Journal of Investment Strategies

Risk.net

Uncertain risk parity

Anish R. Shah

  • Point-estimated covariance can hide risks and leaves risk parity vulnerable to estimation error.
  • Modeling covariance as uncertain instead of fixed captures ambiguity about the present and accounts for changing regimes.
  • Allocating risk under uncertain covariance creates weightings that perform robustly under estimation error and across market conditions.

Risk parity is a portfolio construction technique that scales sections of a portfolio (eg, stocks, bonds, currencies, commodities) so that forecasted contributions to net portfolio risk match the budget. Because risks are measured from a point estimate of covariance, the method is subject to problems of estimation error. This paper treats covariance as uncertain in order to find a risk parity weighting that does not count on perfectly optimized hedges and is robust to changes in regime. Separately, of general interest are the uncertain risk contributions calculated en route. Reporting a portfolio’s uncertain risk decomposition puts a band around numbers and reveals fragility. For example, a market could seem hedged in a long–short portfolio but surface as the biggest risk when parameters are considered across their error range.

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