Folio Lab/Documentation

Inverse Volatility

A closed-form, estimation-light allocation that weights each asset inversely proportional to its standalone volatility. Often used as a robust baseline and as a base-estimator inside hierarchical and ensemble methods.

Overview

Inverse Volatility allocates capital so that each asset receives a weight that scales with the inverse of its trailing-window standard deviation. Unlike mean-variance optimisation, it ignores the off-diagonal entries of the covariance matrix and requires no expected-return estimates, which makes it numerically trivial and very stable to noisy inputs. The portfolio weights are available in closed form.

The estimator sits in the same heuristic family as the equally-weighted (1/N) portfolio and is closely related to risk parity. It is sometimes called the naive risk-parity portfolio because it equalises per-asset volatility contributions but ignores correlations; full risk parity (also called Equal Risk Contribution, ERC) goes further and equalises total marginal risk contributions in the presence of correlations. When asset correlations are roughly homogeneous across the universe, the two coincide; when correlations vary materially, full ERC differs (Maillard, Roncalli and Teiletche, 2010).

Inverse Volatility is also one of the standard inner allocators inside Hierarchical Risk Parity (Lopez de Prado, 2016) where it is applied recursively along a hierarchical clustering tree, and is the default in many risk-parity ETF products in practice.

Mathematical Formulation

Notation

  • — sample standard deviation of asset 's returns over the lookback window
  • — weight allocated to asset
  • — number of assets in the eligible universe

Closed-form weights

The unnormalised weight is the reciprocal of volatility, and weights are renormalised to sum to one:

Equivalently, all assets are scaled to the same volatility-weightedbudget: . This is exactly the risk-parity solution under the simplifying assumption that the correlation matrix is the identity.

Implementation

FolioLab uses skfolio's InverseVolatilityestimator. Weights are long-only by construction and sum to one after normalisation. The lookback window for the volatility estimate inherits the platform's default rolling-window configuration; users can override it through the rolling-backtest knob to see how lookback length affects stability.

When to use it

Inverse Volatility is particularly useful as: (a) an estimation-error-free baseline against which to benchmark more sophisticated optimizers (per DeMiguel, Garlappi and Uppal, 2009, naive baselines are surprisingly hard to beat once estimation error is accounted for); (b) the default leaf-level allocator inside HRP, HERC and similar hierarchical methods; and (c) a stable, interpretable allocation in mandates where the optimizer's output must be explainable to non-technical clients.

It performs poorly when the universe contains highly correlated clusters: two near-identical assets each receive their full inverse-volatility share, which doubles the cluster's exposure relative to a true risk-parity allocation. For correlated universes prefer Risk Budgeting / Risk Parity, HRP, or NCO.

Advantages & Limitations

Advantages

  • Closed form: No optimisation solver, no inversion.
  • Robust: Depends only on per-asset volatilities, not correlations.
  • Stable turnover: Weights move slowly with vol.
  • No return estimates: Sidesteps the hardest part of MVO.
  • Explainable: Each weight has a one-line justification.

Limitations

  • Ignores correlations: Two highly correlated assets each receive their full weight.
  • No view of returns: Cannot tilt toward high-conviction names.
  • Concentration in low-vol names: A very stable asset can dominate.
  • No constraints: Sector caps, turnover bounds and tracking-error budgets are not native.
  • Vol-of-vol risk: A regime change in volatility shifts the whole allocation, even if expected-return rankings are stable.

References

  • Maillard, S., Roncalli, T., & Teiletche, J. (2010). "The Properties of Equally Weighted Risk Contribution Portfolios." The Journal of Portfolio Management, 36(4), 60-70.
  • Leote de Carvalho, R., Lu, X., & Moulin, P. (2012). "Demystifying Equity Risk-Based Strategies: A Simple Alpha Plus Beta Description." The Journal of Portfolio Management, 38(3), 56-70.
  • DeMiguel, V., Garlappi, L., & Uppal, R. (2009). "Optimal Versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?" The Review of Financial Studies, 22(5), 1915-1953.
  • Lopez de Prado, M. (2016). "Building Diversified Portfolios that Outperform Out of Sample." The Journal of Portfolio Management, 42(4), 59-69. (inverse-vol as the leaf allocator inside HRP)
  • Palomar, D. P. (2025). Portfolio Optimization: Theory and Application. Cambridge University Press, Chapter 6 (Portfolio Basics), Section 6.4 (Heuristic Portfolios).
  • skfolio documentation — skfolio.optimization.InverseVolatility.