# Risk Parity

## Bernd Scherer

Risk parity, given its attractive returns and intuitive appeal, has proved to be an economic success for the asset management industry. However, it is not short of critics. This section provides key insights into the main practical issues. The theoretical properties of risk parity and other diversification-based portfolio construction methods are discussed in the previous chapter and will not be repeated here.

## 5.1 A PRACTICAL REVIEW OF RISK PARITY

To achieve diversification, risk parity aims at allocating an identical (percentage) contribution to risk to each individual asset. In other words, all assets become equally important for overall portfolio performance in a risk-parity portfolio. For this to work, risk-parity portfolios tend to overweight low-volatility and low-correlation assets. If we define portfolio risk as portfolio volatility, we can make use of the fact that volatility is linear homogeneous in portfolio weights. Doubling portfolio weights will exactly double portfolio volatility and percentage contributions to volatility add up to 1. Risk parity is achieved if

 \begin{array}{*{20}c} {w_i \frac{{{\textrm{d}}\sigma }}{{{\textrm{d}}w_i }} = w_i \frac{{w

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