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A simulation methodology is applied to the loan loss reserve process of an agricultural lender. Weaknesses of the point‐estimate approach to estimating loan loss reserves are addressed with a “bottom‐up” model. Modeling includes consideration of the producer’s and the lender’s diversification efforts. Implementation of this model will provide the lender a better understanding of the institution’s portfolio risk, as well as the credit risk associated with each loan. This study compares the lender’s loan loss estimates to a distribution of losses with associated probabilities. The comparative results could provide the lender a basis for setting probability levels for determining the regulatory required level of loan loss reserve.

This study aims to examine the theoretical foundations for multivariate portfolio optimization algorithms under illiquid market conditions. In this study, special emphasis is devoted to the application of a risk-engine, which is based on the contemporary concept of liquidity-adjusted value-at-risk (LVaR), to multivariate optimization of investment portfolios.

This paper examines the modeling parameters of LVaR technique under event market settings and discusses how to integrate asset liquidity risk into LVaR models. Finally, the authors discuss scenario optimization algorithms for the assessment of structured investment portfolios and present a detailed operational methodology for computer programming purposes and prospective research design with the backing of a graphical flowchart.

To that end, the portfolio/risk manager can specify different closeout horizons and dependence measures and calculate the necessary LVaR and resulting investable portfolios. In addition, portfolio managers can compare the return/risk ratio and asset allocation of obtained investable portfolios with different liquidation horizons in relation to the conventional Markowitz´s mean-variance approach.

The examined optimization algorithms and modeling techniques have important practical applications for portfolio management and risk assessment, and can have many uses within machine learning and artificial intelligence, expert systems and smart financial applications, financial technology (FinTech), and within big data environments. In addition, it provide key real-world implications for portfolio/risk managers, treasury directors, risk management executives, policymakers and financial regulators to comply with the requirements of Basel III best practices on liquidly risk.

The proposed optimization algorithms can aid in advancing portfolios selection and management in financial markets by assessing investable portfolios subject to meaningful operational and financial constraints. Furthermore, the robust risk-algorithms and portfolio optimization techniques can aid in solving some real-world dilemmas under stressed and adverse market conditions, such as the effect of liquidity when it dries up in financial and commodity markets, the impact of correlations factors when there is a switching in their signs and the integration of the influence of the nonlinear and non-normal distribution of assets’ returns in portfolio optimization and management.

I. INTRODUCTION A typical shortcoming of most current credit portfolio models is the lack of a stochastic modeling of risk factors, such as interest rates or credit spreads, during the revaluation process at the risk horizon. For example, fixed income instruments, such as bonds or loans, are revalued at the risk horizon using the current forward rates and (rating class specific) forward credit spreads for discounting future cash flows. Hence, the stochastic nature of the instrument's value in the future which results from changes in factors other than credit quality is ignored, and the riskiness of the credit portfolio at the risk horizon is underestimated. A further consequence is that correlations between changes of the debtor's default probability and changes of market risk factors and, hence, the exposure at default cannot be integrated into the credit portfolio model. This drawback is especially relevant for portfolios of defaultable market‐driven derivatives. One reason why risk factors not directly related to credit risk are neglected in most current credit portfolio models is that there is still no commonly accepted approach for modeling the credit quality of a debtor and the dependencies between the credit quality changes of different debtors. Hence, it might be over‐ambitious to incorporate correlations between market risk factors and credit quality changes. Even empirical evidence on the sign of the correlation remains inconclusive. Additionally, introducing stochastic market risk factors and modeling the correlation between these risk factors and credit quality changes would significantly increase the computational burden for calculating robust risk measures of credit portfolios.

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.

The purpose of this paper is to develop a prescriptive portfolio selection (PPS) model based on a compromise between the idea of “fast” and “slow” thinking proposed by Kahneman.

“Fast” thinking is effortless and comfortable for investors, while “slow” thinking may result in better performance. These two systems are related to the first two types of analysis in the decision theory: descriptive, normative and prescriptive analysis. However, to compromise between “fast” and “slow” thinking, “overconfidence” is used as a weighting parameter. A case study including a sample of 161 active investors in Tehran Stock Exchange (TSE) is provided. Moreover, the feasibility and optimality of the model are discussed.

Results show that the PPS recommendations are efficient with a shift from the mean-variance efficient frontier; investors prefer PPS portfolios over the advisor recommendations; and investors have no significant preference between PPS and their own expectations.

Two assumptions of this study include: first, investors follow their “fast” system of thinking by themselves. Second, the investors’ “slow” system of thinking is represented by advisor recommendations which are simple expected value of risk and return. Therefore, considering these two assumptions for any application is the main limitation of this study. Moreover, the authors did not have access to more investors in TSE or other financial markets.

This is the first study that includes overconfidence in modeling portfolio selection for the purpose of achieving a portfolio that has a reasonable performance and one that investors are comfortable with.

This research aims to demonstrate portfolio modeling, which leads to Sharia compliance in encountering crises because of COVID-19. The authors proposed modifying the Black–Litterman (BL) model adapted to the Sharia principle. The implementation of BL on Shariah-compliant stock data with capital asset pricing model (CAPM) requires adjustment because of the interest rate in the calculation. Thus, the objective of this study is to develop and evaluate the modified BL for Shariah-compliant stock portfolios in the financial crisis caused by the COVID-19 pandemic.

The Sharia-compliant asset pricing model (SCAPM) with the inflation rate was regarded as the new starting point in the BL model. This proposed model was implemented in Indonesia using monthly returns from the Jakarta Islamic Index (JII) list collected from February 2014 to June 2019. Furthermore, the portfolio performance of BL-SCAPM was compared with two reference portfolios, the mean-variance method and BL-CAPM.

The result presents that the portfolio performance of BL-SCAPM outperformed the MV and BL-CAPM. The impact of the Sharpe ratio of BL-SCAPM was more significant than the reference portfolio. The equal benefit was procured from both portfolios in July and August 2019. After the COVID-19 outbreak was officially declared in January 2020, the performance of BL-SCAPM was still above the BL. Despite a decline in portfolio value before and during the outbreak, the reference portfolio losses were higher than those of BL-SCAPM. Hence, this study manifested that BL-SCAPM outperformed the reference portfolio.

The results illustrate the empirical study which can be implemented for the Shariah-compliant stock market in Indonesia. By evaluating portfolio value on the COVID crisis for long investment, replacing CAPM with SCAPM in the BL model can transform the asset proportion. It decreased the portfolio loss during the crisis. Future research can be developed more from the open problems in this implementation to deliver the portfolio model into the Shariah framework with varied SCAPM in BL.

The attention to BL studies on portfolio building with Sharia-compliant stocks is rarely focused on the Islamic perspective. Hence, the novelty of this research is the idea of modifying the BL model with a Shariah starting point. More generally, this research enriches Shariah financial literacy regarding the stock market and, specifically, its implementation in the Indonesian stock market.

Stock selection models often use momentum and analysts’ expectation data. We find that earnings forecast revisions and direction of forecast revisions are more important than analysts’ forecasts in identifying mispriced securities. Investing with expectations data and momentum variables is consistent with maximizing the geometric mean and Sharpe ratio over the long run. Additional evidence is revealed that supports the use of multifactor models for portfolio construction and risk control. The anomalies literature can be applied in real-world portfolio construction in the U.S., international, and global equity markets during the 1998–2009 time period. Support exists for the use of tracking error at risk estimation procedures.

While perfection cannot be achieved in portfolio creation and modeling, the estimated model returns pass the Markowitz and Xu data mining corrections test and are statistically different from an average financial model that could have been used to select stocks and form portfolios. We found additional evidence to support the use of Arbitrage Pricing Theory (APT) and statistically-based and fundamentally-based multifactor models for portfolio construction and risk control. Markets are neither efficient nor grossly inefficient; statistically significant excess returns can be earned.

The purpose of this paper is to build an easy to implement, pragmatic and parsimonious yet accurate model to determine an exposure at default (EAD) distribution for CCL (contingent credit lines) portfolios.

Using an algorithm similar to the basic CreditRisk+ and Fourier Transforms, the authors arrive at a portfolio level probability distribution of usage.

The authors perform a simulation experiment which illustrates the convolution of two portfolio segments to derive an EAD distribution, chosen randomly from Moody's Default Risk Service (DRS) database of CCLs rated as of 12/31/2008, to derive an EAD distribution. The standard deviation of the usage distribution is found to decrease as we increase the number of puts used, but the mean value remains relatively stable, as the extreme points converge towards the mean to produce a shrinkage in the spread of the distribution. The authors also observe, for the sample portfolio, that an increase in the additional usage rate level also increases the volatility of the associated exposure distribution.

This model, in conjunction with internal bank financial institution research, can be used for banks' EAD estimation as mandated by Basel II for bank CCL portfolios, or implemented as part of a Solvency II process for insurers exposed to credit sensitive unfunded commitments. Apart from regulatory requirements, distributions of stochastic exposure generated can be inputs for different economic capital models and stress testing procedures used to capture an accurate risk profile of the portfolio, as well as providing better insights into the problem of managing liquidity risk for a portfolio of CCLs and similar exposures.

In‐spite of the large volume of CCLs in portfolios of financial institutions all (for commercial banks holding these as well as for insurance companies having analogous exposures), paucity of EAD models, unsuitability of external data and inconsistent internal data with partial draw‐downs have been a major challenge for risk managers as well as regulators in managing CCL portfolios.

The existing literature on the Black-Litterman (BL) model does not offer adequate guidance on how to generate investors’ views in an objective manner. Therefore, the purpose of this paper is to establish a generalized multivariate Vector Error Correction Model (VECM)/Vector Auto-Regressive (VAR)-Dynamic Conditional Correlation (DCC)/Asymmetric DCC (ADCC) framework, and applies it to generate objective views to improve the practicality of the BL model.

This paper establishes a generalized VECM/VAR-DCC/ADCC framework that can be utilized to model multivariate financial time series in general, and produce objective views as inputs to the BL model in particular. To test the VECM/VAR-DCC/ADCC preconditioned BL model’s practical utility, it is applied to a six-asset China portfolio (including one risk-free asset).

With dynamically optimized view confidence parameters, the VECM/VAR-DCC/ADCC preconditioned BL model offers clear advantage over the standard mean-variance method, and provides an automated portfolio optimization alternative to the classic BL approach.

The VECM/VAR-DCC/ADCC framework and its application in the BL model proposed by this paper provide an alternative approach to the classic BL method. Since all the view parameters, including estimated mean return vectors, conditional covariance matrices and pick matrices, are generated in the VECM/VAR and DCC/ADCC preconditioning stage, the model improves the objectiveness of the inputs to the BL stage. In conclusion, the proposed model offers a practical choice for automated portfolio balancing and optimization in a China context.

Without short-sales constraints, mean-variance (MV) and power-utility portfolios generated from historical data are often characterized by extreme expected returns, standard deviations, and weights. The result is usually attributed to estimation error. I argue that modeling error, that is, modeling the portfolio problem with just a budget constraint, plays a more fundamental role in determining the extreme solutions and that a more complete analysis of MV problems should include realistic constraints, estimates of the means based on predictive variables, and specific values of investors’ risk tolerances. Empirical evidence shows that investors who utilize MV analysis without imposing short-sales constraints, without employing estimates of the means based on predictive variables, and without specifying their risk tolerance miss out on remarkably remunerative investment opportunities.