FRM Part II · FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?
An analyst computes daily correlations for 1,000 stock pairs and finds the cross-sectional distribution of correlations is positively centered with a bounded range of [-1, 1]. She then tests the time series of one pair's correlation and finds a first-order autocorrelation of 0.95 in monthly correlation levels but near 0.05 in monthly correlation changes. Which conclusion is best supported?
Correlation levels are persistent while changes are nearly unpredictable, which fits a slowly mean-reverting level. High autocorrelation in levels signals persistence, and low autocorrelation in changes shows no trend momentum, so the series is bounded and modelable.
- ACorrelation levels are persistent, while changes are close to unpredictable, consistent with a slowly mean-reverting levelCorrect
- BCorrelation levels are independent over time, while changes are highly persistent
- CBoth levels and changes are highly persistent, so correlation is a random walk
- DNeither levels nor changes carry information, so correlation cannot be modeled
Explanation
High autocorrelation in levels indicates persistence; low autocorrelation in changes means shocks are not trending month to month. This is characteristic of a slowly mean-reverting process with a stable local level, not independence in levels. Option 2 reverses the findings, and a random walk would not be bounded.
Did you get it right without looking?
One question tells you little. A timed set on Empirical Properties of Correlation: How Do Correlations Behave in the Real World? shows your real accuracy, how long you take and where you lose marks.
More Empirical Properties of Correlation: How Do Correlations Behave in the Real World? questions
- A risk manager observes that the average pairwise correlation among equities is high, around 0.75, in a stressed period. Which statement bes…
- A mean-reverting correlation model is written as dρ = a(μ − ρ)dt + σ dz. The long-run mean μ is 0.40, the current correlation is 0.60 and a …
- A fund holds both domestic and foreign bonds and equities. Based on empirical findings on correlations across markets, which statement is mo…
- An analyst estimates equity correlation using only days on which the market fell sharply (market return below its 5th percentile) and finds …
- Over a long sample, a risk manager observes that the correlation between two stock returns is mean-reverting. Following a month in which the…
- A risk manager at a multi-asset fund notes that the equity-bond return correlation estimated over a calm five-year window is -0.30, but duri…