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This chapter presents a multi-criteria portfolio model with the expected return as a performance measure and the expected worst-case return as a risk measure. The problems are formulated as a single-objective linear program, as a bi-objective linear program, and as a triple-objective mixed integer program. The problem objective is to allocate the wealth on different securities to optimize the portfolio return. The portfolio approach has allowed the two popular financial engineering percentile measures of risk, value-at-risk (VaR) and conditional value-at-risk (CVaR) to be applied. The decision-maker can assess the value of portfolio return, the risk level, and the number of assets, and can decide how to invest in a real-life situation comparing with ideal (optimal) portfolio solutions. The concave efficient frontiers illustrate the trade-off between the conditional value-at-risk and the expected return of the portfolio. Numerical examples based on historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided. The computational experiments prove that both proposed linear and mixed integer programming approaches provide the decision-maker with a simple tool for evaluating the relationship between the expected and the worst-case portfolio return.

It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value‐at‐risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models.

Given the rising need for measuring and controlling of financial risk as proposed in Basel II and Basel III Capital Adequacy Accords, trading risk assessment under illiquid market conditions plays an increasing role in banking and financial sectors, particularly in emerging financial markets. The purpose of this chapter is to investigate asset liquidity risk and to obtain a Liquidity-Adjusted Value at Risk (L-VaR) estimation for various equity portfolios. The assessment of L-VaR is performed by implementing three different asset liquidity models within a multivariate context along with GARCH-M method (to estimate expected returns and conditional volatility) and by applying meaningful financial and operational constraints. Using more than six years of daily return dataset of emerging Gulf Cooperation Council (GCC) stock markets, we find that under certain trading strategies, such as short selling of stocks, the sensitivity of L-VaR statistics are rather critical to the selected internal liquidity model in addition to the degree of correlation factors among trading assets. As such, the effects of extreme correlations (plus or minus unity) are crucial aspects to consider in selecting the most adequate internal liquidity model for economic capital allocation, especially under crisis condition and/or when correlations tend to switch sings. This chapter bridges the gap in risk management literatures by providing real-world asset allocation tactics that can be used for trading portfolios under adverse markets’ conditions. The approach to computing L-VaR has been arrived at through the application of three distinct liquidity models and the obtained results are used to draw conclusions about the relative liquidity of the diverse equity portfolios.

The aim of this paper is to fill a gap in the foreign‐exchange trading risk‐management literature and particularly from the perspective of emerging and illiquid markets, such as in the context of the Moroccan foreign‐exchange market.

This paper, demonstrates a constructive approach, for the management of trading risk exposure of foreign‐exchange securities, which takes into account proper adjustments for the illiquidity of both long and short trading positions. The approach is based on the renowned concept of value at risk (VaR) along with the innovation of a software tool utilizing matrix‐algebra and other optimization techniques.

Several case studies, on the Moroccan Dirham, were achieved with the objective of setting‐up a practical framework of trading risk measurement, management and control reports, in addition to the inception of a practical procedure for the calculation of optimum VaR limits structure.

In this work, the risk‐management procedures that are discussed will aid financial markets' participants, regulators and policymakers, operating within emerging economies, in founding sound and proactive policies to handle foreign‐exchange trading risk exposures. The document includes comprehensive theory, analyses sections, conclusions and recommendations, and full real‐world foreign‐exchange trading risk‐management reports.

Although a substantial literature has examined the statistical and economic meaning of VaR models, this article provides real‐world techniques and optimum asset allocation strategies that are useful for trading portfolios in emerging and illiquid financial markets. This is with the objective of setting‐up the basis of a proactive methodology/procedure for the measurement, management and control of foreign‐exchange exposures in the day‐to‐day trading operations.

The main objective of this paper is to analyze the dynamic volatility spillovers between the investor's behavioral biases, the macroeconomic instability factors and the value at risk of the US Fintech stock market before and during the COVID-19 pandemic.

The authors used the methodologies proposed by Diebold and Yilmaz (2012) and the wavelet approach.

The wavelet coherence results show that during the COVID-19 period, there was a strong co-movement among value at risk and each selected variables in the medium-run and the long-run scales. Diebold and Yilmaz's (2012) method proved that the total connectedness index raised significantly during the COVID-19 period. Moreover, the overconfidence bias and the financial stress index are the net transmitters, while the value at risk and herding behavior variables are the net receivers.

This study offers some important implications for investors and policymakers to explain the impact of the COVID-19 pandemic on the risk of Fintech industry.

The study findings might be useful for investors to better understand the time–frequency connectedness and the volatility spillover effects in the context of COVID-19 pandemic. Future research may deal with investors' ability of constructing portfolios with another alternative index like cryptocurrencies which seems to be a safer investment.

To the best of the authors' knowledge, this is the first study that relies on the continuous wavelet decomposition technique and spillover volatility to examine the connectedness between investor behavioral biases, uncertainty factors, and Value at Risk of US Fintech stock markets, while taking into account the recent COVID-19 pandemic.

The purpose of this article is to introduce a new method of estimating risk as an alternative to value at risk (VaR), drawing on the risk assessment literature in environmental science.

A commonly used and accepted measure of market risk is VaR, defined as the difference between initial portfolio value and a probabilistic lower bound B on the portfolio value at time T. To take account of situations where the portfolio value may fall below B prior to time T, an an alternative to VaR is proposed based on first passage time distributions.

It is argued that the resulting expected minimum portfolio value over the time frame T provides a clear alternative measure of market risk. Analytical expressions are obtained and numerical comparisons given when the distribution of portfolio returns is lognormal.

Analytical results are presented for lognormal distributions for returns. Results for other models can be easily obtained from simulation.

The new measure of risk recognizes that investors might be sensitive to risks of decline in the value of a portfolio at any time within a given time horizon, not just at the end of the anticipated period of investment. The expected minimum portfolio value measures the largest loss that is expected at some stage over that period.

A new measure of risk is presented that arises from literature on risk assessment in environmental science. It is complementary to VaR for assessing risk.

This chapter presents the survey of selected linear and mixed integer programming multi-objective portfolio optimization. The definitions of selected percentile risk measures are presented. Some contrasts and similarities of the different types of portfolio formulations are drawn out. The survey of multi-criteria methods devoted to portfolio optimization such as weighting approach, lexicographic approach, and reference point method is also presented. This survey presents the nature of the multi-objective portfolio problems focuses on a compromise between the construction of objectives, constraints, and decision variables in a portfolio and the problem complexity of the implemented mathematical models. There is always a trade-off between computational time and the size of an input data, as well as the type of mathematical programming formulation with linear and/or mixed integer variables.

Financial asset return series usually exhibit nonnormal characteristics such as high peaks, heavy tails and asymmetry. Traditional risk measures like standard deviation or variance are inadequate for nonnormal distributions. Value at Risk (VaR) is consistent with people's psychological perception of risk. The asymmetric Laplace distribution (ALD) captures the heavy-tailed and biased features of the distribution. VaR is therefore used as a risk measure to explore the problem of VaR-based asset pricing. Assuming returns obey ALD, the study explores the impact of high peaks, heavy tails and asymmetric features of financial asset return data on asset pricing.

A VaR-based capital asset pricing model (CAPM) was constructed under the ALD that follows the logic of the classical CAPM and derive the corresponding VaR-β coefficients under ALD.

ALD-based VaR exhibits a minor tail risk than VaR under normal distribution as the mean increases. The theoretical derivation yields a more complex capital asset pricing formula involving β coefficients compared to the traditional CAPM.The empirical analysis shows that the CAPM under ALD can reflect the β-return relationship, and the results are robust. Finally, comparing the two CAPMs reveals that the β coefficients derived in this paper are smaller than those in the traditional CAPM in 69–80% of cases.

The paper uses VaR as a risk measure for financial time series data following ALD to explore asset pricing problems. The findings complement existing literature on the effects of high peaks, heavy tails and asymmetry on asset pricing, providing valuable insights for investors, policymakers and regulators.

Recent literature discusses the persistence of skewness and tail risk in hedge fund returns. The aim of this paper is to suggest an alternative skewness measure, Azzalini's skewness parameter delta, which is derived as the normalized shape parameter from the skew‐normal distribution. The paper seeks to analyze the characteristics of this skewness measure compared with other indicators of skewness and to employ it in some typical risk and performance measurements.

The paper first provides an overview of the skew‐normal distribution and its mathematical formulation. Then it presents some empirical estimations of the skew‐normal distribution for hedge fund returns and discusses the characteristics of using delta with respect to classical skewness coefficients. Finally, it illustrates how delta can be used in risk management and in a performance measurement context.

The results highlight the advantages of Azzalini's skewness parameter delta, especially with regard to its interpretation. Delta has a limpid financial interpretation as a skewness shock on normally distributed returns. The paper also derives some important characteristics of delta, including that it is more stable than other measures of skewness and inversely related to popular risk measures such as the value‐at‐risk (VaR) and the conditional value‐at‐risk (CVaR).

The contribution of the paper is to apply the skew‐normal distribution to a large sample of hedge fund returns. It also illustrates that using Azzalini's skewness parameter delta as a skewness measure has some advantages over classical skewness coefficients. The use of the skew‐normal and related distributions is a relatively new, but growing, field in finance and not much has been published on the topic. Skewness itself, however, has been the subject of a great deal of research. Therefore, the results contribute to three fields of research: skewed distributions, risk measurement, and hedge fund performance.

It is the purpose of this article to empirically test the risk parameters for larger foreign‐exchange portfolios and to suggest real‐world policies and procedures for the management of market risk with the aid of value at risk (VaR) methodology. The aim of this article is to fill a void in the foreign‐exchange risk management literature and particularly for large portfolios that consist of long and short positions of multi‐currencies of numerous developed and emerging economies.

In this article, a constructive approach for the management of risk exposure of foreign‐exchange securities is demonstrated, which takes into account proper adjustments for the illiquidity of both long and short trading/investment positions. The approach is based on the renowned concept of VaR along with the innovation of a software tool utilizing matrix‐algebra and other optimization techniques. Real‐world examples and reports of foreign‐exchange risk management are presented for a sample of 40 distinctive countries.

A number of realistic case studies are achieved with the objective of setting‐up a practical framework for market risk measurement, management and control reports, in addition to the inception of a practical procedure for the calculation of optimum VaR limits structure. The attainment of the risk management techniques is assessed for both long and short proprietary trading and/or active investment positions.

The main contribution of this article is the introduction of a practical risk approach to managing foreign‐exchange exposure in large proprietary trading and active investment portfolios. Key foreign‐exchange risk management methods, rules and procedures that financial entities, regulators and policymakers should consider in setting‐up their foreign‐exchange risk management objectives are examined and adapted to the specific needs of a model of 40 distinctive economies.

Although a substantial literature has examined the statistical and economic meaning of VaR models, this article provides real‐world techniques and optimum asset allocation strategies for large foreign‐exchange portfolios in emerging and developed financial markets. This is with the objective of setting‐up the basis of a methodology/procedure for the measurement, management and control of foreign‐exchange exposures in the day‐to‐day trading and/or asset management operations.