Risk Parity: Risk Measures, Solvers, and Portfolio Backtests

Summary

This research overview examines risk parity within the broader development of portfolio allocation methods. It describes several risk measures and risk-allocation principles, emphasizing Euler allocation to define each asset’s contribution to portfolio risk. It also explains why variance may be unsuitable as the risk measure for a risk parity model and outlines quadratic programming and Newton methods for solving the allocation problem.

The study compares risk parity with mean-variance allocation and a fixed 40/60 portfolio, then reports backtests across asset groups and portfolio setups. In the tests, very low-volatility cash-like assets can dominate the allocation; when they are excluded, bonds can take their place. Results also vary substantially with the covariance lookback period. A broader mix of domestic and overseas assets is reported as more robust, and risk parity is described as stronger than equal weighting on risk-adjusted returns and risk control, despite lower absolute returns. These are study-specific historical findings, not guarantees; the summary gives no detailed dates, costs, or implementation assumptions.

Key ideas

• Risk parity allocates capital so that portfolio assets make balanced contributions to a chosen measure of risk.
• Euler allocation provides a framework for calculating each asset’s contribution to portfolio risk.
• The study outlines quadratic programming and Newton methods for solving risk parity weights.
• Very low-volatility assets can receive dominant weights under risk parity.
• The reported backtests are sensitive to the covariance lookback period and asset universe.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.