When Correlations of Index Levels Can Mislead Before and After a Regime Shift

Summary

The document questions an analysis that compares the correlation of an uncertainty index and a fixed-income ETF index before and after a financial crisis. It asks whether comparing their levels is technically sound, given the common advice to analyze returns, and how that comparison differs from a cointegration test. It also notes that both series may be more bounded or stationary-looking than typical stock prices.

No answer or empirical result is included, so the document does not establish whether the reported disconnect is genuine. Its questions point to important distinctions: correlation between levels can reflect trends or shared persistence, while correlation between changes addresses co-movement in movements; cointegration asks whether a particular combination of nonstationary series is stationary. Bounded-looking values alone do not establish stationarity, and a pre/post comparison raises questions about structural change and statistical uncertainty. The data, transformations, tests, and sample periods are not provided, limiting any conclusion about the analyst’s method.

Key ideas

• Correlation between index levels and correlation between returns or changes answer different questions.
• Cointegration evaluates whether a combination of series is stationary, rather than simply measuring correlation.
• A bounded or stable-looking index is not necessarily statistically stationary.
• Comparing periods around a crisis may involve structural breaks that affect inference.
• The document supplies questions but no test results or conclusion about the specific analysis.

Tags

# Potential pitfalls in the use of correlation


# Potential pitfalls in the use of correlation












Background: The red line is an index, which goes from 0 to 100, measuring uncertainty in the markets.

The dark blue line is a price index, which has a lower bound at 0, and virtually no upper bound. However since it's a fixed income index, it will tend to hover around 100, compared to a stock index which can exhibit clear strong trends. Please ignore the light blue line.

The analyst in question compared the correlation between the uncertainly index levels (not returns) and ETF index levels (not returns), pre and post the financial crisis and concluded that there is a disconnect post crisis.

My question: Is such an analysis technically correct? I've always read about never regressing prices and always returns. Specifically,

a) Whilst doing a cointegration analysis, we would have regressed the two price time series and looked at the stationarity of the error term. We would have concluded that before the crsis, the error term was stationary and post cris, it is not. How does that analysis compare to simply regressing the two series like it's done here

b) Also, since these two times, by construction are somewhat stationary (as opposed to stock prices), would simply regressing the price series be okay here?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.