Academic literature on the topic 'Risk-free rate'

It is proven, under a set of assumptions differing from the usual ones in the unboundedness of the time interval, that, in an economy in equilibrium consisting of a risk-free cash account and an equity whose price process is a geometric Brownian motion on , the drift rate must be close to the risk-free rate; if the drift rate and the risk-free rate are constants, then and the price process is the same under both empirical and risk neutral measures. Contributing in some degree perhaps to interest in this mathematical curiosity is the fact, based on empirical data taken at various times over an assortment of equities and relatively short durations, that no tests of the hypothesis of equality are rejected.

There is a certain relationship among stock return rate, market return rate and risk-free interest rate, which is worth discussing, and it is helpful for us to analyze stocks and evaluate their prices. I have found that the market return rate and risk-free rate have correlation through multiple regression, and other stock's return rate can affect the target stock to some extent. The stock return rate is positively related to the market interest rate and inversely related to the risk-free interest rate.

Abstract This paper deals with the fire risk of a selected halogen-free electrical cable. The research was objected to a three-core power electric cable for a fixed installation CHKE J3x1.5 (cross section of each copper core was 1.5 mm2) with a declared class of reaction to fire B2ca, s1, d1, a1. The electrical cable was manufactured and supplied by VUKI, a. s., Slovakia. The fire risk of the electric cable was evaluated based on the heat release rate, total heat release, smoke release rate, total smoke release and effective heat of combustion. These parameters were measured using a cone calorimeter at 50 kW m−2 (specimens and cone emitter were placed horizontally during the test). The measured electrical cable showed a maximum heat release rate of nearly 150 kW m−2, a maximum average heat emission rate of almost 100 kW m−2, a total heat release of almost 130 MJ m−2, a maximum smoke release rate of almost 2.5 s−1, a total smoke release of more than 800 m2 m−2, an effective heat of combustion (cable as a whole) of nearly 9 MJ kg−1 and an effective heat of emission (polymeric parts of the cable) of 26.5 MJ kg−1.

The present value of a forward contract for any asset that does not pay a dividend is calculated by discounting its forward price by the risk-free rate. We show that the discount function for assets that have a non-zero correlation with interest rates, has to be adjusted to account for the correlation between the asset and interest rates. Put-Call parity is also violated and needs to be adjusted as well for such assets. It is shown that the risk-free rate is asset dependent. The adjustment to the price is small for short dated forwards, but increases quadratically with time to maturity.

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).

<p>Society expects that buildings and other structures are safe for the people who use them or who are near them. The failure of a building or structure is expected to be an extremely rare event. Thus, society implicitly relies on the expertise of the professionals involved in the planning, design, construction, operation and maintenance of the structures it uses.<p>Structural engineers devote all their effort to meeting society’s expectations effi ciently. Engineers and scientists work together to develop solutions to structural problems. Given that nothing is absolutely and eternally safe, the goal is to attain an acceptably small probability of failure for a structure, a facility, or a situation. Reliability analysis is part of the science and practice of engineering today, not only with respect to the safety of structures, but also for questions of serviceability and other requirements of technical systems that might be impacted by some probability.<p>The present volume takes a rather broad approach to safety and reliability in Structural Engineering. It treats the underlying concepts of safety, reliability and risk and introduces the reader in a fi rst chapter to the main concepts and strategies for dealing with hazards. The next chapter is devoted to the processing of data into information that is relevant for applying reliability theory. Two following chapters deal with the modelling of structures and with methods of reliability analysis. Another chapter focuses on problems related to establishing target reliabilities, assessing existing structures, and on effective strategies against human error. The last chapter presents an outlook to more advanced applications. The Appendix supports the application of the methods proposed and refers readers to a number of related computer programs.<p>This book is aimed at both students and practicing engineers. It presents the concepts and procedures of reliability analysis in a straightforward, understandable way, making use of simple examples, rather than extended theoretical discussion. It is hoped that this approach serves to advance the application of safety and reliability analysis in engineering practice.<p>The book is amended with a free access to an educational version of a Variables Processor computer program. FreeVaP can be downloaded free of charge and supports the understanding of the subjects treated in this book.

Various models proposed to explain the equity premium or risk‐free rate puzzle are explained: external habits (Abel’s “catching up with the Joneses” model and the Campbell‐Cochrane model), rare disasters, Epstein‐Zin‐Weil utility, long run risks, and idiosyncratic uninsurable labor income risk. External habits allow the SDF to be variable without requiring high variability of consumption. The SDF for a representative investor with Epstein‐Zin‐Weil utility depends on consumption and the market return. It is most useful when the world is not IID, as in the long‐run risks model. With uninsurable labor income risk, there is no representative investor even if investors all have the same CRRA utility, and there is additional exibility to explain asset returns.

There is a representative investor at any Pareto optimal competitive equilibrium. If investors have linear risk tolerance with the same cautiousness parameter, then there is a representative investor with the same utility function. When there is a representative investor, there is a factor model with the representative investor’s marginal utility of consumption as the factor. If the representative investor has constant relative risk aversion, then the risk‐free return and log equity premium can be calculated in terms of moments of aggregate consumption. The equity premium and risk‐free rate puzzles are explained. The coskewness‐cokurtosis pricing model and the Rubinstein option pricing model are derived.

The distinction between conditional and unconditional factor pricing models is explained. The conditional CAPM implies that unconditional risk premia are linear in the expected beta and the beta of the beta. The CCAPM and ICAPM are derived as approximate relations in discrete time. Testing conditional models is equivalent to unconditional tests of pricing for managed portfolios. The Gordon growth model is derived, assuming that dividend growth and the single‐period SDF are IID over time. The equity premium and risk‐free rate puzzles are derived from the Gordon growth model with a CRRA investor and lognormal consumption growth. The Campbell‐Shiller linearization implies that dividend yields predict either future returns or future dividend growth.

AbstractThe “natural rate of interest” is the hypothetical, risk-free real rate of interest that would obtain in a closed economy, if net public debt were zero. It is considerably less than the optimal steady-state rate of interest, which is equal to the system’s growth rate. This holds for a very general “meta-model.” The fundamental equation of capital theory holds on the optimal steady-state path: T = Z − D, where T is the overall economic period of production, Z is the representative private “waiting period” of consumers and D is the public debt ratio. Prosperity is at least 30% lower at the natural rate of interest than at the optimal rate.

This chapter describes the effects of the Financial Stability Board review of interest rate benchmarks. The board’s report recommended a number of measures to help improve security, notably by underpinning existing IBORS with transactions data and by developing alternative, nearly risk-free rates. New benchmarks would be developed with reference to the ISOCO Principles published in July 2013. The chapter explains these principles and how they were put into practice.

Derivatives valuation is based on the key principle of no-arbitrage pricing. This chapter presents valuation models for various types of fixed income derivatives, including forward rate agreements (FRAs), interest rate swaps, Eurodollar and Treasury bond futures, bond options, caps and floors, swaptions, and options on interest rate futures. Following the financial crisis that began in the summer of 2007, major changes occurred in the practice of fixed income derivatives valuation, particularly regarding the adoption of overnight indexed swaps (OIS) as a source of the risk-free rate. This chapter shows how OIS discounting is implemented in FRA pricing and swap valuation. Traditional approaches such as cost of carry valuation in futures pricing are illustrated. With respect to option valuation, this chapter explains the risk-neutral pricing approach as well as closed-form solutions such as the Black model. The chapter also provides numeric examples to illustrate the practical use of the presented models and formulas.

This chapter presents facts and concepts regarding long-run stock market returns. It starts out briefly defining stock returns.The chapter then looks at the historical data, starting with US data and then turning to international data. It decomposes stock returns into a risk-free rate and a risk premium. The chapter also introduces concepts that will be used repeatedly throughout the book, such as different kinds of averages (arithmetic and geometric), standard deviations, variances, and other important concepts in finance.The chapter presents stylized facts about long-run stock returns. It does not try to explain what generates these returns. This is the topic of subsequent chapters.

This chapter looks at how 16 million American children live in poverty, putting them at risk for delayed development, disease, and poor educational outcomes. The Earned Income Tax Credit (EITC) is a pro-work, federal tool that has reduced or eliminated poverty for 13.2 million children. However, 20% of eligible households do not claim this tax credit. To lower the US poverty rate, which has plateaued, how might health systems help families maximize this economic credit? A 2018 program suggests it is possible to connect EITC-eligible families to free tax preparation through physician referral, fliers included with visit reminders, in-clinic advertising, and calls to families with upcoming appointments in the pediatric clinic, offering tax services 15 to 25 hours weekly, including evenings and weekends. The program was associated with increased filing rates, receipt of EITC, and use of free tax preparation, all of which increase money for low-income families. Finding such clever, convenient ways to make better use of federal policies to reduce poverty one family at a time creates a novel community resource.

Non-Hodgkin lymphoma (NHL) is the fourth most common malignancy in children, with an even higher incidence in adolescents, and is primarily represented by only a few histological subtypes. Dramatic progress has been achieved, with survival rates exceeding 80%. Most patients with Burkitt lymphoma and diffuse large B-cell lymphoma are cured with short, intensive, pulse chemotherapy. The benefit of the addition of rituximab has been demonstrated for high-risk B-NHL and primary mediastinal B-cell lymphoma. Lymphoblastic lymphoma is treated with intensive, semi-continuous, longer ‘leukaemia-derived’ protocols. Relapses in B-cell and lymphoblastic lymphomas are rare and infrequently curable, even with intensive approaches. Event-free survival rates of about 75% have been achieved in anaplastic large-cell lymphomas with various regimens, including generally a short, intensive ‘B-like’ regimen. The role of immunity appears important in prognosis and needs further exploration in therapy. Anaplastic lymphoma kinase (ALK) inhibitor therapeutic approaches are currently being investigated. For all these paediatric lymphomas, the intensity of induction/consolidation treatments correlates with a high rate of immediate toxicities, but due to low cumulative doses of anthracyclines and alkylating agents, minimal or no long-term toxicity is expected. Challenges that remain include defining the value of prognostic factors, such as early response on positron emission tomography (PET)/computed tomography (CT) and monitoring of minimal disseminated and residual disease, utilizing new biological technologies to improve risk stratification and the development of innovative therapies, both at frontline and relapse. non-Hodgkin lymphoma, NHL, European Intergroup for Childhood NHL, EICNHL, Burkitt lymphoma, anaplastic large-cell lymphoma, ALK, lymphoblastic lymphoma

The history of active worldwide scientific research on mechanisms of aging and the age-associated diseases counts more than five decades. Of these, among the numerous theories of aging, at least 50 years dominated the free radical theory of aging. Since mitochondria were found to be the major producers of free radicals, the research on aging became largely centered on mitochondria. At the end of 80s of the 20th century, physicians have established a new nosological entity named “Metabolic syndrome” comprising several simultaneously existing symptoms and risk factors, which increase with age to 47% in men and 64% for women. The diagnosis of metabolic syndrome (MetS) requires simultaneous presence of at least three out of five medical conditions: visceral obesity, hypertension, high blood sugar, insulin resistance, low serum high-density lipoprotein accompanied with high serum triglycerides. However, from the beginning of the definition of MetS there was, and still is, a rather lovely debate, which of the symptoms must be considered as the main one. In spite of the enormous number of publications on both mechanisms of aging and MetS, there was relatively small progress in understanding the fundamental processes in these closely related problems. On the contrary, the mitochondrial free radical theory was found to be wrong in its current paradigms. In this Chapter we will discuss recent discoveries and hypotheses which open new perspectives in both theoretical and practical approaches to the problems of aging and MetS. We will show how aging and development of MetS are closely related to each other and the normal ontogenesis of human beings. Why men and women have different rates of aging and mechanisms of transition to MetS. We state that MetS is not just a cluster of symptoms, but one of the last steps of individual ontogenesis, namely the first step of eldership when the aging rate may increase manifold.

Proponents of new pipeline projects are often asked by regulators to provide estimates of risk and reliability for their proposed pipeline. On existing pipelines, the availability of operating and assessment data is generally considered to be essential to the task of performing an accurate and defendable risk or reliability assessment. For proposed or new pipelines, the absence of these data presents a significant challenge to those performing the analysis. The reliance on industry incident data presents problems, since the vast majority of loss-of-containment incidents relate to older pipelines in which the design, routing criteria, material properties, material manufacturing processes, and early operating practices differ significantly from those that are characteristic of modern pipelines. As a consequence, much of the available failure incident data does not accurately reflect the threats or the magnitudes of the threats that are associated with modern pipelines. In order to address this problem, ‘adjustment factors’ are often applied against incident data to try to account for threat differences between the source data and the intended application. The selection of these adjustment factors can often be quite subjective, however, and open to judgment; therefore, they can be difficult to justify. With the rapidly growing practice of regular in-line inspection (ILI) on transmission pipelines, an extensive repository of ILI data has been accumulated — much of it relating to modern pipelines. Through the judicious selection of source data, ILI data sets can be mined so that an analogue data set can be created that constitutes a reasonable representation of the attributes of reliability of a specific new pipeline of interest. Key reliability properties, such as tool error distribution, feature incidence rate, feature size distribution, and apparent feature growth rate distribution can be derived from such analogue data. By applying these reliability properties in an analysis along with known pipeline design and material properties and their associated distributions, and by taking consideration of planned inspection intervals, a reliability basis can be derived for estimating pipeline risk and reliability. Estimates of risk and reliability that are derived in this manner employ methodologies that are repeatable, defendable, transparent, and free of subjectivity. This paper outlines an approach for completing risk and reliability estimates on new pipelines, and presents the results of some sample calculations. The reliability estimates illustrated are based on an approach whereby corrosion feature size and growth rates are obtained from analogue ILI datasets, and treated as random variables. In that regard, they constitute the probability of exceeding a limit state that represents an approximation of the condition for failure.

Due to its superior mechanical and electrical properties, as well as low cost, Cu is gradually replacing Au as wire bonding material. However, since copper is a stiffer material, it requires greater bonding force, which in turn increases risk of bond pad cratering and inter-layer dielectric (ILD) fracture. A critical challenge to numerically modeling the pad cratering or ILD fracture is the availability of appropriate constitutive models for the Cu free-air balls (FAB). In this work we first present rate and temperature dependent force-displacement response of micron-sized Cu FAB characterized using a custom-built high-precision microtester. From the experimental force-displacement data, Anand viscoplastic constitutive model parameters are obtained using an inverse finite element analysis procedure, where the material parameters are iterated through an automated procedure until the finite element and experimental force-displacement responses match. The constitutive model parameters to describe the FAB behavior at low and intermediate strain rates and at high temperatures are obtained and reported in this paper.

When installing subsea pipelines on an uneven seabed, the free spans can be vulnerable to fatigue damage caused by vortex induced vibrations (VIV). Indeed, even moderate currents can induce vortex shedding, alternately at the top and the bottom of the pipeline, at a rate determined by the flow velocity. Each time a vortex sheds, a force is generated in both the in-line and cross-flow direction, causing an oscillatory multi-mode vibration. This vortex induced vibration can give rise to fatigue damage of submarine pipeline spans, especially in the vicinity of the girth welds. Traditional design for VIV is recommended in DNV-RP-F105, which limits the allowable free span length and implies whether (and when) seabed interventions are required. The traditional DNV-RP-F105 design method is based on a semi-empirical approach, where the allowable span length depends on the pipe properties (diameter, wall thickness, coating, steel SN_curves, …), the sea state (current velocity, wave induced velocity and period) and the soil conditions (submerged unit weight, undrained shear strength, bearing capacity,…). All these input parameters, however, exhibit a certain extent of scatter and uncertainty. This paper presents a risk based evaluation of free spans, by applying the principles of structural reliability theory to the problem of long free spanning pipelines subjected to VIV. First, a fully deterministic on-bottom roughness analysis is performed to introduce numerical tools for free span analysis. Then, a sensitivity analysis on soil parameters is presented to show significant influence of soil properties on free span predictions. To study the implications of uncertainty in soil properties, a First Order Reliability Method (FORM) analysis is presented at the end of this paper, where the soil properties are introduced as stochastic variables.

Abstract In Romania, in the last decades, was not realized any complex plan of management concerning the environmental rehabilitation of the natural riverbeds, even if there are even in present many places confronted with repeated floods. After the floods from 2004, 2005 and 2014 have been recorded in some places large deposits of sediments or contrary, in other zones with erosion and uncontrolled coastal slides. As an immediate effect, zones with risk for the local population and not only, have appeared. The present paper estimates the capacity of transport for a riverbed in natural conditions, based on the local measurements registered before and after a flood. The model is tested for a tributary of the Bistrita River, the Cracau River, near the Siret basin, an area well-known for such repeated floods sometimes even two or three recorded in the same year, as it was in 2005 and 2008. Three of these floods were confronted with human losses, many dead animals, and agricultural flooded areas. Near the analyzed watercourse there are many localities, with a high density of population. The realized numerical model for the flow with free surface was taking into account the possibility of the permanent changing of the lateral surfaces (riverbeds) during the floods. A continuous balance of the entered and transported sediments is realized, due to the erosion and sediment transportation. The time variation of the discharged liquid and the solid phases are directly connected with the sediment transport. In these conditions, the fine fractions of sediments from the bed’s structure are removed from its surface. In some places, the sediments become “armored” with the coarser part of the bed sediment. It is proposed a mathematical model to simulate the effect of both types of deposits into a fluid flow in open channels, with a movable bed. The entire alluvial stream, until the base rock, is considered with a small thickness so the non-uniformity of the grain size in the vertical distribution in riverbed could be neglected. The boundary conditions in the flood analysis consist of the upstream hydrograph and the stationary level of the downstream watercourse. Knowing the flow rate and the water levels by direct measurements, there is possible to establish the risk zones, far away from the river borders. The primary purpose of this study is to minimize the effects of such uncontrolled floods by determining the risk zones and to present a solution for increasing population safety which lives near the riverbed. Finally, some conclusions and references are mentioned.

Abstract Chip access for flip-chip packages in high-performance microprocessors is performed by removing the lid then by extraction of the die from the package substrate. Residual stresses built in temperature cycled (TC) units result in a low success rate using conventional delidding techniques. A need has developed in failure analysis for stress-free removal of the materials surrounding a flip-chip device. This paper discusses a novel, cost effective, wet chemical process that has been developed for thin die and lid removal of flip-chip packaged units. The process uses n-methy-2-pyrrolidone (NMP) for epoxy-based lid attach and underfill materials. A reflux unit is designed to reduce the risk of fire and explosion when the sample is heated in the solvent to the desired temperature. The method of heating reduces the chance of thermal shock, which could fracture the sample due to rapid heating or cooling.

The research reactor Thetis, in service since 1967 and stopped in 2003, is part of the laboratories of the institution of nuclear science of the University of Ghent. The reactor, of the pool-type, was used as a neutron-source for the production of radio-isotopes and for activation-analyses. The reactor is situated in a water pool with inner diameter of 3 m. and a depth of 7.5 m. The reactor core is situated 5.3m under water level. Besides the reactor, the pool contains pneumatic loops, handling tools, graphite blocks for neutron moderation and other experimental equipment. The building houses storage rooms for fissile material and sources, a pneumatic circuit for transportation of samples, primary and secondary cooling circuits, water cleaning resin circuits, a ventilation system and other necessary devices. Because of the experimental character of the reactor, laboratories with glove boxes and other tools were needed and are included in the dismantling program. The building is in 3 levels with a crawl-space. The ground-floor contains the ventilation installation, the purification circuits with tanks, cooling circuits and pneumatic transport system. On the first floor, around the reactor hall, the control-room, visiting area, end-station for pneumatic transport, waste-storage room, fuel storage-room and the labs are located. The second floor contains a few laboratories and end stations of the two high speed transfer tubes. The lowest level of the pool is situated under ground level. The reactor has been operated at a power of 150 kW and had a max operating power of 250 kW. Belgoprocess has been selected to decommission the reactor, the labs, storage halls and associated circuits to free release the building for conventional reuse and for the removal of all its internals as legal defined. Besides the dose-rate risk and contamination risk, there is also an asbestos risk of contamination. During construction of the installation, asbestos-containing materials were used, which must be removed in controlled conditions. The ventilation system is considered free from nuclear contamination but it contains asbestos. This paper covers the organization of the dismantling work, the technical execution aspect and conclusions already known (dismantling is ongoing as this is written).

The proposed ultrasonic Reactor water Level Monitoring system is intended for monitoring water level in the hot leg of a nuclear reactor during Operation at Reduced Inventory (ORI) with the core in place as may be needed for certain maintenance activities. Since the existing fuel bundles continue the production of heat thorough the decay process, it is critical to maintain a certain water flow rate through the reactor. The Residual Heat Removal System (RHRS) handles this task during the reactor shutdown. The free water surface during ORI subjects the RHRS to the risk of air intake. Such an event would trigger a set of emergency procedures for priming the RHRS and bringing it back online. Some of the possible outcomes of such an event are: extension of outage, handling of the extra regulatory reporting tasks, potential requirements for extra testing after system recovery, possible damage to RHR pump, boiling of reactor water, generation of airborne contamination, and fuel damage. Another risk during ORI is reactor overflow. The major immediate concern is the safety of personnel in case of accidental overflow. This event could result in contamination and the related outage delays. The previously existing systems have always had problems with transducer reliability. This has lead to the need for removal and re-installation of their transducers from outage to outage. However, the proposed system uses a redundant design with permanently mounted transducers. The system uses advanced digital signal processing techniques to determine the water level.

Edison Welding Institute (EWI) and Enterprise Products Operating LP (Enterprise) worked together to develop an in-service welding program. The objective of this project was to relax flow restrictions on current in-service welding procedures to allow for welding onto liquid pipelines with flow rates outside of current flow limits. Enterprise’s current products include liquid propane, liquid ethane, and propane and ethane mixes in addition to other refined products. The current Enterprise in-service welding procedures restrict welding onto liquid pipelines with a flow rate between 1.3 and 4.0 ft/s (0.4 and 1.2 m/s). The minimum flow rate of 1.3 ft/s (0.4 m/s) was used because it was Enterprise’s minimal operating flow rate. The maximum flow rate of 4 ft/s (1.2 m/s) was grandfathered into the procedures. When welding onto an in-service pipeline to repair a damaged section of pipe or to install a branch connection (i.e., hot-tapping) there are two main concerns (burnthrough and hydrogen cracking) and both concerns needed to be evaluated for both flow conditions. The results from the project allow welding onto no-flow liquid pipelines with wall thicknesses between 0.25 and 0.5 in. (6.4 to 12.7 mm). Even though welding onto a no-flow thin-walled liquid pipeline [i.e., less than 0.25 in. (6.4 mm)] would not increase cracking susceptibility, the risk of burnthrough and eutectic iron formation would make the procedure unacceptable. The results of this project also indicated that acceptable welds can be made onto a high flow liquid pipeline [up to 12 ft/s (3.7 m/s)]. It was recommended, however, that Enterprise only use the temper bead welding procedures for such applications. Proper use of the temper bead welding procedures (i.e., proper heat input, weld toe spacing and stringent low hydrogen welding practice) has been shown to produce acceptable, crack-free welds. It is important to note that none of the welds showed signs of cracking, but the hardness levels of the heat input control procedures all exceeded the critical hardness level for their intended carbon equivalent materials. Increasing the flow rate from 4 to 12 ft/s (1.2 to 3.7 m/s) does appear to increase the cooling effect but it is not possible to determine the magnitude of the effect from the results of this work.

Free college proposals have become increasingly popular in many countries of the world. To evaluate their potential effects, we develop and estimate a dynamic model of college enrollment, performance, and graduation. A central piece of the model, student effort, has a direct effect on class completion, and an indirect effect in mitigating the risk of not completing a class or not remaining in college. We estimate the model using rich, student-level administrative data from Colombia, and use the estimates to simulate free college programs that differ in eligibility requirements. Among these, universal free college expands enrollment the most, but it does not affect graduation rates and has the highest per-graduate cost. Performance-based free college, in contrast, delivers a slightly lower enrollment expansion yet a greater graduation rate at a lower per-graduate cost. Relative to universal free college, performance-based free college places a greater risk on students but is precisely this feature that delivers better outcomes. Nonetheless, the modest increase in graduation rates suggests that additional, complementary policies might be required to elicit the large effort increase needed to raise graduation rates.

International financial institutions (IFIs) generally enjoy preferred creditors treatment (PCT). Although PCT rarely appears in legal contracts, when sovereigns restructure bilateral or commercial debts, they normally pay IFIs in full. This paper presents a model where a creditor, such as an IFI, that can commit to lend limited amounts at the risk-free rate and can refrain from lending into arrears is always repaid and adds value. The analysis suggests that IFIs and market lenders can both enhance welfare, even if banning commercial borrowing can sometimes be optimal. To maintain their status, preferred lenders should offer low cost financing in volumes that are consistent with countries' incentives to repay even in bad states. This suggests such lenders should not differentiate lending interest rates according to risk and should not participate in the restructuring of commercial debt.

Verification will be of critical importance to achieving and maintaining a Middle East zone free of weapons of mass destruction (ME WMD). Effective verification arrangements would serve a vital national security objective for each state in the region by reducing tensions, removing the motivation to proliferate, and mitigating the risk of a virtual nuclear arms race (or war). In view of the high levels of tension and mistrust within the zone, ensuring effective verification will be especially demanding. The paper examines specific elements of the future nuclear verification of the zone, including: Which states should be included? What prohibitions and obligations should apply in the zone and how would they be verified? How could elimination of nuclear weapons in the zone be achieved? On what basis would the zone treaty enter into force? The paper also examines a number of existing treaties and arrangements as well as the lessons learned from past verification cases which regional states can draw on in developing verification for a Middle East nuclear-weapon-free zone.

Background/Purpose: Post-operative delirium leads to significant morbidity in elderly patients, yet there is no regimen to prevent POD. Opioid use in the elderly surgical population is of the most significant risk factors for developing POD. The purpose of this scoping review is to recognize that Dexmedetomidine mitigates cognitive dysfunction secondary to acute pain and the use of narcotic analgesia by decreasing the amount of norepinephrine (an excitatory neurotransmitter) released during times of stress. This mechanism of action also provides analgesia through decreased perception and modulation of pain. Methods: The authors developed eligibility criteria for inclusion of articles and performed a systematic search of several databases. Each of the authors initially selected five articles for inclusion in the scoping review. We created annotated literature tables for easy screening by co-authors. After reviewing the annotated literature table four articles were excluded, leaving 11 articles for inclusion in the scoping review. There were six level I meta-analysis/systematic reviews, four level II randomized clinical trials, and one level IV qualitative research article. Next, we created a data-charting form on Microsoft Word for extraction of data items and synthesis of results. Results: Two of the studies found no significant difference in POD between dexmedetomidine groups and control groups. The nine remaining studies noted decreases in the rate, duration, and risk of POD in the groups receiving dexmedetomidine either intraoperatively or postoperatively. Multiple studies found secondary benefits in addition to decreased POD, such as a reduction of tachycardia, hypertension, stroke, hypoxemia, and narcotic use. One study, however, found that the incidence of hypotension and bradycardia were increased among the elderly population. Implications for Nursing Practice: Surgery is a tremendous stressor in any age group, but especially the elderly population. It has been shown postoperative delirium occurs in 17-61% of major surgery procedures with 30-40% of the cases assumed to be preventable. Opioid administration in the elderly surgical population is one of the most significant risk factors for developing POD. With anesthesia practice already leaning towards opioid-free and opioid-limited anesthetic, the incorporation of dexmedetomidine could prove to be a valuable resource in both reducing opioid use and POD in the elderly surgical population. Although more research is needed, the current evidence is promising.

1.1 Macroeconomic summary Economic recovery has consistently outperformed the technical staff’s expectations following a steep decline in activity in the second quarter of 2020. At the same time, total and core inflation rates have fallen and remain at low levels, suggesting that a significant element of the reactivation of Colombia’s economy has been related to recovery in potential GDP. This would support the technical staff’s diagnosis of weak aggregate demand and ample excess capacity. The most recently available data on 2020 growth suggests a contraction in economic activity of 6.8%, lower than estimates from January’s Monetary Policy Report (-7.2%). High-frequency indicators suggest that economic performance was significantly more dynamic than expected in January, despite mobility restrictions and quarantine measures. This has also come amid declines in total and core inflation, the latter of which was below January projections if controlling for certain relative price changes. This suggests that the unexpected strength of recent growth contains elements of demand, and that excess capacity, while significant, could be lower than previously estimated. Nevertheless, uncertainty over the measurement of excess capacity continues to be unusually high and marked both by variations in the way different economic sectors and spending components have been affected by the pandemic, and by uneven price behavior. The size of excess capacity, and in particular the evolution of the pandemic in forthcoming quarters, constitute substantial risks to the macroeconomic forecast presented in this report. Despite the unexpected strength of the recovery, the technical staff continues to project ample excess capacity that is expected to remain on the forecast horizon, alongside core inflation that will likely remain below the target. Domestic demand remains below 2019 levels amid unusually significant uncertainty over the size of excess capacity in the economy. High national unemployment (14.6% for February 2021) reflects a loose labor market, while observed total and core inflation continue to be below 2%. Inflationary pressures from the exchange rate are expected to continue to be low, with relatively little pass-through on inflation. This would be compatible with a negative output gap. Excess productive capacity and the expectation of core inflation below the 3% target on the forecast horizon provide a basis for an expansive monetary policy posture. The technical staff’s assessment of certain shocks and their expected effects on the economy, as well as the presence of several sources of uncertainty and related assumptions about their potential macroeconomic impacts, remain a feature of this report. The coronavirus pandemic, in particular, continues to affect the public health environment, and the reopening of Colombia’s economy remains incomplete. The technical staff’s assessment is that the COVID-19 shock has affected both aggregate demand and supply, but that the impact on demand has been deeper and more persistent. Given this persistence, the central forecast accounts for a gradual tightening of the output gap in the absence of new waves of contagion, and as vaccination campaigns progress. The central forecast continues to include an expected increase of total and core inflation rates in the second quarter of 2021, alongside the lapse of the temporary price relief measures put in place in 2020. Additional COVID-19 outbreaks (of uncertain duration and intensity) represent a significant risk factor that could affect these projections. Additionally, the forecast continues to include an upward trend in sovereign risk premiums, reflected by higher levels of public debt that in the wake of the pandemic are likely to persist on the forecast horizon, even in the context of a fiscal adjustment. At the same time, the projection accounts for the shortterm effects on private domestic demand from a fiscal adjustment along the lines of the one currently being proposed by the national government. This would be compatible with a gradual recovery of private domestic demand in 2022. The size and characteristics of the fiscal adjustment that is ultimately implemented, as well as the corresponding market response, represent another source of forecast uncertainty. Newly available information offers evidence of the potential for significant changes to the macroeconomic scenario, though without altering the general diagnosis described above. The most recent data on inflation, growth, fiscal policy, and international financial conditions suggests a more dynamic economy than previously expected. However, a third wave of the pandemic has delayed the re-opening of Colombia’s economy and brought with it a deceleration in economic activity. Detailed descriptions of these considerations and subsequent changes to the macroeconomic forecast are presented below. The expected annual decline in GDP (-0.3%) in the first quarter of 2021 appears to have been less pronounced than projected in January (-4.8%). Partial closures in January to address a second wave of COVID-19 appear to have had a less significant negative impact on the economy than previously estimated. This is reflected in figures related to mobility, energy demand, industry and retail sales, foreign trade, commercial transactions from selected banks, and the national statistics agency’s (DANE) economic tracking indicator (ISE). Output is now expected to have declined annually in the first quarter by 0.3%. Private consumption likely continued to recover, registering levels somewhat above those from the previous year, while public consumption likely increased significantly. While a recovery in investment in both housing and in other buildings and structures is expected, overall investment levels in this case likely continued to be low, and gross fixed capital formation is expected to continue to show significant annual declines. Imports likely recovered to again outpace exports, though both are expected to register significant annual declines. Economic activity that outpaced projections, an increase in oil prices and other export products, and an expected increase in public spending this year account for the upward revision to the 2021 growth forecast (from 4.6% with a range between 2% and 6% in January, to 6.0% with a range between 3% and 7% in April). As a result, the output gap is expected to be smaller and to tighten more rapidly than projected in the previous report, though it is still expected to remain in negative territory on the forecast horizon. Wide forecast intervals reflect the fact that the future evolution of the COVID-19 pandemic remains a significant source of uncertainty on these projections. The delay in the recovery of economic activity as a result of the resurgence of COVID-19 in the first quarter appears to have been less significant than projected in the January report. The central forecast scenario expects this improved performance to continue in 2021 alongside increased consumer and business confidence. Low real interest rates and an active credit supply would also support this dynamic, and the overall conditions would be expected to spur a recovery in consumption and investment. Increased growth in public spending and public works based on the national government’s spending plan (Plan Financiero del Gobierno) are other factors to consider. Additionally, an expected recovery in global demand and higher projected prices for oil and coffee would further contribute to improved external revenues and would favor investment, in particular in the oil sector. Given the above, the technical staff’s 2021 growth forecast has been revised upward from 4.6% in January (range from 2% to 6%) to 6.0% in April (range from 3% to 7%). These projections account for the potential for the third wave of COVID-19 to have a larger and more persistent effect on the economy than the previous wave, while also supposing that there will not be any additional significant waves of the pandemic and that mobility restrictions will be relaxed as a result. Economic growth in 2022 is expected to be 3%, with a range between 1% and 5%. This figure would be lower than projected in the January report (3.6% with a range between 2% and 6%), due to a higher base of comparison given the upward revision to expected GDP in 2021. This forecast also takes into account the likely effects on private demand of a fiscal adjustment of the size currently being proposed by the national government, and which would come into effect in 2022. Excess in productive capacity is now expected to be lower than estimated in January but continues to be significant and affected by high levels of uncertainty, as reflected in the wide forecast intervals. The possibility of new waves of the virus (of uncertain intensity and duration) represents a significant downward risk to projected GDP growth, and is signaled by the lower limits of the ranges provided in this report. Inflation (1.51%) and inflation excluding food and regulated items (0.94%) declined in March compared to December, continuing below the 3% target. The decline in inflation in this period was below projections, explained in large part by unanticipated increases in the costs of certain foods (3.92%) and regulated items (1.52%). An increase in international food and shipping prices, increased foreign demand for beef, and specific upward pressures on perishable food supplies appear to explain a lower-than-expected deceleration in the consumer price index (CPI) for foods. An unexpected increase in regulated items prices came amid unanticipated increases in international fuel prices, on some utilities rates, and for regulated education prices. The decline in annual inflation excluding food and regulated items between December and March was in line with projections from January, though this included downward pressure from a significant reduction in telecommunications rates due to the imminent entry of a new operator. When controlling for the effects of this relative price change, inflation excluding food and regulated items exceeds levels forecast in the previous report. Within this indicator of core inflation, the CPI for goods (1.05%) accelerated due to a reversion of the effects of the VAT-free day in November, which was largely accounted for in February, and possibly by the transmission of a recent depreciation of the peso on domestic prices for certain items (electric and household appliances). For their part, services prices decelerated and showed the lowest rate of annual growth (0.89%) among the large consumer baskets in the CPI. Within the services basket, the annual change in rental prices continued to decline, while those services that continue to experience the most significant restrictions on returning to normal operations (tourism, cinemas, nightlife, etc.) continued to register significant price declines. As previously mentioned, telephone rates also fell significantly due to increased competition in the market. Total inflation is expected to continue to be affected by ample excesses in productive capacity for the remainder of 2021 and 2022, though less so than projected in January. As a result, convergence to the inflation target is now expected to be somewhat faster than estimated in the previous report, assuming the absence of significant additional outbreaks of COVID-19. The technical staff’s year-end inflation projections for 2021 and 2022 have increased, suggesting figures around 3% due largely to variation in food and regulated items prices. The projection for inflation excluding food and regulated items also increased, but remains below 3%. Price relief measures on indirect taxes implemented in 2020 are expected to lapse in the second quarter of 2021, generating a one-off effect on prices and temporarily affecting inflation excluding food and regulated items. However, indexation to low levels of past inflation, weak demand, and ample excess productive capacity are expected to keep core inflation below the target, near 2.3% at the end of 2021 (previously 2.1%). The reversion in 2021 of the effects of some price relief measures on utility rates from 2020 should lead to an increase in the CPI for regulated items in the second half of this year. Annual price changes are now expected to be higher than estimated in the January report due to an increased expected path for fuel prices and unanticipated increases in regulated education prices. The projection for the CPI for foods has increased compared to the previous report, taking into account certain factors that were not anticipated in January (a less favorable agricultural cycle, increased pressure from international prices, and transport costs). Given the above, year-end annual inflation for 2021 and 2022 is now expected to be 3% and 2.8%, respectively, which would be above projections from January (2.3% and 2,7%). For its part, expected inflation based on analyst surveys suggests year-end inflation in 2021 and 2022 of 2.8% and 3.1%, respectively. There remains significant uncertainty surrounding the inflation forecasts included in this report due to several factors: 1) the evolution of the pandemic; 2) the difficulty in evaluating the size and persistence of excess productive capacity; 3) the timing and manner in which price relief measures will lapse; and 4) the future behavior of food prices. Projected 2021 growth in foreign demand (4.4% to 5.2%) and the supposed average oil price (USD 53 to USD 61 per Brent benchmark barrel) were both revised upward. An increase in long-term international interest rates has been reflected in a depreciation of the peso and could result in relatively tighter external financial conditions for emerging market economies, including Colombia. Average growth among Colombia’s trade partners was greater than expected in the fourth quarter of 2020. This, together with a sizable fiscal stimulus approved in the United States and the onset of a massive global vaccination campaign, largely explains the projected increase in foreign demand growth in 2021. The resilience of the goods market in the face of global crisis and an expected normalization in international trade are additional factors. These considerations and the expected continuation of a gradual reduction of mobility restrictions abroad suggest that Colombia’s trade partners could grow on average by 5.2% in 2021 and around 3.4% in 2022. The improved prospects for global economic growth have led to an increase in current and expected oil prices. Production interruptions due to a heavy winter, reduced inventories, and increased supply restrictions instituted by producing countries have also contributed to the increase. Meanwhile, market forecasts and recent Federal Reserve pronouncements suggest that the benchmark interest rate in the U.S. will remain stable for the next two years. Nevertheless, a significant increase in public spending in the country has fostered expectations for greater growth and inflation, as well as increased uncertainty over the moment in which a normalization of monetary policy might begin. This has been reflected in an increase in long-term interest rates. In this context, emerging market economies in the region, including Colombia, have registered increases in sovereign risk premiums and long-term domestic interest rates, and a depreciation of local currencies against the dollar. Recent outbreaks of COVID-19 in several of these economies; limits on vaccine supply and the slow pace of immunization campaigns in some countries; a significant increase in public debt; and tensions between the United States and China, among other factors, all add to a high level of uncertainty surrounding interest rate spreads, external financing conditions, and the future performance of risk premiums. The impact that this environment could have on the exchange rate and on domestic financing conditions represent risks to the macroeconomic and monetary policy forecasts. Domestic financial conditions continue to favor recovery in economic activity. The transmission of reductions to the policy interest rate on credit rates has been significant. The banking portfolio continues to recover amid circumstances that have affected both the supply and demand for loans, and in which some credit risks have materialized. Preferential and ordinary commercial interest rates have fallen to a similar degree as the benchmark interest rate. As is generally the case, this transmission has come at a slower pace for consumer credit rates, and has been further delayed in the case of mortgage rates. Commercial credit levels stabilized above pre-pandemic levels in March, following an increase resulting from significant liquidity requirements for businesses in the second quarter of 2020. The consumer credit portfolio continued to recover and has now surpassed February 2020 levels, though overall growth in the portfolio remains low. At the same time, portfolio projections and default indicators have increased, and credit establishment earnings have come down. Despite this, credit disbursements continue to recover and solvency indicators remain well above regulatory minimums. 1.2 Monetary policy decision In its meetings in March and April the BDBR left the benchmark interest rate unchanged at 1.75%.