The Uses and Limitations of CORRA Transparency Metrics: Beyond Percentiles and Volumes

Summary

Publishing additional measures of central tendency, such as the mean and mode, alongside CORRA (median) enhances transparency about the shape of the distribution of CORRA-eligible trades. Although the CORRA distribution is dynamic, these three measures collectively can reveal additional information about the distribution of its underlying trades, such as asymmetry and potential multiple peaks of volume. This additional information could help explain larger day-to-day movements in CORRA, if they occur. The added degree of transparency reinforces CORRA’s robustness as a risk-free benchmark and balances the value of additional transparency with the risk of providing too much granular information on the distribution of trades. While these additional CORRA metrics provide value, they also have limitations, as outlined below.

Uses

Incremental measures of central tendency help participants to better understand the shape of a sample distribution of data.1 In a symmetric unimodal distribution (e.g., normal), the mean, mode and median will all be the same. However, this relationship generally does not hold when the distribution is asymmetric. For example, in a unimodal distribution, if the mean is greater than the median and the median is greater than the mode, the distribution typically has a positive skew, or a larger right tail (Figure 1, right side). Conversely, if the mean of a unimodal distribution is less than the median and the median is less than the mode, the distribution usually has a negative skew, or a larger left tail (Figure 1, left side).

When the number of peaks in the distribution is unknown, the publication of the mean, mode and median can provide information on the distribution’s shape and hint at the existence of multiple peaks of volume. In distributions with widely separated peaks, the mean and median usually fall somewhere between the mode and another peak, with the median sometimes on one of the peaks.

This is informative because, in the context of the CORRA distribution, users are likely unaware of the number of potential peaks and may not fully understand the factors driving changes in the CORRA setting. A large change in CORRA from one day to the next, known as “gapping,” could result from either a material shift in the distribution or minor changes in volumes at different rates, particularly when the distribution is not unimodal.

Examples of gapping from August 7, 2024, to August 12, 2024

Despite minimal day-over-day changes in the underlying distribution of trades, CORRA experienced an increase of 3 basis points (bps) from August 7 to August 8, 2024. This substantial shift was largely attributable to the distribution’s non-unimodal shape at the time. In such cases, knowing the median, mean and mode can provide users with some indication of the potential for gapping. For instance, on August 7, the median and mode were equal and the mean was higher, suggesting that the distribution was skewed to the right with the potential presence of other peaks in the distribution, which were elevating the mean above the median and mode (Chart 1). As a result, users who were aware of this skew would likely have been less surprised when, on August 8, CORRA jumped 3 bps from 4.53% to 4.56%, surpassing the mean, which had only a modest increase of about 0.5 bps, while the mode remained unchanged (Chart 2).

At the start of August 9, although CORRA declined by 1 bp to 4.55%, the mode remained unchanged at 4.53%, and the mean was little changed (Chart 3). This would have suggested a slight decrease in the volume to the right of the mode. On August 12, CORRA decreased by 2 bps back to 4.53%, equaling the mode once again (Chart 4). Although the mean also declined, it remained higher than the other two measures, indicating that potential peaks persisted to the right of the mode.

Caveats

While the mean and mode offer additional insights, they have limitations when applied to the CORRA distribution, which is both discrete and subject to daily variations. There have been several instances when CORRA and the mean were relatively close (with an absolute difference of less than 1 bp), yet CORRA still exhibited changes of 2 bps or more on a day-over-day basis. Therefore, although these measures of central tendency can provide additional information about the underlying CORRA distribution, they must be interpreted with caution.

Endnotes