Concentration Risk Herfindahl: Measuring Portfolio Over-Exposure

Key Takeaways

• The Herfindahl-Hirschman Index sums the squared weights across positions; its inverse gives the effective number of positions (N_eff), which reveals how many truly independent bets the portfolio is making.
• A portfolio holding 7 sectors with a 40% technology weight calculates to HHI of 0.24 and N_eff of only 4.1, it behaves like 4 equal-weight sectors, not 7.
• Counting tickers as diversification is a common mistake: 50 names where the top 5 are half the book has an N_eff much closer to 5 than to 50.
• Basel's Large Exposures framework caps any single counterparty at 25% of Tier 1 capital, a direct regulatory limit on single-name concentration risk.

What It Is

A portfolio with 100 equal positions at 1 percent each is not the same as a portfolio with one 50 percent position and fifty 1 percent positions, even if the average correlation is identical. The second portfolio's fate is tied to the big name. Concentration risk is the term for that extra fragility.

The Herfindahl-Hirschman Index compresses the portfolio weight vector into a single number:

HHI = sum(w_i^2) for all positions i

Weights are expressed as fractions (0.05 for 5 percent). HHI ranges from 1/N (perfectly equal-weighted N-position portfolio) to 1 (single position). Regulators, antitrust authorities, and portfolio risk teams all use the same statistic.

The Intuition

Squaring the weights penalises large positions disproportionately. A 10 percent weight contributes 0.01 to HHI. A 20 percent weight contributes 0.04, four times as much, even though it is only twice the nominal size.

The inverse of HHI gives an intuitive effective number of positions, N_eff = 1/HHI. A portfolio with HHI of 0.10 behaves like an equal-weighted portfolio of 10 names, regardless of how many line items are actually on the statement. That number is what most practitioners quote when they want to communicate concentration quickly.

How It Works

In a banking context, concentration appears in several dimensions:

• Single-name concentration. Basel's Large Exposures framework (BCBS 283) caps an individual counterparty exposure at 25 percent of Tier 1 capital, and 15 percent for exposures between G-SIBs.
• Sector concentration. Exposure to one industry, such as commercial real estate or energy, that exceeds prudent thresholds relative to capital.
• Geographic concentration. A portfolio dominated by one country or region, sharing macro shocks.
• Funding concentration. Deposit bases where a handful of customers account for a disproportionate share of liabilities. SR 11-14 asks banks to monitor all of these.

For antitrust applications, the US Department of Justice uses HHI on market shares. Under 0.15 is "unconcentrated", 0.15 to 0.25 is "moderately concentrated", above 0.25 is "highly concentrated". The same thresholds are reasonable rough anchors for portfolio use, though portfolio managers more often target N_eff.

Credit risk models add a granularity adjustment. The internal ratings-based (IRB) capital formula assumes an infinitely granular portfolio. Real portfolios are not, so a Granularity Adjustment (GA) is added, using HHI as an input, to raise capital when concentration is material.

Worked Example

Consider a sector allocation for a 1 billion portfolio:

• Technology: 40 percent
• Healthcare: 20 percent
• Financials: 15 percent
• Consumer staples: 10 percent
• Energy: 8 percent
• Utilities: 4 percent
• Other: 3 percent

HHI = 0.40^2 + 0.20^2 + 0.15^2 + 0.10^2 + 0.08^2 + 0.04^2 + 0.03^2
    = 0.1600 + 0.0400 + 0.0225 + 0.0100 + 0.0064 + 0.0016 + 0.0009
    = 0.2414
N_eff = 1 / 0.2414 ~ 4.14 effective sectors

Despite holding seven sectors, the portfolio behaves like four. The 40 percent tech weight alone contributes two-thirds of the index. If the manager trims tech to 25 percent and redeploys evenly across the other six (to 12.5 percent each), HHI falls to about 0.156 and N_eff rises to 6.4. The portfolio is now genuinely diversified across sectors in an economic sense, not just a label sense.

Frequently Asked Questions

Q: What is concentration risk in simple terms? Concentration risk is what happens when too much of a portfolio's outcome depends on a single name, sector, or counterparty. If that one position fails badly, the whole portfolio suffers materially, diversification has not done its job.

Q: How does the Herfindahl Index affect investment decisions? HHI translates a complex weight vector into a single number and its inverse into an effective position count. A manager with N_eff of 5 despite holding 30 tickers should ask whether the 30-name portfolio is actually a concentrated 5-name bet with many small satellites that add no real diversification.

Q: What is a real-world example of concentration risk and HHI? A sector allocation with 40% in technology across seven sectors has HHI of 0.24 and N_eff of about 4. Trimming tech to 25% and redistributing evenly raises N_eff to 6.4, a genuine improvement in sector diversification, not just a label change.

Q: How can investors reduce concentration risk without reducing returns? Use N_eff as the target rather than position count. Find positions with low correlation to the concentrated holding and add them, even a modest allocation to a genuinely uncorrelated name can raise N_eff significantly. Monitor single-name, sector, and geographic HHI separately.

Q: How is concentration risk different from total volatility? Total volatility captures how much the portfolio value swings day-to-day. Concentration risk captures fragility to a specific idiosyncratic event, the 5% single-name position that defaults with 60% recovery loses 3% of the portfolio outright, independent of overall volatility. Standard deviation misses this; HHI and single-name limits catch it.

Common Mistakes

1. Counting line items as diversification. A portfolio of 50 names where the top five are half the book is not 50-name diversified. N_eff is the honest metric.

2. Ignoring correlation when computing HHI. Herfindahl assumes positions are independent risk units. Two different issuers in the same sector with the same macro exposure are nearly one risk. Adjusting by mapping to underlying factors (factor HHI) catches this.

3. Treating ETFs as one name. A large position in a sector ETF is concentration in that sector, not in one ticker. Look through to holdings for a true concentration view. The same applies to funds of funds and structured notes.

4. Benchmark-implied concentration. Cap-weighted indices are themselves concentrated. Tracking them closely means inheriting their concentration. Measuring active concentration against the benchmark, not against equal weight, is the correct frame for a constrained manager.

5. Static thresholds. A 5 percent single-name limit may be conservative in a 100-stock equity portfolio and too loose in a concentrated credit book. Limits should scale with the portfolio's risk budget and the correlation structure, not live as fixed numbers from an old policy.

Sources

1. Basel Committee on Banking Supervision. "Studies on credit risk concentration." BCBS Working Paper 15. https://www.bis.org/publ/bcbs_wp15.htm
2. Basel Committee on Banking Supervision. "Supervisory framework for measuring and controlling large exposures." BCBS 283. https://www.bis.org/publ/bcbs283.htm
3. Federal Reserve. "SR 11-14: Supervisory Expectations for Risk Management of Concentrations." https://www.federalreserve.gov/supervisionreg/srletters/sr1114.htm
4. US Department of Justice. "Herfindahl-Hirschman Index." https://www.justice.gov/atr/herfindahl-hirschman-index

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.