chapter eleven

11 Asset Allocation by Risk: Introduction to Risk Parity

 

This chapter covers

  • The concept of risk contributions in investment portfolios
  • Different definitions of risk parity portfolios, and means of computing their weights

In the last chapter, we saw two pitfalls of mean-variance optimization:

  1. Without explicit constraints on diversification, mean-variance optimization could result in very concentrated portfolios
  2. The weights of portfolios obtained using mean-variance optimization can be very sensitive to the inputs - expected returns, covariances, and constraints.

We’ll start this chapter by revealing another unattractive property of portfolios that appear to be diversified, and how this motivates allocating assets within a portfolio by risk, rather than by capital - an approach known as risk parity. We’ll cover several different forms of risk parity methods for constructing portfolios according to each approach, and also discuss some of the practical implications of managing a risk parity portfolio.

11.1 Decomposing portfolio risk

11.1.1 Risk contributions

11.1.2 Risk concentration in a “diversified” portfolio

11.1.3 Risk parity as an optimal portfolio

11.2 Calculating risk parity weights

11.2.1 Naive risk parity

11.2.2 General risk parity

11.2.3 Weighted risk parity

11.2.4 Hierarchical risk parity

11.3 Implementation of risk parity portfolios

11.3.1 Applying leverage

11.4 Summary