Research findings relating to anomalous equity returns should ideally be repeatable by others. Usually, only a small subset of the decisions made in a particular backtest workflow are released, which limits reproducability. Data collection and cleaning, parameter setting, algorithm development and report generation are often done with manual point-and-click tools which do not log user actions. This problem is compounded by the fact that the trial-and-error approach of researchers increases the probability of backtest overfitting. Borrowing practices from the reproducible research community, we introduce a set of scripts that completely automate a portfolio-based, event-driven backtest. Based on free, open source tools, these scripts can completely capture the decisions made by a researcher, resulting in a distributable code package that allows easy reproduction of results.

Since the Basel Committee on Banking Supervision first suggested a transition to Expected Shortfall as the primary risk measure for financial institutions, the question on how to backtest it has been widely discussed. Still, there is a lack of studies that compare the different proposed backtesting methods. This thesis uses simulations and empirical data to evaluate the performance of non-parametric backtests under different circumstances. An important takeaway from the thesis is that the different backtests all use some kind of trade-off between measuring the number of Value at Risk exceedances and their magnitudes. The main finding of this thesis is a list, ranking the non-parametric backtests. This list can be used to choose backtesting method by cross-referencing to what is possible to implement given the estimation method that the financial institution uses. / Sedan Baselkommittén föreslog införandet av Expected Shortfall som primärt riskmått för finansiella institutioner, har det debatteras vilken backtesting metod som är bäst. Trots detta råder det brist på studier som utvärderar olika föreslagna backtest. I studien används simuleringar och historisk data för att utvärdera icke-parametriska backtests förmåga att under olika omständigheter upptäcka underskattad Expected Shortfall. En viktig iakttagelse är att alla de undersökta testen innebär ett avvägande i vilken utsträckning det skall detektera antalet och/eller storleken på Value at Risk överträdelserna. Studien resulterar i en prioriterad lista över vilka icke-parametriska backtest som är bäst. Denna lista kan sedan användas för att välja backtest utefter vad varje finansiell institution anser är möjligt givet dess estimeringsmetod.

Submitted by Sara Ribeiro (sara.ribeiro@ucb.br) on 2017-08-17T14:48:23Z No. of bitstreams: 1 LeonardoNascimentoCastroDissertacao2017.pdf: 1765989 bytes, checksum: fb4cfd563d11e2aa428d7c5af632c835 (MD5) / Approved for entry into archive by Sara Ribeiro (sara.ribeiro@ucb.br) on 2017-08-17T14:50:34Z (GMT) No. of bitstreams: 1 LeonardoNascimentoCastroDissertacao2017.pdf: 1765989 bytes, checksum: fb4cfd563d11e2aa428d7c5af632c835 (MD5) / Made available in DSpace on 2017-08-17T14:50:34Z (GMT). No. of bitstreams: 1 LeonardoNascimentoCastroDissertacao2017.pdf: 1765989 bytes, checksum: fb4cfd563d11e2aa428d7c5af632c835 (MD5) Previous issue date: 2017-01-01 / Due to the Crisis of 2008, the Basel Committee accelerated the process for update the Accord and identified some weaknesses such as the inability of V aR to capture the tail risk. Subsequently, it was recommended to substitute V aR, a non-coherent measure of risk due to the absence of subadditivity, by CV aR. However, in 2011 the absence of elicitability for CV aR was shown and this has led some people to believe that it is impossible to perform a backtesting for this risk measure. Elicitability is an mathematical property for model selection and not for validation, although the convexity of its scoring function is required for backtesting. It is important to know the identifiability and testability, which have a relation with elicitability. For a good backtesting in the Trading Book, the testable function must be sharp, which is strictly increasing and decreasing with respect to the predictive and realized variables, respectively, and meet the requirement of ridge backtest, which depends on the least possible V aR. The CV aR, while not being testable or elicitable, is at least conditionally elicitable and therefore also conditionally testable. To validate the CV aR models, simulations were made with the three Acerbi methods, two of this study for testing and another adapted from the quantile approximation. Of these six, none were perfect, but two presented better results than the V aR Backtesting. This study analyzed the risk measures V aR and CV aR by the Historical Simulation, Delta-Normal, Correlated Normal, Monte Carlo and Quasi-Monte Carlo Simulation methods in the 95%, 97.5% and 99% for the Brazilian bond and stock portfolios, as well as the Brazilian Real against the Dollar, Euro and Yen currencies, and used some backtesting for the two measures. This study also proposed a method to improve Backtesting results of V aR. / Devido ?? Crise de 2008 o Comit?? de Basileia acelerou o processo para atualiza????o do Acordo e identificou algumas falhas como, por exemplo, a incapacidade do V aR em captar o risco de cauda. Posteriormente, recomendou-se substituir o V aR, uma medida n??o coerente de risco devido ?? aus??ncia de subaditividade, pelo CV aR. Entretanto, em 2011 foi mostrada a aus??ncia da elicitabilidade para o CV aR e isso induziu algumas pessoas a pensarem ser imposs??vel realizar um backtesting para esta medida de risco. A elicitabilidade ?? uma propriedade matem??tica para a sele????o de modelo e n??o para a valida????o, apesar de que a convexidade de sua fun????o scoring ?? necess??ria para o backtesting. Foram introduzidos os conceitos de identificabilidade e testabilidade, que possuem uma rela????o com a elicitabilidade. Para um bom backtesting no Trading Book, a fun????o test??vel deve ser n??tida, que ?? estritamente crescente e decrescente em rela????o ??s vari??veis preditiva e realizada, respectivamente, e atender o requisito de ridge backtest, que dependa o m??nimo poss??vel do V aR. O CV aR, apesar de n??o ser elicit??vel nem test??vel, ?? pelo menos condicionalmente elicit??vel e, portanto, tamb??m condicionalmente test??vel. Para validar os modelos do CV aR, foram feitas simula????es com os tr??s m??todos de Acerbi, dois desta pesquisa para teste e outro adaptado da Aproxima????o dos N??veis de V aR. Destes seis, nenhum foi perfeito, mas dois apresentaram resultados melhores que o Backtesting do V aR. Esta pesquisa analisou as medidas de risco V aR e CV aR pelos m??todos Simula????o Hist??rica, Delta-Normal, Normal Correlacionado, Simula????o Monte Carlo e Quase-Monte Carlo nos intervalos de confian??a de 95%, 97,5% e 99% para as carteiras de t??tulos e a????es brasileiras, al??m das cota????es do Real frente ??s moedas D??lar, Euro e Iene, e utilizou alguns testes de ader??ncia para as duas medidas. Esta pesquisa tamb??m prop??s um m??todo para melhorar os resultados do Backtesting do V aR.

After the financial crisis of 2008 regulators found that the derivative market, where financial institutions traded OTC derivatives with each other, played a significantrole in triggering the crisis. This led to the emergence of Counterparty Credit Risk(CCR) which is used to measure the exposure banks have to their counterparties. In simple terms CCR is a mix of Market and Credit risk which defines the risk that your counter party will go into bankruptcy. CCR involves the risk factors used in market risk since all of the derivatives are based on underlying assets such as interest rate and currencies. The thesis will focus on how one can backtest individual risk factors driving the value of OTC derivatives. We will present different Monte Carlo simulation techniques that are being used to simulate and represent all possible future outcomes for the risk factors. In order to better understand the performance of a chosen model and how to adjust the calibration window for the ingoing parameters, two different approaches are presented,Quantitative Backtesting and Statistical Backtesting. As an extension to this, a portfolio of interest rate Swaps are backtested whose value are driven by the evolution of the underlying risk factors. The backtesting ofthe portfolio is done with netting. The time horizon for the backtesting procedureis 2010-2020 giving the user up to 261 independent observations with a forecast length of 14 days. Both of the backtesting methods provide the practitioner with a graphical results guiding the user to choose an appropriate model and calibration method for simulating the risk factors. We found that a combination of the two approaches provides the best result. Hence, no backtesting method is superior the other. Instead they complement each other and should be used simultaneously. Using the two backtesting methods one can find a model that perfectly fit the underlying distribution of risk factors, theoretically. However, one should be careful since there will always be uncertainty about the future and there is no guarantee that tomorrow will follow historical evolution exactly.

Portfolio rebalancing has become a popular tool for institutional investors the last decade. Adaptive asset allocation, an approach suggest by William Sharpe is a new approach to portfolio rebalancing taking market capitalization of asset classes into consideration when setting the normal portfolio and adapting it to a risk profile. The purpose of this thesis is to evaluate the traditional approach of portfolio rebalancing with the adaptive one. The comparison will consist of backtesting and two simulation methods which will be compared computationally measuring time and memory usage (Monte Carlo and Latin Hypercube Sampling). The comparison was done in Excel and in R respectively. It was found that both of the asset allocation approaches gave similar result in terms of the relevant risk measurements mentioned but that the traditional was a cheaper and easier alternative to implement and therefore might be more preferable over the adaptive approach from a practical perspective. The sampling methods were found to have no difference in memory usage but Monte Carlo sampling had around 50% less average running time while at the same time being easier to implement. / Portfölj rebalansering har blivit ett populärt verktyg för institutionella investerare det senaste årtiondet . Adaptiv tillgångsallokering, en taktik föreslagen av William Sharpe är en typ av rebalansering där hänsyn tas till marknadsvärdet av tillgångsklasserna samtidigt som man anpassar det efter en riskprofil. Syftet med detta arbete är att evaluera den traditionella strategin kontra den adaptiva strategin där jämförelsen kommer bestå av backtesting (tillämpa strategin på historisk data) samt två simulationsmetoder(Monte Carlo och LHS). Simulationernas implementering kommer jämföras med avseende på tid och minnesanvändning. Jämförelserna gjordes i Excel och i R respektivt. Resultatet av studien visar att att båda strategierna gav liknande resultat med avseende på de riskmått som finns med men att den traditionella strategin var billigare och enklare att implementera och kan därför vara den strategi att föredra från ett praktiskt perspektiv. Simulationsmetoderna visade ingen skillnad i minnesanvänding men däremot att Monte Carlo var både lättare att implementera samt hade ca 50% mindre körtid i genomsnitt.

Risk measurement tools and strategies have until recently been calibrated for a low-for-long interest rate environment. However, in the current higher interest rate environment, banking supervisory entities have intensified their regulatory pressure on institutions to enhance their assessment and monitoring of interest rate risk and credit spread risk. The European Banking Authority (EBA) has released updated guidelines on the assessment and monitoring of Credit Spread Risk in the Banking Book (CSRBB), which will replace the current guidelines by 31st December 2023. The new guidelines identify the CSRBB as a separate risk category apart from Interest Rate Risk in the Banking Book (IRRBB), and specifies the inclusion of liabilities in therisk calculations. This paper proposes a CSRBB model that conforms to the updated EBA guidelines. The model uses a historical simulation Value at Risk (HSVaR) and Expected Shortfall (ES) approach, and includes a 90-day holding period, as suggested by Finansinspektionen (FI). To assess the effectiveness of the model, it is compared with a standardised model of FI, and subjected to backtesting. Additionally, the paper suggests modifications to the model to obtain more conservative results. / Riskmätningsverktyg och strategier har sedan nyligen anpassats till en lågräntemiljö. Dock till följd av den nuvarande högre räntemiljön har tillsynsmyndigheter för bankväsendet satt ökat tryck på institutioners utvärdering och rapportering av ränterisk och kreditspreadrisk. Den Europeiska Bankmyndigheten (EBA) har publicerat uppdaterade riktlinjer för bedömning och rapportering av kreditspreadsrisken i bankboken (CSRBB), som ersätter de nuvarande riktlinjerna den 31 december 2023. De nya riktlinjerna identifierar CSRBB som en separat riskkategori från ränterisk i bankboken (IRRBB) och specificerar inkluderingen av skulder i riskberäkningarna. Denna uppsats föreslår en CSRBB-modell som följer EBAs uppdaterade riktlinjer. Modellen använder en Value at Risk (VaR) metodik baserat på historiska simulationer och Expected Shortfall (ES), samt antar en 90-dagars innehavsperiod som föreslås av Finansinspektionen (FI). Modellens effektivitet utvärderas genom en jämförelse med FIs standardmodell för kreditspreadrisken i bankboken, samt genom backtesting. Slutligen diskuteras möjliga justeringar av modellen för att uppnå mer konservativa resultat.

Most of the literature on Value at Risk concentrates on the unconditional nonparametric or parametric approach to VaR estimation and much less on the direct modeling of conditional quantiles. This thesis focuses on the direct conditional VaR modeling, using the flexible quantile regression and hence imposing no restrictions on the return distribution. We apply semiparamet- ric Conditional Autoregressive Value at Risk (CAViaR) models that allow time-variation of the conditional distribution of returns and also different time-variation for different quantiles on four stock price indices: Czech PX, Hungarian BUX, German DAX and U.S. S&P 500. The objective is to inves- tigate how the introduction of dynamics impacts VaR accuracy. The main contribution lies firstly in the primary application of this approach on Cen- tral European stock market and secondly in the fact that we investigate the impact on VaR accuracy during the pre-crisis period and also the period covering the global financial crisis. Our results show that CAViaR models perform very well in describing the evolution of the quantiles, both in abso- lute terms and relative to the benchmark parametric models. Not only do they provide generally a better fit, they are also able to produce accurate forecasts. CAViaR models may be therefore used as a...

This study employs Extreme Value Theory and several univariate methods to compare their Value-at-Risk and Expected Shortfall predictive performance. We conduct several out-of-sample backtesting procedures, such as uncondi- tional coverage, independence and conditional coverage tests. The dataset in- cludes five different stock markets, PX50 (Prague, Czech Republic), BIST100 (Istanbul, Turkey), ATHEX (Athens, Greece), PSI20 (Lisbon, Portugal) and IBEX35 (Madrid, Spain). These markets have different financial histories and data span over twenty years. We analyze the global financial crisis period sep- arately to inspect the performance of these methods during the high volatility period. Our results support the most common findings that Extreme Value Theory is one of the most appropriate risk measurement tools. In addition, we find that GARCH family of methods, after accounting for asymmetry and fat tail phenomena, can be equally useful and sometimes even better than Extreme Value Theory based method in terms of risk estimation. Keywords Extreme Value Theory, Value-at-Risk, Expected Shortfall, Out-of-Sample Backtesting Author's e-mail ozturkdurmus@windowslive.com Supervisor's e-mail ies.avdulaj@gmail.com

The purpose of this thesis is to identify the best volatility model for Value-at-Risk(VaR) estimations. We estimate 1 % and 5 % VaR figures for Nordic indices andstocks by using two symmetrical and two asymmetrical GARCH models underdifferent error distributions. Out-of-sample volatility forecasts are produced usinga 500 day rolling window estimation on data covering January 2007 to December2014. The VaR estimates are thereafter evaluated through Kupiec’s test andChristoffersen’s test in order to find the best model. The results suggest thatasymmetrical models perform better than symmetrical models albeit the simpleARCH is often good enough for 1 % VaR estimates.

Banking has a unique role in the well-being of an economy. This role makes banks one of the most heavily regulated and supervised industries. In order to strengthen the soundness and stability of banking systems, regulators require banks to hold adequate capital. While credit risk was the only risk that was covered by the original Basle Accord, with the 1996 amendment, banks have also been required to assign capital for their market risk starting from 1998. In this research, the impact of the market risk capital regulations on bank capital levels and derivative activities is investigated. In addition, this study also evaluates the impact of using different approaches that are allowed to be used while calculating the required market risk capital, as well as the accuracy of VaR models. The implementation of the market risk capital regulations can influence banks either by increasing their capital or by decreasing their trading activities and in particular trading derivative activities. The literature review concerning capital regulations illustrates that in particular the impact of these regulations on bank capital levels and derivative activities is an issue that has not yet been explored. In order to fill this gap, the changes in capital and derivatives usage ratios are modelled by using a partial adjustment framework. The main results of this analysis suggest that the implementation of the market risk capital regulations has a significant and positive impact on the risk-based capital ratios of BHCs. However, the results do not indicate any impact of these regulations on derivative activities. The empirical findings also demonstrate that there is no significant relationship between capital and derivatives. The market risk capital regulations allow the use of either a standardised approach or the VaR methodologies to determine the required capital amounts to cover market risk. In order to evaluate these approaches, firstly differences on bank VaR practices are investigated by employing a documentary analysis. The documentary analysis is conducted to demonstrate the differences in bank VaR practices by comparing the VaR models of 25 international banks. The survey results demonstrate that there, is no industry consensus on the methodology for calculating VaR. This analysis also indicates that the assumptions in estimating VaR models vary considerably among financial institutions. Therefore, it is very difficult for financial market participants to make comparisons across institutions by considering single VaR values. Secondly, the required capital amounts are calculated for two hypothetical foreign exchange portfolios by using both the standardised and three different VaR methodologies, and then these capital amounts are compared. These simulations are conducted to understand to what extent the market risk capital regulations approaches produce different outcomes on the capital levels. The results indicate that the VaR estimates are dependent upon the VaR methodology. Thirdly, three backtesting methodologies are applied to the VaR models. The results indicate that a VaR model that provides accurate estimates for a specific portfolio could fail when the portfolio composition changes. The results of the simulations indicate that the market risk capital regulations do not provide a `level playing field' for banks that are subject to these regulations. In addition, giving an option to banks to determine the VaR methodology could create a moral hazard problem as banks may choose an inaccurate model that provides less required capital amounts.