Risk parity and risk budgeting

Risk parity flips the Markowitz frame. Instead of optimising expected returns subject to risk, allocate capital so that each asset contributes equally to portfolio risk. Pioneered by Bridgewater's All Weather (Dalio, 1996) and popularised by AQR and others, risk parity has become a multi-hundred-billion-dollar institutional allocation philosophy.

The risk-contribution identity

σ_p = Σᵢ RC_i
RC_i = w_i · (Σw)_i / σ_p

Each asset's risk contribution is its weight times its marginal contribution. Risk contributions sum to portfolio volatility (Euler's theorem applied to σ_p, which is homogeneous of degree 1 in w).

Equal risk contribution (ERC)

Choose w such that RC_i = σ_p / n for every i. Equivalently:

w_i · (Σw)_i = w_j · (Σw)_j   for all i, j

This non-linear system has no closed-form solution in general but is solvable by iterative methods (Spinu 2013, Maillard et al. 2010). Modern solvers handle ERC for 50-asset universes in milliseconds.

Comparison with other allocations

• Equal-weight (1/n): equal capital allocation. High-vol assets dominate risk.
• Inverse-vol: w_i ∝ 1/σ_i. Equal risk contribution ONLY when correlations are zero.
• Minimum-variance: ignores all expected returns; concentrates in low-vol corner.
• Risk parity (ERC): equal risk contribution accounting for correlations.

Bridgewater's All Weather logic

Allocate equal risk to four macro environments: growth-up, growth-down, inflation-up, inflation-down. Each environment is best served by different asset classes (equities, nominal bonds, commodities/TIPS, IL-bonds). The portfolio is then unleveraged from the equal-risk weights, and finally levered up (or down) to a target volatility.

Leverage and the risk-parity argument

Unlevered risk parity is typically low-vol (5-8% annual). To achieve equity-like returns, risk parity portfolios are typically levered 1.5-2× through repo/bond futures. The argument: a levered risk-parity portfolio offers a higher Sharpe than a 60/40 portfolio — because 60/40 concentrates 90%+ of its risk in equities, whereas risk parity diversifies risk across asset classes.

The 2008 case for risk parity

Risk parity portfolios dramatically outperformed 60/40 in 2008 because their bond allocation was much larger. In subsequent low-rate years (2010-2020) the strategy continued to deliver as long-bonds rallied. Then 2022 — when stocks AND bonds fell together — was the worst year on record for risk parity, raising the question of whether the bond rally tailwind was structural or transient.

Strengths of risk parity

• Stable allocations: no dependence on expected returns (mostly).
• Diversification across risk types: doesn't concentrate in equity beta.
• Levered Sharpe is plausibly higher than 60/40 over long horizons.
• Transparent: rules-based, communicable, doesn't depend on PM judgment.

Weaknesses

• Sensitive to vol estimation: covariance estimation noise propagates into weights.
• Bond leverage adds dependence on funding markets — repo blowups (2008, 2020) hurt.
• Negative skew: levered portfolios are more vulnerable to fat-tail events.
• Critique: 'risk parity in normal times, but in a crisis everyone delevers at once and the strategy fails.'