DOCSLIB.ORG

Basics of Financial Mathematics

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Basics of Financial Mathematics MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION Federal State-Funded Educational Institution of Higher Vocational Education «National Research Tomsk Polytechnic University» Department of Higher Mathematics and Mathematical Physics BASICS OF FINANCIAL MATHEMATICS A study guide 2012 BASICS OF FINANCIAL MATHEMATICS Author A. A. Mitsel. The study guide describes the basic notions of the quantitative analysis of financial transactions and methods of evaluating the yield of commercial contracts, investment projects, risk-free securities and optimal portfolio of risk-laden securities. The study guide is designed for students with the major 231300 Applied Mathematics, 230700 Application Informatics, and master’s program students with the major 140400 Power Engineering and Electrical Engineering. CONTENTS Introduction Chapter 1. Accumulation and discounting 1.1. Time factor in quantitative analysis of financial transactions 1.2. Interest and interest rates 1.3. Accumulation with simple ınterest 1.4. Compound interest 1.5. Nominal and effective interest rates 1.6. Determining the loan duration and interest rates 1.7. The notion of discounting 1.8. Inflation accounting at interest accumulation 1.9. Continuous accumulation and discounting (continuous interest) 1.10. Simple and compound interest rate equivalency 1.11. Change of contract terms 1.12. Discounting and accumulation at a discount rate 1.13. Comparison of accumulation methods 1.14. Comparing discounting methods Questions for self-test Chapter 2. Payment, annuity streams 2.1. Basic definitions 2.2. The accumulated sum of the annual annuity 2.3. Accumulated sum of annual annuity with interest calculation m times a year 2.4. Accumulated sum of p – due annuity 2.5. Accumulated sum of – due annuity with p m,1 m 2.6. The present value of the ordinary annuity 2.7. The present value of the annual annuity with interest calculation times a year 2.8. The present value of the – due annuity ( m 1) 2.9. The present value of the – due annuity with m1, p m 2.10. The relation between the accumulated and present values of annuity 2.11. Determining annuity parameters 2.12. Annuity conversion Questions for self-test Chapter 3. Financial transaction yield 3.1. The absolute and average annual transaction yield 3.2. Tax and inflation accounting 3.3. Payment stream and its yield 3.4. Instant profit Questions for self-test Chapter 4. Credit calculations 4.1. Total yield index of a financial and credit transaction 4.2. The balance of a financial and credit transaction 4.3. Determining the total yield of loan operations with commission 4.4. Method of comparing and analyzing commercial contracts 4.5. Planning long-term debt repayment Questions for self-test Chapter 5. Analysis of real investments 5.1. Introduction 5.2. Net present value 5.3 internal rate of return 5.4. Payback period 5.5. Profitability index 5.6. Model of human capital investment Questions for self-test Chapter 6. Quantitative financial analysis of fixed income securities 6.1. Introductioon 6.2. Determining the total yield of bonds 6.3. Bond portfolio return 6.4. Bond evaluation 6.5. The evaluation of the intrinsic value of bonds 6.6. Valuation of risk connected with investments in bonds Questions for self-test Chapter 7. Bond duration 7.1. The notion of duration 7.2. Connection of duration with bond price change 7.3. Properties of the duration and factor of bond convexity 7.4. Time dependence of the value of investment in the bond. Immunization property of bond duration 7.5. Properties of the planned and actual value of investments Questions for self-test Chapter 8. Securities portfolio optimization 8.1. Problem of choosing the investment portfolio 8.2. Optimization of the wildcat security portfolio 8.3. Optimization of the portfolio with risk-free investment possibility 8.4. Valuating security contribution to the total expected portfolio return 8.5. A pricing model on the competitive financial market 8.6. The statistical analysis of the financial market Questions for self-test Bibliography Part 1. Lecture Course Introduction The main goal of the science of finances consists in studying how the financial agents (persons and institutions) distribute the resources limited in time. The accent exactly on the time, but not other distribution types studied in economics (in regions, industries, enterprises), is a distinguishing feature of the financial science. The solutions made by the persons with regard to the time distribution of resources are financial decisions. From the point of view of the person(s) taking the such decisions, the resources distributed refer to either expenses (expenditures) or earnings (inflows). The financial decisions are based on commensuration of the values of expenses and profit streams. In the term payment the temporal character of resource distribution is reflected. The problems concerning the time distribution of resources (in the most general sense), are financial problems. Since the solution of financial problems implies the commensuration of values of expenses (expenditures) and the results (earnings), the existence of some common measure to evaluate the cost (value) of the distributed resources is supposed. In practice, the cost of the resources (assets) is measured in these or those currency units. However, it is only one aspect of the problem. The other one concerns the consideration of time factor. If the problem of time distribution of resources is an identifying characteristic of financial problems, then the financial theory must give means for commensuration of values referring to different time moments. This aspect of the problem has an aphoristic expression time is money. The ruble, dollar, etc. have different values today and tomorrow. Besides, there is one more crucially important aspect. In all the real financial problems which one must face in practice, there is an uncertainty referring to both the value of the future expenses and income, and the time points which they refer to. This very fact that the financial problems are connected with time stipulates the uncertainty characteristic of them. Talking of uncertainty, we imply, of course, the uncertainty of the future, but not past. The uncertainty of the past is usually connected (at least in financial problems) with the lack of information and in this sense, in principle, it is removable along with the accumulation and refinement of the data; whereas, the uncertainty of the future is not removable in principle. This uncertainty is that is characteristic of financial problems leads to the risk situation at their solution. Due to uncertainty, any solution on the financial problems may lead to the results different from the expected ones, however thorough and thoughtful the solution may be. The financial theory develops the concepts and methods for financial problem solution. As any other theory, it builds the models of real financial processes. Since such basic elements as time, value, risk, and criteria for choosing the desired distribution of resources obtain a quantitative expression, these models bear the character of mathematical models, if necessary. The majority of the models studied in the modern financial theory, have a strongly marked mathematical character. Along with that, the mathematical means used to build and analyze the financial models, vary from the elementary algebra to the fairly complicated divisions of random processes, optimal management, etc. Although, as it was mentioned, the uncertainty and risk are inseparable characteristics of financial problems, in a number of cases it is possible to neglect them either due to the stability of conditions in which the decision is made, or in idealized situations, when the model considered ignores the existence of these or those risk types due to its specificity. Financial models of this type are called the models with total information, deterministic models, etc. The study of such models is important because of two factors. First, in a number of cases, these models are fairly applicable for a direct use. This refers to, tor instance, the majority of models of the classical and financial mathematics devoted to models of the simplest financial transactions, such as bank deposit, deal on the promissory note, etc. Second, one of the ways for studying the models in the uncertainty conditions is modeling, i.e. the analysis of possible future situations or scenarios. Each scenario corresponds to a certain, fairly determined, future course of events. The analysis of this scenario is made, naturally, within the deterministic model. Then, on the basis of the carried out analysis of different variants of event development, a common solution is made. Chapter 1 Accumulation and Discounting 1.1. Time Factor in Quantitative Analysis of Financial Transactions The basic elements of financial models are time and money. In essence, financial models re- flect to one extent or another the quantitative relations between sums of money referring to vari- ous time points. The fact that with time the cost or, better to say, the value of money changes now due to constant inflation, is obvious to everyone. The ruble today and the ruble tomorrow, in a week, month or year – are different things. Perhaps, it is less obvious, at least not for an economist, that even without inflation, the time factor nevertheless influences the value of money. Let us assume that possessing a ―free‖ sum you decide to place it for a time deposit in a bank at a certain interest. In time, the sum on your bank account increases, and at the term end, under favorable conditions, you will get a higher amount of money than you placed initially. Instead of the deposit, you could buy shares or bonds of a company that can also bring you a certain profit after some time. Thus, also in this case, the sum invested initially turns into a larger amount after some time period. Of course, you may choose to not undertake anything and simply keep the money at home or at a bank safe.
Load more

Recommended publications
  • Deflation and the Fisher Equation
    Economic SYNOPSES short essays and reports on the economic issues of the day 2010 ■ Number 27 Deflation and the Fisher Equation William T. Gavin, Vice President and Economist rving Fisher (1867-1947), one of America’s greatest federal funds rate was 2.18 percent and, in the 1980s, it I monetary economists, is famous for many reasons. was a whopping 4.61 percent. One of the most important is the Fisher equation, which states that the nominal interest rate is equal to the real interest rate plus the expected inflation rate. This is a So, according to Irving Fisher, statement about equilibrium in the market for bonds, not one reason to worry about deflation is about the factors that determine these two components. that the federal funds rate is expected Depending on which market rate is used, the expected real return will include a premium for various sources of to be held near zero as the economy risk. For most of post-WWII U.S. history, estimates of this grows out of this recession. risk premium in the federal funds market have been small relative to estimates of the risk-free real interest rate and the expected inflation rate, so they are ignored in this essay. With the federal funds rate near zero since December The chart shows the Fed’s policy rate—the federal funds 2008 and expected to remain there for the next year or two, rate—and the consumer price index (CPI) inflation trend. the Fisher equation has important implications for the The trend is measured as a 25-month centered moving expected inflation rate.
    [Show full text]
  • A Lower Bound on Real Interest Rates by Jesse Aaron Zinn
    Real Interest Rate in Developed Economies Median and Range Source: Federal Reserve Bank of San Francisco See the note at the end of article. A Lower Bound on Real Interest Rates By Jesse Aaron Zinn Peer Reviewed 1 Jesse Aaron Zinn is an Assistant Professor of Economics in the College of Business at Clayton State University. His research interests include macroeconomics, public finance, and developmental economics. He earned his PhD in Economics at University of California, Santa Barbara. Abstract In this short article, the author demonstrates that real interest rates cannot be lower than -1 (i.e. -100%). He discusses how the textbook approximation to the Fisher equation can lead to the erroneous belief that there is no lower bound on real interest rates. He also speculates that the widespread use of the Fisher equation is why we had yet to realize that a lower bound on real rates exists. This leads him to advocate using and teaching the exact Fisher equation, rather than its approximation. Introduction Negative real interest rates have been common in the United States and other countries since the financial crisis of 2007-8. In fact, Japan has often had negative real interest rates going back to the early 1990s. In some countries, such as Denmark and Switzerland, there have been cases where nominal interest rates have also turned negative, disproving the idea that zero is an impenetrable lower bound on nominal rates. These phenomena have, no doubt, lead many to wonder how low rates can go. The objective of this short piece is to demonstrate the existence of a lower bound on real rates of interest.
    [Show full text]
  • Real Interest Rate and Fisher Equation
    6. Real interest rate, Fisher equation, Fisher effect 1. Real interest rate The real interest rate of an economy represents the purchasing power of the economy’s nominal interest rate : it is the nominal rate expressed in terms of goods. That the nominal interest rate between period and period 1 is means that, by lending 1 currency unit in , one gets 1 currency units in 1. That the real interest rate between period and period 1 is means that, by lending 1 unit of goods int , one gets 1 units of goods in 1. Thus, expresses purchasing power: the amount of goods obtained from each unit of good lent. 2. An example on the real interest rate Let “goods” be represented by the CPI basket. There are two periods, 1 and 2. The nominal interest rate between 1 and 2 is 10%. The cost of the CPI basket in 1 is 204 EUR. The cost of the CPI basket in 2 is 220 EUR; see the sketch on the right. With this information, the CPI inflation rate is 220 204 7.84%. 204 If 612 EUR are lent in 1. Then 612 1 612 1 0.10 673.2 EUR are obtained in 2. In 1, the purchasing power of 612 EUR is 612/ 612/204 3 baskets. In 2, the purchasing power of 673.2 EUR is 673.2/ 673.2/220 3.06 baskets. The real interest rate measures the change in purchasing power of the money lent. Specifically, transforms 3 baskets into 3.06 baskets. Thus, satisfies 3 1 3.06, so 0.02 2%.
    [Show full text]
  • IRVING FISHER – Forerunner of Monetarism
    PROFILES OF WORLD ECONOMISTS IRVING FISHER – forerunner of monetarism doc. Ing. Ján Iša, DrSc. Irving Fisher (1867 to 1947), who the theory of capital and interest, the theo- J. A. Schumpeter labelled as the greatest ry of index numbers and accounting, the theoretical economist of America, signifi- ”Phillips curve” and economic research cantly contributed to numerous spheres of methodology. economic theory and statistics. Perhaps he Fisher was the first American mathemati- is most known for his contribution to the de- cal economist, entrepreneur, reformer and velopment of the modern quantity theory, lecturer. Irving Fisher was born on 27th February, 1867 in Saugerti- He was appointed a full professor of economics in 1898 and es (New York) and lived in New Haven (Connecticut). Over ti- worked at Yale University actively up until 1920, afterwards me Fisher attended gradually schools in Peace Dale (Rhode Is- devoting his time mainly to writing books (of his 28 books pub- land), New Haven (Connecticut) and Saint Louis (Missouri). lished 18 dealt with economic theory) and a number of various Just at the time when he had finished secondary school and ga- activities outside the university. He taught only on a part-time ined a place at Yale College, his father died, leaving Irving 500 basis and therefore had less of an influence on students and, in dollars for his college education. contrast to other eminent architects of economic science (for At Yale University he studied mathematics, science, sociolo- example J. M. Keynes); he did not create a distinctive economic gy and philosophy. His most eminent teachers were the mathe- school.
    [Show full text]
  • Nber Working Paper Series Searching for Irving Fisher
    NBER WORKING PAPER SERIES SEARCHING FOR IRVING FISHER Kris James Mitchener Marc D. Weidenmier Working Paper 15670 http://www.nber.org/papers/w15670 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 January 2010 We thank Michael Bordo, Richard Burdekin, Andy Rose, Eric Swanson, and participants at UC Berkeley, the San Francisco Fed, and the ASSA meetings for comments and suggestions. Mitchener acknowledges the generous financial support of the Hoover Institution while in residence as the W. Glenn Campbell and Rita Ricardo-Campbell National Fellow. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peer- reviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2010 by Kris James Mitchener and Marc D. Weidenmier. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Searching for Irving Fisher Kris James Mitchener and Marc D. Weidenmier NBER Working Paper No. 15670 January 2010 JEL No. E4,G1,N2 ABSTRACT There is a long-standing debate as to whether the Fisher effect operated during the classical gold standard period. We break new ground on this question by developing a market-based measure of general inflation expectations during the gold standard. Since the gold-silver price ratio was widely used to track inflation during the gold standard period, we are able to derive a measure of inflation expectations using the interest-rate differential between Austrian silver and gold perpetuity bonds with identical terms.
    [Show full text]
  • MONEY and BANKING
    MONEY and BANKING: ECON 3115 Revised, Fall 2011 Professor Benjamin Russo Chapter 4: Understanding Interest Rates To simplify discussion these notes ignore important economic differences between financial intermediaries and financial markets. Instead, the notes treat the financial system as one big happy family. Outline I) What is the „Present Value‟ of an Asset? How is Present Value Calculated? II) Interest Rates and Yield to Maturity III) Interest Rates versus Rates of Return IV) Interest Rate Risk V) “The” Interest Rate and Economic Efficiency VI) The Real Interest Rate versus the Nominal Interest Rate I) What is the „Present Value‟ of an Asset? How is Present Value Calculated? 1) Present Value (PV) is a fundamental concept in financial economics. For this reason, you need to understand the concept and how to calculate it. Start with the concept. Generally speaking, the PV of an asset is the current value of future income the asset is expected to produce, after the future income is discounted by the "opportunity cost of owning the asset." The opportunity cost of owning an asset is the future income that could have been earned if the owner had bought the next best alternative asset. E.G., suppose Ms. Penny-pincher ranks four different assets with the colorful names Red, Blue, Green, and Fuchsia. Ms. P. ranks Blue highest, and buys only Blue. She ranks Green second highest, but does not buy Green. Thus, Ms. P. foregoes the opportunity to earn income from Green. The foregone Green income is the opportunity cost of owning Blue. 2) The opportunity cost of owning an asset often is called the "time value of money" because it is the value one could have achieved, over time, had "money" been invested differently.
    [Show full text]
  • Fisher's Equation and the Inflation Risk Premium in a Simple
    Fisher's Equation and the In¯ation Risk Premium in a Simple Endowment Economy Pierre-Daniel G. Sarte ne of the more important challenges facing policymakers is that of assessing in¯ation expectations. Goodfriend (1997) points out that O one can interpret the meaning of a given interest rate policy action primarily in terms of its impact on the real rate of interest. However, evaluating this impact requires not only that one understands the various links between the nominal rate and expected in¯ation but also that one can quantify these relationships. To ®nd an approximate measure of expected in¯ation, one often turns to the behavior of long bond rates. Two key ideas explain why this approach might be appropriate. First, Fisher's theory holds that the real rate of interest is just the difference between the nominal rate of interest and the public's expected rate of in¯ation. Second, the long-term real rate is generally thought to exhibit very little variation.1 Alternatively, and still based on Fisher's theory, one might use the yield spread between the ten-year Treasury note and its in¯ation-indexed counterpart as an estimate of expected in¯ation. In January 1997, the U.S. Treasury indeed began issuing ten-year in¯ation-indexed bonds. While economic analysts typically attempt to capture in¯ation expectations using Fisher's equation, this method has its ¯aws. When in¯ation is stochastic, Fisher's relation may not actually hold. Barro (1976), Benninga and Protopa- padakis (1983), as well as Cox, Ingersoll, and Ross (1985), show that the decomposition of the nominal rate into a real rate and expected in¯ation should The opinions expressed herein are the author's and do not represent those of the Federal Reserve Bank of Richmond or the Federal Reserve System.
    [Show full text]
  • Chapter 8 - Theories of FX Determination – Part 2 Goal Get a Formula for St
    Rauli Susmel FINA 4360 – International Financial Management Dept. of Finance Univ. of Houston Chapter 8 - Theories of FX Determination – Part 2 Goal get a formula for St. St = f( id, if,Id, If,…) Last Lecture Effect of LOOP (arbitrage through trade) on FX Markets. Derive “equilibrium” (i.e., no-trade) St: Absolute PPP: St = Pd / Pf (Rejected, existence of transaction costs, borders a problem) Relative PPP: ef, Id - If (Rejected in the short-run, some long-run support) This Lecture Continue the search for a functional form that explains St. 8.2 International Fisher Effect (IFE) IFE builds on the law of one price, but for financial transactions. Idea: Expected returns to international investors who invest in money markets in their home country should be equal to the expected returns they would get if they invest in foreign money markets once adjusted for currency fluctuations. Exchange rates will be set in such a way that international investors cannot profit from interest rate differentials. The "effective" T-day return on a foreign bank deposit is: rd (f) = (1 + if * T/360) (1 + ef,T) -1. On the other hand, the effective T-day return on a home bank deposit is: rd (d) = id * T/360. Setting rd (d) = rd (f) and solving for ef,T = (St+T/St - 1) we get: S (1 i *T /360) e IFE T t 1 d 1 (IFE). f ,T S (1 i *T /360) t f IFE Using a linear approximation: e f,T (id - if) x T/360. IFE e f,,T represents an expectation –i.e., E[ef,,T].
    [Show full text]
  • DEVOLUTION of the FISHER EQUATION: Rational Appreciation to Money Illusion*
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE GRIPS Policy Information Center provided by InsitutionalDiscussion Repository at the Paper National Graduate : 08-04 Institute for Policy Studies DEVOLUTION OF THE FISHER EQUATION: Rational Appreciation to Money Illusion* James R. Rhodes. June 2008 .Professor of Economics, National Graduate Institute for Policy Studies (GRIPS), 7-22-1 Roppongi, Minato-ku, Tokyo 106-8677 Japan TEL: +81-(0)3-6439-6220 E-mail: [email protected] *The author is indebted to Levis Kochin for providing the original stimulus for this paper and to the late Milton Friedman for sustaining interest. Thanks are also due Joerg Bibow, Yang Ming Chang, Dana Ferrell, Thomas Humphrey, the late Mark Meador, Perry Mehrling, Francisco de A. Nadal-De Simone, Sumimaru Odano, Frank Packer, Kenichi Sakakibara, Kenji Yamamoto, and several anonymous referees for helpful comments on earlier versions of the paper. Supplementary Notes on the Fisher Equations contains elaborations and extensions of material contained in the paper. Supplementary Notes is available from the author. © 2008 by James R. Rhodes. All rights reserved. GRIPS Policy Information Center Discussion Paper : 08-04 DEVOLUTION OF THE FISHER EQUATION: Rational Appreciation to Money Illusion Abstract In Appreciation and Interest Irving Fisher (1896) derived an equation connecting interest rates in any two standards of value. The original Fisher equation (OFE) was expressed in terms of the expected appreciation of money [percent change in E(1/P)] whereas the ubiquitous conventional Fisher equation (CFE) uses expected goods inflation [percent change in E(P)]. Since Jensen‟s inequality implies the non-equivalence of the two equations, the OFE is not subject to standard criticisms of non-rationality leveled against the CFE.
    [Show full text]
  • An Empirical Investigation of the International Fisher Effect
    2002:042 SHU BACHELOR’S THESIS An Empirical Investigation of the International Fisher Effect EMIL SUNDQVIST Social Science and Business Administration Programmes ECONOMICS PROGRAMME Department of Business Administration and Social Sciences Division of Economics Supervisor: Stefan Hellmer 2002:042 SHU • ISSN: 1404 – 5508 • ISRN: LTU - SHU - EX - - 02/42 - - SE An Empirical Investigation of the International Fisher Effect EMIL SUNDQVIST Social Science and Business Administration Programme Economics Programme Department of Business Administration and Social Sciences Division of Economics Supervisor: Stefan Hellmer V TABLE OF CONTENTS ABSTRACT I SAMMANFATTNING II LIST OF FIGURES V Chapter 1 INTRODUCTION 5 1.1 Purpose 6 1.2 Method 6 1.3 Scope 7 1.4 Outline 8 Chapter 2 THEORETICAL FRAMEWORK 8 2.1 Purchasing Power Parity 9 2.1.1 Empirical evidence 10 2.2 The Fisher Effect 11 2.2.1 Empirical evidence 14 2.3 The International Fisher Effect 14 2.3.1 Empirical evidence 17 Chapter 3 THE REGRESSION MODEL 17 3.1 The efficient market hypothesis 18 3.2 The regression model 19 3.3 The data 20 Chapter 4 THE REGRESSION RESULTS AND ANALYSIS 22 4.1 The regression results for United States-Sweden 23 4.2 The regression results for United States-Japan 25 4.3 The regression results for United States-United Kingdom 26 4.4 The regression results for United States-Canada 27 V 4.5 The regression results for United States-Germany 29 Chapter 5 CONCLUSIONS 31 REFERENCES 35 V LIST OF FIGURES Figure 2.1 Purchasing Power Parity 6 Figure 2.2 The Fisher Effect 9 Figure 2.3
    [Show full text]
  • Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation? Author(S): Martin D
    American Finance Association Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation? Author(s): Martin D. D. Evans and Karen K. Lewis Source: The Journal of Finance, Vol. 50, No. 1 (Mar., 1995), pp. 225-253 Published by: Wiley for the American Finance Association Stable URL: http://www.jstor.org/stable/2329244 . Accessed: 08/10/2013 16:26 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Wiley and American Finance Association are collaborating with JSTOR to digitize, preserve and extend access to The Journal of Finance. http://www.jstor.org This content downloaded from 128.91.113.15 on Tue, 8 Oct 2013 16:26:34 PM All use subject to JSTOR Terms and Conditions THE JOURNAL OF FINANCE * VOL. L, NO. 1 * MARCH 1995 Do Expected Shifts in Inflation Affect Estimates of the Long-Run Fisher Relation? MARTIN D. D. EVANS and KAREN K. LEWIS* ABSTRACT Recent empirical studies suggest that nominal interest rates and expected inflation do not move together one-for-one in the long run, a finding at odds with many theoretical models. This article shows that these results can be deceptive when the process followed by inflation shifts infrequently.
    [Show full text]
  • Irving Fisher, the UIP Puzzle And
    Irving Fisher and the UIP Puzzle Rachel A.J. Campbell Maastricht University and Tilburg University Faculty of Economics and Business Administration, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands, tel. +31 43 388-4827, e-mail: [email protected]. Kees G. Koedijk Tilburg University and CEPR Department of Economics, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands, tel. +31 13 466-2915, e-mail: [email protected]. James R. Lothian (corresponding author) Fordham University Graduate School of Business, Fordham University, 113 West 60th Street, New York, NY 10023, USA, tel. +1 212 636-6147, e-mail: [email protected] ; [email protected] . Ronald J. Mahieu Tilburg University Department of Econometrics & Operations ResearchFinancial Management, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands, tel. +31 13 466 8752, e-mail: [email protected]. February 2009 JEL Classification: F31, B19 Keywords: Exchange rates, forward discount bias, international parities, expectation errors, Irving Fisher. _________________ We would like to thank Richard Ballie, Menzie Chinn, John Cochrane, John Devereux, Hans DeWachter, Martin D.D. Evans, Paul de Grauwe, Franz Palm, Yusif Simaan, Daniel Thornton, Mathijs Van Dijk, Christian Wolff, Jun Yang and to seminar participants at Fordham University, Trinity College Dublin and University College Cork for helpful comments. Abstract In this paper we empirically verify much of the seminal work by Irving Fisher on uncovered interest parity, which he conducted over a century ago. Like Fisher, we find that the departures from UIP are connected to individual episodes in which errors surrounding exchange-rate expectations are persistent, but eventually transitory.
    [Show full text]