This blog post is a refactored version of this Twitter thread
Let’s do dispersion trading for the uninitiated.
What Is Dispersion Trading?
Why Is Dispersion Trading A Correlation Bet?
 The 2 stocks rip in opposite directions.
 The index is unchanged.

The stocks move exactly together in a big way.

You win on your stock straddles but you will lose more on your index short.
Why?
The index is cheaper than the sum of the legs in straddle space. To understand why, we will need some simple math.
An Intuitive Equation
Correlation represents the spread between an index’s vol and the vol of the components.
 Index variance
 Avg stock variance
 Avg cross corr of each stock to every other stock
Be careful, you need to take square roots to move from var space to vol space which is how prices are more commonly interpreted. In other words, you must square the ratio of index vol to stock vol you get the implied corr.
Implied correlation = .44
The Shape Of Correlation Risk
Here’s index vol relation to corr for a fixed stock vol of 30%
If you structure a trade vega neutral or premium neutral you will be short correlation convexity.
 As corr increases: you get shorter vol as the index short will grows faster than the stock vol longs.
 As corr falls: vice versa. You get longer vol as it falls!
 You may choose to overweight stock long vega to flatten the curvature, but now you increase exposure to owning options.
 What do you want your local gamma/theta profile to be? How do you want your “shocked” portfolio to look (matrix approach would ask “what’s my p/l with spot down 10% and correlation doubling?”)
 How much basis or synthetic basket risk you want to take with names you include or not since this is a “dirty” trade in the first place?
The Correlation Surface
If you put the 3D options glasses on, you’ll notice that correlation has its own surface!
 Upside implied correlations are cheaper than downside correlations.
 Implied correlation has a term structure as well.
Implied correlation surfaces vary across sectors as well. Energy, biotech, bank etfs. The sector indices have implied correlations between basket components.
Then consider FX vol markets. They care about the rate vols of the individual fiat legs and, you guessed it, the correlation.
How about a US investor trading options on a foreign index of an exporter nation. Like Japan. There’s an implied correlation between the yen and the equity index itself. Google the term quanto if you want to explore that idea.
Broader Risk Lessons
The risk for any portfolio of long/short trades (either delta one or volatility) is as correlations increase your gross positions become exposed. You can’t hide behind “nets” when corrs explode higher. This is especially dangerous because most “hedged” portfolios are levered.
Imagine a beta neutral trade where you are long 2 units of “alpha stock” and short 1 unit of index (assume they are the same vol, but “alpha” stock is .50 corr).
 When correlations increase towards 100%, you are no longer neutral but long equiv of 1 unit of index into a falling market, increasing correlation mkt.
Relative value books tend to blow up as corrs increase since corrs are used to weight positions.  A portfolio that wins as correlation increases (which is itself correlated with equity risk premia) should cost carry!
This is, in fact what we find. Implied correlation trades at a premium to realized correlation (and correlation swaps which have linear risks). You pay a premium to hold a long implied correlation position. Those selling correlation via dispersion trades are capturing a risk premia or source of carry correlated with conventional risk premia.
Index options “should” be overpriced because it’s a systematic risk premium. The dispersion traders are the ones who bet when the overpricing is “excessive”. I wouldn’t advise trying that at home though.
Parting Thoughts
How do implied correlations correlate to systematic risk premia? How do they compare to realized corrs?These types of questions are the start of seeing the world as one big spiderweb of risk premia and cross correlations.
Armed with this understanding, go build the dashboard to find the cheapest hedges, the most efficient basis, or the most levered shot at correlation regimes shifting. In other words, you don’t have to have a view on whether assets are cheap or not. You can look for situations where implied correlations are [over]confident in particular regimes persisting.