The Solvency II Standard Formula, Linear Geometry, and Diversification*J. Risk Financial Manag.* **2017**, *10*(2), 11; doi:10.3390/jrfm10020011 - 18 May 2017**Abstract **

The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance

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The core of risk aggregation in the Solvency II Standard Formula is the so-called square root formula. We argue that it should be seen as a means for the aggregation of different risks to an overall risk rather than being associated with variance-covariance based risk analysis. Considering the Solvency II Standard Formula from the viewpoint of linear geometry, we immediately find that it defines a norm and therefore provides a homogeneous and sub-additive tool for risk aggregation. Hence, Euler’s Principle for the reallocation of risk capital applies and yields explicit formulas for capital allocation in the framework given by the Solvency II Standard Formula. This gives rise to the definition of *diversification functions*, which we define as monotone, subadditive, and homogeneous functions on a convex cone. Diversification functions constitute a class of models for the study of the aggregation of risk and diversification. The aggregation of risk measures using a diversification function preserves the respective properties of these risk measures. Examples of diversification functions are given by seminorms, which are monotone on the convex cone of non-negative vectors. Each ${L}^{p}$ norm has this property, and any scalar product given by a non-negative positive semidefinite matrix does as well. In particular, the Standard Formula is a diversification function and hence a risk measure that preserves homogeneity, subadditivity and convexity.
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A Risk Management Framework for Cloud Migration Decision Support*J. Risk Financial Manag.* **2017**, *10*(2), 10; doi:10.3390/jrfm10020010 - 22 April 2017**Abstract ****Keywords:** risk management framework; risk assessment; cloud migration; security; analytic hierarchy process (AHP); business value
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Capital Regulation, the Cost of Financial Intermediation and Bank Profitability: Evidence from Bangladesh*J. Risk Financial Manag.* **2017**, *10*(2), 9; doi:10.3390/jrfm10020009 - 17 April 2017**Abstract **

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In response to the recent global financial crisis, the regulatory authorities in many countries have imposed stringent capital requirements in the form of the BASEL III Accord to ensure financial stability. On the other hand, bankers have criticized new regulation on the ground

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In response to the recent global financial crisis, the regulatory authorities in many countries have imposed stringent capital requirements in the form of the BASEL III Accord to ensure financial stability. On the other hand, bankers have criticized new regulation on the ground that it would enhance the cost of funds for bank borrowers and deteriorate the bank profitability. In this study, we examine the impact of capital requirements on the cost of financial intermediation and bank profitability using a panel dataset of 32 Bangladeshi banks over the period from 2000 to 2015. By employing a dynamic panel generalized method of moments (GMM) estimator, we find robust evidence that higher bank regulatory capital ratios reduce the cost of financial intermediation and increase bank profitability. The results hold when we use equity to total assets ratio as an alternative measure of bank capital. We also observe that switching from BASEL I to BASEL II has no measurable impact on the cost of financial intermediation and bank profitability in Bangladesh. In the empirical analysis, we further observe that higher bank management and cost efficiencies are associated with the lower cost of financial intermediation and higher bank profitability. These results have important implications for bank regulators, academicians, and bankers.
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An Empirical Study on the Impact of Basel III Standards on Banks’ Default Risk: The Case of Luxembourg*J. Risk Financial Manag.* **2017**, *10*(2), 8; doi:10.3390/jrfm10020008 - 12 April 2017**Abstract **

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We study how the Basel III regulations, namely the Capital-to-Assets Ratio (CAR), the Net Stable Funding Ratio (NSFR) and the Liquidity Coverage Ratio (LCR), are likely to impact banks’ profitability (i.e., ROA), capital levels and default. We estimate historical series of the new

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We study how the Basel III regulations, namely the Capital-to-Assets Ratio (CAR), the Net Stable Funding Ratio (NSFR) and the Liquidity Coverage Ratio (LCR), are likely to impact banks’ profitability (i.e., ROA), capital levels and default. We estimate historical series of the new Basel III regulations for a panel of Luxembourgish banks for a period covering 2003q2–2011q3. We econometrically investigate whether historical LCR and NSFR components, as well as CAR positions are able to explain the variation in a measure of a bank’s default risk (approximated by Z-score) and how these effects make their way through banks’ ROA and CAR.We find that the liquidity regulations induce a decrease in average probabilities of default. We find that the liquidity regulation focusing on maturity mismatches (i.e., NSFR) induces a decrease in average probabilities of default. Conversely, the impact on banks’ profitability is less clear-cut; what seems to matter is banks’ funding structure rather than the characteristics of the portfolio of assets. Additionally, we use a model of bank behavior to simulate the banks’ optimal adjustments of their balance sheets as if they had to adhere to the regulations starting in 2003q2. Then, we predict, using our preferred econometric model and based on the simulated data, the banks’ Z-score and ROA. The simulation exercise suggests that basically all banks would have seen a decrease in their default risk during a crisis episode if they had previously adhered to Basel III.
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On the Power and Size Properties of Cointegration Tests in the Light of High-Frequency Stylized Facts*J. Risk Financial Manag.* **2017**, *10*(1), 7; doi:10.3390/jrfm10010007 - 7 February 2017**Abstract **

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This paper establishes a selection of stylized facts for high-frequency cointegrated processes, based on one-minute-binned transaction data. A methodology is introduced to simulate cointegrated stock pairs, following none, some or all of these stylized facts. AR(1)-GARCH(1,1) and MR(3)-STAR(1)-GARCH(1,1) processes contaminated with reversible and

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This paper establishes a selection of stylized facts for high-frequency cointegrated processes, based on one-minute-binned transaction data. A methodology is introduced to simulate cointegrated stock pairs, following none, some or all of these stylized facts. AR(1)-GARCH(1,1) and MR(3)-STAR(1)-GARCH(1,1) processes contaminated with reversible and non-reversible jumps are used to model the cointegration relationship. In a Monte Carlo simulation, the power and size properties of ten cointegration tests are assessed. We find that in high-frequency settings typical for stock price data, power is still acceptable, with the exception of strong or very frequent non-reversible jumps. Phillips–Perron and PGFF tests perform best.
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Modeling NYSE Composite US 100 Index with a Hybrid SOM and MLP-BP Neural Model*J. Risk Financial Manag.* **2017**, *10*(1), 6; doi:10.3390/jrfm10010006 - 5 February 2017**Abstract **

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Neural networks are well suited to predict future results of time series for various data types. This paper proposes a hybrid neural network model to describe the results of the database of the New York Stock Exchange (NYSE). This hybrid model brings together

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Neural networks are well suited to predict future results of time series for various data types. This paper proposes a hybrid neural network model to describe the results of the database of the New York Stock Exchange (NYSE). This hybrid model brings together a self organizing map (SOM) with a multilayer perceptron with back propagation algorithm (MLP-BP). The SOM aims to segment the database into different clusters, where the differences between them are highlighted. The MLP-BP is used to construct a descriptive mathematical model that describes the relationship between the indicators and the closing value of each cluster. The model was developed from a database consisting of the NYSE Composite US 100 Index over the period of 2 April 2004 to 31 December 2015. As input variables for neural networks, ten technical financial indicators were used. The model results were fairly accurate, with a mean absolute percentage error varying between 0.16% and 0.38%.
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Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors*J. Risk Financial Manag.* **2017**, *10*(1), 5; doi:10.3390/jrfm10010005 - 2 February 2017**Abstract **

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We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in Kamdem (2005) and are present also in at least thirty other papers referencing it, including the

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We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in Kamdem (2005) and are present also in at least thirty other papers referencing it, including the recent survey by Nadarajah et al. (2014) on estimation methods for expected shortfall. In particular, we show that the correction we provide in the popular multivariate Student t setting eliminates understatement of expected shortfall by a factor varying from at least four to more than 100 across different tail quantiles and degrees of freedom. As such, the resulting economic impact in ﬁnancial risk management applications could be signiﬁcant. We further correct such errors encountered also in closely related results in Kamdem (2007 and 2009) for mixtures of elliptical distributions. More generally, our ﬁndings point to the extra scrutiny required when deploying new methods for expected shortfall estimation in practice.
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Determination of the Optimal Retention Level Based on Different Measures*J. Risk Financial Manag.* **2017**, *10*(1), 4; doi:10.3390/jrfm10010004 - 25 January 2017**Abstract **

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This paper deals with the optimal retention level under four competitive criteria: survival probability, expected profit, variance and expected shortfall of the insurer’s risk. The aggregate claim amounts are assumed to be distributed as compound Poisson, and the individual claim amounts are distributed

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This paper deals with the optimal retention level under four competitive criteria: survival probability, expected profit, variance and expected shortfall of the insurer’s risk. The aggregate claim amounts are assumed to be distributed as compound Poisson, and the individual claim amounts are distributed exponentially. We present an approach to determine the optimal retention level that maximizes the expected profit and the survival probability, whereas minimizing the variance and the expected shortfall of the insurer’s risk. In the decision making process, we concentrate on multi-attribute decision making methods: the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) methods with their extended versions. We also provide comprehensive analysis for the determination of the optimal retention level under both the expected value and standard deviation premium principles.
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Capital Structure Arbitrage under a Risk-Neutral Calibration*J. Risk Financial Manag.* **2017**, *10*(1), 3; doi:10.3390/jrfm10010003 - 19 January 2017**Abstract **

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By reinterpreting the calibration of structural models, a reassessment of the importance of the input variables is undertaken. The analysis shows that volatility is the key parameter to any calibration exercise, by several orders of magnitude. To maximize the sensitivity to volatility, a

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By reinterpreting the calibration of structural models, a reassessment of the importance of the input variables is undertaken. The analysis shows that volatility is the key parameter to any calibration exercise, by several orders of magnitude. To maximize the sensitivity to volatility, a simple formulation of Merton’s model is proposed that employs deep out-of-the-money option implied volatilities. The methodology also eliminates the use of historic data to specify the default barrier, thereby leading to a full risk-neutral calibration. Subsequently, a new technique for identifying and hedging capital structure arbitrage opportunities is illustrated. The approach seeks to hedge the volatility risk, or vega, as opposed to the exposure from the underlying equity itself, or delta. The results question the efficacy of the common arbitrage strategy of only executing the delta hedge.
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Acknowledgement to Reviewers of the *Journal of Risk and Financial Management* in 2016*J. Risk Financial Manag.* **2017**, *10*(1), 2; doi:10.3390/jrfm10010002 - 10 January 2017**Abstract **
The editors of the *Journal of Risk and Financial Management *would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...]
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Portfolio Optimization and Mortgage Choice*J. Risk Financial Manag.* **2017**, *10*(1), 1; doi:10.3390/jrfm10010001 - 3 January 2017**Abstract **

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This paper studies the optimal mortgage choice of an investor in a simple bond market with a stochastic interest rate and access to term life insurance. The study is based on advances in stochastic control theory, which provides analytical solutions to portfolio problems

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This paper studies the optimal mortgage choice of an investor in a simple bond market with a stochastic interest rate and access to term life insurance. The study is based on advances in stochastic control theory, which provides analytical solutions to portfolio problems with a stochastic interest rate. We derive the optimal portfolio of a mortgagor in a simple framework and formulate stylized versions of mortgage products offered in the market today. This allows us to analyze the optimal investment strategy in terms of optimal mortgage choice. We conclude that certain extreme investors optimally choose either a traditional fixed rate mortgage or an adjustable rate mortgage, while investors with moderate risk aversion and income prefer a mix of the two. By matching specific investor characteristics to existing mortgage products, our study provides a better understanding of the complex and yet restricted mortgage choice faced by many household investors. In addition, the simple analytical framework enables a detailed analysis of how changes to market, income and preference parameters affect the optimal mortgage choice.
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The Effect of Monitoring Committees on the Relationship between Board Structure and Firm Performance*J. Risk Financial Manag.* **2016**, *9*(4), 14; doi:10.3390/jrfm9040014 - 5 December 2016**Abstract **

The purpose of this study is to investigate the impact of board structure on the performance of French firms in the presence of several monitoring committees. We studied 80 publicly listed French firms spanning from 2001 to 2013. We concluded that large board

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The purpose of this study is to investigate the impact of board structure on the performance of French firms in the presence of several monitoring committees. We studied 80 publicly listed French firms spanning from 2001 to 2013. We concluded that large board size has a negative effect on market performance. While large board size in combination with the existence of at least three committees enhances accounting performance and does not have any impact on market performance, the existence of a board dominated by independent directors with the presence of at least three committees seems to have only a negative impact on accounting performance. Our findings indicate that monitoring committees are beneficial for shareholders only for corporations with a large board size.
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Credit Scoring by Fuzzy Support Vector Machines with a Novel Membership Function*J. Risk Financial Manag.* **2016**, *9*(4), 13; doi:10.3390/jrfm9040013 - 7 November 2016**Abstract **

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Due to the recent financial crisis and European debt crisis, credit risk evaluation has become an increasingly important issue for financial institutions. Reliable credit scoring models are crucial for commercial banks to evaluate the financial performance of clients and have been widely studied

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Due to the recent financial crisis and European debt crisis, credit risk evaluation has become an increasingly important issue for financial institutions. Reliable credit scoring models are crucial for commercial banks to evaluate the financial performance of clients and have been widely studied in the fields of statistics and machine learning. In this paper a novel fuzzy support vector machine (SVM) credit scoring model is proposed for credit risk analysis, in which fuzzy membership is adopted to indicate different contribution of each input point to the learning of SVM classification hyperplane. Considering the methodological consistency, support vector data description (SVDD) is introduced to construct the fuzzy membership function and to reduce the effect of outliers and noises. The SVDD-based fuzzy SVM model is tested against the traditional fuzzy SVM on two real-world datasets and the research results confirm the effectiveness of the presented method.
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The Design and Risk Management of Structured Finance Vehicles*J. Risk Financial Manag.* **2016**, *9*(4), 12; doi:10.3390/jrfm9040012 - 28 October 2016**Abstract **

Special investment vehicles (SIVs), extremely popular financial structures for the creation of highly-rated tranched securities, experienced spectacular demise in the 2007-2008 financial crisis. These financial vehicles epitomize the shadow banking sector, characterized by high leverage, undiversified asset pools, and long-dated assets supported by

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Special investment vehicles (SIVs), extremely popular financial structures for the creation of highly-rated tranched securities, experienced spectacular demise in the 2007-2008 financial crisis. These financial vehicles epitomize the shadow banking sector, characterized by high leverage, undiversified asset pools, and long-dated assets supported by short-term debt, thus bearing material rollover risk on their liabilities which led to defeasance. This paper models these vehicles, and shows that imposing leverage risk control triggers can be optimal for all capital providers, though they may not always be appropriate. The efficacy of these risk controls varies depending on anticipated asset volatility and fire-sale discounts on defeasance. Despite risk management controls, we show that a high failure rate is inherent in the design of these vehicles, and may be mitigated to some extent by including contingent capital provisions in the ex-ante covenants. Post the recent subprime financial crisis, we inform the creation of safer SIVs in structured finance, and propose avenues of mitigating risks faced by senior debt through deleveraging policies in the form of leverage risk controls and contingent capital.
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Portfolios Dominating Indices: Optimization with Second-Order Stochastic Dominance Constraints vs. Minimum and Mean Variance Portfolios*J. Risk Financial Manag.* **2016**, *9*(4), 11; doi:10.3390/jrfm9040011 - 4 October 2016**Abstract **

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The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD) constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. The

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The paper compares portfolio optimization with the Second-Order Stochastic Dominance (SSD) constraints with mean-variance and minimum variance portfolio optimization. As a distribution-free decision rule, stochastic dominance takes into account the entire distribution of return rather than some specific characteristic, such as variance. The paper is focused on practical applications of the portfolio optimization and uses the Portfolio Safeguard (PSG) package, which has precoded modules for optimization with SSD constraints, mean-variance and minimum variance portfolio optimization. We have done in-sample and out-of-sample simulations for portfolios of stocks from the Dow Jones, S&P 100 and DAX indices. The considered portfolios’ SSD dominate the Dow Jones, S&P 100 and DAX indices. Simulation demonstrated a superior performance of portfolios with SD constraints, versus mean-variance and minimum variance portfolios.
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On Setting Day-Ahead Equity Trading Risk Limits: VaR Prediction at Market Close or Open?*J. Risk Financial Manag.* **2016**, *9*(3), 10; doi:10.3390/jrfm9030010 - 9 September 2016**Abstract **

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This paper investigates the information content of the ex post overnight return for one-day-ahead equity Value-at-Risk (VaR) forecasting. To do so, we deploy a univariate VaR modeling approach that constructs the forecast at market open and, accordingly, exploits the available overnight close-to-open price

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This paper investigates the information content of the ex post overnight return for one-day-ahead equity Value-at-Risk (VaR) forecasting. To do so, we deploy a univariate VaR modeling approach that constructs the forecast at market open and, accordingly, exploits the available overnight close-to-open price variation. The benchmark is the bivariate VaR modeling approach proposed by Ahoniemi et al. that constructs the forecast at the market close instead and, accordingly, it models separately the daytime and overnight return processes and their covariance. For a small cap portfolio, the bivariate VaR approach affords superior predictive ability than the ex post overnight VaR approach whereas for a large cap portfolio the results are reversed. The contrast indicates that price discovery at the market open is less efficient for small capitalization, thinly traded stocks.
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The Nexus between Social Capital and Bank Risk Taking*J. Risk Financial Manag.* **2016**, *9*(3), 9; doi:10.3390/jrfm9030009 - 29 July 2016**Abstract **

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This study explores social capital and its relevance to bank risk taking across countries. Our empirical results show that the levels of bank risk taking are lower in countries with higher levels of social capital, and that the impact of social capital is

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This study explores social capital and its relevance to bank risk taking across countries. Our empirical results show that the levels of bank risk taking are lower in countries with higher levels of social capital, and that the impact of social capital is mainly reflected by the reduced value of the standard deviation of return on assets. Moreover, the impact of social capital is found to be weaker when the legal system lacks strength. Furthermore, the study considers the impacts of social capital of the banks’ largest shareholders in these countries and finds that high levels of social capital present in these countries exert a negative effect on bank risk taking, but the effect is not strongly significant.
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The Determinants of Equity Risk and Their Forecasting Implications: A Quantile Regression Perspective*J. Risk Financial Manag.* **2016**, *9*(3), 8; doi:10.3390/jrfm9030008 - 7 July 2016**Abstract **

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Several market and macro-level variables influence the evolution of equity risk in addition to the well-known volatility persistence. However, the impact of those covariates might change depending on the risk level, being different between low and high volatility states. By combining equity risk

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Several market and macro-level variables influence the evolution of equity risk in addition to the well-known volatility persistence. However, the impact of those covariates might change depending on the risk level, being different between low and high volatility states. By combining equity risk estimates, obtained from the Realized Range Volatility, corrected for microstructure noise and jumps, and quantile regression methods, we evaluate the forecasting implications of the equity risk determinants in different volatility states and, without distributional assumptions on the realized range innovations, we recover both the points and the conditional distribution forecasts. In addition, we analyse how the the relationships among the involved variables evolve over time, through a rolling window procedure. The results show evidence of the selected variables’ relevant impacts and, particularly during periods of market stress, highlight heterogeneous effects across quantiles.
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Probability of Default and Default Correlations*J. Risk Financial Manag.* **2016**, *9*(3), 7; doi:10.3390/jrfm9030007 - 5 July 2016**Abstract **

We consider a system where the asset values of firms are correlated with the default thresholds. We first evaluate the probability of default of a single firm under the correlated assets assumptions. This extends Merton’s probability of default of a single firm under

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We consider a system where the asset values of firms are correlated with the default thresholds. We first evaluate the probability of default of a single firm under the correlated assets assumptions. This extends Merton’s probability of default of a single firm under the independent asset values assumption. At any time, the distance-to-default for a single firm is derived in the system, and this distance-to-default should provide a different measure for credit rating with the correlated asset values into consideration. Then we derive a closed formula for the joint default probability and a general closed formula for the default correlation via the correlated multivariate process of the first-passage-time default correlation model. Our structural model encodes the sensitivities of default correlations with respect to the underlying correlation among firms’ asset values. We propose the disparate credit risk management from our result in contrast to the commonly used risk measurement methods considering default correlations into consideration.
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Down-Side Risk Metrics as Portfolio Diversification Strategies across the Global Financial Crisis*J. Risk Financial Manag.* **2016**, *9*(2), 6; doi:10.3390/jrfm9020006 - 21 June 2016**Abstract **

This paper features an analysis of the effectiveness of a range of portfolio diversification strategies, with a focus on down-side risk metrics, as a portfolio diversification strategy in a European market context. We apply these measures to a set of daily arithmetically-compounded returns,

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This paper features an analysis of the effectiveness of a range of portfolio diversification strategies, with a focus on down-side risk metrics, as a portfolio diversification strategy in a European market context. We apply these measures to a set of daily arithmetically-compounded returns, in U.S. dollar terms, on a set of ten market indices representing the major European markets for a nine-year period from the beginning of 2005 to the end of 2013. The sample period, which incorporates the periods of both the Global Financial Crisis (GFC) and the subsequent European Debt Crisis (EDC), is a challenging one for the application of portfolio investment strategies. The analysis is undertaken via the examination of multiple investment strategies and a variety of hold-out periods and backtests. We commence by using four two-year estimation periods and a subsequent one-year investment hold out period, to analyse a naive 1/N diversification strategy and to contrast its effectiveness with Markowitz mean variance analysis with positive weights. Markowitz optimisation is then compared to various down-side investment optimisation strategies. We begin by comparing Markowitz with CVaR, and then proceed to evaluate the relative effectiveness of Markowitz with various draw-down strategies, utilising a series of backtests. Our results suggest that none of the more sophisticated optimisation strategies appear to dominate naive diversification.
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