Relative Value Volatility Trading
Derivatives-based Portfolio Solutions


Volatility investors can trade volatility pairs in the same way as trading equity pairs. For indices, this can be done via options, variance swaps or futures on a volatility index (such as the VIX or vStoxx). For indices that are popular volatility trading pairs, if they have significantly different skews this can impact the volatility market. Single-stock relative value volatility trading is possible, but less attractive due to the wider bid-offer spreads.

When a pair trade between two equities is attempted, the main driver of profits is from a mean reversion of the equity prices. With volatility relative value trading, there are two ways of profiting:
  • Mean reversion. In the same way an equity pair trade profits from a mean reversion of stock prices, a volatility pair trade can profit from a mean reversion of implied volatility. For short-term trades, mean reversion is the primary driver for profits (or losses). For relative value trades using forward starting products (eg, futures on volatility indices), this is the only driver of returns as forward starting products have no carry. The method for finding suitable volatility pair trades that rely on a short-term mean reversion are similar to that for a vanilla pair trade on equities.
  • Carry. For an equity pair trade, the carry of the position is not as significant as, typically, the dividend yields of equities do not differ much from one another and are relatively small compared to the movement in spot. However, the carry of a volatility trade (difference between realised volatility and implied volatility) can be significant. As the duration of a trade increases, the carry increases in importance. Hence, for longer term volatility pair trades it is important to look at the difference between realised and implied volatility..

While the skew of different indices is dependent on correlation, traders tend to keep the absolute difference in implied volatility stable due to mean reversion. This is why if equity markets move down, the implied volatility of the S&P500 or FTSE (as they are large diversified indices that hence have high skew) tends to come under pressure, while the implied volatility of country indices with fewer members, such as the DAX, are likely to be supported. The SX5E tends to lie somewhere in between, as it has fewer members than the S&P500 or FTSE but is more diverse than other European country indices. Should markets rise, the reverse tends to occur (high skew indices implieds are lifted, low skew implieds are weighed on).

Difference between implieds is key, not the absolute level of each implied
We note that for returns due to mean reversion, it is not the absolute level of volatility that is key but the difference. For example, let us assume stock A implieds trade between 20% and 25% while stock B implieds trade between 30% and 35%. If stock A is at 25% implied (top of range) while stock B implied is at 30% implied (bottom of range), a short A volatility long B volatility position should be initiated. This is despite the 25% implied of A being less than the 30% implied of B.

In dispersion trading, a (normally short) index volatility position is traded against a basket of (normally long) single-stock volatility positions. This position of index volatility vs basket could be considered to be a pair trade where one leg is the index and the other leg is the basket. A pair trade can be carried out via straddles / strangles or variance swaps, just like dispersion. We shall assume that the pair trade is being carried out by delta hedging options, for trading via variance swaps simply replaces notional in the table below with the vega of the variance swap. The weighting of the legs in order to be vega / theta or gamma flat is similar to dispersion trading, as can be seen below.

Sign of theta, vega and gamma depends on which way round the pair trade is initiated
The sign of theta, vega and gamma are based on a trade of shorting the lower volatility security and going long the higher volatility security (on an absolute basis) in order for easy comparison to dispersion trading (where, typically, the lower absolute volatility of the index is shorted against a long of the higher absolute volatility of the single stocks). For the reverse trade (short the higher absolute volatility security and long the lower absolute volatility security), the signs of the greeks need to be reversed.

Theta and vega weighted are the most common methods of weighting pair trades. Dollar gamma weighted is rarely used and is included for completeness purposes only. Theta-weighted trades assume proportional volatility changes (eg, if stock A has 20% implied and stock B has 25% implied, if stock A rises from 20% to 30% implied that is a 50% increase and stock B rises 50% to 37.5% implied). Vega-weighted trades assume absolute volatility changes (eg, if stock A has 20% implied and stock B has 25% implied, if stock A rises from 20% to 30% that is a 10 volatility point increase and stock B rises 10 volatility points to 35% implied).

Pair trade between two securities of same type should be theta weighted
If a pair trade between two securities of the same type (ie, two indices, or two single stocks) is attempted, theta weighting is the most appropriate. This is because the difference between a low volatility security and a high volatility security (of the same type) usually increases as volatility increases (ie, a proportional move). If a pair trade between an index and a single stock is attempted, vega weighting is the best as the implied volatility of an index is dependent not only on single-stock implied volatility but also on implied correlation. As volatility and correlation tend to move in parallel, this means the payout of a vega-weighted pair trade is less dependent on the overall level of volatility (hence the volatility mispricing becomes a more significant driver of the P&L of the trade)

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