Those who trade equity derivatives for a living are familiar with the complexities of trading volatility. In general, traders seek to exploit option mispricings through delta-neutral strategies in which a hedge position in the underlying stock is dynamically adjusted through the life of the option. While the Black-Scholes framework provides a straight forward formula with regard to initiating (delta) and adjusting (gamma) the stock hedge, the process of realizing profits from volatility trading is far from exact. Profit uncertainty arises from the path dependent nature of an option's gamma and vega. These Greeks are a complex function of the relationship of the spot price to the strike price, time, and volatility.
To illustrate these path dependencies, we provide the following chart. The chart (gamma profile) shows the gamma profile of an option based on two hypothetical paths of the underlying stock and changes in time. We assume in each case that the daily return for the stock is drawn from a normal distribution with 50% annualized volatility. As is quickly evident, the gamma profile can vary substantially depending on how the stock price behaves in relation to the strike price.
The single stock variance swap is an OTC equity derivative product that addresses some of the limitations of traditional delta-neutral option strategies. The payoff of the swap contract is based on the realized variance of the returns of the equity in relation to a variance strike price agreed to by the parties on trade date. The distinguishing characteristic of this vehicle is that it provides the investor with constant exposure to realized volatility. The gamma of the contract does not hinge on the relationship of the stock price to the strike price, nor is it impacted by the passage of time. In this way, the trader knows exactly the daily break-even change in the stock price for a variance swap.
There are many potential applications of single stock variance swaps. First, the swap may be used to express a long or short view on future volatility. Here, a trader could buy or sell the swap outright, or as part of a volatility pairs trade. An example of this would be to buy a variance swap on Altera Corp. and sell a variance swap on Xilinx Inc. These two semi-conductor stocks typically exhibit similar volatility characteristics. Should their implied volatilities diverge sufficiently, a long/short variance swap structure would be an effective method for seeking to capture this divergence.
The second potential application of single stock variance swaps is as a defensive instrument. Investors with long exposure to a single stock may find that overlaying a long variance swap can help mitigate losses in instances when the stock suffers a substantial sell-off. This strategy is conditioned on the expectation that volatility will rise should the stock price fall sharply. For example, the recent decline in the price of Tyco International has resulted in a spike in both realized and implied volatility levels. Since 1/2/02, the stock has fallen roughly 20% and realized volatility has spiked to 65%.
A third application for the single stock variance swap is in the area of "dispersion trading". In this strategy, an investor sells options on an index and buys options on the individual stocks that comprise the index. The objective is to profit from the high level of implied correlation among the stocks. Dispersion trades are often difficult to manage due to inherent trading frictions and rebalancing costs. Since the variance swap isolates volatility exposure without the path dependent draw backs of delta-neutral option strategies, it is can be an effective vehicle for a dispersion trade.
To provide an example, we use the Semiconductor HOLDRs (SMH) Index and the largest three stocks (INTC, TXN, AMAT) in the index. These three stocks comprise 50% of the index weight. Suppose an investor sells an SMH variance swap at 55% on 100,000 per volatility point. The investor also buys single stock variance swaps on INTC, TXN, and AMAT (weighting the units in each swap to reflect each stock's weight in the index) for a weighted average strike price of 55%. The investor now has a very direct trade in place: should the weighted average realized volatility of the package of stocks exceed the realized volatility of the SMH, the transaction will be profitable. If not, the investor will lose money. In the chart on the previous page we illustrate how this spread has behaved historically.
The single stock variance swap is a new product that provides direct long or short access to realized volatility. The swap may be a useful alternative for traders who are currently using delta-neutral option strategies to trade volatility and are seeking more stable gamma and vega profiles. Additionally, those investors with long exposure to a single stock may find the variance swap attractive as a defensive vehicle that can be used to mitigate losses suffered from a sharp decline in the stock price.
This week's Learning Curve was written by Dean Curnutt,principal and equity derivative strategist at Banc of America Securities.
