Inverse-volatility weights

Calculation contract

w_i = (1 / sigma_i) / sum_j(1 / sigma_j)

Method and interpretation

A 10%, 20%, 40% volatility vector creates weights in the ratio 4:2:1. The common normalization sets total capital weight to one. Multiplying every volatility by the same positive scale leaves the weights unchanged.

This reference is useful for checking a proposed weighting implementation, including its asset order and zero-input policy. It does not estimate volatility from prices. Choose and document the estimator, lookback and cutoff elsewhere before passing a vector here.

Where the reference stops

Correlations are absent. In general the output is not an equal-risk-contribution solution, and a low historical volatility estimate can concentrate capital. Zero is rejected instead of receiving an infinite weight. All inputs must use one frequency.

Published synthetic inputs

{
  "volatilities": [
    0.1,
    0.2,
    0.4
  ]
}

Frozen calculation output

{
  "weights": [
    0.5714285714285714,
    0.2857142857142857,
    0.14285714285714285
  ],
  "weight_sum": 1
}

Positive same-frequency decimal volatilities only. Correlations are not used; this is not a general equal-risk-contribution solver.

Verification coverage

• Scale invariance, normalization and equal-volatility equality.
• Zero, negative, null and string values rejected.

Unit and independent-reference checks test arithmetic and rejection rules, not future investment performance.

Method references

• MOSEK: risk budgeting and contributions

Read the assumptions in context