Risk-based Asset Allocation Research Articles

A Study of Hierarchical Risk Parity in Portfolio Construction

<p style="text-align: justify;"><span style="font-family: 'times new roman', times, serif; font-size: 14pt;">The construction and optimization of a portfolio is a complex process that has been a historically active research area in finance. For portfolios with highly correlated assets, the performance of traditional risk-based asset allocations methods such as the mean-variance (MV) model is limited when numerous assets are correlated. A novel clustering-based asset allocation method, called Hierarchical Risk Parity (HRP), provides an opportunity to mitigate these limitations in portfolio construction. HRP utilizes the hierarchical relationships between the covariance of assets in a portfolio to determine weight distributions, eliminating the need for the inversion of the covariance matrix that is required by most traditional risk-based asset allocation methods. This research examines the viability of Hierarchical Risk Parity (HRP) method in portfolio construction of a US equity portfolio and compares the performances of HRP to traditional asset allocation methods exemplified by the mean-variance (MV) method. The results of this research show that the performance of the HRP method is comparable to the performance of the MV method. Given these findings, HRP provides an advantageous approach for portfolio construction in practical scenarios where correlated assets are present in the portfolios.</span></p>

Risk-Based Asset Allocation in Factor Investing: Exploring the Inverse Factor Volatility Strategy

This study evaluates the effectiveness of the Inverse Factor Volatility strategy within the context of factor investing, comparing its performance to the conventional Risk Parity strategy. Using quantitative techniques, including portfolio construction and performance metrics analysis, this research employs data from five individual equities spanning the years 2000 to 2022. The methodology involves constructing portfolios based on Inverse Factor Volatility and Risk Parity principles and analyzing performance metrics, including mean returns, risk-adjusted returns, and drawdowns. The findings indicate that, compared to Risk Parity, Inverse Factor Volatility offers superior drawdowns, risk-adjusted returns, and mean returns. These results suggest that Inverse Factor Volatility may be a more effective strategy for portfolio management and could represent an advancement over traditional factor investing methods. The conclusions of this study hold significant implications for portfolio managers seeking to optimize their investment strategies.

Comparative Study of the Equal-Weight Method and Hierarchical Risk Parity in Portfolio Construction

Purpose: Portfolio optimization is a process in which the capital is allocated among the portfolio assets such that the return is maximized while the risk is minimized. Portfolio construction and optimization has long been an active research area in finance. For the portfolios with highly correlated assets, the performance of traditional risk-based asset allocation methods such as, the mean-variance (MV) method is limited because quadratic optimizers require an inversion of the covariance matrix of the portfolio to distribute weight among the portfolio assets. Methods: A possible solution to the limitations of traditional risk-based asset allocation methods can be provided by a hierarchical clustering-based Machine Learning method because it uses hierarchical relationships between the covariance of assets in the portfolio to distribute the weight, and inversion of the covariance matrix is not required. A comparison of the performance of a simple non-optimization technique called the Equal-weight (EW) method to the two optimization methods, the Mean-variance method and the HRP method, which is a machine learning method, was conducted in this research. Results: It was found that in terms of cumulative returns, the equal-weight method has outperformed several more sophisticated optimization techniques, the mean-variance method, and the HRP method. For most of the period, the Sharpe ratio of the HRP method was observed to be similar to the mean-variance method and equal-weight method. Implications: This research supports the idea that HRP is a feasible method to construct portfolios with correlated assets because the performance of HRP is comparable to the performances of the traditional optimization method and the non-optimization method.

Constructing inverse factor volatility portfolios: A risk-based asset allocation for factor investing

In this study, we investigate risk-based asset allocation approaches for factor investing strategies by constructing a multifactor portfolio based on the inverse weighting method. We propose the inverse factor volatility (IFV) strategy, which is the simplified variant of a factor risk parity, assuming constant factor correlation. In IFV portfolio construction, the portfolio's weights are determined by using scaled inverse factor volatility treated as a proxy for a targeted exposure in the optimization. Based on daily stock and index returns on global markets from 2002 to the end of 2017, we implemented the empirical analysis of IFV portfolios among three stock markets: Japan, Euro, and the US. The results obtained reveal that the IFV portfolios significantly outperformed market capitalization weighted portfolios by successfully acquiring factor risk premiums.

The impact of sectorial and geographical segmentation on risk-based asset allocation techniques

In the last decades, risk-based portfolio construction techniques have enjoyed a widespread diffusion in the financial community. This study aims at evaluating how these portfolio construction techniques produce different results depending on whether the segmentation of the stock market investment universe is based on sectorial or geographical criteria. An empirical analysis, applied on the global equity market, is carried out by making use of the typical and most advanced statistical and financial evaluation measures. Geographical segmentation is carried out in relation to the listing market, while sectorial segmentation is made in relation to the productive sectors to which individual companies belong. Our comparative analysis provides substantially coherent results, demonstrating a significant preference for the sectorial criterion compared to the geographic one. In conclusion, this result can be attributed to the subdivision of the investment universe into sectorial indices characterized by greater internal coherence and better external differentiation, in addition to the lower concentration of sectorial segmentation compared to the geographical one.

Momentum with Volatility Timing

The growing adoption of factor investing simultaneously prompted the active topic of factor timing approaches for the dynamic allocation of multi-factor portfolios. The trend represents a natural development of filling the gap between passive and active management. The paper addresses this direction by introducing the volatility-timed winners approach that applies past volatilities as a timing predictor to mitigate momentum factor underperformance for time intervals spanning the market downturn and post-crisis period. The proposed approach was confirmed with Spearman rank correlation and demonstrated in relation to different strategies including momentum volatility scaling, risk-based asset allocation, time series momentum and MSCI momentum indexes. The corresponding analysis generalized existing volatility scaling strategies and brought together the two branches of the smart-beta domain, factor investing and risk-based asset allocation.

Multifactor Portfolio Construction by Factor Risk Parity Strategies: An Empirical Comparison of Global Stock Markets

Since the financial crisis in 2008, factor investing has attracted the attention of investment managers and asset owners. A factor-based investment portfolio can enjoy effective diversification and acquire factor risk premiums at lower cost than active managers can. In equity investments, “smart beta” investing has been established as a common investment style and the multifactor strategy has become the most popular in recent years. This study makes an additional contribution to empirical research for risk-based asset allocation in multifactor investing. We verified the effectiveness of the factor risk parity (FRP) strategy by constructing active equity FRP portfolios for four stock markets, Japan, the United States, United Kingdom, and Euro countries. For the Japanese market, four factors considered to be effective in the market were adopted for constructing FRP portfolios. For the other markets, we constructed FRP portfolios by equalizing factor risk contributions between the cyclical and defensive factors. We found that the FRP strategy is a prospective method for capturing factor risk premiums, since it can adequately allocate risk to factors that contribute positive returns in the active FRP portfolios.

Monetary Policy and Risk-Based Asset Allocation

This paper focuses on the effects of the Fed’s monetary policy on stock and bond returns co-movement and their implications to risk-based asset allocation. Using a regime-switching model that controls for the economic effects of monetary policy we identify three co-movement regimes. We document that risk-based portfolio strategies poorly perform in the low correlation regime which features inflation shocks. We find outperformance evidence under the negative correlation regime with a high stock market risk and a very accommodating Fed policy. Less effectiveness is demonstrated under the positive correlation regime where bonds are regarded as risky assets and interest rate volatility is fueled by monetary policy.

Introduction into Multi-Factor Investing

Asset managers worldwide face the new market reality: significantly decreased global economic growth, the lowest interest rates and inflation, an increase in asset cross-correlation due to accelerated globalization and spikes of event driven volatility, high assets valuation levels. In response to market changes the new approaches to asset management have been developed: risk based asset allocation and factor investing. In this introductory document we briefly cover historical evolution of asset management from traditional methods to alternative beta and “pure” alpha strategies. Then we describe each category and analyze it based on our own examples. At the end we outline the new trends and future fields of research in modern asset management and alpha generating strategies.

Monetary Policy and Risk-Based Asset Allocation

This paper focuses on the effects of the Fed’s monetary policy on stock and bond returns co-movement and their implications to risk-based asset allocation. Using a regime-switching model that controls for the economic effects of monetary policy we identify three co-movement regimes. We document that risk-based portfolio strategies poorly perform in the low correlation regime which features inflation shocks. We find outperformance evidence under the negative correlation regime with a high stock market risk and a very accommodating Fed policy. Less effectiveness is demonstrated under the positive correlation regime where bonds are regarded as risky assets and interest rate volatility is fueled by monetary policy.

Risk-based strategies: the social responsibility of investment universes does matter

In this article we extend the research on risk-based asset allocation strategies by exploring how using an SRI universe impacts the properties of risk-based portfolios. We focus on four risk-based asset allocation strategies: the Equally Weighted (EW), the Most Diversified Portfolio (MDP), the Minimum Variance (MV) and the Equal Risk Contribution (ERC). Using different estimators of the matrix of covariances, we apply these strategies to the EuroStoxx universe of stocks, the Advanced Sustainability Performance Index (ASPI) and the complement of the ASPI in the EuroStoxx universe from March 15, 2002 to May 1, 2012. We observe several impacts but one is particularly important in our mind. We observe that risk-based asset allocation strategies built on the entire universe, concentrate their solution on non-SRI stocks. Such risk-based portfolio is therefore under-weighted in socially responsible firms.

A Generalized Risk Budgeting Approach to Portfolio Construction

Risk-based asset allocation models have received considerable attention in recent years. This increased popularity is due in part to the difficulty in estimating expected returns as well as the financial crisis of 2008 which has helped reinforce the key role of risk in asset allocation. In this study, we propose a generalized risk budgeting (GRB) approach to portfolio construction. In a GRB portfolio assets are grouped into possibly overlapping subsets and each subset is allocated a pre-specified risk budget. Minimum variance, risk parity and risk budgeting portfolios are all special instances of a GRB portfolio. The GRB portfolio optimization problem is to find a GRB portfolio with an optimal risk-return profile where risk is measured using any positively homogeneous risk measure. When the subsets form a partition, the assets all have the same expected return and we restrict ourselves to long-only portfolios, then the GRB problem can in fact be solved as a convex optimization problem. In general, however, the GRB problem is a constrained non-convex problem, for which we propose two solution approaches. The first approach uses a semidefinite programming (SDP) relaxation to obtain an (upper) bound on the optimal objective function value. In the second approach we develop a numerical algorithm that integrates augmented Lagrangian and Markov chain Monte Carlo (MCMC) methods in order to find a point in the vicinity of a very good local optimum. This point is then supplied to a standard non-linear optimization routine with the goal of finding this local optimum. It should be emphasized that the merit of this second approach is in its generic nature: in particular, it provides a starting-point strategy for any non-linear optimization algorithm.

Diversifying risk parity

Striving for maximum diversification we follow the 2009 work of Meucci in measuring and managing a multi-asset class portfolio. Under this paradigm the maximum diversification portfolio is equivalent to a risk parity strategy with respect to the uncorrelated risk sources embedded in the underlying portfolio assets. We characterize the mechanics and properties of this diversified risk parity strategy. Moreover, we explore the risk and diversification characteristics of traditional risk-based asset allocation techniques such as 1/N, minimum-variance or risk parity and show the diversified risk parity strategy to be very meaningful when benchmarked against these alternatives.

Risk-Based Asset Allocation Under Markov-Modulated Pure Jump Processes

We consider a risk-based asset allocation problem in a Markov, regime-switching, pure jump model. With a convex risk measure of the terminal wealth of an investor as a proxy for risk, we formulate the risk-based asset allocation problem as a zero-sum, two-person, stochastic differential game between the investor and the market. The HJB dynamic programming approach is used to discuss the game problem. A semi-analytical solution of the game problem is obtained in a particular case.

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.

Risk-Based Allocation of Principal Portfolios

Risk-based asset allocation strategies are mainly used to diversify nominal asset weights. In this paper, we discuss the diversification of risk factors. The analysis is based on the idea of Partovi and Caputo (2004), who use principal component analysis to transform a portfolio into a set of uncorrelated principal portfolios. Risk-based asset allocation strategies can be applied to these uncorrelated sources of risk. A similar route has been taken by Meucci (2009) with his idea of a maximum entropy portfolio. We discuss the relation of this approach with the concept of principal risk parity. Both strategies are backtested against nominal diversification strategies in a multi-asset portfolio. We find no evidence that risk diversification does outperform nominal diversification and discuss possible reasons for this.

A Risk-Based Asset Allocation Framework for Unstable Markets

Individual investors need to shift from trying to beat the market to creating a strategy that will enable them to achieve their important financial goals regardless of the future behavior of financial markets. The wealth allocation framework is an intuitive goals-driven framework of three portfolios: safety, investment, and aspirational. The central problem in the framework is risk allocation—that is, allocating assets optimally among the three risk–return portfolios to maximize the probability of achieving specified goals. In this case, asset allocation can be viewed as a special case of risk allocation.

A BSDE approach to risk-based asset allocation of pension funds with regime switching

An asset allocation problem of a member of a defined contribution (DC) pension fund is discussed in a hidden, Markov regime-switching, economy using backward stochastic differential equations, (BSDEs). A risk-based approach is considered, where the member selects an optimal asset mix with a view to minimizing the risk described by a convex risk measure of his/her terminal wealth. Firstly, filtering theory is adopted to transform the hidden, Markov regime-switching, economy into one with complete observations and to develop, (robust), filters for the hidden Markov chain. Then the optimal asset allocation problem of the member is formulated as a two-person, zero-sum stochastic differential game between the member and the market in the economy with complete observations. The BSDE approach is then used to solve the game problem and to characterize the saddle point of the game problem. An explicit expression for the optimal asset mix is obtained in the case of a convex risk measure with quadratic penalty and it can be considered a generalized version of the Merton ratio. An explicit expression for the optimal strategy of the market is also obtained, which leads to a risk-neutral wealth dynamic and may provide some insights into asset pricing in the economy with inflation risk and regime-switching risk. Numerical examples are provided to illustrate financial implications of the BSDE solution.

Diversifying Risk Parity

Striving for maximum diversification we follow Meucci (2009) in measuring and managing a multi-asset class portfolio. Under this paradigm the maximum diversification portfolio is equivalent to a risk parity strategy with respect to the uncorrelated risk sources embedded in the underlying portfolio assets. Our paper characterizes the mechanics and properties of this diversified risk parity strategy. Moreover, we explore the risk and diversification characteristics of traditional risk-based asset allocation techniques like 1/N, minimum-variance, or risk parity and demonstrate the diversified risk parity strategy to be quite meaningful when benchmarked against these alternatives.