Equal Risk Contribution Portfolio Research Articles

Centrality-Based Equal Risk Contribution Portfolio

This article combines the traditional definition of portfolio risk with minimum-spanning-tree-based “interconnectedness risk” to improve equal risk contribution portfolio performance. We use betweenness centrality to measure an asset’s importance in a market graph (network). After filtering the complete correlation network to a minimum spanning tree, we calculate the centrality score and convert it to a centrality heuristic. We develop an adjusted variance–covariance matrix using the centrality heuristic to bias the model to assign peripheral assets in the minimum spanning tree higher weights. We test this methodology using the constituents of the S&P 100 index. The results show that the centrality equal risk portfolio can improve upon the base equal risk portfolio returns, with a similar level of risk. We observe that during bear markets, the centrality-based portfolio can surpass the base equal risk portfolio risk.

A Novel way to Diversify Portfolio Weights

There is broad agreement among academics and practitioners that, in general, a diversified portfolio delivers more robust out-of-sample performance than a concentrated one. This paper develops a new method to diversify portfolio weights, which does not rely on expected returns or volatilities and is therefore robust to measurement error in these variables. It uses pair-wise regressions to estimate how much variation each asset explains in terms of another asset. The optimization function finds the portfolio weights that maximize the unexplained variation of the portfolio. We benchmark our method against established methods from the literature, such as the minimum volatility and the equal risk contribution portfolios. We demonstrate that our method adheres to established diversification properties and it performs well in empirical tests.

Enhancing portfolio resilience during crisis periods: Lessons from BRICS indices and multi asset strategies

This paper uses Markowitz’s mean-variance model to construct an investment portfolio incorporating multiple assets – BRICS equity indices, Gold, crude oil, bonds, and cryptocurrencies. The optimally created risky portfolios outperform alternative portfolio optimization methods – the naive portfolio and the equal risk contribution portfolio; and established indices – the S&P 500 and the MSCI Emerging Equity Index in terms of metrics – adjusted Sharpe ratio, modified Sharpe ratio, and the modified Value at Risk. The findings are validated across different periods, including the COVID-19 period and the Russian invasion of Ukraine, including various in and out of sample periods. The findings highlight the benefits of portfolio diversity, mainly using BRICS indices, Gold, and Brent Crude oil, and challenge the notion of limited diversification benefits in BRICS indices found in previous studies. This paper further suggests the potential of emerging market bonds ETF as a diversification option during turbulent economic periods and highlights the limitations of cryptocurrencies in optimizing multi asset portfolios. By adopting the recommended multi asset portfolios, investors can enhance their risk-return trade-offs and achieve superior performance compared to the S&P500 and MSCI emerging indices. Lastly, the paper recommends future research opportunities in measuring portfolio performance and hedging strategies considering risk-adjusted return measurements, transaction expenses, and dynamic rebalancing techniques.

The best-fitting model(s) of equal risk contribution: evidence from environmental-friendly portfolio

PurposeThis research aims to select the best-fitting model(s) of equal risk contribution portfolios (ERC). ERC is a robust estimation in the absence of reasonable expectations about future returns.Design/methodology/approachThe portfolio consists of five environmental-friendly exchange-traded funds (ETFs). It applies equal risk optimization, beneficial when the assets are firmly linked, such as the ETFs. This paper operationalizes 20 covariance models in portfolio construction, and a portfolio with classic covariance is the benchmark to beat. To select the best-fitting model(s), the paper applies statistical inferences of the model confidence set. This research also constructs the newly-developed minimum connectedness optimization method and utilizes maximum drawdown as the primary evaluation tool.FindingsThe outbreak of COVID-19 hugely impacts the portfolio drawdown. The results also show that the classic covariance is hard to beat, partly explained by estimation error and model misspecification. This paper suggests that equal risk contribution can benefit from copula-based covariance. It consistently and significantly outperforms the other models in various robustness tests.Practical implicationsIn the absence of substantial predictions about future returns and the existence of strongly linked assets, selecting appropriate portfolio components by risk contribution is a sound choice.Originality/valueThis is the first paper to select the best-fitting model(s) of ERC portfolio during the COVID-19.

Evaluating Hierarchical Equal Risk Contribution Portfolios in the Chinese Stock Market

This paper investigates the usefulness of the Hierarchical Equal Risk Contribution algorithm to exploit correlation structure in China’s equity market over 2001-2020. By running a horse race of different combinations of metrics and linkages, we demonstrate that the winner strategy always beats traditional portfolio construction techniques. Better-performing risk-based hierarchy strategies vary with stock-sorting methods by size, mean return, volatility, and Sharpe ratio. However, our treatment results in extremely imbalanced asset allocation, implying that we capture information other than the standard Chinese industrial classification.

Risk Parity for Multi-Asset Futures Allocation – A Practical Analysis of the Equal Risk Contribution Portfolio

Since the early beginning of investing as it was commonly seen as a form of gambling for the rich and wealthy, the idea of Harry Markowitz was revolutionising the way of thinking and how portfolios should be constructed. However, today the traditional mean-variance portfolios are still not fully adopted by practitioners. After the financial crisis of 2008, a type of portfolio called risk parity arise and attracted the attention of numerous investors. In this paper, a risk parity portfolio named equal risk contribution portfolio is constructed based on a rolling window of 300 days. The portfolio is built on 21 future contracts downloaded from Quandl. It includes assets from four asset classes with a data range from June 2005 to March 2020. A performance and risk analysis is made for each asset, asset class and year. Many findings from the literature are reflected in our results, such as strong diversification and a higher Sharpe Ratio than the equally weighted Benchmark. The impact of the financial crisis of 2008 and the good performance of risk parity during this period can also be seen. To a certain extent, the COVID-19 crisis, in which our risk parity portfolio performs well, can also be observed.

Long-term dependency between sovereign bonds and sectoral indices of India: evidence using Hurst exponent and wavelet analysis

PurposeThe purpose of this study is to provide a new way to optimize a portfolio and to show that combining the Hurst exponent and wavelet analysis may help to increase portfolio returns.Design/methodology/approachThe authors use the Hurst exponent and wavelet analysis to study the long-term dependencies between sovereign bonds and sectoral indices of India. The authors further construct and evaluate the performance of three portfolios constructed on the basis of Hurst standard deviation (SD) – global minimum variance (GMV), most diversified portfolio (MDP) and equal risk contribution (ERC).FindingsThe authors find that an ERC portfolio generates positive superior return as compared other two. Since our sample includes periods of two crisis – post-2007 financial crisis and the ongoing pandemic, this study reveals that combining government bond with equities and gold provides a higher returns when the portfolios are constructed using the risk exposures of each asset in the overall portfolio risk.Practical implicationsThe findings provide guidance to portfolio managers by helping them to select assets using the Hurst approach and wavelet analysis thereby increasing the portfolio returns.Originality/valueIn this study, the authors use a combination of Hurst exponent and wavelet analysis to understand the long-term dependencies among various assets and provide a new methodology to optimize a portfolio. As far as the authors’ knowledge, no study in the past has attempted to provide a joint framework for portfolio optimization and therefore this study is the first to apply this methodology.

Machine Learning for Recession Prediction and Dynamic Asset Allocation

The authors introduce a novel application of support vector machines (SVM), an important machine learning algorithm, to determine the beginning and end of recessions in real time. Nowcasting, forecasting a condition in the present time because the full information will not be available until later, is key for recessions, which are only determined months after the fact. The authors show that SVM has excellent predictive performance for this task, capturing all six recessions from 1973 to 2018 and providing the signal with minimal delay. The authors take advantage of the timeliness of SVM signals to test dynamic asset allocation between stocks and bonds. A dynamic risk budgeting approach using SVM outputs appears superior to an equal-risk contribution portfolio, improving the average returns by 85 bps per annum without increased tail risk. TOPICS:Big data/machine learning, financial crises and financial market history, portfolio construction, tail risks

Taking the right course navigating the ERC universe

We study the equal risk contribution (ERC) investment strategies exploring how these portfolios perform relative to traditional risk-only (minimum variance portfolio), risk–return (Markowitz portfolio) and naive (1/n) investment schemes when expanding the asset class universe. We propose a combinatorial mechanism to expand the investment universe of all feasible ERC portfolios and then combine them, thus realizing an ERC efficient frontier consistent with the mutual fund separation theorem (Merton in J Financ Quant Anal 7:1851–1872, 1972). In doing this, we mitigate the out-of-sample estimation error in portfolio weights and better diversify asset allocation against unpredictable extreme events. Simulation, bootstrapping and empirical experiments indicate that the corresponding tangency portfolio, computed through the regression-based approach introduced in Britten-Jones (J Finance 54:655–671, 1999), offers better risk-adjusted performance relative to risk-only, risk–return-based competitors as well as the 1/n strategy.

The Hierarchical Equal Risk Contribution Portfolio

Building upon the fundamental notion of hierarchy, the Risk Parity (HRP) and the Clustering based Asset Allocation (HCAA), the Hierarchical Equal Risk Contribution Portfolio (HERC) aims at diversifying capital allocation and risk allocation. HERC merges and enhances the machine learning approach of HCAA and the Top-Down recursive bisection of HRP. In more detail, the modified Top-Down recursive division is based on the shape of dendrogram, follows an Equal Risk Contribution allocation and is extended to downside risk measures such as conditional value at risk (CVaR) and Conditional Drawdown at Risk (CDaR). The out-of-sample performances of hierarchical clustering based portfolios are evaluated across two empirical datasets, which differ in terms of number of assets and composition of the universe (multi-assets and individual stocks). Empirical results highlight that HERC Portfolios based on downside risk measures achieve statistically better risk-adjusted performances, especially those based on the CDaR.

Long-only equal risk contribution portfolios for CVaR under discrete distributions

Portfolios in which all assets contribute equally to the conditional value-at-risk (CVaR) represent an interesting variation of the popular risk parity investment strategy. This paper considers the use of convex optimization to find long-only equal risk contribution (ERC) portfolios for CVaR given a set of equally likely scenarios of asset returns. We provide second-order conic and non-linear formulations of the problem, which yields an ERC portfolio when CVaR is both positive and differentiable at the optimal solution. We identify sufficient conditions for differentiability and develop a heuristic that obtains an approximate ERC portfolio when the conditions are not satisfied. Computational tests show that the approach performs well compared to non-convex formulations that have been proposed in the literature.

Minimum risk versus capital and risk diversification strategies for portfolio construction

In this paper, we propose an extensive empirical analysis on three categories of portfolio selection models with very different objectives: minimization of risk, maximization of capital diversification, and uniform distribution of risk allocation. The latter approach, also called Risk Parity or Equal Risk Contribution (ERC), is a recent strategy for asset allocation that aims at equally sharing the risk among all the assets of the selected portfolio. The risk measure commonly used to select ERC portfolios is volatility. We propose here new developments of the ERC approach using Conditional Value-at-Risk (CVaR) as a risk measure. Furthermore, under appropriate conditions, we also provide an approach to find a CVaR ERC portfolio as a solution of a convex optimization problem. We investigate how these classes of portfolio models (Minimum-Risk, Capital-Diversification, and Risk-Diversification) work on seven investment universes, each with different sources of risk, including equities, bonds, and mixed assets. Then, we highlight some strengths and weaknesses of all portfolio strategies in terms of various performance measures.

Nowcasting Recessions Using the SVM Machine Learning Algorithm

We introduce a novel application of support vector machines (SVM), an important machine learning algorithm, to determine the beginning and end of recessions in real time. Nowcasting, forecasting a condition in the present time because the full information will not be available until later, is key for recessions, which are only determined months after the fact. We show that SVM has excellent predictive performance for this task, capturing all six recessions from 1973 to 2018 and providing the signal with minimal delay. We take advantage of the timeliness of SVM signals to test dynamic asset allocation between stocks and bonds. A dynamic risk budgeting approach using SVM outputs appears superior to an equal-risk contribution portfolio, improving the average returns by 85 bps per annum without increased tail risk.

Economic benefits of using realized covariance forecasts in risk-based portfolios

ABSTRACTThis article examines the economic benefit of using the realized covariance matrix forecasts, for constructing the risk-based portfolios. We use the two-scale realized covariance estimator (TSC), the jump robust two-scale realized covariance estimator (RTSC) and the realized bipower covariance estimator (BPC), to forecast the daily realized covariance matrix. Using these covariance matrix forecasts, we implement three risk-based portfolios: the global minimum variance portfolio, the equal risk contribution portfolio and the most diversified portfolio. There is evidence that the portfolio performance improves by using TSC or RTSC estimators as compared to the daily-returns-based estimator. The performance gains are robust to the choice of risk-based portfolio strategy, the degree of investor’s relative risk-aversion, the market conditions and the choice of time intervals.

Performance of risk-based portfolios under different market conditions: Evidence from India

This study evaluates the performance of risk-based portfolios under different market conditions. We compare four strategies, namely, the equally weighted portfolio (EW), the global minimum variance portfolio (GMV), the most diversified portfolio (MDP) and the equal risk contribution portfolio (ERC). No single strategy consistently dominates the others, under different market conditions. As expected, the GMV has the least downside risk. Although there is no clear winner among the risk-based portfolios, there is evidence that they generally outperform the market capitalization based portfolio.

Diversified Equity Portfolios: The Case to Use Risk-Based Weights to Construct an Investable Equity Index

When making a passive equity investment investors typically use indexes that are weighted by the market capitalization of the constituents. Using S&P 500 US equity sectors I will show that market cap weights provide inefficient diversification. As an alternative to the market cap weighted S&P 500 index I will introduce an investable risk-based index using SPDR sector ETFs. The risk-based weights are calculated using a risk parity methodology and over the life of the portfolio (03-26-1999 to 02-28-2015) create a cumulative return net of estimated trading costs of 79.5% compared to the S&P 500 return of 55.9%1. In addition to its higher returns, the sector equal risk contribution portfolio (ERP) has lower risk measured by standard deviation, conditional value at risk, and drawdowns.

Computing equal risk contribution portfolios

For institutional investors, optimizing the trade-off between risk and reward poses significant modeling and computational challenges. Notably, small errors in the estimated returns of financial assets can lead to optimized portfolios that incur far too much risk for the returns they actually deliver. Given these adverse effects, portfolio construction techniques that are based exclusively on risk have grown in popularity. For instance, equal risk contribution (ERC) portfolios seek to equalize the risk contributions of all assets, so that the portfolio is fully diversified from a risk perspective. This paper reviews the nonlinear optimization models that underlie the ERC approach and, in response to the reported difficulty of solving such optimization problems, compares the performance of several nonlinear programming algorithms when constructing ERC portfolios. Our results suggest that performance worsens with a poor choice of algorithm or a bad problem formulation. We provide alternative formulations and also develop heuristic procedures that construct an approximation to the ERC portfolio in an efficient manner.

Practical Applications of Risk-Based Asset Allocation: A New Answer to an Old Question?

Risk is overtaking expected returns in portfolio construction for many investment managers. <b>Wai Lee</b>, Managing Director at <b><i>Neuberger Berman</i></b>, advises investors to clearly state their goals and question whether the intended portfolio meets them. Lee urges investors to de-emphasize numerical simulations and portfolio fine tuning. This Practical Applications report is about his award-winning article <b>Risk-Based Asset Allocation: <i>A New Answer to an Old Question?</i></b>, which might have drawn a frosty reception from some of his peers because it is highly critical of increasingly popular risk-based strategies. Lee examines four risk-based asset allocation portfolios: <b>equally weighted, global minimum variance, most-diversified portfolio</b> and <b>equal risk-contribution portfolio</b>, also dubbed <b>risk parity</b>. The one common characteristic these strategies share is that the only input required to determine portfolio composition is a model of risk, he tells us. Noticeably absent is an explicit model of expected returns, Lee cautions.

Dynamic Risk-Based Asset Allocation

In asset allocation, the equal risk contribution (ERC) approach has rapidly gained popularity: portfolio weights are dynamically set such that the asset classes contribute equally to the portfolio risk. As such, the portfolio loads automatically less on the more risky asset and, by diversifying across asset classes, portfolio drawdowns are reduced. When the equity subportfolio is allocated based on market capitalization weights, the ERC portfolio allocation tends to be dominated by the bond allocation. While the resulting portfolio has a low risk, it is - in today's market regime of low interest rates - also characterized by only moderate expected returns. For this reason, American fund managers have advocated to overlay the ERC portfolio with leverage. Such a leveraged risk-diversified portfolio is commonly referred to as a risk-parity strategy. This paper explores two leverage-free alternatives to increase tactically the equity allocation and preserve a completely risk-based asset allocation approach, which dynamically adjusts to the changing risk regimes. The first one consists of replacing the market capitalization-weighted equity index with a low-risk equity index. The second suggestion to increase the equity allocation is to deviate from an equal risk contribution objective to a 60/40 risk allocation strategy. We show that these two modifications increase significantly the weight of the equity portion in the portfolio, while still keeping the total risk of the dynamically rebalanced portfolios at a low level.

Market crises and the 1/N asset-allocation strategy

We consider portfolio management strategies where the investment style switches based on the value of a crisis indicator. A variety of strategies is considered in historical backtests on different datasets. Our findings show that certain simple switching strategies achieve statistically significant out-performance when compared to the equally-weighted portfolio with respect to the Sharpe ratio and Omega. In our backtest, the 1/N strategy and equal-risk contribution portfolio perform best during normal times. On the other hand, during turbulent times, risk considerations seem to play a major role leading to minimum variance as the preferred strategy.