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Relation between VIX, S&P500 and the CDX-Index

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The VIX-index is a measure of implied volatility in the S&P 500 and is often referred to as a fear index.  CDX.NA.IG is a credit default swap-index consisting of 125 North American investment grade companies and the S&P 500 is a stock index consisting of the 500 largest companies in USA. In [1], authors use ordinary least square (OLS) regression to study if VIX can be explained by CDS and S&P 500. and find that the VIX ,  CDX.NA.IG  (will be referred as CDX in this article for short) and  S&P 500  have a high correlation. Figure 1.   A mean-reverting pattern of inverse relationship of VIX and S&P 500 played out cleanly in 2022. VIX VIX  is measured as the weighted 30-day implied standard derivation of annual changes in S&P 500.  For example if the value of VIX is 20, then S&P 500 is expected to increase or decrease by 20% over the next year. [2]   This will be true in 68% of the cases, because stand...