More positions are not the same thing as more diversification

riskPublished 20 October 20261 min readmulti asset

Key points

• Weights of 60, 30 and 10 have a squared-weight index of 0.46.
• The index is about the allocation, not about volatility.
• Correlations are not inferred from the weights.

What is going on

Square each holding’s decimal weight and add them. Equal weights spread the index lower. One large weight pulls it up. For 0.60, 0.30 and 0.10 the sum of squares is 0.36 + 0.09 + 0.01 = 0.46. Investor.gov describes diversification as spreading risk, not as removing it. A sector label or a shared factor can sit underneath many names. The explorer will also apply shocks you type: the portfolio result is the sum of weight times shock. If you do not type a shock, it does not invent one.

Why it matters

A portfolio that looks diversified by count can be concentrated by the same companies inside the funds. Currency can dominate a foreign weight that looked small in the home currency. The allocation calculator takes holdings you enter. It does not build a covariance matrix.

What to watch

Check the weights add to the total you think they do. Name the largest holding and the top three. Ask which of them would fall together.

Risks

A low index is not a small possible loss. This page does not estimate volatility from the weights.