The term correlation is used to describe 2 trade-able assets with price that tend to move in same direction(or opposite directions). However, are there assets that exhibit inverse volatility correlation? What I mean is that: If asset A is experiencing exploding volatility, then B would be experiencing little volatility(and the other way round). The direction of price is not important here, just the amount of volatility.
Sure, you can search for any possible correlation pairs. Just do your own correlation analysis, or pay someone to do it for you. It's a time-consuming job as the time-series data of n*(n-1)/2 pairs need to be analyzed...
If you just mean to look at vols of one asset to be relationally larger (smaller) than a related asset, that is common. High beta against lower beta will give you exposure to a volatility differential. Duration risk against nearer term will do the same for rate risk. For two assets to have inversely correlated volatility, cash would have to be flowing between them. In other words, they are acutely negatively correlated, but also correlated relative to investor flows (or a long/long spread is correlated!). Just some thoughts. This is related to liquidity. When one asset class becomes risky, risk is suppressed in a competing asset that is liquid enough to accept the flows. Big levered trades that are long/short (or long/long) can produce this type of thing when they unwind. Example, 60/40 split. Index vols up, bond vols down, or like the DOW/RUT spread trade unwinding and the hedge leg going limit up or having monster rallies intra-day. LOL Index traders watch the yield curve because it's so correlated to index vol. Rate fly (grey) and VIX futures (blue). This is the day of the CPI print.
To find anything that has a consistent inverse volatility correlation will prove difficult, perhaps non-existent.
It appears form the picture that Vix futures and rate experience volatility and direction correlation and not inverse volatility correlation? You mentioned 60/40 split. I am not sure I understand what you mean there. Do you mean a portfolio of bonds and stocks could experience inversely correlated volatility(price direction is irrelevant)? I am curious to know if: The implied volatility of inverse SPY ETF is inversely correlated to the VIX?