Will My Risk Parity Strategy Outperform?
Robert Anderson (University of California, Berkeley), et al. | July 2012
We gauge the return-generating potential of four investment strategies: value weighted, 60/40 fixed mix, unlevered and levered risk parity. We have three main findings. First, even over periods lasting decades, the start and end dates of a backtest can have a material effect on results; second, transaction costs can reverse ranking, especially when leverage is employed; third, a statistically significant return premium does not guarantee outperformance over reasonable investment horizons.

Risk Parity Research Summary
Wesley Gray (Empiritrage), et al. | May 2012
Our conclusion on risk parity as an asset allocation system is mixed. On one hand, the backtested results are solid. However, one must use significant amounts of leverage, it is unclear what the benchmark is when assessing risk parity portfolios, and there are open questions as to whether slight perturbations in estimation techniques affect results. In a future research report we will address these research questions—as well as others–in detail.
The Trend is Our Friend: Risk Parity, Momentum and Trend Following in Global Asset Allocation
Steve Thomas (City University London), et al. | August 2012
We examine the effectiveness of applying a trend following methodology to global asset allocation between equities,bonds,commodities and real estate.The application of trend following offers a substantial improvement in risk-adjusted performance compared to traditional buy-and-hold portfolios. We also find it to be a superior method of asset allocation than risk parity. Momentum and trend following have often been used interchangeably although the former is a relative concept and the latter absolute. By combining the two we find that one can achieve the higher return levels associated with momentum portfolios but with much reduced volatility and drawdowns due to trend following. We observe that a flexible asset allocation strategy that allocates capital to the best performing instruments irrespective of asset class enhances this further.
Diversified Risk Parity Strategies for Equity Portfolio Selection
Harald Lohre (Deka Investment), et al. | May 2012
We investigate a new way of equity portfolio selection that provides maximum diversification along the uncorrelated risk sources inherent in the S&P 500 constituents. This diversified risk parity strategy is distinct from prevailing risk-based portfolio construction paradigms. Especially, the strategy is characterized by a concentrated allocation that actively adjusts to changes in the underlying risk structure. In addition, x-raying the risk and diversification characteristics of traditional risk-based strategies like 1/N, minimum-variance, risk parity, or the most-diversified portfolio we find the diversified risk parity strategy to be superior. While most of these alternatives crucially pick up risk-based pricing anomalies like the low-volatility anomaly we observe the diversified risk parity strategy to more effectively exploit systematic factor tilts.
Efficient Algorithms for Computing Risk Parity Portfolio Weights
Denis Chaves (Research Affiliates), et al. | July 2012
This paper presents two simple algorithms to calculate the portfolio weights for a risk parity strategy, where asset class covariance information is appropriately taken into consideration to achieve “true” equal risk contribution. Previous implementations of risk parity either (1) used a naïve 1/vol solution, which ignores asset class correlations, or (2) computed “true” risk parity weights using relatively complicated optimizations to solve a quadratic minimization program with non-linear constraints. The two iterative algorithms presented here require only simple computations and quickly converge to the optimal solution. In addition to the technical contribution, we also compute the parity in portfolio “risk allocation” using the Gini coefficient. We confirm that portfolio strategies with parity in “asset class allocation” can actually have high concentration in its “risk allocation”.
Diversification Return and Leveraged Portfolios
Edward Qian (PanAgoro) | Summer 2012 (Journal of Portfolio Management)
It is widely accepted that portfolio rebalancing adds diversification return to fixed-weight portfolios, but this is only true for long-only unleveraged portfolios. Qian provides analytical results regarding portfolio rebalancing and the associated diversification returns for different kinds of portfolios including long-only, long-short, and leveraged. He shows that portfolio rebalancing is linked to underlying portfolio dynamics. For long-only unleveraged portfolios, rebalancing amounts to a mean-reverting strategy, and the diversification return is always non-negative. But for short (or inverse) and leveraged portfolios, portfolio rebalancing on the top-down level amounts to a trend-following strategy that detracts from diversification return. Qian analyzes diversification returns of risk parity portfolios and shows that the diversification return of a leveraged long-only portfolio can generally be decomposed into two parts, both of which are related to a scaled unleveraged portfolio. The first part is the positive diversification return from rebalancing among individual assets at the bottom- up level, which is amplified by leverage. The second part is the negative diversification return caused by the leverage of the overall portfolio. His numerical examples show that diversification return is, in general, positive for leveraged risk parity portfolios when the leverage ratio is not too high. In addition, he shows that low correlations between different assets are crucial in achieving positive diversification return and reducing portfolio turnover for risk parity portfolios.