Composition of robust equity portfolios

Robust portfolios resolve the sensitivity issue identified as a concern in implementing mean–variance analysis. Because robust approaches are not widely used in practice due to a limited understanding regarding the portfolios constructed from these methods, we present an analysis of the composition of robust equity portfolios. We find that compared to the Markowitz mean–variance formulation, robust optimization formulations form portfolios that contain a fewer number of stocks, avoid large exposure to individual stocks, have higher portfolio beta, and show low correlation between weight and beta of the stocks composing the portfolio. These properties are also found for global minimum-variance portfolios.     

On the robustness of risk-based asset allocations

Since the subprime crisis, portfolios based on risk diversification are of great interest to both academic researchers and market practitioners. They have also been employed by several asset management firms and their performance appears promising. Since they do not rely on estimates of expected returns, they are assumed to be robust. The same argument holds for minimum variance and equally weighted portfolios. In this paper, we consider a Monte Carlo simulation, as well as an empirical global portfolio dataset, to study the effect of estimation errors on the outcomes of two recently proposed asset allocations, the equally weighted risk contribution (ERC) and the principal component analysis (PCA) portfolio. The ERC portfolio is more robust to changes in the input parameters and has a smaller estimation error than the Markowitz approaches, whereas the PCA portfolio is even more unstable than the classical approaches. In the worst-case scenario, neither approach delivers what it promises. However, in every case the resulting return?Crisk relationship is dominated by the Markowitz approaches.     

Safety-first portfolio optimization for US investors in emerging global,Asian and Latin American markets

Risk averse US investors with safety-first objectives in portfolio optimization hold small weights (maximum 10%) in emerging markets when constructing portfolios of the Standard and Poor's 500 (SP), and the Emerging Markets Composite Global (CG), Asia (AS) and Latin American (LA) indexes, respectively. The Composite Global and Asia weights are even smaller than their minimum variance weights. Yet, these optimal safety-first portfolios are dominant in terms of risk and return over the global minimum or higher variance portfolios. In contrast, safety-first optimization for Latin America is hardly different from the minimum variance and not clearly dominant over other mean–variance portfolios. Overall, safety-first limits portfolio losses associated with infrequent catastrophic events and otherwise optimize performance.     

Spectral risk measures and portfolio selection

This paper deals with risk measurement and portfolio optimization under risk constraints. Firstly we give an overview of risk assessment from the viewpoint of risk theory, focusing on moment-based, distortion and spectral risk measures. We subsequently apply these ideas to an asset management framework using a database of hedge funds returns chosen for their non-Gaussian features. We deal with the problem of portfolio optimization under risk constraints and lead a comparative analysis of efficient portfolios. We show some robustness of optimal portfolios with respect to the choice of risk measure. Unsurprisingly, risk measures that emphasize large losses lead to slightly more diversified portfolios. However, risk measures that account primarily for worst case scenarios overweight funds with smaller tails which mitigates the relevance of diversification.     

Optimal commodity asset allocation with a coherent market risk modeling

This paper fills a fundamental gap in commodity price risk management and optimal portfolio selection literatures by contributing a thorough reflection on trading risk modeling with a dynamic asset allocation process and under the supposition of illiquid and adverse market settings. This paper analyzes, from a portfolio managers' perspective, the performance of liquidity adjusted risk modeling in obtaining efficient and coherent investable commodity portfolios under normal and adverse market conditions. As such, the author argues that liquidity risk associated with the uncertainty of liquidating multiple commodity assets over given holding periods is a key factor in formalizing and measuring overall trading risk and is thus an important component to model, particularly in the wake of the repercussions of the recent 2008 financial crisis. To this end, this article proposes a practical technique for the quantification of liquidity trading risk for large portfolios that consist of multiple commodity assets and whereby the holding periods are adjusted according to the specific needs of each trading portfolio. Specifically, the paper proposes a robust technique to commodity optimal portfolio selection, in a liquidity-adjusted value-at-risk (L-VaR) framework, and particularly from the perspective of large portfolios that have both long and short positions or portfolios that consist of merely pure long trading positions. Moreover, in this paper, the author develops a portfolio selection model and an optimization-algorithm which allocates commodity assets by minimizing the L-VaR subject to applying credible operational and financial constraints based on fundamental asset management considerations. The empirical optimization results indicate that this alternate L-VaR technique can be regarded as a robust portfolio management tool and can have many uses and applications in real-world asset management practices and predominantly for fund managers with large commodity portfolios.     

Socially responsible investment portfolios: Does the optimization process matter?

This study investigates the impact of the choice of optimization technique when constructing Socially Responsible Investment (SRI) portfolios. Corporate Social Performance (CSP) scores are price sensitive information that is subject to considerable estimation risk. Therefore, uncertainty in the input parameters is greater for SRI portfolios than conventional portfolios, and this affects the selection of the appropriate optimization method. We form SRI portfolios based on six different approaches and compare their performance along the dimensions of risk, risk-return trade-off, diversification and stability. Our results for SRI portfolios contradict those of the conventional portfolio optimization literature. We find that the more “formal” optimization approaches (Black-Litterman, Markowitz and robust estimation) lead to SRI portfolios that are both less risky and have superior risk-return trade-offs than do more simplistic approaches; although they also have more unstable asset allocations and lower diversification. Our conclusions are robust to a series of tests, including the use of different estimation windows and stricter screening criteria.     

Focusing on the worst state for robust investing

Despite its shortcomings, the Markowitz model remains the norm for asset allocation and portfolio construction. A major issue involves sensitivity of the model's solution to its input parameters. The prevailing approach employed by practitioners to overcome this problem is to use worst-case optimization. Generally, these methods have been adopted without incorporating equity market behavior and we believe that an analysis is necessary. Therefore, in this paper, we present the importance of market information during the worst state for achieving robust performance. We focus on the equity market and find that the optimal portfolio in a market with multiple states is the portfolio with robust returns and observe that focusing on the worst market state provides robust returns. Furthermore, we propose alternative robust approaches that emphasize returns during market downside periods without solving worst-case optimization problems. Through our analyses, we demonstrate the value of focusing on the worst market state and as a result find support for the value of worst-case optimization for achieving portfolio robustness.     

Dynamic hedge fund portfolio construction: A semi-parametric approach

In this article, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. We compare the standard mean–variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semi-parametric methodology, which is based on extreme value theory, copula and Monte Carlo simulation. We compare the semi-parametric approach with the standard, non-parametric approach, used to compute CVaR, CDaR and Omega, and the benchmark parametric approach, based on both static and dynamic mean–variance optimization. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the parametric mean–variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.     

Optimal asset allocation using a combination of implied and historical information

This paper investigates the contribution of option-implied information for strategic asset allocation for individuals with minimum-variance preferences and portfolios with a variety of assets. We propose a covariance matrix that exploits a mixture of historical and option-implied information. Implied variance measures are proposed for those assets for which option-implied information is available. Historical variance and correlation measures are applied to the remaining assets. The performance of this novel approach for constructing optimal investment portfolios is assessed out-of-sample using statistical and economic measures. An empirical application to a sophisticated portfolio comprised by a combination of equities, fixed income, alternative securities and cash deposits shows that implied variance measures with risk premium correction outperform variance measures constructed from historical data and implied variance without correction. This result is robust across investment portfolios, volatility and portfolio performance metrics, and rebalancing schemes.     

A note on the returns from minimum variance investing

Disappointed with the performance of market weighted benchmark portfolios yet skeptical about the merits of active portfolio management, investors in recent years turned to alternative index definitions. Minimum variance investing is one of these popular concepts. I show in this paper that the portfolio construction process behind minimum variance investing implicitly picks up risk-based pricing anomalies. In other words the minimum variance tends to hold low beta and low residual risk stocks. Long/short portfolios based on these characteristics have been associated in the empirical literature with risk adjusted outperformance. This paper shows that 83% of the variation of the minimum variance portfolio excess returns (relative to a capitalization weighted alternative) can be attributed to the FAMA/FRENCH factors as well as to the returns on two characteristic anomaly portfolios. All regression coefficients (factor exposures) are highly significant, stable over the estimation period and correspond remarkably well with our economic intuition. The paper also shows that a direct combination of market weighted benchmark portfolio and risk based characteristic portfolios will provide a statistically significant improvement over the indirect pickup via the minimum variance portfolio.     

Learning risk preferences from investment portfolios using inverse optimization

The level of risk an investor can endure, known as risk-preference, is a subjective choice that is tightly related to psychology and behavioral science in decision making. This paper presents a novel approach of measuring risk preference from existing portfolios using inverse optimization on mean–variance portfolio allocation framework. Our approach allows the learner to continuously estimate real-time risk preferences using concurrent observed portfolios and market price data. We demonstrate our methods on robotic investment portfolios and real market data that consists of 20 years of asset pricing and 10 years of mutual fund portfolio holdings. Moreover, the quantified risk preference parameters are validated with two well-known risk measurements currently applied in the field. The proposed methods could lead to practical and fruitful innovations in automated/personalized portfolio management, such as Robo-advising, to augment financial advisors’ decision intelligence in a long-term investment horizon.     

Thematic portfolio optimization: challenging the core satellite approach

In recent years, thematic exchange-traded funds (ETF) have increased in economic significance. Investors in thematic ETFs have more than just financial objectives and gain a non-monetary added value from a thematic portion in their portfolios. Therefore, traditional portfolio optimization models which target only financial criteria cannot suit these investors’ needs anymore. Nevertheless, to account for their thematic interests, investors adapt a core satellite strategy in which conventional core portfolios and thematic satellite portfolios are combined. Thus, these portfolios are separately optimized without further considering inter-portfolio correlation effects. Since modern portfolio theory has originally been established to, inter alia, optimize these correlation effects, portfolios can only be efficient by chance. Therefore, this study targets the correlation effects between conventional and thematic portfolios and uses a tri-criterion thematic portfolio optimization model as an overall framework. Throughout a two-part analysis with tradable ETFs and a simulation with 250,000 draws and 1,750,000 portfolio optimizations performed, the status quo is compared to the tri-criterion model. Quantifying the suboptimality, simulation results show a mean portfolio improvement of 6.23% measured as relative yield enhancement. Further, our analysis concludes that the more narrowly a theme is defined and the more particular it is, relative yield enhancements can increase up to 46.88%.

     

Portfolio selection with mental accounts and background risk

Das et al. (2010) develop a model where an investor divides his or her wealth among mental accounts with motives such as retirement and bequest. Nevertheless, the investor ends up selecting portfolios within mental accounts and an aggregate portfolio that lie on the mean–variance frontier. Importantly, they assume that the investor only faces portfolio risk. In practice, however, many individuals also face background risk. Accordingly, our paper expands upon theirs by considering the case where the investor faces background risk. Our contribution is threefold. First, we provide an analytical characterization of the existence and composition of the optimal portfolios within accounts and the aggregate portfolio. Second, we show that these portfolios lie away from the mean–variance frontier under fairly general conditions. Third, we find that the composition and location of such portfolios can differ notably from those of portfolios on the mean–variance frontier.     

Portfolio credit-risk optimization

This paper evaluates several alternative formulations for minimizing the credit risk of a portfolio of financial contracts with different counterparties. Credit risk optimization is challenging because the portfolio loss distribution is typically unavailable in closed form. This makes it difficult to accurately compute Value-at-Risk (VaR) and expected shortfall (ES) at the extreme quantiles that are of practical interest to financial institutions. Our formulations all exploit the conditional independence of counterparties under a structural credit risk model. We consider various approximations to the conditional portfolio loss distribution and formulate VaR and ES minimization problems for each case. We use two realistic credit portfolios to assess the in- and out-of-sample performance for the resulting VaR- and ES-optimized portfolios, as well as for those which we obtain by minimizing the variance or the second moment of the portfolio losses. We find that a Normal approximation to the conditional loss distribution performs best from a practical standpoint.     

The Effect of Shortfall as a Risk Measure for Portfolios with Hedge Funds

Abstract:  Current research suggests that the large downside risk in hedge fund returns disqualifies the variance as an appropriate risk measure. For example, one can easily construct portfolios with nonlinear pay-offs that have both a high Sharpe ratio and a high downside risk. This paper examines the consequences of shortfall-based risk measures in the context of portfolio optimization. In contrast to popular belief, we show that negative skewness for optimal mean-shortfall portfolios can be much greater than for mean-variance portfolios. Using empirical hedge fund return data we show that the optimal mean-shortfall portfolio substantially reduces the probability of small shortfalls at the expense of an increased extreme crash probability. We explain this by proving analytically under what conditions short-put payoffs are optimal for a mean-shortfall investor. Finally, we show that quadratic shortfall or semivariance is less prone to these problems. This suggests that the precise choice of the downside risk measure is highly relevant for optimal portfolio construction under loss averse preferences.     

Noise sensitivity of portfolio selection under various risk measures

We study the sensitivity to estimation error of portfolios optimized under various risk measures, including variance, absolute deviation, expected shortfall and maximal loss. We introduce a measure of portfolio sensitivity and test the various risk measures by considering simulated portfolios of varying sizes N and for different lengths T of the time series. We find that the effect of noise is very strong in all the investigated cases, asymptotically it only depends on the ratio N/T, and diverges (goes to infinity) at a critical value of N/T, that depends on the risk measure in question. This divergence is the manifestation of a phase transition, analogous to the algorithmic phase transitions recently discovered in a number of hard computational problems. The transition is accompanied by a number of critical phenomena, including the divergent sample to sample fluctuations of portfolio weights. While the optimization under variance and mean absolute deviation is always feasible below the critical value of N/T, expected shortfall and maximal loss display a probabilistic feasibility problem, in that they can become unbounded from below already for small values of the ratio N/T, and then no solution exists to the optimization problem under these risk measures. Although powerful filtering techniques exist for the mitigation of the above instability in the case of variance, our findings point to the necessity of developing similar filtering procedures adapted to the other risk measures where they are much less developed or non-existent. Another important message of this study is that the requirement of robustness (noise-tolerance) should be given special attention when considering the theoretical and practical criteria to be imposed on a risk measure.     

Dynamic spillover effects among green bond,renewable energy stocks and carbon markets during COVID-19 pandemic: Implications for hedging and investments strategies

This study has been inspired by the emergence of socially responsible investment practices in mainstream investment activity as it examines the transmission of return patterns between green bonds, carbon prices, and renewable energy stocks, using daily data spanning from 4th January 2015 to 22nd September 2020. In this study, our dataset comprises the price indices of S&P Green Bond, Solactive Global Solar, Solactive Global Wind, S&P Global Clean Energy and Carbon. We employ the TVP-VAR approach to investigate the return spillovers and connectedness, and various portfolio techniques including minimum variance portfolio, minimum correlation portfolio and the recently developed minimum connectedness portfolio to test portfolio performance. Additionally, a LASSO dynamic connectedness model is used for robustness purposes. The empirical results from the TVP-VAR indicate that the dynamic total connectedness across the assets is heterogeneous over time and economic event dependent. Moreover, our findings suggest that clean energy dominates all other markets and is seen to be the main net transmitter of shocks in the entire network with Green Bonds and Solactive Global Wind, emerging to be the major recipients of shocks in the system. Based on the hedging effectiveness, we show that bivariate and multivariate portfolios significantly reduce the risk of investing in a single asset except for Green Bonds. Finally, the minimum connectedness portfolio reaches the highest Sharpe ratio implying that information concerning the return transmission process is helpful for portfolio creation. The same pattern has been observed during the COVID-19 pandemic period.     

Is gold good for portfolio diversification? A stochastic dominance analysis of the Paris stock exchange

This paper aims to assess the role of gold quoted in Paris in the diversification of French portfolios from 1949 to 2012 using the stochastic dominance (SD) approach. The principal advantage of this method is that there is no restriction on the distribution of the returns. Our results show that stock portfolios including gold stochastically dominate those without gold at the second and third orders. This implies that risk-averse investors would be better off by including gold in their stock portfolios to maximize their expected utilities. The study on sub-periods shows that this result holds especially in unstable or crisis times. However, these results do not hold for bond or risk-free portfolios, for which the portfolios without gold dominate those with gold. To check the robustness of our results, our SD analysis of a mixed portfolio (50% stocks, 30% bonds and 20% the risk-free asset) provides results similar to those for portfolios with stocks only, except from 1971 to 1983. Portfolios including gold quoted in London show results similar to those from Paris. The results of mean–variance performance measures confirm the findings of previous studies that gold is good for the diversification of stock portfolios but not for bond portfolios.     

Strategic International Diversification and Monthly Seasonality

To the author's knowledge no other studies have dealt with the effect of international diversification on stock market monthly seasonality. The aim of this study is to investigate this effect in various ways: stock market monthly seasonality is analyzed by incorporating exchange rates and trading costs in international portfolio returns. The variance of the world portfolio is decomposed into six components. Stochastic dominance approach is used to show the robustness of the results. Five trading strategies are compared to help international investors be more informed. All the results show that monthly seasonality is clearly present in an economic sense and robust. Particularly, when exchange rates are incorporated into portfolio returns. January has the highest return and the lowest risk in the world portfolio.     

Risk parity portfolio optimization under a Markov regime-switching framework

We formulate and solve a risk parity optimization problem under a Markov regime-switching framework to improve parameter estimation and to systematically mitigate the sensitivity of optimal portfolios to estimation error. A regime-switching factor model of returns is introduced to account for the abrupt changes in the behaviour of economic time series associated with financial cycles. This model incorporates market dynamics in an effort to improve parameter estimation. We proceed to use this model for risk parity optimization and also consider the construction of a robust version of the risk parity optimization by introducing uncertainty structures to the estimated market parameters. We test our model by constructing a regime-switching risk parity portfolio based on the Fama–French three-factor model. The out-of-sample computational results show that a regime-switching risk parity portfolio can consistently outperform its nominal counterpart, maintaining a similar ex post level of risk while delivering higher-than-nominal returns over a long-term investment horizon. Moreover, we present a dynamic portfolio rebalancing policy that further magnifies the benefits of a regime-switching portfolio.