Risks, Volume 9, Issue 4 (April 2021) – 22 articles

The central issue of this paper is analysis and resulting proposals to help unsophisticated pension participants achieve pension portfolios that match their level of risk aversion when there is a large amount of unexplained heterogeneity in risk aversion. Target date funds are commonly used as the default investment in defined contribution plans in the U.S., UK and other countries. These funds recognize that individuals usually should hold less risky investment portfolios as their expected retirement date approaches because their ability to bear financial market risk declines as the time horizon decreases. However, these funds do not account for differences in risk aversion among people with the same target date. Empirical studies find large amounts of unexplained heterogeneity in risk aversion. Target date funds cannot deal with this issue simply by sorting people into demographic groupings, other than age, that are known to affect risk aversion, such as gender. Financial education can help people do a better job of managing financial market risk in their pension portfolios, but we argue that it is unreasonable to expect millions of pension participants to attain advanced levels of financial literacy. This paper considers three innovations in target date funds that can help individual pension participants do a better job of managing financial market risk. The analysis can be applied to other situations where defaults are used for investing pension participants’ portfolios. The paper suggests new lines of research relating to individual differences in risk aversion. Full article

The aim of this article is to use multiple discriminant analysis (MDA) and logit models to assess the risk of bankruptcy of companies in the Polish tourism sector in the crisis conditions caused by the COVID-19 pandemic. A review of the literature is used to select models appropriate to analyze the risk of bankruptcy of tourism enterprises listed on the Warsaw Stock Exchange (WSE). The data are from half-year financial statements (the first half of 2019 and 2020, respectively). The obtained results are compared with the current values of the Altman EM-score model and selected financial ratios. An analysis allowed the estimation of the risk of bankruptcy of enterprises from the tourism sector in Poland as well as the assessment of the prognostic value of these models in the tourism sector and the risk of a collapse of this market in Poland. The article fills the research gap created by the negligible use of solvency analysis of the tourism sector and constitutes the basis for estimating the risk of collapse of the tourism sector in a crisis situation. Full article

A new method to estimate longevity risk based on the kernel estimation of the extreme quantiles of truncated age-at-death distributions is proposed. Its theoretical properties are presented and a simulation study is reported. The flexible yet accurate estimation of extreme quantiles of age-at-death conditional on having survived a certain age is fundamental for evaluating the risk of lifetime insurance. Our proposal combines a parametric distributions with nonparametric sample information, leading to obtain an asymptotic unbiased estimator of extreme quantiles for alternative distributions with different right tail shape, i.e., heavy tail or exponential tail. A method for estimating the longevity risk of a continuous temporary annuity is also shown. We illustrate our proposal with an application to the official age-at-death statistics of the population in Spain. Full article

Although a large number of mortality projection models have been proposed in the literature, relatively little attention has been paid to a formal assessment of the effect of model uncertainty. In this paper, we construct a Bayesian framework for embedding more than one mortality projection model and utilise the finite mixture model concept to allow for the blending of model structures. Under this framework, the varying features of different model structures can be exploited jointly and coherently to have a more detailed description of the underlying mortality patterns. We show that the proposed Bayesian approach performs well in fitting and forecasting Japanese mortality. Full article

The objective of this research was to demonstrate the (nonlinear) risks of sovereign insolvency and explore the applicability of stochastic modeling in public debt management, given a structural economic model of stochastic government debt dynamics. A stochastic optimal control model was developed to model public debt dynamics based on the debt accounting identity, where the interest-growth differential obeys a continuous random process. This stochasticity represents both the interest rate risk of public debt and the variability of the growth rate of the nominal Gross Domestic Product combined. The optimal fiscal policy was analyzed in terms of the model parameters. The model was simulated, and results were visualized. The insolvency risk was demonstrated by examining the variance of the optimal process. The model was amended with hidden credit risk premia and fiscal multipliers, which forces the debt dynamics to be nonlinear in the debt ratio. The results, on the other hand, confirm that the volatility of the interest-growth differential is crucial in terms of sovereign solvency and in addition, it demonstrates the large risks stemming from the multiplier effect, which underlines the need for prudent debt management and fiscal policy. Full article

The main aim of this article is to examine the inter-relationships among the top cryptocurrencies on the crypto stock market in the presence and absence of the COVID-19 pandemic. The nine chosen cryptocurrencies are Bitcoin, Ethereum, Ripple, Litecoin, Eos, BitcoinCash, Binance, Stellar, and Tron and their daily closing price data are captured from coinmarketcap over the period from 13 September 2017 to 21 September 2020. All of the cryptocurrencies are integrated of order 1 i.e., I(1). There is strong evidence of a long-run relationship between Bitcoin and altcoins irrespective of whether it is pre-pandemic or pandemic period. It has also been found that these cryptocurrencies’ prices and their inter-relationship are resilient to the pandemic. It is recommended that when the investors create investment plans and strategies they may highly consider Bitcoin and altcoins jointly as they give sustainability and resilience in the long run against the geopolitical risks and even in the tough time of the COVID-19 pandemic. Full article

In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company’s surplus process is assumed to follow a Brownian motion with drift, and the reinsurance price is modelled by a continuous-time Markov chain with two states. The presence of regime-switching substantially complicates the optimal reinsurance problem, as the surplus-independent strategies turn out to be suboptimal. We develop a recursive approach that allows to represent a solution to the corresponding Hamilton–Jacobi–Bellman (HJB) equation and the corresponding reinsurance strategy as the unique limits of the sequence of solutions to ordinary differential equations and their first- and second-order derivatives. Via Ito’s formula, we prove the constructed function to be the value function. Two examples illustrate the recursive procedure along with a numerical approach yielding the direct solution to the HJB equation. Full article

Choosing solutions under risk and uncertainty requires the consideration of several factors. One of the main factors in choosing a solution is modeling the decision maker’s attitude to risk. The expected utility theory was the first approach that allowed to correctly model various nuances of the attitude to risk. Further research in this area has led to the emergence of even more effective approaches to solving this problem. Currently, the most developed theory of choice with respect to decisions under risk conditions is the cumulative prospect theory. This paper presents the development history of various extensions of the original expected utility theory, and the analysis of the main properties of the cumulative prospect theory. The main result of this work is a fuzzy version of the prospect theory, which allows handling fuzzy values of the decisions (prospects). The paper presents the theoretical foundations of the proposed version, an illustrative practical example, and conclusions based on the results obtained. Full article

The appropriate choice of a threshold level, which separates the tails of the probability distribution of a random variable from its middle part, is considered to be a very complex and challenging task. This paper provides an empirical study on various methods of the optimal tail selection in risk measurement. The results indicate which method may be useful in practice for investors and financial and regulatory institutions. Some methods that perform well in simulation studies, based on theoretical distributions, may not perform well when real data are in use. We analyze twelve methods with different parameters for forty-eight world indices using returns from the period of 2000–Q1 2020 and four sub-periods. The research objective is to compare the methods and to identify those which can be recognized as useful in risk measurement. The results suggest that only four tail selection methods, i.e., the Path Stability algorithm, the minimization of the Asymptotic Mean Squared Error approach, the automated Eyeball method with carefully selected tuning parameters and the Hall single bootstrap procedure may be useful in practical applications. Full article

This work aims to verify an authorial forecasting method from a system of interdependent equations, which is based on empirical equations of the structural form and is mainly intended for econometric micromodels. The prediction procedure will be analogous to the so-called chain prediction that is used for recursive models. The difference—compared with the prediction from a recursive model—entails the necessity of using one of the reduced-form empirical equations to begin the procedure of constructing a sequence of forecasts from successive structural-form empirical equations. The research results presented above indicate that the above-proposed iterative forecasting method from structural-form equations of a system of interdependent equations guarantees synchronization of forecasts as part of a closed cycle of relations. A different number of iterations is required to obtain convergent forecasts. It can be noticed that the further ahead the forecasted period is, the more iterations should be carried out to obtain convergent forecasts. Small business management with the use of forecasting can be done remotely. Rapid updates of statistical information will require cloud-based communication. Completion of data in a cloud will allow, on one hand, accurate assessment of expired forecasts and, on the other, to update the predictor equations. This can be carried out at any place with Internet access. Full article

The new class of matrix-tilted Archimedean copulas is introduced. It combines properties of Archimedean and elliptical copulas by introducing a tilting matrix in the stochastic representation of Archimedean copulas, similar to the Cholesky factor for elliptical copulas. Basic properties of this copula construction are discussed and a further extension outlined. Full article

We evaluate the impact of timing on decision outcomes when both the timing and the relevant decision are chosen under uncertainty. Sports betting provides the testing ground, as we exploit an original dataset containing more than one million online bets on games of the Italian Major Soccer League. We find that individuals perform systematically better when they place their bets farther away from the game day. The better performance of early bettors holds controlling for (time-invariant) unobservable ability, learning during the season, and timing of the odds. We attribute this result to the increase of noisy information on game day, which hampers the capacity of late (non-professional) bettors to use very simple prediction methods, such as team rankings or last game results. We also find that more successful bettors tend to bet in advance, focus on a smaller set of events, and prefer games associated with smaller betting odds. Full article

The broadly used pay-as-you-go (PAYG) pension system is intrinsically wrong. The essence of the problem is that the PAYG system distributes the yield of raising children, i.e., of human capital investment (which is essentially the pension contribution), in such a way that it disregards the extent to which individuals have contributed to this, and even whether it has occurred at all. This error can be corrected if we take the pension contribution to be the yield on an investment of human capital, and as such use this to pay back the costs and expenses of the raising of the contribution payer—overall to those who paid these costs and expenses at the time. Accordingly, the central question of my study is whether it is possible to construct a consistent pension system based on the above foundations, and how my ideas may be inserted into the Diamond–Samuelson model. The method of the study was logical analysis and the construction of a theoretical mathematical model. The results of the study show that it is possible to construct a public pension system that operates according to a different logic than today’s system, a system which is free from the effects of demographic fluctuations, which does not motivate the refusal to have children, and which will remain self-sufficient under all circumstances. The study achieves this by presenting a possible pension system of this kind in detail. Via the suitable modification of the Diamond–Samuelson model, I have succeeded in showing that the pension system I am proposing increases the willingness to have children up to the social optimum, in contrast to the fully (but traditionally) funded and PAYG systems. This system currently only exists in theory and may be regarded as a major theoretical innovation, which naturally has certain (although not particularly extensive) antecedents. Its introduction could enable the resolution of the contradictions of existing pension systems and could also provide a solution to the as yet unsolved problem of the increasingly expensive regeneration of human capital, and as such, its potential practical implications are immeasurable. Full article

The aim of this paper is to present life expectancy of both genders depending on their income and to determine the impact of a possible regularity on the state pension policy. The study was based on the income of pensioners in Poland (over 5 million people receiving old-age pension). The results obtained made it possible to formulate several important conclusions: the rich live longer; the impact of income on life expectancy is much stronger among men than women; and with age, income has less and less impact on life expectancy. Consequently, in the capital model that is in force in Poland, the state should take this fact into account in its pension policy when calculating the amount of the benefit. Full article

Modern management means making managerial decisions in many situations—including the administrative ordering of matters of a bankrupt enterprise. The situation in which the court approves the opening of bankruptcy proceedings is strictly regulated by law. This does not mean, however, that such a decision is made under conditions of certainty as to its consequences. The risk of making a wrong decision has significant consequences for everyone who is interested in it (the bankrupt company, its partners, employees, banks, the tax office). The purpose of this article is to explain the importance and significance of the various types of information that are used to reliably assess the value of a failing enterprise’s assets. The information of individual types is analyzed in the decision-making process which leads to the right decision on whether to start bankruptcy proceedings. Therefore, in the theoretical part, the authors prepare a list of types of information used in the mentioned process. Then the authors present the results of a survey (103 specialists in the field of bankruptcy), which allows to assess the real meaning of information of individual types. The main contribution for which the present paper is responsible is the description of the verified tool which functioned in the form of the survey that was applied in the study and the result arising from conducting it. This survey was used to achieve the main objective that was focused on constructing the hierarchy of significance of different types of information relating to the risk of conducting bankruptcy proceedings. The main findings show that in general insolvency specialists prioritize the information (financial and also not financial) not originating from financial reporting. Full article

The COVID-19 virus has hit the economy around the world. In Poland, SMEs have the greatest problems with doing business. Border blockades and the quarantine for enterprises in virtually all industries throughout Poland greatly complicated the supply systems and the inventory management process. Up to now, SMEs have acted in group purchasing organizations to improve their competitive position. This form of activity also positively affects their financial security. Therefore, in this paper, the inventory management among this group of companies during the COVID-19 pandemic was analyzed. The purpose of the paper was to show how inventory management strategies changed during the COVID-19 pandemic in SMEs operating in industry GPOs. The analysis was carried out on a group of 88 Polish commercial enterprises operating in purchasing groups. The research period covered the years 2017–2019 and March–June 2020. The research showed a change in inventory management strategy in SMEs during the pandemic time of COVID-19. For the first four months, managers of enterprises tried to pursue a conservative policy and to accumulate stocks in the event of a shortage of supplies. This article also presents the form of security that was applied for SMEs operating in group purchasing organizations (GPOs) to avoid forced downtime caused by the COVID-19 pandemic. Full article

The COVID-19 pandemic has shown how important it is to prepare one’s own financial budget for the unexpected loss of income. In this dimension, the financial education of the society plays an invaluable role. It allows us to account for events that may adversely affect personal finances in our budget management decisions. Therefore, the aim of the article is to check whether households with a higher level of financial and debt literacy have better management skills from the perspective of a household’s budget, which in the face of a crisis reduces the risk of individuals not paying their liabilities. Thus, at the turn of June and July 2020, we conducted surveys among 1300 Polish citizens. Using the multinomial logistic regression, we show that people with a higher financial and debt literacy are less affected by overindebtedness. During the crisis, people who have a higher debt literacy are better prepared to manage credit liabilities; in this situation, financial literacy is less important. In addition, the type of credit experience turned out to be significant. Respondents who have experience with consumer loans (potentially high-margin products) are more likely to have debt repayment problems than those with mortgage loans experiences. Full article

This paper considers a mean-variance portfolio selection problem when the stock price has a 3/2 stochastic volatility in a complete market. Specifically, we assume that the stock price and the volatility are perfectly negative correlated. By applying a backward stochastic differential equation (BSDE) approach, closed-form expressions for the statically optimal (time-inconsistent) strategy and the value function are derived. Due to time-inconsistency of mean variance criterion, a dynamic formulation of the problem is presented. We obtain the dynamically optimal (time-consistent) strategy explicitly, which is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Finally, we provide numerical studies to show the impact of main model parameters on the efficient frontier and illustrate the differences between the two optimal wealth processes. Full article

Protecting against unexpected yield curve, inflation, and longevity shifts are some of the most critical issues institutional and private investors must solve when managing post-retirement income benefits. This paper empirically investigates the performance of alternative immunization strategies for funding targeted multiple liabilities that are fixed in timing but random in size (inflation-linked), i.e., that change stochastically according to consumer price or wage level indexes. The immunization procedure is based on a targeted minimax strategy considering the M-Absolute as the interest rate risk measure. We investigate to what extent the inflation-hedging properties of ILBs in asset liability management strategies targeted to immunize multiple liabilities of random size are superior to that of nominal bonds. We use two alternative datasets comprising daily closing prices for U.S. Treasuries and U.S. inflation-linked bonds from 2000 to 2018. The immunization performance is tested over 3-year and 5-year investment horizons, uses real and not simulated bond data and takes into consideration the impact of transaction costs in the performance of immunization strategies and in the selection of optimal investment strategies. The results show that the multiple liability immunization strategy using inflation-linked bonds outperforms the equivalent strategy using nominal bonds and is robust even in a nearly zero interest rate scenario. These results have important implications in the design and structuring of ALM liability-driven investment strategies, particularly for retirement income providers such as pension schemes or life insurance companies. Full article

Nepotism and cronyism are forms of favoritism towards certain people in the workplace. For this reason, they constitute a problem for organization managers, ethicists and psychologists. Identifying the impact of COVID-19 pandemic on the increase of nepotism and cronyism may provide a basis for organizations to assess their extent and to take possible measures to prevent their negative effects. At the same time, the research presented in the article may provide a basis for further research work related to nepotism and cronyism at the times of other threats, different from the pandemic. The aim of the article is to examine the impact of the COVID-19 pandemic on growing acceptance for nepotism and cronyism in Polish enterprises. Qualitative and quantitative methods have been included in the conducted research. Qualitative study aimed at improving knowledge of nepotism and cronyism and the impact of the COVID-19 pandemic on these phenomena, followed by a quantitative study conducted in order to verify the information obtained in the qualitative study. This research has demonstrated that Nepotism and cronyism in the workplace, are phenomenon that are basically evaluated negatively. They adversely influences social and economic development, but the impact of COVID-19 pandemic on nepotism and cronyism is not significant. Full article

This article describes the techniques employed in the production of a synthetic dataset of driver telematics emulated from a similar real insurance dataset. The synthetic dataset generated has 100,000 policies that included observations regarding driver’s claims experience, together with associated classical risk variables and telematics-related variables. This work is aimed to produce a resource that can be used to advance models to assess risks for usage-based insurance. It follows a three-stage process while using machine learning algorithms. In the first stage, a synthetic portfolio of the space of feature variables is generated applying an extended SMOTE algorithm. The second stage is simulating values for the number of claims as multiple binary classifications applying feedforward neural networks. The third stage is simulating values for aggregated amount of claims as regression using feedforward neural networks, with number of claims included in the set of feature variables. The resulting dataset is evaluated by comparing the synthetic and real datasets when Poisson and gamma regression models are fitted to the respective data. Other visualization and data summarization produce remarkable similar statistics between the two datasets. We hope that researchers interested in obtaining telematics datasets to calibrate models or learning algorithms will find our work ot be valuable. Full article