# Equity Market Breadth and What It Means for Implied Correlation

### A brief primer on implied correlation

**Equity Market Breadth and What It Means for Implied Correlation**

Only about 9% of the S&P500 stocks have been leading this latest rally while the rest have been rangebound. Of course, these are the tech and especially AI stocks that are in vogue now after NVDA’s stellar earnings report.

Another way to look at this is through the view of implied correlation. This is what the options market is expecting to be the correlation between the stocks in the index on a going forward basis, similar in concept to implied volatility for options. In fact, implied correlation is derived from the relationship between the implied volatility of CME S&P index future options and the implied volatility of the single stock constituents of the index of the same tenor.

More precisely, we can use the following generalized formula:

where sigma_i is the implied volatility of stock I and w_i is the weight of stock I, and N=500 for the 500 stocks in the index. Now for those intimidated by the math, the important thing to note here is that when the implied volatility of the index is high relative to that of the single stocks, the implied correlation is high, and vice versa, which makes intuitive sense.

Recently as noted above, the breadth of stocks leading the rally in the market has been low and even the sectors outside of tech have had mixed performance, and the market expects this trend to continue. We can see the trend in implied correlation recently using the ticker COR3M on TradingView (note the CBOE instead of doing the above calculation for all 500 stocks, uses the top 50 stocks in the index to simplify things):

As can be seen this has been dropping off a cliff and is at 2 year lows, which as from the formula above means that implied volatility on the S&P 500 index is going down at a faster rate than implied volatility of the constituent stocks.

Now you may say that hey this is just the same as saying the VIX is going down, but the difference here is that traders at banks and hedge funds will look at this as a relative value arbitrage opportunity since betting on correlation going up is often viewed as a safer trade than betting on volatility. Since there are many reasons to expect stocks to have positive correlation, the trader would view this as having a rather limited downside.

What is also interesting is that the 3mth implied correlation was at 29% on May 18, the last time the VIX was below 16, and now it is at 22%. This to me looks like capitulation of some of the above relative value traders either getting a tap on the shoulder by their risk manager or perhaps some lightening of their positions going into the less liquid summer months.

Is this sell off over? Hard to say but these are certainly the kind of mispricings that would start to get the attention of other players in the market outside of the specialists in these trades, so depending on your perspective it would make sense to either go long VIX (buy index vol) or sell single stock options here.

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I like what you're doing here and am excited to learn more about this way of approaching trading.

You're gonna kill the normies without a "Get off Zero" post or series. I'm pretty mathy, and I instinctively skipped the formula.