How Variance Dispersion Can Become Short Volatility

Summary

The note explains how a variance dispersion position can acquire short volatility exposure after a market decline. The example starts with a vega-neutral portfolio that is short an index option and long options on individual stocks, with deltas hedged at inception. As the market falls, the options move farther from at-the-money and their vegas decline.

The explanation then considers vega convexity: higher implied volatility can increase the vega of out-of-the-money options. If the index volatility smile is steeper than the single-stock smiles, the short index option can gain more vega from that effect than the long single-stock options. The portfolio can therefore shift to net short vega, despite being initially vega neutral. This is a qualitative scenario, not a universal outcome; the change depends on how spot, implied volatility, and the respective smiles move.

Key ideas

• A variance dispersion trade can begin with a short index option and long single-stock options sized to be vega neutral.
• A market decline can move both sets of options farther from at-the-money and reduce their vegas.
• Higher implied volatility can raise the vega of out-of-the-money options through vega convexity.
• A steeper index smile can cause the short index option to gain more vega than the single-stock options, shifting the portfolio short vega.

Tags

# How variance dispersion trades become short volatility


# How variance dispersion trades become short volatility












From this document, http://quantlabs.net/academy/download/free_quant_instituitional_books_/[JP%20Morgan]%20Variance%20Swaps.pdf, on page 56, it states that

> Losses from short correlation through variance dispersion can occasionally be very large, especially since the trade becomes short volatility following adverse moves in correlation.

I cannot see how short correlation through variance dispersion becomes short volatility.

## Answer by mbison (score 2, accepted)

https://quant.stackexchange.com/a/32958

Suppose you are short the index option, and long the single stock options (all vanillas). You size it in such a way that at inception you have flat vega, you hedge out all your deltas.

Now assume the market moves down. All your options move away from ATM and they all have less vega (both your long single stock options, as well as ur short index option).

OTM options are long vega convexity: when implied moves up, vega moves up. So while all your options lost vega due to moving away from the money. They will gain incremental vega due to a higher vol (assuming vol moves along the smile).

Index smile is steeper than single stock smile. So the index option - which you are short- gains more vegas relative to the single due to vega convexity. Combining it all, you are short vegas now. (both index and single lost vega due to spot move, but index lost less due to steeper smile).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.