Correlated Positions & Concentration Risk

Diversification counts independent sources of uncertainty, not rows in a trade log. One hundred positions can fail together because they resolve from the same event or were all valued by the same stale signal.

Portfolio variance #

For position PnLs $X_i$,

$$Var\left(\sum_iX_i\right)=\sum_iVar(X_i)+2\sum_{i<j}Cov(X_i,X_j).$$

Ignoring covariance drops every cross-position term. If correlations are positive, the resulting risk estimate is too small.

Three common concentration patterns #

1. Same event: election winner, turnout, and party-seat contracts can all jump on one result.
2. Same signal: several sports markets use one injury feed; one bad update biases all valuations.
3. Same execution path: latency or venue outage causes many stale fills together.

Numeric example #

Buying 100 shares across one contract at $q=0.65$, $p=0.60$ is not 100 Bernoulli trials. All shares settle identically: total PnL is +40 if YES and -60 if NO. Treating them as independent would invent smooth diversification that does not exist.

Life example #

Owning ten apartments in one floodplain is ten assets but one flood exposure. Address count does not diversify the common hazard.

Application to no-hedge #

Maintain limits by settlement event, event family, reference venue/feed, strategy version, and time window. Stress a common reference error and simultaneous adverse fill. Apply position sizing to the cluster total, not independently to each order.