Concentration Risk and Position Limits

Concentration risk is the risk that a single position, sector, factor, or strategy dominates the portfolio's outcome. It is the most common cause of catastrophic trading losses — not because the positions were bad, but because they were too large relative to the book. Position limits are the structural defense: hard caps that prevent any single exposure from becoming large enough to end the trading account.

Where concentration hides

Concentration is rarely as obvious as "all my money in one stock." It hides in:

• Common factor exposure: Twenty tech stocks are concentrated in a single growth-and-rate factor despite looking like diversification.
• Common underlying: Long an equity index future and long its largest constituent are the same bet twice.
• Strategy clustering: Five strategies that all enter on momentum breakouts share a regime dependency and fail together in choppy markets.
• Counterparty concentration: All positions cleared through one prime broker carry the broker's default risk.

Measuring concentration

• Herfindahl-Hirschman Index (HHI): $\sum w_i^2$, where $w_i$ is position weight. HHI of 1 means perfect concentration; $1/n$ means equal weighting. Effective number of positions is $1/\text{HHI}$.
• Top-N share: What fraction of portfolio risk sits in the largest 1, 3, or 5 positions?
• Factor exposure decomposition: Run each position's returns against common factors (market, size, value, momentum, volatility) and aggregate. The largest factor exposure is the hidden concentration.

Setting position limits

Effective limits layer multiple constraints:

• Per-position limit: No single position exceeds a fixed percentage of equity — typically 2% to 10% depending on strategy type and liquidity.
• Per-factor limit: Aggregate exposure to any single risk factor caps below a threshold tied to total risk budget.
• Per-strategy limit: Each strategy's allocation is bounded so that strategy failure cannot exceed a survivable drawdown.
• Hard ceiling regardless of model: Even when risk models bless a larger position, an absolute cap on capital at risk per name prevents model error from concentrating the book.

The math of concentration loss

If a position with weight $w$ suffers a loss $L$, the portfolio impact is $w \cdot L$. A 5% position that loses 50% costs the portfolio 2.5% — survivable. A 40% position that loses 50% costs the portfolio 20% — often career-ending. Position size is the multiplier that converts a bad outcome into a survivable one or a fatal one.

The expected contribution of position $i$ to portfolio variance is approximately:

$$\text{Risk Contribution}i = \frac{w_i \sum_j w_j \sigma{ij}}{\sigma_p}$$

In a risk-budgeted portfolio, no single position's risk contribution should exceed a defined share of total.

Limits are worthless without enforcement. Set them in calm conditions and obey them under stress, when the temptation to "let this one run" is greatest.