes in strike level.

Because realised volatility cannot be less than zero, a long variance swap position has a known maximum loss, which turns out to be ½ x strike x vega notional. The maximum loss on a short variance swap is often limited by the inclusion of a cap on volatility. Without a cap, the short's potential losses are unlimited. Typically, a cap is set at 2.5 x strike, which turns out to give a maximum loss of 2.625 x strike x vega notional.

3. How do its returns act as a diversifying asset?

Increasingly, investors have come to view volatility itself as an asset class, one that can diversify investment returns or hedge unwelcome investment scenarios. For example, volatility typically rises in a bear market, so holding a long volatility position (being long variance swaps) can help to hedge an equity portfolio. However, as with any asset, the path to riches is to buy when cheap and sell when expensive. And here investors can look to exploit the mean-reverting nature of volatility to add alpha to portfolios. For example, systematically selling volatility has historically been profitable, with returns akin to selling credit protection.


4. How are they priced relative to ATM volatilities?

Variance swaps price slightly above at-the-money (ATM) implied volatility levels. Both variance swap strikes and ATM volatilities can be interpreted as market estimates of future volatility, and therefore it should be no surprise that they are well correlated. However, a variance swap payout is convex, which simply means that long variance swap positions receive more for a given increase in volatility than they lose for a similar decrease in volatility. The value of this benefit is the main reason for the slightly higher price of variance swaps, relative to ATM volatilities.

5. How widely used are variance swaps in institutional portfolios?

The variance swap market has grown steadily in recent years with institutional investors increasingly using variance swaps for hedging purposes or for portfolio diversification. For example, life assurance companies now offer many products with guaranteed benefits (e.g. variable annuities, with-profits funds) and these expose them to short volatility positions that may be offset by using variance swaps. Estimating total traded volumes is problematic, as with any OTC market, but recent estimates for daily traded volumes on indices are in the region of $3-5 million vega notional (source: Risk Magazine).This represents a 5- to 10-fold increase, compared to volumes three years ago. We estimate that around 20% of volatility exposure traded in the market is now done using variance swaps.


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