>FUNDAMENTAL RELATIONSHIP BETWEEN AN INDEX’S VOLATILITY AND THE CORRELTAION AND AVERAGE VOLATILITY OF ITS COMPONENTS

Overview

In this document, we derive and analyse the fundamental relationship between an index’s volatility and the correlation and average volatility of its components:



This relationship holds in practice when correlation is above 0.15, and the number of components is above 202.

■ Section 1 reviews the definition of realised and implied correlation.
■ Section 2 derives the relationship from fundamentals.
■ Section 3 evaluates the strength of the relationship using statistical methods.
■ Appendix A is a short reference of statistical formulas.

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