Measuring Stock Market Dispersion: The Herd Behavior Index Approach

Dispersion in the stock market refers to the degree of variation in individual stock returns within an index or sector. High dispersion indicates significant differences in performance among stocks. Conversely, low dispersion suggests that stocks are moving more uniformly, often driven by broad market trends.

Usually, dispersion is measured by implied correlation. Reference [1] proposed a method to measure dispersion called the Herd Behavior Index (HIX). It is calculated as the ratio of the variance of a stock index to the variance of a hypothetical index that represents the extreme case of comonotonicity or perfect herd behavior. The variance is determined using model-free methods involving options, similar to the calculation of the VIX. The authors pointed out,

In this paper we made a modest contribution to this complicated matter by proposing a measure for the degree of co-movement or herd behavior present in equity markets. This measure compares the currently observed market situation with the comonotonic situation under which the whole system is driven by a single factor. More precisely, it compares an estimate of the variance of the market index with an estimate of the corresponding worst-case or comonotonic variance. In line with the VIX methodology, the estimate for the variance of the market index is based on the full spectrum of current option information on the index. Although the worst-case market situation is not observed, the comonotonic variance can easily be determined from the option prices on the constituents of the market index.

In short, the authors developed the Herd Behavior Index to measure stock market dispersion. They also explained how it differs from the implied correlation index,

Measuring the degree of co-movement with the HIX/CIX has several advantages compared to implied correlation. The HIX/CIX is able to capture all kinds of dependences between stock prices, whereas the implied correlation is a weighted average of pairwise correlations amongst the asset returns and hence, only focuses on linear dependences. Furthermore, making abstraction of the approximations involved in its calculation, the HIX reaches its maximal value of 1 if and only if the underlying random variables are comonotonic. On the other hand, there is no direct link between the degree of herd behavior and the value of the implied correlation.

This is an innovative proposal, but its practical application and effectiveness remain to be seen. One can apply it, for example, to option dispersion trading. A high HIX value suggests buying individual options and selling index options. The position can then be closed when the market stabilizes and the HIX decreases. Further research is needed to assess the profitability of this strategy and the effectiveness of the Herd Behavior Index in general.

Let us know what you think in the comments below or in the discussion forum.

References

[1] Jan Dhaene, Daniël Lindersy, Wim Schoutensz, David Vyncke, The Herd Behavior Index: A new measure for the implied degree of co-movement in stock markets, Insurance: Mathematics and Economics Volume 50, Issue 3, May 2012, Pages 357-370

Article Source Here: Measuring Stock Market Dispersion: The Herd Behavior Index Approach

source https://harbourfronts.com/measuring-stock-market-dispersion-herd-behavior-index-approach/