**PAIR TRADES CAN BE THETA OR VEGA WEIGHTED**

*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).*

**Pair trade between an index and a single should be vega weighted**

*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)*

#### My comments

Vega and scaled vega weighting is used for fixed spread relationships.

Practically this means that a vega neutral book is very exposed to a regime change in vol. For example a relative move in vols in which all vols double or half. This is because a vega neutral book is roughly unit neutral as ATM vegas are not sensitive to vol level. Note this is not true for skewed or wingy options as they ARE sensitive to vol levels

Theta weighting is also known as percent vega weighting.

Theta is proportional to vol level just as percent vega is normalized by vol level. This type of weighting implies vols move in proportion to one another. The weakness of this method it is subject to distortion in the wings which are already weighted in proportion to vega because OTM options have a volga.
Be careful using percent vega if a book is packed with wings