Setting Concentration Limits for Credit Portfolios with HHI
Summary
The document asks how to set internal concentration limits for a retail credit portfolio and whether the Herfindahl-Hirschman Index (HHI) is suitable. It defines HHI as the sum of squared exposure weights and notes that its range depends on the number of exposures: equal weights produce the minimum, while a single exposure produces the maximum. It also describes a normalized version that maps this range to zero through one.
A proposed practical approach is to create sample portfolios with different exposure allocations and ask industry experts, or the portfolio manager, which ones appear concerning. The HHI values of those portfolios can then serve as reference points for choosing a threshold, such as using an average or a more conservative low value among the portfolios judged concentrated. The document does not supply a universal cutoff or establish that this calibration is validated. Limits should reflect the portfolio's risk appetite and credit context; the suggested thresholding process is a judgment-based starting point.
Key ideas
- HHI is calculated by summing the squared shares of portfolio exposures.
- The HHI range depends on the number of exposures, with equal weighting at the minimum and a single exposure at the maximum.
- A normalized HHI rescales the measure to run from zero to one.
- One proposed calibration method is to compare portfolios that experts or managers judge concentrated with their HHI values.
- The document offers no universal cutoff, so any threshold remains dependent on risk appetite and judgment.
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Full text
# How to create/define concentration risk limits for credit portfolios
# How to create/define concentration risk limits for credit portfolios
How do you create/define concentration risk limits for credit portfolios?
I've seen a lot of recommendation for HHI for example, but how do I define what is high or low concentration?
The idea of the analysis is not regulatory but for my own control of the portfolio positions and credit risk distribution. The portfolio is composed of basically retail credits.
Are there better alternatives to HHI?
Edit: Pleb commented on $HHI_t = \sum_{i=1}^d(w_t^i)^2$ where $HHI_t \in [\frac{1}{d}, 1]$, because if I have a single exposition then I have maximum value and if I have expositions with equal weights, then $HHI_t = \sum_{i=1}^d(\frac{1}{d})^2 = d\frac{1}{d^2} = \frac{1}{d}$. We could normalize it to be $HHI_t \in [0, 1]$ by subtracting $\frac{1}{d}$ on the nominator and denominator, then $cHHI_t = \frac{HHI_t - \frac{1}{d}}{1- \frac{1}{d}}$. But then, how further from 0 is a worrying point? How high should be my HHI before I start to worry and notice I have a concentration problem? Let's say I have to redistribute my expositions somehow if I hit a certain value. How do I define that value? Is there a metric in which that value is easier to define?
Its intuitive to think its highly correlated with my risk apetite. But how do I use that to obtain a concentration limit?
Edit2: Also from Pleb: Together with industry experts (or by yourself) its possible to scout which portfolio would seem concentrated (simply by altering the weights). That way, you go through different allocations in order to pinpoint the portfolios that seem concentrated. Then, calculate the cHHIt metric for the portfolios that are deemed concentrated. The point of reference can then be the average of all cHHIt, or more conservative, the smallest cHHIt and define the threshold there.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.