Risk Parity (Equal Risk Contribution)
Does equal risk contribution prevent concentration in a portfolio?
Estimate each asset?s contribution to portfolio risk under a stated covariance matrix and choose weights that equalize those ex ante contributions. Recheck them after correlations change; equal estimated contributions do not ensure equal realized losses or superior returns.
Equal risk contribution is an ex ante allocation construction, not a guaranteed return improvement.
Evidence map
| Aspect | Finding |
|---|---|
| Idea | Allocate so each asset contributes the same amount to total portfolio risk, rather than the same capital. |
| Key result / formula | Total risk splits additively (Euler's theorem): sigma_p = sum_i RC_i, with risk contribution RC_i = w_i*(Sigma w)_i / sigma_p and marginal risk MRC_i = d sigma_p / d w_i. |
| Practical rule | Use ERC/inverse-vol when you trust covariances but not expected returns; add modest leverage to reach a target return (levered risk parity). |
Idea
This stops the highest-vol asset (usually equities) from dominating portfolio risk and maximizes ex-ante risk diversification.
Key result / formula
Equal-Risk-Contribution (ERC) sets w_i*(Sigma w)_i equal for all i. For uncorrelated assets this reduces to inverse-volatility weighting, w_i proportional to 1/sigma_i. Maillard, Roncalli & Teiletche (2010) prove the ERC portfolio's volatility lies between the minimum-variance and 1/N portfolios, and it requires no expected-return input.
Practical rule
Weakness: it can over-weight low-vol/crowded assets (bonds) and ignores valuation — pair with a vol target and leverage limits.
Worked weights
For two uncorrelated assets with annual volatilities of 10% and 20%, inverse-volatility weights are proportional to 1/0.10 and 1/0.20, giving about 67% and 33%. Their standalone volatility contributions then match under the zero-correlation assumption. If their correlation changes, equal risk contributions require the full covariance matrix; the simple inverse-vol rule is only a special case. Re-estimate covariance on past data at each rebalance, calculate realized risk contributions and include the turnover cost. Leveraging the lower-volatility sleeve to meet a return target increases financing and liquidation risk. Risk parity equalizes estimated risk, not economic valuation or expected returns.
Additional check
For the two-asset example, the 67/33 weights produce equal approximate risk contributions only with zero correlation; report the covariance estimate and both realized contributions after each rebalance.
Source
Maillard, Roncalli & Teiletche, "The Properties of Equally-Weighted Risk Contribution Portfolios," Journal of Portfolio Management 36(4) 2010, SSRN 1271972; Qian, "Risk Parity Portfolios" (PanAgora, 2005). Primary source