Risk Parity

Risk parity is an approach to asset allocation in which capital is divided so that each holding contributes the same amount of risk to the portfolio. Because some assets are far more volatile than others, equal risk does not mean equal money: low-risk assets such as government bonds receive large weights and high-risk assets such as shares receive small ones. Many risk parity funds then apply leverage to raise the expected return of the whole portfolio to a chosen level.

The method is offered as an alternative to traditional mixes such as 60 percent shares and 40 percent bonds, and to the optimization of modern portfolio theory, which needs forecasts of expected returns. Risk parity needs only estimates of risk and of how assets move together. It is used mainly by institutional investors and specialist funds.

In a 60/40 portfolio the split of money hides the split of risk. Suppose shares have a volatility of 15 percent a year, bonds 5 percent, and the two are uncorrelated. The variance contributed by shares is $(0.60 \times 15)^2 = 81$ and by bonds $(0.40 \times 5)^2 = 4$. Shares therefore account for 81 out of 85, or about 95 percent, of the portfolio's variance. The portfolio is diversified by name but its results are driven almost entirely by the stock market.

Risk parity aims for genuine diversification across sources of return that respond differently to economic conditions, typically shares, nominal bonds, inflation-linked bonds and commodities.

The risk contribution of asset $i$ to portfolio volatility is:

• $w_i$ is the portfolio weight of asset $i$.
• $\Sigma$ is the covariance matrix of asset returns, and $(\Sigma w)_i$ is the $i$-th element of that matrix multiplied by the vector of weights.
• $\sigma_p$ is the volatility of the whole portfolio.

The contributions add up to $\sigma_p$, and a risk parity portfolio is the set of weights at which all of them are equal. In general this must be solved numerically. A widely used shortcut ignores correlations and weights each asset by the inverse of its volatility:

With shares at 15 percent volatility and bonds at 5 percent, the inverse volatilities are 0.0667 and 0.2, which sum to 0.2667. The weights are $0.0667 / 0.2667 = 25$ percent in shares and 75 percent in bonds. Each side then carries $0.25 \times 15 = 3.75$ and $0.75 \times 5 = 3.75$ points of volatility. For two assets this shortcut gives exact risk parity whatever the correlation.

The unleveraged portfolio above has a volatility of about 5.3 percent if the assets are uncorrelated, well below that of a 60/40 mix, and a correspondingly lower expected return. To reach a target such as 10 percent volatility, the manager scales all positions up by borrowing or, more commonly, by holding futures, which require only a margin deposit. Here the scaling factor would be about 1.9.

The argument for doing so is that a well-diversified portfolio has a higher Sharpe ratio than a concentrated one, so leveraging it is a more efficient way to seek return than concentrating in shares. Many funds combine the method with volatility targeting, adjusting leverage as measured risk changes.

The best-known early example is the All Weather strategy launched by the hedge fund firm Bridgewater Associates in 1996. The term risk parity was introduced in 2005 by Edward Qian of PanAgora Asset Management. Interest grew sharply after the 2008 financial crisis, in which conventional balanced portfolios suffered large losses from their equity holdings. Later variants include hierarchical risk parity, published by Marcos López de Prado in 2016, which groups related assets before allocating risk.

• Dependence on bonds. The approach holds large leveraged positions in bonds. It performed well during the long decline in interest rates from the 1980s, and critics question whether that record can be repeated.
• Correlation risk. The method relies on shares and bonds not falling together. In 2022, when inflation and rising rates pushed both down, many risk parity funds recorded heavy losses.
• Leverage and forced selling. Leverage magnifies losses, and rules that cut positions when volatility jumps can require selling into falling markets.
• Estimation. Volatility and correlation are estimated from past data and change over time.
• Risk is not return. Equalizing risk says nothing about whether each asset is priced to reward that risk.

Supporters respond that no allocation method is free of assumptions, and that balancing risk remains more robust than concentrating it. Outcomes also depend on implementation, including the rebalancing frequency and the cost of financing.