Chapter 14 Portfolio Risk Budgeting

Updated: May 15, 2021

Copyright © Eric Zivot 2015, 2020, 2021

The idea of portfolio risk budgeting is to decompose a measure of portfolio risk into risk contributions from the individual assets in the portfolio. In this way, an investor can see which assets are most responsible for portfolio risk and can then make informed decisions, if necessary, about re-balancing the portfolio to alter the risk. Portfolio risk budgeting reports, which summarize asset contributions to portfolio risk, are becoming standard in industry practice. In addition, it has become popular to consider portfolio construction using risk budgeting to create so-called “risk-parity” portfolios. In risk-parity portfolios, portfolio weights are constructed so that that each asset has equal risk contributions to portfolio risk.92

We first motivate risk budgeting using the portfolio return variance and standard deviation as measures of portfolio risk. We then show how Euler’s theorem can be used to do risk budgeting for portfolio risk measures that are homogenous of degree one in the portfolio weights. Such risk measures include portfolio return standard deviation (volatility) and Value-at-Risk for general return distributions.

  • Need to finish introduction

The R packages used in this chapter are IntroCompFinR and PerformanceAnalytics.


  1. Two hedge funds, Bridgewater and AQR capital management have helped to make risk parity investing popular. ↩︎