Not Equal: A Comparison of “Risk Parity” and “Equal Risk Contribution”

The term “Risk Parity” is often confusing because it is defined and applied differently depending on the firm.  With the advent of multiple variations in tactical asset allocation and indexing strategies, it is perhaps not a stretch to claim that Risk Parity is as vague and elusive  as using the term “hedge fund” to describe a style of investment management. I have created a table below to clarify two different variations that are often used interchangeably and are not the same.   A good history of the origins of risk parity can be found here: http://en.wikipedia.org/wiki/Risk_parity. Systematic Investor– an excellent blog-  provides some useful R code and testing here: http://systematicinvestor.wordpress.com/2012/03/19/backtesting-asset-allocation-portfolios/. Meb Faber– always a great resource for new ideas- provides an application of Risk Parity to asset allocation as well as a good list of articles here: http://www.mebanefaber.com/2012/03/22/risk-parity-vs-endowment-model-vs-permanent-portfolio/

In my opinion, it is best to simply consider Risk Parity as a broad class of risk-budgeting schemes where the risk of each asset in the portfolio is leveraged (if necessary) to have the same volatility. Essentially, each asset has “equal risk”, and thus the portfolio is considered to be more diversified since returns and risk are less dependent on any one asset. In contrast, Roncalli http://www.thierry-roncalli.com/riskparity.html  coins the term “Equal Risk Contribution” (ERC)  which is a distinct sub-class of Risk Parity that seeks to equalize risk contributions from each asset to the portfolio. If both methods sound the same after reading various articles, that is because for the often cited two-asset case  they have the same mathematical solution and explanation for their validity. Nevertheless, not all Risk Parity portfolios are the same-  it is necessary to understand the differences between the equal risk and equal risk contribution approach to avoid improper application or interpretation. Below is a table that helps to define the similarities and differences of the two approaches and the relative advantages of each in the context of portfolio allocation.

Features and Qualities Shared By Equal Risk Contribution (ERC) and Risk Parity (RP)

Algorithm Characteristics	Equivalency	Equal Risk Contribution (ERC)	Risk Parity (RP)
Requires Historical/Expected Asset Returns	≈	No	No
Considered Heuristic Algorithms That Lack Strong Theoretical Support	≈	Yes	Yes
Generally Uses Leverage	≈	Yes	Yes
Generally Uses a Target Portfolio Risk	≈	Yes	Yes
Allocation Across All Assets in the Universe Selected	≈	Yes	Yes
Low Turnover Relative to Traditional Models	≈	Yes	Yes
Comparatively Less Sensitive to Estimation Error than Traditional Models	≈	Yes	Yes
Generally Superior Return and Sharpe to Equal Weight Portfolios	≈	Yes	Yes
Better Returns and Sharpe than 60/40 Balanced Stock/Bond Portfolios	≈	Yes	Yes
Solution for a Two-Asset Portfolio	≈	inverse volatility weighted	inverse volatility weighted
Conditions for Being Equivalent to Equal Weight Portfolios	≈	Equal Asset Volatility and Constant Correlation	Equal Asset Volatility and Constant Correlation
Conditions for Being Optimal on the Efficient Frontier	≈	Equal Sharpe Ratios and Constant Correlations	Equal Sharpe Ratios and Constant Correlations

Features and Qualities That Favor Equal Risk Contribution (ERC)

Algorithm Characteristics	Equivalency	Equal Risk Contribution (ERC)	Risk Parity (RP)
Objective Function	â‰	volatility of risk contributions=0	inverse volatility weighted
Uses Beta/Covariance Data	â‰	Yes	No
Always Assumes Constant Correlation Matrix	â‰	No	Yes
Holdings Have Equal Risk Contributions to Portfolio Volatility	â‰	Yes	No
Performance Highly Sensitive to the Universe of Assets Selected	â‰	No	Yes (ie. 5 equities and 1 bond create imbalance)
Flexibility of Use for Risk Budgeting and Factor Tilts	â‰	winner	loser
Out of Sample Risk (Given the same target)	â‰	winner	loser
Out of Sample Return (Given the same target or leverage constrained)	â‰	winner	loser
Out of Sample Drawdowns	â‰	winner	loser
Out of Sample Sharpe Ratios	â‰	winner	loser
Out of Sample Diversification (Concentration and Average Correlation)	â‰	winner	loser
Favorable Hybrid Between Minimum Variance and Equal Weight	â‰	Yes	No
Can Be Equivalent to Minimum Variance	â‰	When Correlation Matrix is Minimized	Not Possible

Features and Qualities That Favor Risk Parity (RP) or Equal Risk

Algorithm Characteristics	Equivalency	Equal Risk Contribution (ERC)	Risk Parity (RP)
Simple to Calculate for the Mathematically Challenged (Napkin Factor)	â‰	loser	winner
Intuitively Easy to Understand and Use in Most Software Packages	â‰	No	Yes
Best Sounding Name/Cool Factor	â‰	loser	winner
Practical Use for Dynamic Allocation With Long-Term Monthly Data	â‰	loser	winner
Sensitivity to Covariance Estimation Error	â‰	loser	winner
Generally Requires a Sophisticated Solver for Optimization	â‰	Yes	No
Speed of Calculation for Large Universe	â‰	Slow	Fast
Performance on very large data sets with limited sample size	â‰	loser (too many covariances relative to sample size	winner (fewer variables to estimate relative to sample size)