Realistic Portfolio Research Articles

The low-volatility effect in African frontier equity markets

ABSTRACT This study investigated the extent to which the low-risk anomaly is present in a pooled sample of nine African frontier equity markets from March 2004 to July 2023. Portfolio-level analysis was used to investigate the total stock returns of equally weighted quintile portfolios sorted on historical volatility. The presence of a monotonic relationship between historical volatility and subsequent returns was evaluated using monotonicity tests, controlling for possible mediating variables. The results revealed evidence of a statistically significant low-volatility premium, except during bull markets. These findings imply that investors can expect to earn higher returns by allocating to stocks with lower historical volatility, but only during bear markets. These results hold for realistic portfolio construction constraints, such as (il)liquidity and high transaction costs.

Using GAN-generated market simulations to guide genetic algorithms in index tracking optimization

Index tracking is the problem of building a portfolio that replicates the performance of a market index. The recent applications involving deep learning in index tracking are more focused on the learned information rather than on the framework that consumes this information. The problem is that, until now, a way to enable the extension of the index tracking models that adopt machine learning was not yet proposed. Nowadays, the mathematical programming framework is more flexible when considering model extensions to build realistic portfolios. Thus, this study presents ways to combine generative adversarial networks (GANs) within this framework to generate market simulations incorporated into a base index tracking model. It was verified how the simulations generated by GANs can impact the out-of-sample performance of the portfolio and how to deal with their instability, by using real data from the Brazilian market. To achieve this, two evolutionary metaheuristics were proposed to solve the multiple scenario index tracking problem. The proposed evolutionary algorithms minimize the tracking errors of a portfolio in multiple market simulations generated by GANs. The performance of the proposed algorithms was compared against another evolutionary metaheuristic that solves the index tracking problem using historical data. It was possible to observe that the scenario-based dominance genetic algorithm (SDM-SBDGA-GAN) was able to perform better than the real data genetic algorithm (RDM-GA) and the sample average approximation genetic algorithm (SDM-SAAGA-GAN). These results open doors for new applications of synthetic data in the construction of portfolios using more realistic constraints and other tracking objectives. This work also brings discussions about problems related to the application of GANs in this context.

Analysing Grid-Level Effects of Photovoltaic Self-Consumption Using a Stochastic Bottom-up Model of Prosumer Systems

Self-consumption of the energy generated by photovoltaics (PV) is playing an increasingly important role in the power grid. “Prosumer” systems consume part of the produced energy directly to meet the local demand, which reduces the feed-in into as well as the demand from the grid. In order to analyse the effects of PV self-consumption in the power grid, we introduce a stochastic bottom-up model of PV power generation and local consumption in the control area of the German transmission system operator TransnetBW. We set up a realistic portfolio of more than 100,000 PV/prosumer systems to generate representative time series of PV generation and consumption as a basis to derive self-consumption and feed-in. This model allows for the investigation of the time-dependent behaviour in detail for the full portfolio whereas measurements are presently only available as aggregated feed-in time series over a nonrepresentative subset of systems. We analyse the variation of self-consumption with PV generation and consumption at the portfolio level and its seasonal, weekly and diurnal cycles. Furthermore, we study a scenario of 100% prosumers as a limiting case for a situation without subsidized feed-in tariffs and local energy storage.

Treynor Ratio guided risk-return model for TSO-DSO mutualism considering energy and price volatility

Treynor Ratio (TR), a reward to volatility measure in finance, is used to quantify excess return per unit risk taken by the investor, where risk implies volatility in returns relative to market portfolio return. In this paper, TR is modified (TR EP ) to suggest the hourly weight of each risky energy asset at which it is worth using in the transmission and distribution levels to sustain the volatility of the market and to yield reasonable returns to both TSO and DSO. Uncertainties in the wind and solar energy sources pose energy-risk and fluctuations in grid power price poses financial risk, and both impact the TSO-DSO profit trade-off. Here, beta is used as the risk measure that evaluates the effect of uncertainty in each energy source on operators’ profit relative to the collective effect of all the energy sources available in the system. When risk is modelled using absolute measures like standard deviation or variance which are independent of market portfolio returns, it discourages risky assets more, to keep a risk-averse profile. By co-optimizing TR EP values of TSO and DSO, more realistic portfolios are built by maximizing their expected profits per unit risk in relative terms. The resultant portfolio utilizes higher share of distributed energy resources (DERs) and renewable energy, thereby improving the role of DSOs in the market. The operators’ returns are found to be closer to the market portfolio returns at risks well within the market portfolio risk level.

Rebalancing with transaction costs: theory, simulations, and actual data

In the absence of transaction costs and the presence of independent returns, a buy-and-hold strategy theoretically generates higher expected returns than a fixed-weight strategy, where the portfolio weights are regularly readjusted/rebalanced to some initial level. This higher expected return comes with higher volatility. The resulting trade-off leads to different rankings of the Sharpe ratio depending on the statistical moments of the assets. We also focus on Maximum Drawdown. We theoretically discuss causes affecting the ranking of the Sharpe ratio, and we introduce an easy-to-implement methodology to deal with proportional transaction costs. Under transaction costs, the buy-and-hold strategy as the cheaper approach should be the winner. In various simulation experiments, we investigate the relevance of transaction costs on rebalancing strategies. Eventually, we consider several realistic portfolios with a risk-free asset, bonds, stock indices, commodities and real estate that allow us to demonstrate that in practice rebalancing has value.

Sparse grid method for highly efficient computation of exposures for xVA

Every “x”-adjustment in the so-called xVA financial risk management framework relies on the computation of exposures. Considering thousands of Monte Carlo paths and tens of simulation steps, a financial portfolio needs to be evaluated numerous times during the lifetime of the underlying assets. This is the bottleneck of every simulation of xVA.In this article, we explore numerical techniques for improving the simulation of exposures. We aim to decimate the number of portfolio evaluations, particularly for large portfolios involving multiple, correlated risk factors. The usage of the Stochastic Collocation (SC) method Grzelak et al. (2019)[, together with Smolyak’s (1963), Judd et al. (2014) sparse grid extension, allows for a significant reduction in the number of portfolio evaluations, even when dealing with many risk factors. The proposed model can be easily applied to any portfolio and size.We report that for a realistic portfolio comprising linear and non-linear derivatives, the expected reduction in the portfolio evaluations may exceed 6000 times, depending on the dimensionality and the required accuracy. We give illustrative examples and examine the method with realistic multi-currency portfolios consisting of interest rate swaps and swaptions.

Cost of trading factor strategies

Recent academic literature claims that style premia are not robust to trading costs. Several papers written by practitioners counter that the assumptions made by academics on how style portfolios rebalance are too conservative. In this paper we analyse the cost of trading factor strategies using a market impact model estimated from actual transactions data, realistic and multiple portfolio construction techniques and up-to-date data. Our results suggest that, for realistic portfolio sizes, the typical costs of rebalancing a single-factor strategy are unlikely to erode the factor premium.
 In addition, by building portfolios across different factors and with alternative portfolio construction techniques, we are able to assess the degree of similarity amongst strategies over time, which can be viewed as a measure of crowding. The properties of our new crowding indicator are illustrated through an extensive empirical investigation. We then assess its relation to volatility, liquidity and market impact and find that increases in our crowding measure tend to be followed by increases in the volatility of a strategy’s returns.

Portfolio selection with tail nonlinearly transformed risk measures—a comparison with mean-CVaR analysis

We compare portfolio selection under the tail nonlinearly transformed risk measure (TNT) with mean-CVaR analysis for normally distributed returns. TNT arises as a natural extension to CVaR that additionally distorts the portfolio returns' outcomes by means of a concave transformation function. We first address the portfolio setting where no risk-free asset exists. Here, the global minimum CVaR portfolio, also under fairly realistic asset returns, may not exist. TNT is able to resolve this shortcoming: its additional transformation of the portfolio outcomes ensures that the global minimum TNT portfolio and, accordingly, the ()-efficient frontiers, do always exist. Second, we analyze the setting where the risk-free asset is available. In this case, Tobin's theorem holds both for CVaR and TNT, under the condition that the respective investors are sufficiently risk averse. Under TNT, this condition is less restrictive, Tobin's theorem holds more often. We third address the choice of optimal portfolios under CVaR and TNT. Under CVaR, optimal portfolios exhibit plunging: either the investor invests entirely in the risky tangency portfolio or she invests entirely in the risk-free asset; diversification is never optimal. TNT, in contrast, yields more realistic portfolio structures. Below a certain minimum risk premium, we do not find any risky investment. Once this minimum risk premium is passed, the risky investment is continuous and strictly monotonously increasing in the risk premium. This pattern is in line with empirical evidence on the stock market participation puzzle and the equity premium puzzle.

Portfolio Construction Using First Principles Preference Theory and Machine Learning

The author develops a novel approach to portfolio construction that builds on the first principles preference theory, incorporating characteristics of portfolios beyond the mean and variance of returns typical of the state-of-the art mean–variance optimization. Specifically, the author adds skewness and kurtosis of return distributions to the framework. This portfolio framework is proposed with the intent to make it easily accessible conceptually and easily implementable in practice so that it will be of pragmatic value to investment professionals. This imperative of practical feasibility leads to the utilization of standard machine learning techniques that proved effective in overcoming the methodological intricacies associated with mean–variance optimization. Furthermore, the author allows for a multiplicity of optimal portfolio outcomes, leaving to the investor some—albeit constrained—discretion in portfolio choice within a class of similarly optimal portfolios. In a Monte Carlo setting that is rich enough to incorporate co-skewness and tail dependencies aside from simple correlation structures between returns, the suggested framework generates more realistic portfolio solutions than mean–variance optimization. TOPICS:Big data/machine learning, portfolio management, portfolio theory, portfolio construction, simulations Key Findings • This article presents a portfolio construction framework that builds on first principles preference theory, incorporating higher moment return characteristics beyond mean and co-variance typical of mean–variance optimization. Specifically, we also characterize portfolio performance based on return skewness and kurtosis. • Our portfolio framework is easily accessible conceptually and easily implementable in practice, providing pragmatic value to practitioners. The utilization of standard machine learning techniques that proved effective in overcoming the intricacies of mean–variance optimization makes our framework feasible and stable. • We allow for a multiplicity of optimal portfolios. The investor has some discretion over a class of similarly optimal portfolios. In a Monte Carlo study that accounts for correlations, co-skewness, and tail-dependencies, our framework generates more realistic portfolios than mean–variance optimization.

Beyond expected utility: Subjective risk aversion and optimal portfolio choice under convex shortfall risk measures

We conduct a decision-theoretic analysis of convex shortfall risk measures regarding their flexibility to represent subjective risk aversion, and discuss the implications for the choice of optimal portfolios. As convex shortfall risk measures are closely related to the expected utility functional, we draw upon the expected utility framework as our benchmark. First, we show that, unlike expected utility, convex shortfall risk measures do always represent constant absolute risk aversion. This constitutes a significant limitation when changing initial wealth of, e.g., investors, is relevant. Interestingly, though, it is exactly this limitation that provides additional degrees of freedom in representing subjective risk aversion beyond expected utility when initial wealth is fixed, as, e.g., in returned-based portfolio selection models in the tradition of Markowitz (1952). Second, we apply convex shortfall risk measures to the standard portfolio problem between a riskless and a risky asset. We provide a procedure that allows inferring the optimal portfolios under convex shortfall risk measures from certain optimal expected utility-portfolios. The procedure incorporates the additional degrees of freedom in modeling subjective risk aversion and, thus, allows more flexible and realistic portfolios compared to expected utility. Third, we address the optimal portfolio choice between a riskless and a risky asset in the presence of an additional background risk. Again, we prove a correspondence result between optimal portfolios under convex shortfall risk measures and expected utility and obtain more flexible and realistic portfolios compared to expected utility. We also compare the optimal risky investments without and with background risk and provide a necessary and sufficient condition for a reduction of the risky investment.

A regime-switching factor model for mean–variance optimization

We formulate a novel Markov regime-switching factor model to describe the cyclical nature of asset returns in modern financial markets. Maintaining a factor model structure allows us to easily derive the asset expected returns and their corresponding covariance matrix. By design, these two parameters are calibrated to better describe the properties of the different market regimes. In turn, these regime-dependent parameters serve as the inputs during mean–variance optimization, thereby constructing portfolios adapted to the current market environment. Through this formulation, the proposed model allows for the construction of large, realistic portfolios at no additional computational cost during optimization. Moreover, the viability of this model can be significantly improved by periodically re-balancing the portfolio, ensuring proper alignment between the estimated parameters and the transient market regimes. An out-of-sample computational experiment over a long investment horizon shows that the proposed regime-dependent portfolios are better aligned with the market environment, yielding a higher ex post rate of return and lower volatility than competing portfolios.

Evaluation of the efficiency of social investments of metallurgical enterprises according to the decoupling approach

Purpose. To develop a comprehensive methodology for assessing the effectiveness of social investment of metallurgical enterprises by a decoupling approach, which facilitates to form a clear idea of the investors intentions to support socially important initiatives and to make a realistic portfolio in terms of achieving the impact goals. Methodology. During the present research, the statistical methods of time series processing and correlation-regressive analysis are used in determining the dependence of the Decoupling Factor of social values on the amount of capital investment to create them. Decoupling analysis is applied in assessing the effectiveness of social investments of Metinvest Holding and the formation of its portfolio in terms of achieving impact goals. Strategic analysis is put to use in forecasting the effectiveness of social investment Metinvest Holding on the medium perspective. Findings. It is stated that the strategic orientation of transformational changes in the economy is currently the sustainable development of industrial enterprises, the achievement of which, in particular, is possible with the consistent application of the arsenal of fair working conditions, professional growth and welfare of employees, among which social investment has become widespread in foreign practice. The international standards on corporate social responsibility of companies are analyzed and the content component of the concept of social investment is revealed according to the functional approach. Emphasis is placed on the need to assess the effectiveness of social investment by the decoupling approach. The essence of the decoupling and its significance in the process of social investment are revealed. The authors method for evaluating the effectiveness of social investment by the decoupling approach is proposed. The classification of decoupling effect types according to P.Tapio has been modified by distinguishing types of social-decoupling effect. The expediency of supplementing GRI400 Social Standards with the group of indicators GRI-420 Efficiency of Social Investments is substantiated. Originality. The theoretical and methodological provisions in the field of social investment are deepened by developing an authors methodology for assessing the effectiveness of social investment by decoupling approach. In contrast to the existing transformational changes in the economy, the methodology helps to make a clear understanding about the investors intentions and his/her realistic portfolio in terms of achieving the set impact goals. Taking into account the requirements of the UN Resolution Transforming our world: the 2030 Agenda for Sustainable Development, the ISO 26000 Social Responsibility Guide (2010) and the AA1000 AS Social Reporting Standard, it is proposed to supplement GRI-400 Social Standards with a group of indicators for assessing the effectiveness of social investment by the decoupling approach. Practical value. The scientific results on assessing the effectiveness of social investment of industrial enterprises by the decoupling approach should be used in making management decisions to invest capital in improving the working conditions of employees.

Rebalancing With Transaction Costs: Theory, Simulations, and Actual Data

In the absence of transaction costs and the presence of independent returns, a buy-and-hold strategy can be shown to generate higher expected returns than a fixed-weight strategy, where the portfolio weights are regularly readjusted/rebalanced to some initial level. This higher expected return comes, however, at a cost: higher volatility. The resulting trade-off leads to different rankings of the Sharpe ratio depending on the statistical moments of the assets. We theoretically discuss causes affecting the ranking of the Sharpe ratio, and we introduce an easy-to-implement methodology to deal with proportional transaction costs. Under transaction costs, the buy-and-hold strategy as the cheaper approach should be the winner. In various simulation experiments, we investigate the relevance of transaction costs on rebalancing strategies. Eventually, we consider a realistic portfolio with a risk-free asset, bonds, and various stock indices that allows us to demonstrate that in practice, as long as transaction costs remain small, rebalancing has value for realistic portfolios.

A Regime-Switching Factor Model for Mean-Variance Optimization

We formulate a novel Markov regime-switching factor model to describe the cyclical nature of asset returns in modern financial markets. Maintaining a factor model structure allows us to easily derive the asset expected returns and their corresponding covariance matrix. By design, these two parameters are calibrated to better describe the properties of the different market regimes. In turn, these regime-dependent parameters serve as the inputs during mean–variance optimization, thereby constructing portfolios adapted to the current market environment. Through this formulation, the proposed model allows for the construction of large, realistic portfolios at no additional computational cost during optimization. Moreover, the viability of this model can be significantly improved by periodically re-balancing the portfolio, ensuring proper alignment between the estimated parameters and the transient market regimes. An out-of-sample computational experiment over a long investment horizon shows that the proposed regime-dependent portfolios are better aligned with the market environment, yielding a higher ex post rate of return and lower volatility than competing portfolios.

Long horizon predictability: An asset allocation perspective

Consider investors with a 10-year investment horizon who rebalance their portfolio at the monthly frequency. Should they use information from monthly returns, 10-year returns or intermediate returns to build their optimal portfolios? When stock and bond returns are i.i.d., the frequency of returns is not relevant. However, when they are predictable, it is. Using a new estimation approach and before correcting for overlapping observations, we show that the positive impact of predictability on investors’ welfare is stronger for longer prediction horizons and the more so as the investment horizon enlarges. This welfare improvement is achieved by adopting realistic portfolio positions. When we correct for the persistence in the predictive regression residuals due to overlapping observations, our results are preserved for short to medium investment horizons although the added value of long horizon predictability is reduced. Our results are robust to various checks and also hold out-of-sample. Overall, short to medium term investors should exploit long horizon predictability even though they rebalance their portfolios at high frequency.

Stock Returns and the Cross-Section of Characteristics: A Tree-Based Approach

We build regression trees to determine which firm characteristics are most likely to drive future returns. Out of 30 attributes, those related to momentum appear to have, by far, the most marked impact. This prominence is verified at the sector level as well. The second order effects are propelled by volatility and liquidity variables. Finally, we show that a realistic portfolio strategy based on the short-term RSI characteristic outperforms the naive 1/N portfolio by 2.4% per annum, once the transaction costs have been taken into account. One possible explanation for these higher returns is the immunity of the strategy to the momentum crash phenomenon.

Efficient exposure computation by risk factor decomposition

The focus of this paper is the efficient computation of counterparty credit risk exposure on portfolio level. Here, the large number of risk factors rules out traditional PDE-based techniques and allows only a relatively small number of paths for nested Monte Carlo simulations, resulting in large variances of estimators in practice. We propose a novel approach based on Kolmogorov forward and backward PDEs, where we counter the high dimensionality by a generalization of anchored-ANOVA decompositions. By computing only the most significant terms in the decomposition, the dimensionality is reduced effectively, such that a significant computational speed-up arises from the high accuracy of PDE schemes in low dimensions compared to Monte Carlo estimation. Moreover, we show how this truncated decomposition can be used as control variate for the full high-dimensional model, such that any approximation errors can be corrected while a substantial variance reduction is achieved compared to the standard simulation approach. We investigate the accuracy for a realistic portfolio of exchange options, interest rate and cross-currency swaps under a fully calibrated 10-factor model.

On Coherent Risk Measures Induced by Convex Risk Measures

We study the close relationship between coherent risk measures and convex risk measures. Inspired by the obtained results, we propose a class of coherent risk measures induced by convex risk measures. The robust representation and minimization problem of the induced coherent risk measure are investigated. A new coherent risk measure, the Entropic Conditional Value-at-Risk (ECVaR), is proposed as a special case. We show how to apply the induced coherent risk measure to realistic portfolio selection problems. Finally, by comparing its out-of-sample performance with that of CVaR, entropic risk measure, as well as entropic value-at-risk, we carry out a series of empirical tests to demonstrate the practicality and superiority of the ECVaR measure in optimal portfolio selection.

Efficient randomized quasi-Monte Carlo methods for portfolio market risk

We consider the problem of simulating loss probabilities and conditional excesses for linear asset portfolios under the t-copula model. Although in the literature on market risk management there are papers proposing efficient variance reduction methods for Monte Carlo simulation of portfolio market risk, there is no paper discussing combining the randomized quasi-Monte Carlo method with variance reduction techniques. In this paper, we combine the randomized quasi-Monte Carlo method with importance sampling and stratified importance sampling. Numerical results for realistic portfolio examples suggest that replacing pseudorandom numbers (Monte Carlo) with quasi-random sequences (quasi-Monte Carlo) in the simulations increases the robustness of the estimates once we reduce the effective dimension and the impact of the non-smoothness of the integrands.

Convex risk measures based on generalized lower deviation and their applications

Considering the implementability and the properties that a reasonable and realistic risk measure should satisfy, we propose a new class of risk measures based on generalized lower deviation with respect to a chosen benchmark. Besides convexity and monotonicity, our new risk measure can reflect the investor's degree of risk aversion as well as the fat-tail phenomenon of the loss distribution with the help of different benchmarks and weighted functions. Based on the new risk measure, we establish a realistic portfolio selection model taking market frictions into account. To examine the influence of the benchmarks and weighted functions on the optimal portfolio and its performance, we carry out a series of empirical studies in Chinese stock markets. Our in-sample and out-of-sample results show that the new risk measure and the corresponding portfolio selection model can reflect the investor's risk averse attitude and the impact of different trading constraints. Most importantly, with the new risk measure we can obtain an optimal portfolio which is more robust and superior to the optimal portfolios obtained with the traditional expected shortfall risk measures.