The goal of this thesis is to measure the concentration risk of a portfolio as a part of a investment risk considered from the view of insurance companies by various methods and also to compare achieved results. Concentration risk in credit portfolios originates in uneven distribution of invested funds to individual obligors and it is important to manage it. In the theoretical part there are two methods presented - one is being used in practice CreditMetrics), the other one, the EU Directive, will be put into effect in the near future (Solvency II). In the practical part the methods are applied on model portfolios and the results are compared in order to decide how the methods reflect the concentration risk.

A credit portfolio where each obligor contributes infinitesimally to the risk is said to be infinitely granular. The risk related to the fact that no real credit portfolio is infinitely granular, is called name concentration risk. Under Basel II, banks are required to hold a capital buffer for credit risk in order to sustain the probability of default on an acceptable level. Credit risk capital charges computed under pillar 1 of Basel II have been calibrated for a specific level of name concentration. If a bank deviates from this benchmark it is expected to address this under pillar 2, which may involve increased capital charges. Here, we look at some of the difficulties that a bank may encounter when computing a name concentration risk add-on under pillar 2. In particular, we study the granularity adjustment for the Vasicek and CreditRisk+ models. An advantage of this approach is that no vendor software products are necessary. We also address the questions of when the granularity adjustment is a coherent risk measure and how to allocate the add-on to exposures in order to optimize the credit portfolio. Finally, the discussed models are applied to real data

På en teknisk nivå utgör beräkningen av sektorkoncentrationsrisk ett särskilt utmanande problem. I befintlig teori är riktlinjer till såväl hur industrisektorer ska indelas som risknivån beräknas begränsade. Syftet med studien är att utvärdera och analysera olika tillvägagångssätt till sektorkoncentrationsrisk i kreditportföljer. Detta har utförts i två separata delar där både indelningen i sektorer och riskberäkningen behandlats. Sektorindelningen har utvärderats genom att jämföra korrelationsstrukturen mellan två speciellt intressanta indelningsmetodiker; enligt Morgan Stanely Capital Investment (MSCI) och den av Finansinspektionen föreslagna sektorindelningen (SFSA). Riskberäkningen har utvärderats genom att applicera en rad olika koncentrationsmått på portföljer av varierande koncentrationsgrad. Resultaten visar att en minimering av inter-sektoriella korrelationer samt en maximering av intra-sektoriella korrelation är av stor vikt då sektorer indelas. Med andra ord, för att koncentrationen ska generera en faktisk risk krävs det att sektorerna är tydligt särskilda samt internt homogena. Utöver detta ska individuella exponeringar tydligt kunna placeras inom en sektor och de behandlade sektorerna ska inte vara av diversifierad natur. Resultaten tyder vidare på att MSCI presterar bättre för att hantera sektorkoncentrationsrisk på alla dessa punkter. När det kommer till riskberäkningen, visar resultaten att förutom  ördelningen av exponeringar är även sektorspecifika kreditkvaliteter samt korrelationsstrukturer av vikt för att bestämma risknivån. Risken från koncentration är större om risknivån är hög eller om exponeringen är mot korrelerade sektorer. Men framförallt tyder resultaten på att en uniformt fördelat portfölj inte är att se som okoncentrerad. För att ta hänsyn till naturliga koncentrationer är det därför av yttersta vikt att koncentration istället ses i förhållande till den aggregerade kreditmarknaden. / On a technical level, the measurement of sector concentration risk poses a particularlychallenging problem. Existing literature lacks direct suggestions both regarding how sectors are to be divided and the risk-level measured. The purpose of the study is to evaluate and analyse different measures of - and approaches to sector concentration risk in credit portfolios. This has been addressed both by analysing sectorial division and which aspects that are of interest for determining the concentration imposed risk- level. The sectorial division has been addressed by comparing the correlation structures of two especially interesting sector classification methods; the standardised Morgan Stanley Capital Investment industry classification (MSCI) and the proposed sector classification of the Swedish Financial Supervisory Authority (SFSA).  The sector concentration risk measurement has been analysed through employing different risk-measures on portfolios with varying concentration levels. The results show that in order to capture the risk-level from concentration, the main approach for sectorial division should seek to minimise inter-sector correlations and maximise intra-sector correlations. I.e. sectors should be distinct from each other and internally homogeneous. Moreover, an unambiguous sorting of individual exposures towards one sector should be possible and the considered sectors should not be of a diversified nature. It is also found that MSCI outperforms SFSA for assessing  sector concentration risk on all fronts. When it comes to the risk measure, it is found that apart from exposure distribution; credit qualities and correlation structures are of great interest. The risk induced from a concentrated exposure is greater if credit qualities are low or if the exposure is high towards highly correlated sectors. But  above all, the results imply that a uniform distribution is not to be seen as unconcentrated. In order for concentration measurement to incorporate natural concentrations it is thereby greatly important that concentration instead is considered as relative towards the aggregate credit market.

The Own Risk and Solvency Assessment, ORSA, is referred to as the heart of the regulation to be for European insurance companies - Solvency II. The aim of the ORSA process is to provide an overall and holistic view of the insurer’s risks by analyzing their current financial status and business strategy at hand. There is no predefined way to implement this process, which means that the companies are forced to develop a model themselves, as they see fit. In collaboration with a regional insurance company in Sweden we develop a structure and framework for an ORSA-model, flexible enough to be used by similar insurers yet standardized enough to overcome the issue of constrained resources within these smaller organizations. We apply a risk-factor based approach and tie together a balance sheet projection and stress testing, designed to be further developed as the individual insurer see fit. The suggested approach yields partially satisfying results and we consider the model to be particularly well-suited for assessing risk in the context of the small, non-life insurer. / Den egna risk- och solvensutvärderingen, ORSA, kallas hjärtat av det kommande regelverket för europeiska försäkringsbolag - Solvens II. Syftet med ORSA-processen är att ge en övergripande helhetsbild av försäkringsgivarens risker genom att analysera deras finansiella ställning och affärsstrategi. Det finns inget fördefinierat sätt att genomföra denna process, vilket innebär att företagen tvingas att utveckla en modell på egen hand, på ett sätt som de finner lämpligt. I samarbete med ett regionalt försäkringsbolag i Sverige utvecklar vi en struktur och en grund för en ORSA-modell. En modell som är tillräckligt flexibel för att kunna användas av liknande försäkringsgivare men samtidigt standardiserad nog att lösa problemet med begränsade resurser i dessa mindre organisationer. Vi tillämpar en riskfaktor-baserad metod, prognostiserar resultat- och balansräkning för bolaget och utför stresstester. Metoden är utformad för att utvecklas vidare av den enskilde försäkringsgivaren så som de finner lämpligt. Den föreslagna metoden ger delvis tillfredsställande resultat och vi anser att det är en grund väl lämpad att använda som utgångspunkt för att konstruera riskmätningsmetoder för små, skadeförsäkringsbolag.

One of banks core businesses today is to, in various ways, lend capital to the market and in return receive interest rate. But giving out credit comes with great risk and, therefore, precautions need to be taken. It is impossible to forecast exactly which obligor (borrower) that will default on its exposure. However, with well functioning risk management, institutions can lower the severity of their loss. In this study, we consider using a multi-factor model to calculate concentration risk for Swedish credit portfolios, which is a type of credit risk that is usually caused by high concentration of credit exposures distributed over few industrial sectors. In its existing form, the multi-factor model uses fixed sector correlations with predetermined sectors as input. Instead, we propose to use a data-driven approach based on data from the Stockholm stock exchange. In a simulation study, we find that the distributions of total credit loss are somewhat different under the original approach than under our proposed approach. This suggests that further research is needed to investigate whether the two approaches are interchangeable.

【第一篇論文中文摘要】 集中度風險於結構式商品的量化與分析：以房屋抵押貸款證券為例 "Martin and Wilde (2002)與Gordy (2003)" 針對巴塞爾協定(Basel Accords)中金融機構之投資組合所內藴之集中度風險提出了相對應的微粒化調整(Granularity Adjustment)風險量化準則，然而該模型僅止於單因子架構下探究單一信用標的集中度風險之量化。本文將其架構延用至結構式商品中，允許債權群組內之信用標的具不同區域別，我們採用Hull and White(2010)之跨池違約相關性描述，並結合Pykhtin (2004)中延拓單因子聯繫模型至多因子之方式，進而求取債權群組之單一資產集中度(Name Concentration)與區域類別集中度(Sector Concentration)風險的量化。本文以房屋抵押貸款證券(Mortgage Backed Securities, MBSs)為例，於集中度風險的考量下，藉由檢視不同風險情境下分券之損失起賠點，重新評估房屋抵押貸款證券AAA投資級分券信用評級之合理性。研究結果顯示，AAA評等之分券高度曝險於系統性風險，且於高風險情境下，標的房貸之區域集中現象擴大了違約相關性對債權群組損失分配的影響，致使AAA分券之損失起賠點得以超過其實際擔保額度(subordination)範圍。 【第二篇論文中文摘要】 美國銀行放款多角化對其報酬與風險之影響：相關性與傳染的觀點 本文目的在於分析銀行放款的多角化行為對其報酬與風險之影響。研究發現納入銀行放款投資組合相關性之考量，亦即標的資產之相關性結構以及資產間因契約關係所隱含跨投資組合之傳染途徑，將降低多角化之成效。文中透過因子模型(factor model)建構資產之報酬，同時決定其相關性結構，其中將資產間殘差項相關性作為傳染指標，進一步分析投資組合內標的資產間的平均相關係數、傳染與多角化程度間的關聯性。我們以美國銀行作為研究樣本，分別以赫芬達-赫希曼指數估算投資組合權重分配之集中度、使用組合內標的產業股票報酬資訊來計算投資組合內相關程度，接著利用標的產業與投資組合外產業間的殘差相關性來捕捉產業傳染效果，將此三項指標作為衡量多角化指標，分析其在1987年至2014年間聯貸投資組合多角化情形並試圖分析放款多角化對銀行績效之影響。透過契約關係的界定進而探討顧客傳染如何影響銀行績效。 研究發現於市場處於平穩期間(tranquil period)，所有多角化指標銀行放款均呈現放款多角化程度越高越有助於提高銀行的報酬並降低其風險。然而於危機期間(turmoil period)，銀行應將放款權重集中於部分產業、建構相關性較低之組合或選擇較低之傳染效果之產業作為放款的對象，用以提高銀行績效。隱含在危機期間銀行應該選擇適度之多角化策略，若僅以赫芬達-赫希曼指數作為多角化之衡量將顯示危機期間越集中越有助於銀行的表現，此舉將造成解釋上的偏誤。說明於投資組合多角化的衡量上，不該忽略由相關性結構所引發之集中度風險。 / 【Essay I】 Quantification and Analysis of Concentration Risk in Structured Products: the Case of Mortgage Backed Securities Granularity adjustments, introduced by Martin and While (2002) and Gordy (2003), allow one to quantify the concentration exposures of credit portfolios due to imperfect diversification. However, they focus solely on name concentrations under an Asymptotic Single Risk Factor (ASRF) framework. In this study, by adapting the multi-pool correlation structure of Hull and White (2010) under the multi-factor setting of Pykhtin (2004), we derive quantitative measures of name and sector concentration that facilitate subsequent analysis of the risk profiles embedded in Mortgage Backed Securities (MBSs). Under different stress scenarios, we examine the impacts of concentration exposures on the internal credit enhancements, in particular, the AAA tranche attachment points. We show that, under severe market conditions, the presence of sector concentrations in the underlying mortgage pools can further amplify the effects of default correlation on the portfolio loss distributions. As a direct consequence, the predetermined subordination level determined by the assignment of tranche attachment points can be exceeded. 【Essay II】 How Loan Portfolio Diversification Affects U.S. Banks’ Return and Risk: Correlation and Contagion Perspectives. In this paper we investigate how loan portfolio diversification affects the banks’ return and risk. We argue that, the dependence structure of bank loan portfolios, namely, the correlation structure among loan assets and the presence of contagion channels due to contractual relationships across the border of portfolio, contributes to the costs of diversification. Under the factor model framework, we derive a theoretical model to depict the asset returns and their dependence structure. Based on data of US bank loans collected from 1987-2014, our empirical study employs HHI, intra-portfolio correlation, and contagion as proxies for diversification to examine how loan portfolio diversification affects the banks’ profitability and riskiness. In addition, contractual relationships are identified and we investigate how customer contagion affects the bank’s performance. We find that all diversification measures exhibit a positive effect on the performance of U.S. banks during tranquil periods. However, for turmoil periods, banks with loan portfolios of more concentrated weight distributions, lower intra-portfolio correlation, or lower consumer contagion effects would have improved returns and reduced risk. In other words, during crisis, banks should choose an appropriate concentration strategy rather than focus on selected industries as determined solely by the HHI.