Equal capital need not mean equal influence on fluctuations.
More volatile shares can dominate an equal-money share/bond mix. A common risk-parity version equalises contributions to estimated portfolio volatility, often assigning more money to less volatile exposures.
Position sizes, fluctuations and relationships all matter. The result depends on risk definition, estimates and instruments.
Risk balance is not every kind of risk targeting
Other approaches balance broader economic exposures or use different models. All Weather shares ideas without specifying an identical portfolio. An overall volatility target need not balance contributions across assets.
AQR describes implementation, not independent proof of superior returns.
Keep the result inside its model.
Solid: shares. Hatched: bonds. Each bar totals 100% of its own named quantity.
50% / 50% capital
Money: shares 50%, bonds 50%
Variance contributions: shares 94.1%, bonds 5.9%
Portfolio volatility ≈10.31% annually.
20% / 80% capital
Money: shares 20%, bonds 80%
Variance contributions: shares 50.0%, bonds 50.0%
Portfolio volatility ≈5.66% annually.
Neither bar measures a loss probability.
Its 5.66% estimate is not a maximum possible loss or a promise about next year. Precise arithmetic supplies no certainty about the inputs.
Compute variance shares before taking the square root
At zero correlation each contribution is weight²×volatility²; no covariance term. For 50/50, weighted volatilities 10% and 2.5% give squared contributions 0.0100 and 0.000625. Total 0.010625 has square root ≈10.31%; shares of variance are 94.1%/5.9%.
For 20/80, both weighted volatilities are 4%. Each squared contribution is 0.0016; total 0.0032 gives ≈5.66%. Each asset contributes half.
These variance shares also equal shares of the usual volatility-risk contributions. With correlated holdings, include covariance terms in the contribution calculation; the normalised shares still coincide.
Balancing and scaling are separate choices.
Borrowing or derivatives can amplify a balanced mix, adding financing, collateral and forced-reduction risks. A small derivative deposit can support substantial notional.
Risk balancing does not always require borrowing. Inspect actual leverage rather than infer it from the label; raising overall exposure differs from balancing relative contributions.
Stress can change the estimated relationships.
Volatilities/correlations change; inflation shocks can weaken share/bond offsets. One fitted period can misrepresent another. Volatility balance also misses liquidity gaps, sudden losses, currency mismatch and payment deadlines.
Changing inputs also change operating consequences
Correlated contributions require co-movement, not adding standalone estimates. ECB history establishes no future correlation. Revised estimates can trigger turnover or position reductions after losses; faster and slower reactions each have weaknesses around shocks/reversals.
Historical comparisons neither prescribe personal implementation nor prove all strategies behave alike.
Equal modelled risk is not household suitability.
It determines neither affordable loss, a bond’s fit for a nearby bill nor spending currency. Read exposure, measure, leverage permissions, costs and discretion.
Compare an appropriate overall risk level with a simpler alternative. Delegation moves calculations and settlements inside a fund; financing consequences, uncertain estimates and the allocation decision remain with its owner.