Dissertations / Theses on the topic 'Risk-free rate'

The current research was undertaken to assess if the prices in the South African capital market imply a risk free rate that is not equal to the theoretical risk free rate. The research was conducted by means of a literature review and desktop-research-based analysis of the market price based yield curve. The literature review was conducted to establish the importance of the risk free rate in the financial systems dynamics. The literature review highlighted that all the portfolio theories and performance-measure indicators have the risk free rate at the core of their methodology. This implies that the risk free rate is the most important concept that determines the market demand of different instruments. Next, a comparison has been drawn between the BESA published bond yield curve and a market-price-based yield curve developed by the researcher. The findings establish that the market price derived risk free rate is higher than the theoretical risk free rate. It was also found that the shape of the yield curve is different from the BESA projected yield curve, and that it is indicative of future problems in the South African capital market. The implications of investors‟ perceptions of the higher risk free rate are discussed and it is revealed that the foreign investors consider the country risk and the default risk associated with the South African government as higher than the BESA may perceive it to be.
Thesis (MCom (Risk Management))--North-West University, Vaal Triangle Campus, 2013

Dissertação para obtenção do Grau de Doutor em Estatística e Gestão do Risco
The main theme of this thesis is the calibration of a short rate model under the risk neutral measure. The problem of calibrating short rate models arises as most of the popular models have the drawback of not fitting prices observed in the market, in particular, those of the zero coupon bonds that define the current term structure of interest rates. This thesis proposes a risk neutral Gaussian short rate model based on Gaussian processes for machine learning regression using the Vasicek short rate model as prior. The proposed model fits not only the prices that define the current term structure observed in the market but also all past prices. The calibration is done using market observed zero coupon bond prices, exclusively. No other sources of information are needed. This thesis has two parts. The first part contains a set of self-contained finished papers, one already published, another accepted for publication and the others submitted for publication. The second part contains a set of self-contained unsubmitted papers. Although the fundamental work on papers in part two is finished as well, there are some extra work we want to include before submitting them for publication. Part I: - Machine learning Vasicek model calibration with Gaussian processes In this paper we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. We stress that the only prices needed for calibration are market observed zero coupon bond prices and that the parameters are directly obtained in the arbitrage free risk neutral measure. - One Factor Machine Learning Gaussian Short Rate In this paper we model the short rate, under the risk neutral measure, as a Gaussian process, conditioned on market observed zero coupon bonds log prices. The model is based on Gaussian processes for machine learning, using a single Vasicek factor as prior. All model parameters are learned directly under the risk neutral measure,using zero coupon bonds log prices only. The model supports observations of zero coupon bounds with distinct maturities limited to one observation per time instant. All the supported observations are automatically fitted.
M2A/ISEL financing conference trips; ISEL - financing conference fees; ISEL/IPL the PROTEC scholarship; CMA/FCT/UNL - financing conference trips

Syftet med uppsatsen är att diskutera det så kallade equity premium puzzle. Jag

analyserar teoretiskt den intertemporala konsumtionsbaserade CAPM (C-CAPM),

sammanställer en del av litteraturdiskussionen som finns på området samt empiriskt

testar C-CAPM på svensk data. Fenomenet equity premium puzzle innebär att

överavkastningen på aktier är så stor att det inte stämmer med den ekonomiska teorin.

Enligt teorin beror C-CAPMs riskpremie på kovariansen mellan konsumtionen och

aktieavkastningen. Litteraturen visar att forskare inte har lyckats förklara equity

premium puzzle genom att ändra antagandena i grundmodellen. Den empiriska

undersökningen visar att equity premium puzzle även uppkommer på svensk data.

This diploma thesis analyses various approaches to calculate risk-free interest rate. In the beginning it deals with the term risk-free asset a various types of bases we could start calculating from. The paper suggests using spot rates and searches for alternative interest rates on the market. These are subsequently applied to real data coming from Czech market. Specifically they are the bootstrapping method and also the method of deriving risk-free interest rate from interest swap rate. Closing thoughts are dealing with various problems an appraiser may encounter while calculating risk-free rate. For example the problem of using nominal/real rates, nonexistent long-term government bonds or the presence of a default risk for particular government. This diploma thesis closes with a decision tree that could serve as a lead for appraiser in the process of estimating risk-free interest rate.

1.3. Research Questions.

With this in mind, the research questions of this work are:

1. Is the Capital Asset Pricing Model still applicable despite the heavy impact of the financial crisis on the financial systems?

2. What happens to this model when the risk free rate approaches zero?

3. Is there a relationship between the riskiness of an asset and the risk-free interestrate when the latter is approaching the zero level?

Bakgrund: Marknadens riskpremie kan förklaras som den förväntade avkastning en investerare kräver för att acceptera en viss risk. Hur riskpremien skall bestämmas har stått i fokus för omfattande debatter de senaste åren men fortfarande har ingen ultimat lösning infunnit sig. Det finns två huvudsakliga tillvägagångssätt för att uppskatta riskpremien. Det ena att använda historisk data över aktieutvecklingen och därefter förvänta sig att en framtida utveckling kommer att vara likvärdig. Den andra är att göra uppskattningar av den framtida utvecklingen, så som framtida utdelningar, framtida vinster, BNP och inflation och därifrån göra en uppskattning utav riskpremien. Att använda sig av historiska värden har tidigare varit en accepterad metod både i den akademiska och finansiella värden men då den på senare tid har mötts av omfattande kritik, har modeller baserade på uppskattningar av framtiden vuxit sig starkare.

Syfte: Syftet med denna uppsats är att ge en djupgående beskrivning av hur svenska finansiella företag uppskattar och hanterar riskpremium för den svenska aktiemarknaden. Därigenom fanns en avsikt att studera vilken metod som främst användes, hur viktigt riskpremium i form av ett investeringsinstrument var, och morgondagens betydelse av riskpremium.

Metod: Författarna använde sig av en kvalitativ metod, där det empiriska materialet samlades in med hjälp av personliga intervjuer. Intervjufrågor av öppen karaktär skickades ut till respondenterna i förväg, och intervjuerna ägde därefter rum i Stockholm och Göteborg. I den teoretiska referensramen användes både så kallad primär och sekundär litteratur för att kunna redogöra en övergripande bild av problemområdet. Den primära litteraturen, som framförallt ligger till grund för kapitel tre, sågs extra viktig att inkludera då den möjliggjorde en minskad subjektivitet som annars hade riskerat att belasta uppsatsen.

Resultat: Resultaten visade en varierad syn mellan respondenterna där vissa ansåg att riskpremien hade ringa betydelse och andra att det var en mycket viktig variabel. Överlag fanns det dock ett ökat intresse de senaste åren. Även val av metod varierade och vare sig historisk data eller framtida uppskattningar kunde sägas ha ett övertag bland användarna. Avslutningsvis såg författarna ett ökat intresse för de ingående variablerna i modeller som baseras på framtida förväntade värden och kunde därav visa att den framtida debatten sannolikt kommer att behandla vilka variabler som bör inkluderas i denna typ av modeller och hur de bör uppskattas.

Small and medium enterprises (SMEs) are recognised as important for the economic success of countries all over the world because of their contribution to the gross domestic product (GDP), to innovation, to export revenue, to the provision of goods and services to society and large enterprises, to social stability, to employment creation, and to the improvement of economic welfare. These organisations operate within an economic environment characterised by volatility, highly demanding dynamism and tough competition, which often seriously threaten their performance and their survival. The South African business environment in general is constantly changing in the face of an unreceptive economic environment and a subtle political setting which breeds a highly competitive market. For SMEs to withstand the hazards of such a precarious and unfavourable competitive climate, they need to engage in market-oriented strategies. While market orientation research in large organisations has been studied etensively, little attention has been paid to the market orientation of SMEs. Market orientation models have been developed and tested only for developed countries, which recognise the substantial importance of market orientation in the modern business arena. Despite its importance, market orientation and its implementation and relationship with business performance has not been widely researched in developing economies. This need for a market orientation model that is applicable to developing countries underlies this research, the principal purpose of which is to develop a market orientation–business performance conceptual model and test it in a developing country setting. For this purpose, the researcher applied the market orientation constructs as guided by various proponents in the field. Market orientation was identified from the large body of literature and a conceptual framework of market orientation–business performance was proposed. The conceptual framework considered barriers to market orientation, determinants and enablers of market orientation and market orientation with its dimensions (customer emphasis, information generation, intelligence dissemination and intelligence responsiveness or taking action) and economic and non-economic performance as consequences. This framework was then tested in order to identify the link between barriers to market orientation, determinants of market orientation, overall market orientation and business performance. Such efforts have been observed in previous market orientation literature but those studies did not distinguish barriers from determinants. The objective of this study was to establish the relationship between market orientation and the performance of SMEs measured by financial and non-financial measures of business performance. It also sought to ascertain the barriers to market orientation and the determinants/enablers of market orientation and their relationship with market orientation. Another objective was to examine the extent to which SMEs in South Africa have adopted market-oriented practices. A quantitative method was used. Surveys were conducted with 273 SMEs respondents, which were identified using a convenience sampling method. Data from owners/managers of these SMEs were collected using structured questionnaires. This study is different from previous studies on various grounds. Firstly, this study on market orientation is particularly focused on SMEs. Secondly, this study considered barriers to market orientation and determinants of market orientation separately, as having two divergent effects on market orientation. Thirdly, this study considered both the economic and non-economic performance measures as business performance indicators, factorising all the dimensions and modelling the relationship structures. Finally, this study was conducted in a developing economy (South Africa) where limited market orientation studies have been carried out with emphasis on market orientation among SMEs. Quantitative research methods were used to arrive at a valid and convergent conclusion about market orientation and its relationship with business performance. For this purpose, quantitative survey data were obtained from officials of both marketing and non-marketing departments of SMEs in the Vaal Triangle (South Africa). The hypotheses of the study were tested using t-tests statistics, analysis of variance (ANOVA), confirmatory factor analysis (CFA), and structural equation modelling (SEM) goodness of fit. The findings of the study supported the hypotheses of the study and confirmed the applicability of the proposed market orientation framework. The findings also indicated that the market orientation of SMEs in South Africa is determined by four fundamental factors (top management emphasis, market-based reward system, inter-departmental connectedness and management risk posture). In addition, the findings identified four key barriers to market orientation (centralisation and formalisation, inter-departmental conflict, competitive intensity and turbulence). The study also found a significant effect of market orientation on business performance. The findings of this study are consistent with those of previous market orientation studies undertaken in developed countries. At the final stage, the first conceptual model of market orientation–business performance applicable to SMEs in a developing country (South Africa) was offered on the basis of the findings of this study. This conceptual model provides insights and groundwork for further research. Therefore, in order to verify its generic application, it is hoped that this model will be used as a starting point for further studies and be tested in other countries in the world, both developed and developing.
PhD (Business Management)|cNorth-West University, Vaal Triangle Campus|d2013

The Heath-Jarrow-Morton (HJM) model represents the latest in powerful arbitrage-free technology for modeling the term structure and managing interest rate risk. Yet risk management strategies in the form of immunization portfolios using duration, convexity, and M-square are still widely used in bond portfolio management today. This study addresses the question of how traditional risk measures and immunization strategies perform when the term structure evolves in the HJM manner. Using Monte Carlo simulation, I analyze four HJM volatility structures, four initial term structure shapes, three holding periods, and two traditional immunization approaches (duration-matching and duration-and-convexity-matching). I also examine duration and convexity measures derived specifically for the HJM framework. In addition I look at whether portfolios should be constructed randomly, by minimizing their M-squares or using barbell or bullet structures. I assess immunization performance according to three criteria. One of these criteria corresponds to active portfolio management, and the other two correspond to passive portfolio management. Under active portfolio management, an asset portfolio is successfully immunized if its holding period return is greater than or equal to the holding period return of the liability portfolio. Under passive portfolio management, the closer the returns of the asset portfolio to the returns of the liability portfolio, the better the immunization performance. The results of the study suggest that, under the active portfolio management criterion, and with the duration matching strategy, HJM and traditional duration measures have similar immunization performance when forward rate volatilities are low. There is a substantial deterioration in the immunization performance of traditional risk measures when there is high volatility. This deterioration is not observed with HJM duration measures. These results could be due to two factors. Traditional risk measures could be poor risk measures, or the duration matching strategy is not the most appropriate immunization approach when there is high volatility because yield curve shifts would often be large. Under the active portfolio management criterion and with the duration and convexity matching strategy, the immunization performance of traditional risk measures improves considerably at the high volatility segments of the yield curve. The improvement in the performance of the HJM risk measures is not as dramatic. The immunization performance of traditional duration and convexity measures, however, deteriorates at the low volatility segments of the yield curve. This deterioration is not observed when HJM risk measures are used. Overall, with the duration and convexity matching strategy, the immunization performance of portfolios matched with traditional risk measures is very close to that of portfolios matched with the HJM risk measures. This result suggests that the duration and convexity matching approach should be preferred to duration matching alone. Also the result shows that the underperformance of traditional risk measures under high volatility is not due to their being poor risk measures, but rather due to the reason that the duration matching strategy is not an appropriate immunization approach when there is high volatility in the market. Under the passive portfolio management criteria, the performances of traditional and HJM measures are similar with the duration matching strategy. Less than 29% of the duration matched portfolios have returns within one basis point of the target yield, whereas almost all are within 100 basis points of the target yield. These results suggest that the duration matching strategy might not be sufficient to generate cash flows close to those of the target bond. The duration measure assumes a linear relation between the bond price and the yield change, and the nonlinearities that are not captured by the duration measure might be important. When the duration and convexity matching strategy is used, more than 36% of the portfolios are within one basis point of the target with HJM risk measures. This dramatic improvement in the immunization performance of HJM measures is not guaranteed for traditional risk measures. In fact, there are certain cases in which the performance of traditional risk measures deteriorates with the duration and convexity matching strategy. In this respect, choosing the correct risk measure is more important than the immunization strategy when passive portfolio management is pursued. Under active portfolio management criterion, there is no significant difference among bullet, barbell, minimum M-square, and random portfolios with both duration matching and duration and convexity matching strategies. Under the passive portfolio management criterion, bullet portfolios produce closer returns to the target for short holding periods when the duration matching strategy is used. With the duration and convexity matching strategy, bullet, barbell and minimum M-square portfolios produce closer returns to the target for short holding periods. Random portfolios perform as well as bullet, barbell and minimum M-square portfolios for medium to long holding periods. These results suggest that when the duration matching strategy is used, bullet portfolios are preferable to other portfolio formation strategies for short holding periods. When the duration and convexity matching strategy is used, no portfolio formation strategy is better than the other. Under the active portfolio management criterion, minimum M-square portfolios are successfully immunized under each yield curve shape and volatility structure considered. Under the passive portfolio management criterion, minimum M-square portfolios perform better for short holding periods, and their performance deteriorates as the holding period increases, irrespective of the volatility level. This suggests that the performance of minimum M-square portfolios is more sensitive to the holding period rather than the volatility. Therefore, minimum M-square portfolios would be preferred in the markets when there are large changes in volatility. Overall, the results of the study suggest that, under the active portfolio management criterion and with the duration matching strategy, traditional duration measures underperform their HJM counterparts when forward rate volatilities are high. With the duration and convexity matching strategy, this underperformance is not as dramatic. Also no particular portfolio formation strategy is better than the other under the active portfolio management criterion. Under the passive portfolio management criterion, the duration matching strategy is not sufficient to generate cash flows closer to those of the target bond. The duration and convexity matching strategy, however, leads to substantial improvement in the immunization performance of the HJM risk measures. This improvement is not guaranteed for the traditional risk measures. Under the passive portfolio management criterion, bullet portfolios are preferred to other portfolio formation strategies for short holding periods. For medium to long holding periods, however, the portfolio formation strategy does not significantly affect immunization performance. Also, the immunization performance of minimum M-square portfolios is more sensitive to the holding period rather than the volatility.
Ph. D.

A solução da maioria dos problemas práticos enfrentados por administradores financeiros passa pela identificação prévia do custo de oportunidade para investimentos de diferentes prazos e riscos. Este trabalho busca, no conjunto de seus capítulos, realizar uma avaliação crítica das propriedades da estrutura temporal de taxas de juros em reais e de sua utilização como variável exógena fundamental na análise financeira. Sem a pretensão de esgotar qualquer dos temas abordados, procurou-se estabelecer a curva de juros para investimentos livres de riscos em moeda nacional e, através de um conjunto de testes empíricos e observações informais de séries de dados de mercado, identificar peculiaridades que possam invalidar a implementação no Brasil de modelos desenvolvidos no contexto internacional. Dados os aspectos característicos do mercado doméstico evidenciados nos estudos, foram apresentados modelos explicativos tanto para a formação das taxas prefixadas de período quanto para a determinação da remuneração de operações financeiras indexadas à taxa referencial TR.
The solution to most of the problems facing financial managers requires prior identification of the cost of money for different maturities and risks. This paper aims, in its overall content, to examine the Brazilian currency yield curve’s properties and its supporting role in financial analysis. With no intention of exhausting any of the tackled subjects, the Real risk-free term structure was defined and a set of empirical tests performed to identify, with the support of additional data observation, local market’s peculiarities that might prevent international models from being accurately applied in Brazil. Given the domestic market’s distinguishing features emphasized in the studies, models were proposed to explain how short term interest rates are determined in the marketplace for derivatives, and to allow the pricing of financial instruments indexed to the so called TR benchmark (Taxa Referencial).

The income evaluation is one of the basic methods to establish a price of a real estate. It deals with a discount rate. But there is any obligatory methods how to establish the discount rate. The principle of yield property valuation method is the determination of future net profits transferred to the present value. The amount of the discount rate is affected by the large amount of criteria that take into account the risks associated with the property. The risk represents the financial loss which the owner of real estate created if the immovable thing ceased to produce such income, which is calculated in the valuation. But at present experts the risks associated with the real estate does not quantify and discount rate is determined mostly by the professional estimate. The main aim of the Ph.D. Theses is to propose a methodology to more accurately determine the discount rate. This methodology will be based on the free risk rate and risk premiums. The free risk rate shall be determined on the basis of income on government bonds, which are considered the least risky asset. Risk premiums will reflect the technical quality of the property, economy of real estate and legal level of real estate through eleven criteria. The discount rate could be by this methodology simply calculated using the software support of Microsoft Excel.

The work deals with the theoretical basis and the practical approach for determining the risk-free rate of return. The aim of the work is to form recommendations which should analysts follow in determining the risk-free rate of return in the Czech Republic. The first part focuses on theoretical basis of risk-free rate of return and market interest rates. Further, the criteria of risk-free investments are defined in this chapter. The second and third part focuses on determination of the risk-free rate of return using yield to maturity of government bond and yield curve which was derived with using the Nelson-Siegel model. The table of forward rates at the end of each month from January 1999 to April 2010 is attached.

Thesis Variants of determining the risk free rate in the business valuation is dedicated to the issue of estimating risk free rate for the calculation of the discount rate. The objective of this work is to demonstrate the influence of methods to estimate the risk free rate to business valuation based on the example of a selected company valuation. The first part is dedicated to the cost of equity, cost of debt and weighted average cost of capital. Next chapter focuses on the definition of risk-free interest rate and rating as an indicator of credit risk. The thesis also deals with theoretical methods for estimating the risk-free interest rate and their practical application. Values calculated on the basis of theoretical approaches are then applied in the calculation of the discount rate to calculate the present value of the cash flows of company.

The main contribution of the diploma thesis is to give a comprehensive picture of the switch from LIBOR to OIS discounting. Prior to the global financial crisis, LIBOR (London Interbank Offered Rate) represented an approximation of the risk-free rate in the valuation of interest rate derivatives. The collapse of Lehman Brothers in 2008 resulted in sharp widening of the LIBOR-OIS spread, an indicator of the interbank market stress. Many derivative practitioners have become concerned about the choice of an appropriate risk-free rate. Traditional valuation approaches using LIBOR discounting have been reviewed. Meanwhile, the OIS (Overnight Indexed Swap) rate has become a better proxy for the risk-free rate, at least for collateralized or centrally cleared transactions. Firstly, the research aims to discover the divergences between LIBOR rates, popular pre-crisis proxies for the riskfree rate, and OIS rates, their post-crisis alternatives. Secondly, it covers the interbank lending market, and analyzes individual LIBOR-OIS spreads for the USD, EUR, GBP and CZK currency. Thirdly, it explores the transition to OIS discounting in connection with an influence on a wide spectrum of interest rate derivatives. Therefore, any potential effects are demonstrated on numerical valuation examples of interest rate swaps in the USD, EUR, and GBP currency. Finally, the diploma thesis addresses a topic of collateral management and clarifies different approaches using LIBOR or OIS rates for collateralized or non-collateralized transactions.

El presente trabajo de investigación analiza el estado del arte de los ajustes y adaptaciones que se han impuesto al modelo Capital Asset Pricing Model (CAPM) para habilitar su aplicabilidad en mercados emergentes, con el fin de valorar correctamente los activos financieros y estimar la rentabilidad esperada en función del riesgo, es justo mencionar que, desde la publicación del modelo han surgido constantes críticas que lo califican de ineficaz en mercados emergentes, basándose particularmente en que, el modelo representa el riesgo a través de una sola variable que es medida por el riesgo sistemático y que fue originalmente diseñada para mercados desarrollados; en tal sentido, se han presentado propuestas de diversos especialistas que con sus teorías recomiendan ajustar el beta o ponderarlo, otras propuestas sugieren incluir variables como el diferencial de crédito, riesgo país y lambda, con lo que sostienen que es significativamente importante la necesidad de tener que adecuar el modelo a mercados emergentes caracterizados particularmente por ser riesgosos y tener alta volatilidad debido a los constantes cambios en sus variables económicos y financieros.
The following research analyzes the state of the art of the adjustments and adaptations imposed on the Capital Asset Pricing Model (CAPM) in order to enable its applicability on emerging markets, with the aim to value properly financial assets as well as estimate the expected profitability depending on the risk, It is fair to mention that, since the publication of the model, there has been severe criticism on its effectiveness for emerging markets, based on the fact that, the model displays the risk through a single variable that is measured by the systematic risk and that was originally designed for developed markets; in this sense, several proposals have been introduced by specialists suggesting wiht his theories to either adjust the Beta or weighted it, and other proposals suggest including variables such as credit spread, country risk and lambda, with which they maintain that it would be of the utmost importance to adapt the model to emerging markets, particularly characterized for being risky and have feature high volatility due to the constant fluctuations both in their economic and financial variables.
Trabajo de Suficiencia Profesional

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Segundo Sampaio (2002), os modelos intertemporais de equilíbrio começaram a ter a sua eficácia na determinação do retorno dos ativos questionada após a publicação do artigo de Mehra e Prescott em 1985. Tendo como objeto de análise os dados observados no mercado norte-americano, os autores não foram capazes de reproduzir a média histórica do prêmio do retorno das ações em relação ao retorno dos títulos públicos de curto prazo através de parâmetros comportamentais dentro de intervalos considerados plausíveis. Através das evidências, os autores, então, puderam verificar a necessidade de coeficientes exageradamente altos de aversão ao risco para equiparação do prêmio de risco histórico médio das ações norte-americanas, enigma que ficou conhecido como equity premium puzzle (EPP). Foi possível também a constatação de outro paradoxo: a necessidade de taxas de desconto intertemporais negativas para obtenção da média histórica da taxa de juros, o risk-free rate puzzle (RFP). Este trabalho tem como objetivo adaptar os dados do modelo proposto por Mehra e Prescott (2003) ao mercado brasileiro e notar se os puzzles apresentados anteriormente estão presentes. Testa-se o CCAPM com dados brasileiros entre 1995:1 e 2013:4 adotando preferências do tipo utilidade esperada e através da hipótese de log-normalidade conjunta dos retornos. Utiliza-se o método de calibração para avaliar se há EPP no Brasil. Em linha com alguns trabalhos prévios da literatura nacional, como Cysne (2006) e Soriano (2002) que mostraram a existência do puzzle nos períodos de 1992:1-2004:2 e 1980:1-1998:4, respectivamente, conclui-se que o modelo usado por Mehra e Prescott (2003) não é capaz de gerar o prêmio de risco observado na economia brasileira. Sampaio (2002), Bonomo e Domingues (2002) e Issler e Piqueira (2002), ao contrário, não encontram evidências da existência de um EPP brasileiro.

Mestrado em Ciências Actuariais
A recente instabilidade dos mercados financeiros contribuiu para o aumento do debate em torno da avaliação das responsabilidades e dos ativos das empresas de seguros e de resseguros. Tal decorre do desvio significativo que os preços de mercado podem sofrer em relação aos fundamentos económicos implícitos, refletindo a aversão ao risco e o interesse próprio dos investidores. Este texto é o relatório de um estágio curricular realizado no Instituto de Seguros de Portugal. O projeto subjacente consistiu no estudo aprofundado de dois inovadores instrumentos, agora propostos pelas instâncias da União Europeia, para a imunização dos efeitos cíclicos no cálculo das provisões técnicas, em ambiente Solvência II: o counter-cyclical premium e o matching premium. Ambos atuam sobre a Estrutura Temporal das Taxas de Juro, mas enquanto que o primeiro é utilizado apenas em períodos de elevado stress financeiro, o outro tem em vista as empresas que utilizam uma estratégia de buy-and-hold de ativos.
The recent instability of financial markets has raised the debate on the area of the valuation of the liabilities and assets of the insurance and reinsurance undertakings. This follows from the significant deviation that market prices may suffer in relation to their implied economic fundamentals, reflecting the risk aversion and self-interest of investors. This internship report explains the insightful study that was developed about two new instruments, as proposed by European Union bodies: the counter-cyclical premium and the matching premium. The purpose is the immunization of cyclical effects in the calculation of technical provisions, under Solvency II environment. They are both added to the risk free interest rate term structure, but while the first is applied only during stressed periods the other can be used whenever insurers take a buy-and-hold strategy, being able to hold the relevant assets until maturity. The internship was with the Portuguese Insurance and Pension Funds Supervisory Authority (Instituto de Seguros de Portugal).

The work is focussed on the determination of capital structure in its market values, determination of the cost of non-own capital, and determination of the cost of equity, primarily by using the CAPM method. In terms of the CAPM procedure the work deals with the main parameters required by the method, such as risk-free yield rate, risk market premium, and beta coefficient. Furthermore, attention is given to modifications resulting from the inaccuracies of the CAPM method to make the method correspond as much as possible with the actual yield and risk of shares historically achieved at the capital market, and likewise to modifications needed when applying the CAPM method to the valuation of Czech businesses. The recommended procedure of determining the market discount rate for the valuation of an enterprise is applied on an example. Data obtained from the capital market of the Czech Republic are used to calculate the risk premium of the Czech capital market and beta coefficient of selected ten shares out of the Czech capital market, giving an assessment of the possibility of using the data obtained from the Czech capital market for the valuation of businesses incorporated in the Czech Republic.

Using three different models, we examine the determinants of average stock returns on the Stockholm Stock Exchange during 2012-2016. By using time-series data, we find that a Fama-French three-factor model (directed at capturing size and book-to-market ratio) functions quite well in the Swedish stock market and is able to explain the variation in returns better than the traditional CAPM. Additionally, we investigated if the addition of a Price/Earning variable to the Fama-French model would increase the explanatory power of the expected returns of the different dependent variables portfolios. We conclude that the P/E ratio does not influence the expected returns in the sample we used.

碩士
銘傳大學
經濟學研究所
91
After the index option lists on the future market, it affects properly in the financial market in Taiwan. Beside adrenalize the stock market and future market, it offers investors other kinds of tools such as hedge and arbitrage. In Black and Scholes(1973) European-style option model, this study focuses on the part of the risk-free interest rate, and researches the price of option whether it contains the sensitivity of interest rate or not, which is the option market can be affected by the change of interest rate or not. The result shows when call and put are deeply In-The-Money, the change of interest rate affects the price of call and put significantly. When call and put are deeply Out-of-The-Money, the change of interest rate will not affect the price of call and put. Above result fits the hypothesis of Black and Scholes(1973) European-style option model.

碩士
亞洲大學
健康管理研究所
95
Objective: Since the implementation of National Health Insurance, the method for payment is fee-for-service. The highest payment unit in medical equipment usage is per outpatient treatment in ESWL. This study is to understand the stone-free rate after ESWL and analysis the factors that affect the recurrence rate.Materials and Methods: Between Jul. 2000 to Jun 2001, total 706 patients underwent ESWL in Cheng-Ching general hospital. We retrospectively reviewed the stone-free rate and recurrence rate after ESWL. Furthermore,we investigated the factors that contributed the stone-free rate and recurrence rate with Logistic regression analysis. Results: There are 506 males and 200 females in this study. Mean age was 47.23 y/o (range from 16 to 86 y/o). Totally 763 renal units were enrolled. In these 763 renal units, 439 were stone-free after ESWL and the other 324 were not. The stone-free rate is 57.53%. Stone recurred in 123 of 439 renal units (28%). The stone size, number and location are significant factors that affect the stone-free rate. The stone free rate of upper ureteral and upper renal calyceal stones are higher than lower calyceal stone. Patients with an early onset of stone formation had the higher recurrence rate. In addition, lower calyceal stone is easier recurred than upper ureteral stone. Conclusion: ESWL is a less invasive and effective method for urolithiasis.However, lower stone-free rate and higher recurrence rate resulted in higher utilization of ESWL. Complete image study and a proper management will increase the stone free rate. In additional to age and stone location, education on changing in diet habit and life style is important.

The paper discusses implications of prevailing low interest rates ondiscounted cash flow valuations. Applying the traditional theoretical framework can lead to absurd results for intrinsic value. I find evidence that investment banks use artificially high numbers for risk-free rates and equity premia to boost weighted average cost of capital. I argue that valuations that are solely based on discounted cash flows lack meaningfulness in the current environment. They needto be accompanied by other techniquessuchas multiple valuations. In Lisa and minevaluation ofWacker Neuson SEwe did not only “sanity-check”the DCF price target but used anequally weightedblended price target of DCF and multiplesas a result of these findings.

Thesis (M.Comm.)-University of KwaZulu-Natal, Pietermaritzburg, 2009.
The Capital Asset Pricing Model (CAPM), despite criticism and debate regarding its validity, remains the most widely employed model to estimate the cost of equity for use in capital budgeting decisions, both in the U.S. and in South Africa. The risk-free rate specified in the model is generally estimated with the use of a government security, but there is some concern as to the appropriateness of this practice in the South African market. An alternative approach was derived by Black (1972), known as the minimum-variance zero-beta portfolio returns; but the suitability of this parameter in the South African market has not yet been examined. The objective of this study therefore is to determine the best method to estimate the risk-free rate for applications of the CAPM in South Africa. A set of theoretical requirements that an asset must closely satisfy to be considered a suitable proxy for the risk-free rate are derived, with the most commonly employed proxies being compared to these criteria to ascertain their appropriateness. The zero-beta portfolio returns are computed, in conjunction with the rate that investors have historically viewed as the minimum required return, denoted by the intercept of the CAPM. Hypothesis tests of the equality of the two estimates of the risk-free rate and the minimum required return are conducted, as well as a comparison of the forecasting accuracy of the model using the different risk-free rate values. The results of the analysis indicate that the South African proxies diverge substantially from the criteria, and are likely to overstate the true-risk-free rate. In complete contrast to this, the hypothesis tests reveal that the proxies understate the intercept estimate, whilst the zero-beta portfolio returns closely approximate this value. This finding that the zero-beta portfolio returns, which are larger than the proxy yields, are more suitable appears counter-intuitive given the goal to identify the minimum return from investing. This result can possibly be explained by the fact that the CAPM intercept represents the average of the riskless lending and borrowing rates, whilst the proxy only denotes the former. The borrowing rate is likely to be higher than the lending rate; thus giving reason for the average being greater. However, the possibility also remains that the results observed may be a consequence of the incorrect specification of the market portfolio, that the tests employed are inapt, or that the model itself is inappropriate. The forecasting analysis confirms the greater accuracy associated with employing the zero-beta portfolio returns as the risk-free rate compared to the use of a proxy, but the improvement is small. Thus the choice for the practitioner is whether the increase in accuracy is justified by the difficulty and time involved with estimating the zero-beta portfolio returns.

碩士
國立政治大學
金融學系
107
Under the IFRS 17 standard, it’s required to change from the locked-in discount rate which is applied around the world, to the current discount rate. In this paper, we use the Smith-Wilson model, which based on IANs and ICS to perform stability and cash flow test to observe the rationality of the ultimate forward rate setting. According to the result of the testing, it can be shown that using the Taiwan government bonds of 1y, 5y and 10y to interpolate the first ten-year interest curve is the most stable situation while the second-order interpolation of the advanced information is the second best. However, the performance of 1y to 10y Taiwan government bond is the worst among three different situations. Therefore, when it comes to the usage of market data in the future, issues such as market liquidity should be taken into consideration. Moreover, in the cash flow test it can be found that the second-order interpolation method has the result with smaller fluctuation compared with the other. Through the analysis outcomes, it can be seen that the risk-free interest rate curve will be affected by many factors, so the detailed discussion on the use of observable interval data and the given final forward rate will directly influence the stability of the line segment. Furthermore, the setting on the UFR is also an important issue.

Classificação JEL: C52, C58, E21, E44, G12
A partir do modelo Epstein-Zin-Weil (EZW), que separa o Coeficiente Relativo de Aversão ao Risco (CRAR) da Elasticidade Intertemporal de Substituição (EIS) do consumo, estudou-se a adequabilidade empírica na explicação dos retornos dos activos e variação do consumo, atendendo à importância da resolução dos puzzles relacionados com o Equity Premium. Para tal, partiu-se do trabalho de Zhang (2006), que estimou o modelo EZW considerando o cálculo do portfólio óptimo (incluindo o capital humano) em detrimento da utilização do portfólio de mercado como proxy. Aplicaram-se três métodos distintos de estimação e inferência estatística (GEL, Kleibergen e restrições de momento condicionais – todos estes novos contributos à literatura EZW), a duas amostras, uma parcial até 2001 no sentido de comparar com o trabalho de Zhang e outra actualizada até 2013, tendo-se ainda considerado quatro conjuntos distintos de instrumentos: Zhang (2006), Stock e Wright (2000), Yogo (2004) e Chen, Favilukis e Ludvigson (2013). As estimações do modelo EZW com recurso ao método GEL por comparação com o GMM, confirmam a pertinência empírica do modelo, em especial nos casos da utilização dos instrumentos de Yogo e Zhang, evidenciando-se a significância estatística dos modelos estimados, e valores plausíveis para o CRAR e EIS, em geral abaixo de 10 e em torno da unidade, respectivamente. No âmbito da estimação por intervalos, com recurso à estatística de Kleibergen (2005) robusta a weak identification, os resultados foram no mesmo sentido, em especial para os instrumentos de Yogo. Quanto às estimações que consideram restrições de momento condicionais, conclui-se que confirmam os resultados anteriores, apesar de serem métodos computacionalmente difíceis de aplicar face à não linearidade acentuada do modelo. Relacionaram-se as estimações dos Stochastic Discount Factors (SDF´s), no âmbito das restrições de momento condicionais, com os ciclos económicos, e concluiu-se que em períodos de recessão os SDF´s aumentam, fruto das precautionary savings realizadas pelos consumidores perante incerteza quanto ao rendimento, adiando consumo (poupando e investindo em activos) para quando o consumo marginal for mais valorizado. Dois períodos recentes onde este fenómeno aconteceu foi na crise do sub-prime em 2008 e das dívidas soberanas em 2011. Com os resultados obtidos nas estimações, sugere-se que o modelo EZW, com cálculo do portfólio da riqueza conforme Zhang (2006), é relevante na explicação do valor dos activos financeiros, bem como na resolução do equity premium e risk free rate puzzles.
Considering the Epstein-Zin-Weil Model (EZW), which separates the Relative Risk Aversion (RRA) and the Consumption Elasticity Intertemporal Substitution (EIS) coefficients, we studied the empirical adequacy in explaining the assets returns and consumption changes, in order to shed some light about the Equity Premium related puzzles. We follow the work of Zhang (2006), who estimated the EZW model including human capital in the calculation of the optimal portfolio instead of the usual proxy - market portfolio. In the empirical work we applied three different estimation and statistical inference methods (GEL, Kleibergen and conditional moment restrictions estimation - all these new contributions to EZW literature), considering two samples, until 2001 in order to compare to Zhang’s work and the updated untill 2013, and also considering four distinct sets of instruments: Zhang (2006), Stock and Wright (2000), Yogo (2004) and Chen, Favilukis and Ludvigson (2013). The EZW model estimation results, using the GEL method and comparing with GMM, confirm the empirical relevance of the model, particularly using Yogo and Zhang instruments, showing the statistical significance of the estimated models, and plausible values for the RRA and EIS coefficients, generally below 10 and around 1, respectively. Similar conclusions are obtained when considering the confidence sets robust to weak identification of Kleibergen (2005), especially for the Yogo instruments. Regarding the estimations that consider the model’s conditional moment restrictions, in general, they confirm the previous results, although these methods are computationally difficult to apply, given the sharp non linearity of the EZW model. Comparing the estimations of the Stochastic Discount Factors (SDF's), under the conditional moment restrictions, with economic cycles, we conclude that during recessions the SDF's increase, in result of consumers precautionary savings facing uncertainty about income, adding consumption (savings invested in assets) for when marginal consumption is valuable. Recently, we observed this phenomenon in 2008 sub-prime crisis and in 2011 sovereign debts crisis. Considering the estimations results obtained, it is suggested that the EZW model with the calculation of the wealth portfolio as in Zhang (2006) is relevant in explaining the asset prices, as well as a possible resolution of the equity premium and risk free rate puzzles.

Stress testing is a useful and increasingly popular method of analysing the resilience of financial systems to adverse events. It has been introduced recently to the pensions sector, in some countries, as well. This dissertation aim is to present results from a stress testing based on three different scenarios, two of them with adverse financial market scenarios and the last one related with longevity. The main goals of this test are to observe the impact of the shocks applied to the prime financial assets available in the financial market and to understand their significance in the pension fund portfolio.
O Teste de Stress é um método cada vez mais útil e popular de análise da resiliência dos sistemas financeiros a eventos adversos. Só recentemente, estes têm sido introduzidos, em alguns países, no sector dos Fundos de Pensões. Esta dissertação pretende apresentar os resultados de testes de stress com base em três diferentes cenários, dois deles baseados em panoramas adversos nos mercados financeiros e um relacionado com a longevidade de vida. Os principais objetivos deste teste são observar o impacto dos diversos choques aplicados aos principais ativos financeiros disponíveis no mercado e entender a sua significância junto dos Fundos de Pensões.

This thesis focuses on the equity premium puzzle, risk-free rate puzzle and possible solutions of these two quantitative conundrums. Original formulation of both puzzles is introduced and comprehensive literature survey is presented to show the developments regarding this topic. These include risk-based explanations, non-risk based explanations and behavioral finance perspective. Main contribution of this study dwells in estimation of these two puzzles for the Czech Republic. Using consumption-based asset pricing model with time separable preferences, presence of the two puzzles is estimated employing annual Czech data from 1995 to 2011. The equity premium puzzle is not present in the Czech Republic, as the coefficient of risk aversion 5.57  . On the other hand, the risk-free rate puzzle is as severe as in developed economies. Furthermore, the individual time preference parameter  is estimated to be larger than one - a counterintuitive result suggesting consumers prefer unit of consumption tomorrow to unit of consumption today. Robustness of the results is confirmed when different proxy for a risk-free rate is used. Results do not change significantly and the risk-free rate puzzle persists. Direction for future research of the financial market puzzles in the Czech Republic is suggested.

The objective of this study is to estimate the CAPM for the two Portuguese retail companies listed in the PSI-20 (JMT and SON) and assess how the two of them evolve regarding the Portuguese market index. This study covered sixteen years (pre and post-subprime crisis) and, based on estimation results, we established a comparison between the relation of each company with the PSI-20. We also analysed the differences before and after the 2008 financial crisis. For this purpose, the estimation of α and β coefficients was done by using the OLS method, and the adequacy of the model was checked by verifying the statistical significance of the regression coefficients and the fulfilment of the OLS assumptions. Finally, the main conclusion is that the two companies tend to behave differently concerning the Portuguese market index. All the beta estimates were statistically significant, meaning that changes in the PSI-20 returns will influence the changes on each company’s returns, which is in line with the CAPM. However, except for two periods for JMT, the alpha estimates were statistically significant, meaning that there were additional factors other than the market risk premium that explained the expected value of excess returns. We could also note that the expected returns for JMT went from a negative value (pre-crisis) to a positive value (post-crisis), while for SON there was a decline in the alpha value.
O objetivo deste estudo é estimar o CAPM para as duas empresas de distribuição portuguesas que estão listadas no PSI-20 (JMT e SON) e avaliarmos como é que elas evoluem em relação ao índice de mercado português. Este trabalho abrangeu um período de dezasseis anos (pré e pós-crise do subprime) e, com base nos resultados das estimativas, fizemos uma comparação entre a relação de cada empresa com o PSI-20. Posteriormente analisámos as diferenças entre o antes e o após da crise financeira de 2008. Para isso, estimámos os coeficientes α e β através do método OLS e a adequação do modelo foi verificada através da significância estatística dos coeficientes da regressão e do cumprimento das hipóteses do método. Por fim, a principal conclusão é que as duas empresas tendem a comportar-se de maneira diferente em relação ao índice de mercado português. Todas as estimativas do beta são estatisticamente significativas, o que significa que as mudanças na rendibilidade do PSI-20 influenciam as mudanças nos retornos de cada empresa, o que está alinhado com o CAPM. No entanto, com exceção de dois períodos para a JMT, as estimativas para o alfa são estatisticamente significativas, o que significa que, além do prémio de risco de mercado, há outros fatores que explicam o valor esperado dos retornos em excesso. Também pudemos observar que os retornos esperados para a JMT passaram de um valor negativo (pré-crise) para um valor positivo (pós-crise), enquanto para a SON houve um declínio no valor de alfa.

碩士
逢甲大學
統計與精算所
99
This study constructed a risk free term structure based on the Taiwan government bond market, with maturities of up to 120 years. In Taiwan, only government bonds with maturities of up to 30 years could be observed. Additionally, the short-term interest rate also has had spurious volatility and caused the GARCH volatility models to be difficult to converge in the estimation of long-term volatility levels. This paper suggested a threshold GARCH model to infer the equilibrium volatility term structure. Furthermore, this paper used the Vasicek equilibrium interest rate model to extrapolate the long-term interest rate to the Unconditional Forward Rates (UFR) suggested by Quantitative Impact Study 5 (QIS5). The proposed method avoided the arbitrage determination of parameters in QIS5. The numerical analysis showed that the proposed method produced liability values for long-term annuities that were less than that of QIS5.

With the exception of holders of default-free instruments, a key risk run by investors is credit risk. To meet the need of investors to hedge this risk, the market uses credit derivatives. The South African credit derivatives market is still in its infancy and only the very simplistic instruments are traded. One of the reasons is due to the technical sophistication required in pricing these instruments. This dissertation introduces the key concepts of risk neutral probabilities, arbitrage free pricing, martingales, default probabilities, survival probabilities, hazard rates and forward spreads. These mathematical concepts are then used as a building block to develop pricing formulae which can be used to infer valuations to the most popular credit derivatives in the South African financial markets.
Operations Research
M.Sc. (Operations Research)