Risk Parity¶
One-line definition¶
Weighting a portfolio so every asset contributes equally to total risk, rather than equally to capital (equal-weight) or by expected return (mean-variance).
Formula¶
Solved via the standard convex reformulation (Maillard, Roncalli, Teiletche 2010):
minimize 0.5 * w'*Sigma*w - sum(log(w_i)), then renormalize w to sum
to 1.
This is equivalent to equal component risk contribution
(component_risk_contribution from risk contribution)
without needing to solve the equal-contribution condition directly.
Why PMs care¶
A capital-weighted 60/40 portfolio is not risk-balanced — equities typically dominate total risk despite being a minority of capital allocation. Risk parity is the explicit fix: lower-vol assets (like bonds) get more capital weight so their risk contribution matches higher-vol assets.
Worked example¶
Verified in tests/test_robust.py: with two uncorrelated assets at equal
volatility, risk parity gives 50/50 weights (matches equal-weight, as
expected). With asset 2 at 2x the volatility of asset 1, risk parity
weights ~2:1 toward asset 1 — and the resulting component risk
contributions are equal, confirming the property.
Common mistakes¶
- assuming risk parity means equal weights — it means equal risk contribution, which is only the same thing when assets have equal volatility and zero correlation
- ignoring that risk parity often implies leveraging lower-vol assets (like bonds) to bring their risk contribution up to match equities