Concentration risk: single-stock, employer-stock and sector limits, and the effective number of holdings

What you will learn

• How to calculate the effective number of holdings from position weights.
• How much single-stock risk disappears with 5, 20 or 50 names.
• Why employer stock is the most dangerous concentration.
• Concrete caps for single stocks, employer stock and sectors, applied with look-through.

Explanation

Concentration risk is the part of portfolio risk that comes from a few positions being large. One stock and 500 stocks can have the same beta, but only the single stock can go to zero because of one company's problems. That company-specific part is idiosyncratic risk; markets pay no premium for it because diversification removes it for free.

Counting positions is a poor measure: 20 holdings with one at 60 percent is still concentrated. The standard tool is the Herfindahl–Hirschman Index (HHI), the sum of squared weights, and its inverse, the effective number of holdings:

HHI = Σ wi² and N(eff) = 1 / HHI

An equal-weighted portfolio of 12 names has N(eff) = 12; any unequal one has fewer. The course "ETFs, Funds & Long-Term Investing" applies this to indices; here we apply it to your own account with a look-through of the funds you hold.

How fast does it fall? With N stocks of equal volatility σ and average pairwise correlation ρ, portfolio variance is σ² × (ρ + (1 − ρ)/N). The term σ²ρ is the floor you cannot diversify away; σ²(1 − ρ)/N shrinks with N, and most of the shrinkage happens in the first 20 to 30 names.

Employer stock needs its own limit because it doubles up on the risk you already carry through your salary (lesson 7's human capital). If the company fails you lose job and portfolio in the same month, as Enron (2001) and Wirecard (2020) employees did. In Germany employee share programmes enjoy a tax-free allowance under § 3 Nr. 39 EStG (raised to €2,000 per year in 2024; check the current figure), often with a discount and a holding period. Take the discount if you wish, but apply the same cap as to any other stock and sell down when the holding period ends; check tax details with a Steuerberater.

Reference points: the UCITS rules (the EU framework for retail funds) allow a fund at most 10 percent in one issuer, and positions above 5 percent may together not exceed 40 percent (the "5/10/40 rule"). A private investor can be stricter. Common written caps: single stock 5 percent at cost and 10 percent at market; employer stock 10 percent including unvested grants; any one sector (GICS level, course "Sector & Industry Analysis") 25–30 percent on a look-through basis.

Worked example

Hypothetical example: a €200,000 portfolio: global equity ETF €100,000 (50 percent), employer stock €60,000 (30 percent), four other stocks of €10,000 each (5 percent each). Fees, taxes and cash are excluded.

Step 1 – HHI: 0.50² + 0.30² + 4 × 0.05² = 0.25 + 0.09 + 0.01 = 0.35. N(eff) = 1 / 0.35 = 2.9. Six lines behave like fewer than three equal positions.

Step 2 – look-through: the ETF holds over a thousand stocks with a largest weight near 5 percent, so its largest look-through position is about 0.05 × 0.50 = 2.5 percent of the portfolio and its HHI contribution is tiny. The employer stock alone supplies 0.09 of the 0.35.

Step 3 – risk versus N: single-stock volatility 35 percent, average pairwise correlation 0.3.

Going from 1 to 20 names removes 14.7 of the 15.8 removable points; 20 to 50 adds only 0.7.

Step 4 – employer scenario: the employer's shares fall 60 percent. Loss = 0.6 × €60,000 = €36,000, or 18 percent of the portfolio, while the job is at risk too. Under a 10 percent cap (€20,000) the same event costs €12,000, or 6 percent.

Common mistake

Practice activity

On paper: a €150,000 portfolio holds a world ETF €75,000, stock A €37,500, stock B €22,500 and stock C €15,000. (a) Compute HHI and N(eff). (b) Stock A is the employer; which caps are breached? (c) How much of A must be sold to meet a 10 percent employer cap, ignoring taxes?

Key takeaways

• Diversification is measured by squared weights: N(eff) = 1 / Σwi², with look-through of funds.
• With typical correlations, 20–30 equal-weighted stocks remove most idiosyncratic risk; a broad ETF does it more cheaply.
• Employer stock combines portfolio risk with job risk; cap it near 10 percent and sell down as holding periods end.
• Write caps for single stocks, employer stock and sectors, and re-check them after large moves.

Next step

Next we stress-test a multi-asset portfolio against a rate shock, an equity drawdown and an inflation surprise, using duration and beta to turn each into euros.