Measuring Concentration in Long-Short FX Portfolios

Summary

The document asks whether the Herfindahl-Hirschman Index can measure concentration in an FX portfolio built from currency pairs that share USD as a leg. It focuses on the complication that Markowitz portfolio weights may be negative, using a short USDJPY position as an example, and asks whether signed weights can be inserted directly into the usual HHI formula or whether another measure is more appropriate.

No answer, calculation, or comparison of alternative metrics is included, so the document offers no evidence that resolves the question. The issue highlights that a concentration measure designed for nonnegative shares may behave differently when applied to signed portfolio weights. A useful analysis would need to define what concentration means for long-short exposures and consider whether pair weights capture underlying currency exposures, since multiple USD pairs can create overlapping positions. The text is best read as a framing of a portfolio construction and risk measurement problem, not as guidance endorsing a particular formula.

Key ideas

• The document considers HHI as a concentration measure for an FX portfolio of USD currency pairs.
• Markowitz weights may be negative, which complicates applying a measure based on nonnegative shares.
• A short currency-pair position raises the question of whether signed weights should enter the index directly.
• Pair-level weights may obscure overlapping exposures to the individual currencies.
• The document poses the measurement problem but supplies no recommended metric or worked example.

Tags

# Herfindahl-Hirsch-Index for FX Portfolios


# Herfindahl-Hirsch-Index for FX Portfolios












Assume we have an FX portfolio with $n$ currency pairs, such that $w_i$ is the weight of currency pair $i \in \{1, \dots, n\}$ in the portfolio, and $\sum_{i=1}^n w_i = 1$. All pairs have USD as one of the legs (USD is the base currency of the portfolio, and I would like to allocate to other currencies using Markowitz). I would like to compute a concentration measure of the portfolio, and believe that the Herfindahl-Hirsch-Index could be an option (see Chammas, Portfolio Concentration link ). However, Chammas assumes that the portfolio only contains long positions. How should I proceed if one of the portfolio weights is negative?

For example, lets assume that the weight of the USDJPY is $-0.5$. Can I simply input that weight in the computation of the HHI?

Is there a more appropriate concentration measure than the HHI for my problem?

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