Financial Economics Proposals New Minor ………….…… p.1 New Concentration …..… p.14 Proposal for new Minor in Financial Economics, offered by the Economics Department. October 1, 2009 Dr. Patrick Bayer, Chair, Department of Economics. I. Description and rationale Part A: Describe the proposed minor, and explain how it fits into the educational mission. The economic turmoil in the financial markets over the past year has once again turned the attention of many to how deeply such sudden change can affect myriad elements of society. Duke does not currently offer undergraduates a targeted academic path to study in-depth the economic subfield of “financial economics” – the subfield that investigates the financial sector and its interaction with the “real” sector of the economy. In the current curriculum, students learn about these subjects in scattered classes, largely in the Economics Department. But clearly financial economics is a complex and very important part of the modern world – and a university like Duke can make positive contributions to its proper role in society. Through its teaching, its research and its engagement with the financial services community, Duke should thus lead rather than lag in preparing our students to meaningfully shape the financial sector of the economy – and to use their knowledge to make a beneficial difference. The Department of Economics proposes a Minor in financial economics as a way to increase all Duke students’ understanding of the financial sector within the context of a broader liberal arts curriculum. Given Duke’s long-standing liberal arts focus to undergraduate education, it is important to view this proposed minor in financial economics as a new complement within a broad curriculum rather than as the pre-professional training in finance that it is in undergraduate business programs at peer institutions. While the enormous existing student demand for classes in financial economics is undoubtedly driven in part by their desire to ultimately find employment in the financial sector, our aim in meeting this demand is driven by the broader goal of integrating financial economics into courses that explore the relationship between the abstruse financial side of the economy and the more visible “real” sectors of the economy. The importance of an understanding of this relationship is perhaps most clearly demonstrated in the current crisis as it relates to home mortgages and their impact on the macro-economy as well as the individual lives of households caught in the midst of this crisis. But the connections to real issues at the center of a liberal arts economics education reach far beyond this most obvious example. In addition to traditional course offerings in financial economics, we can envision, for instance, offering courses on: • • • how the financial sector affects the disadvantaged and the urban underclass the role of micro-credit in developing economies the role of the legal system in appropriately functioning financial markets • • • • • 2 How in disparities in educational opportunities, arise from the problem of financial borrowing constraints the interaction of formal financial markets with informal family mechanisms for dealing with risk and uncertainty the role of psychology in “behavioral finance” the problem of retirement security in a global society the cross-cultural notions of the ethics that govern financial institutions. It is, in fact, difficult to conceive of any subfield in economics that does not have deep connections to financial economics – and it is in these connections that we recognize the potential of financial economics as a fertile component of a liberal arts education. Ultimately, it is not to the Economics Department’s comparative advantage to impart preprofessional skills, but rather the advantage lies in developing skills that are valued in the marketplace while providing a bigger picture framework -- one in which students see the decisions made in financial sectors as intimately connected to broader intellectual questions of deep social significance. In this sense, when properly framed as part of a liberal arts education, a minor in financial economics is consistent with the students’ desire to gain more intimate knowledge of the financial services sector and with the broader goals of a liberal arts curriculum. At the same time, we do not believe that opportunities to gain a greater understanding of the financial sector ought to be restricted exclusively to economics majors, but that there ought to be paths for students that have acquired the necessary skills to gain such understanding even as their primary major rests in another department. In fact, we believe that students will benefit a great deal more in the long run from confronting the salient issues in the financial sector through programs that frame these within the larger context in which the financial sector operates. In this way, our students can be prepared to confront the challenges of our time while they accumulate the knowledge that will permit them to effectively compete with students from our peer institutions that take a narrower view of undergraduate finance education via business-focused majors. Our approach furthermore fits well with Duke’s larger strategic plan of equipping students to put their knowledge in the broader service of society. Our department, as outlined in its recent self-study, is well equipped to begin offering a minor of this type. Unusual among economics departments around the country, our department has a tradition of faculty strength in the area of financial econometrics complemented by outstanding teaching in financial economics. And, with the support infrastructure of the EcoTeach center, much initial logistical support is in place to begin our effort in this direction prior to additional teaching and support resources coming on line as the program expands in size. Part B: Relationship with other majors, minors, certificates, including areas of potential overlap. The potential of this minor raises several questions regarding its relationship with existing areas of undergraduate focus. First, because training in financial economics is currently offered within the economics major, to what extent will the new minor affect our own department’s economics major? Second, how much of the student interest in financial economics is related to interest in the business world more generally, and 3 therefore how will the creation of a minor in financial economics impact the Markets and Management (MMS) certificate? Third, how much of the interest in financial economics currently resides among a subset of students majoring in mathematically oriented subjects (like math, statistics and computer science), as well as students in the Pratt and Sanford Schools? With respect to economics majors, we are developing a parallel concentration in financial economics within the major – thus creating positive spillovers for economics majors. It is likely that some students who currently major (or double-major) in economics in order to gain access to existing courses in financial economics may decide to major in another department and complement that major with this new minor. Given the substantial math and statistics pre-requisites in the proposed minor, our analysis suggests that the number of economics majors is likely to decline by approximately 10% (see part C of this section). Given the large size of the economics major, we do not view such a potential decline in the number of majors as a major impediment to implementing expanded opportunities for students in other departments. Instead we view the expanded course offerings in financial economics that would result from the creation of a minor as a net positive for those students who continue to major in economics. Given the potential impact this minor would have on the MMS certificate, we have engaged with the leadership of the MMS certificate to discuss its likely impact. Just as the Department of Economics may see a modest decline in the number of majors from the creation of a minor, it is possible that the MMS certificate would see a similarly modest decline. But, just as we view the creation of new courses as a net benefit to the major, the leadership of MMS views such expanded course offerings as strengthening their own efforts. It is, in fact, natural for training in financial economics to emanate primarily from the economics department, allowing MMS to focus on areas of comparative advantage and leveraging the department’s efforts to strengthen their own programs. Finally, if Economics is likely to experience a modest decline in the number of majors, it is likely that other mathematically oriented majors will see an increase in their number of majors as some students combine the minor in financial economics with major training in math, statistics, computer science or engineering. Given the statistics and math prerequisites for the minor, it is furthermore likely that math and statistics will see a modest increase in enrollments as students prepare for the new minor. Part C: Discuss potential impact on existing undergraduate or graduate academic programs at Duke. Talk about likely demand. As indicated in the previous part, we anticipate a modest decline in the number of economics majors, a modest decline in the number of students obtaining the MMS certificate and a modest increase in other quantitative majors outside economics. At the same time, we argue that the minor would result in an increased diversity of course offerings that will strengthen the economics major as well as the MMS program. Between 15 and 30 students from the Pratt School double major in economics in any given year. 1 We think that the majority of these students would switch their economics major to a financial economics minor. The number of other quantitatively oriented 1 For the years 2005 through 2010, for instance, the numbers of Pratt double majors in economics were 15, 14, 27, 18, 17 and 17(est.). 4 double-majors (from math, statistics and computer science) has recently increased, from about 4 in 2005 to an estimated 15 in 2010. Again, we think that some of these students will switch their economics major into a minor in financial economics. At the same time, it is likely that the financial economics minor would attract a number of quantitatively oriented students from Pratt and other majors – in particular those students who currently are on the margin of getting a double major with economics in order to take financial economics courses but choose not to do so because of the larger number of pre-requisites into the major. For those students, the financial economics minor would in essence lower the barriers for obtaining access to material they would like to study but currently cannot. The vast majority of joint majors from other departments would likely remain double majors due to the higher math pre-requisites for the minor in financial economics and presumably because many of them are attracted to the economics major by factors other than the department’s course offerings in financial economics. Our overall conclusion for the economics major is that we should therefore expect to lose between 15 and 30 majors while attracting in the neighborhood of 50 new minors. We are less able to predict precisely how the other affected areas are likely to be impacted but, as suggested above, anticipate a modest increase in majors for some of the more quantitative departments, a modest decrease for the MMS certificate – but with an improved set of course offerings benefiting students in all of these areas. 5 II. Detailed Description: Requirements and Curriculum Students pursuing the financial economics minor will be expected to take a minimum of five courses, two of which are required, while the remaining courses may be selected from a menu of options. Pre-requisites for the minor include both mathematics and statistics courses. A. Three Pre-requisite Courses (Required): Mathematics skills and tools are essential pre-requisites to a thorough grasp of financial theory and its applications. We impose additional, relatively high mathematics requirements for the financial economics minor to compensate for the fact that these students will not have as much economic intuition, since they will not be taking the core economics theory courses. Because the students who pursue the minor will have more mathematical training, they will be comfortable with the quantitative level of the financial economics courses and hence able to focus their efforts on learning the economic intuition behind the models. Their classmates who have an economics background will be focusing more on mastering the technical tools, being more comfortable with the economic ideas embodied in them. • MATH 103: Multivariate Calculus. (Higher level math courses are also acceptable.) • MATH 104: Linear Algebra and Applications OR MATH 107: Linear Algebra and Differential Equations. • STAT 103: Probability and Statistical Infererence. (Certain higher level stats courses are also acceptable.) B. Two Financial Economics Core Courses (required): Core courses for the minor include both introductory economics and introductory finance. • ECON 51D: Economic Principles. Instructor: Fullenkamp, Leachman. Enrollment: 400 each semester. Pre-reqs: None. This course introduces basic macroeconomic concepts such as inflation, unemployment, and economic growth, as well as micro concepts such as preferences and the relationship between supply, demand, and price. Students are also introduced to different perspectives on monetary and fiscal policy. All of these concepts are necessary precursors to the fundamental underpinnings of financial markets. This course is open to all undergraduate students, with no pre-requisites. 6 • Econ XXX: Intermediate Economics For Finance. Instructor: Burnside, Rasiel. Enrollment: 150 each semester. Pre-reqs: Econ 51D, Math 104 or 107 or Econ 105, Stat 103. Currently under development. This course integrates intermediate level micro- and macroeconomics with topics in finance to provide a gateway course into both the financial economics minor as well as the concentration in financial economics for majors. Students will either be strong in their intermediate economics tool-kit (by having taken Econ 105 (and Econ 55 that is a pre-requisite to Econ 105)) or sophisticated in their mathematical preparation (by having taken Math 104 or 107). The former will most likely involve economics majors who are interested in a concentration in financial economics and require additional technical preparation for the concentration. The latter are most likely noneconomics majors who are pursuing a Minor in Financial economics and require additional economic intuition to supplement their technical training. C. Three Elective Courses: These will be chosen from among a list of approved courses, some of which are already taught within the department (see Appendix I for a list of existing and proposed courses). Courses will include offerings in the three primary aspects of financial economics: corporate finance, asset pricing, and time series econometrics. Courses in all three of these areas are currently taught within the department. The department also offers, or will add, courses in areas of finance that overlap with other disciplines such as psychology and public policy. These include Behavioral Finance (which integrates insights from psychology) and Public Finance (which intersects with Public Policy). III Proposed Bulletin Text Minor Requirements: Economics 1A and 2A; or 51D. Mathematics 103 and either Mathematics 104 or Mathematics 107. Econ XXX [Intermediate Economics For Finance]. Three additional 100 level or above economics courses, to be selected from the following: Economics 157, 166, 168, 183, 187, 200ES, 220, 225/Math 215, BME 120, and others with approval of DUS. 7 IV: List of Current Courses available for the minor Pre-requisite courses Mathematics 103, 104, and 107 are service courses offered by the mathematics department each semester, with high enrollment caps. All of these courses are prerequisites for a number of different majors; adding these as pre-requisites for the financial economics minor should not materially affect demand for these courses, especially since the students most likely to be interested in the financial economics minor will likely take these courses anyway as part of their major requirements. Statistics 103 is currently a pre-requisite for the economics major. It is offered each semester with high enrollment caps. Required Courses Economics 51D: Economic Principles. This is one of the largest courses in the university, with enrollment exceeding 400 in some semesters. Students from a broad range of majors take this class, and the class size varies considerably from semester to semester. The economics department does not anticipate that the addition of 30-40 financial economics minors will impose excess demand. Economics XXX: Intermediate Economics for Finance. This course will apply intermediate level micro and macroeconomic models to topics in financial economics. Course to be developed. Expected enrollment: 100. See Section IIB for more details. Elective Courses Appendix I contains a list of existing courses that will be approved for the financial economics minor, as well as a list of proposed new courses, some of which will be taught by a new Professor of the Practice to be hired by the Economics department. It is anticipated that the list of approved electives will change over time as offerings evolve. 8 V: Description of New Courses to be offered for the minor Some additional financial economics electives will be taught by a new Professor of the Practice of economics, to be recruited to the department. See Appendix 1. VI: Identification of Teaching Faculty A. List of Faculty, including titles Tim Bollerslev, Juanita and Clifton Kreps Professor of Economics Craig Burnside, Professor of Economics Tracy Falba, Associate Director of Undergraduate Studies Connel Fullenkamp, Associate Professor of the Practice of Economics Lori Leachman, Professor of the Practice of Economics Andrew Patton, Associate Professor of Economics Emma Rasiel, Assistant Professor of the Practice of Economics Barbara Rossi, Associate Professor of Economics CJ Skender, Senior Lecturer George Tauchen, William Henry Glasson Professor of Economics New Professor of the Practice of Economics Arlie Petters, Benjamin Powell Professor of Math Larry Boyd, Associate Director, Duke’s Center for Entrepreneurship and Research Commercialization All of these faculty members have indicated willingness to participate. B. Teaching Responsibilities and how they may be impacted by the new minor Since the courses these faculty will be teaching are applicable to their usual audience (i.e. Econ majors) this imposes minimal costs on either those faculty or the department in terms of teaching availability. C. Estimate the need for new faculty, and funding sources. We anticipate that will need one more Professor of the Practice to teach additional financial economics electives. An initiative is underway to solicit five-year seed funding for this position. 9 VII: Administration Program Direction: Professors Emma Rasiel, Connel Fullenkamp, and Thomas Nechyba. Advising: Initially, this will be managed as part of the overall Economics advising team; potentially in conjunction with new Professor of the Practice who would have specific responsibilities in this regard. Administrative Support: Initially, administrative support will be incorporated into the EcoTeach Center, whose staff currently handle as many as 700 Economics majors. Depending on the eventual size of the minor, it may be necessary to create additional support. Should this prove to be the case, the new Professor of the Practice may be asked to take on the role of administering the financial economics minor in conjunction with the Ecoteach staff. VIII: Available Funding The Economics Department, in cooperation with A&S and Corporate Development, is pursuing a proposal to solicit 5-year (external) seed funding for this effort. We anticipate that such funding will be in place prior to the launch of the minor. IX: Library Resources Library resources currently used by students for the existing financial economics courses will serve students opting for the proposed new minor. X: Letters of Support 1. 2. 3. 4. Letter of support from Dean of Trinity College Letters from Chair and DUS in the economics department. Letters from Chair and DUS in Statistics and Math Letter from Associate Dean in Pratt 10 Appendix 1: Electives for the Financial Economics Minor Part A: Existing courses • Econ 157: Financial Markets and Investment. Instructor: Rasiel, Patton or staff. Enrollment: 60. The structure and workings of financial markets. Topics include risk-return relationships, aspects of portfolio selection, the capital asset pricing model, arbitrage pricing theory, fixed income analysis, and aspects of derivatives. • Econ 166: Global Capital Markets. Instructor: Rasiel. Enrollment: 24 (permission of instructor required). This course introduces students to the roles of various participants in the financial markets, including investment banks, money managers, and so on. Students are expected to stay current with business and finance news and issues. There are no prerequisites for this class; however, faculty consent is required for enrollment. • Econ 168: Asset Pricing and Portfolio Management Instructor: Rasiel or staff. Enrollment: 125. Pricing models for asset classes such as bonds and equities, as well as derivative securities including futures and options. on equity indices, currencies and commodities. Portfolio risk analysis, speculation and hedging techniques. • Econ 183: Managerial Accounting. Instructor: Skender. Enrollment: 75 The accounting model of the firm, transaction analysis, the use of accounting information by management. Topics include procedures to process accounting data, income determination, financial statement analysis, cost behavior, budgeting, and short-run decisions. The construction and interpretation of corporate financial reports. How a firm's performance is presented in the income statement, and how different revenue and expense recognition practices affect this performance measure. • Econ 187: Public Finance Instructor: Falba or staff. Enrollment: 30 Allocation and distribution of public funds. Use of and tradeoffs between taxation and borrowing. Economic, social, ethical and demographic implications of federal and state allocation decisions. • Econ 195.12: Financial Risk Management Instructor: Fullenkamp. Enrollment: 30 This course investigates the main types of financial risks and the techniques used to measure and manage these risks. Special attention will be paid to the instruments used to manage risk, and the interaction between public policy and industry practice. Implications for regulatory environment are also examined. • Econ 195.49: Behavioral Finance. Instructor: Rasiel. Enrollment: 30 The field of Behavioral Finance uses psychology to explain so-called anomalies that we observe in the financial markets—apparent mis-pricings and inefficiencies that are not consistent with the classical economic models of rational behavior. Using some of 11 the more popular and accepted theories of human behavior from the fields of psychology and decision-making, we will characterize some prevalent features of irrational behavior in the financial markets. • Econ 200ES: Financial Derivatives / Financial Engineering. Instructor: Tauchen. Pre-reqs: financial economics core courses Pricing models for derivative securities including futures, and options on equity indices, currencies and commodities, and interest rate and currency swaps. Uses of derivatives for both hedging and speculative purposes. • Econ 220: Time Series Econometrics. Instructor: Rossi. Pre-reqs: Econ 139 and Linear Algebra or Instructor Permission Enrollment: 25 Empirical research in macroeconomics and international finance, providing students with a series of econometric tools for empirical analysis of time-series and an introduction to the current empirical research in macroeconomics, international finance, and forecasting. Small project and simple empirical research required. • Econ 225 / Math 215: Mathematical Finance. Instructor: Petters. Pre-reqs: Math 103, 104, 135 or equivalent, or consent of instructor. An introduction to the basic concepts of mathematical finance. Topics include modeling security price behavior, Brownian and geometric Brownian motion, mean variance analysis and the efficient frontier, expected utility maximization, Ito's formula and stochastic differential equations, the Black-Scholes equation and option pricing formula. • BME 120: Introduction to Business in Technology-Based Companies. Instructor: Boyd. Introduction to key areas of business, including finance, marketing, management and intellectual property in the context of a technological start-up. 12 Part B: Proposed new courses The department anticipates hiring one new Professor of the Practice who will teach additional financial economics courses that will serve as electives for both the financial economics minor and the economics major. We anticipate that the new professor will offer some of the following options. Other existing members of the Economics department may also offer one or more of these courses as special topics from time to time. • Econ XXX: Intermediate Economics For Finance. Instructor: Burnside, Rasiel. Enrollment: 150 each semester. Pre-reqs: Econ 51D, Math 104 or 107 or Econ 105, Stat 103. Currently under development. This course integrates intermediate level micro- and macroeconomics with topics in finance to provide a gateway course into both the financial economics minor as well as the concentration in financial economics for majors. See Section IIB for more information. • Econ 195.XX: International Finance. Instructor: Leachman. Enrollment: 40. Currently under development. This course analyzes how managers of international corporations do or should behave in terms of hedging their international exposure. Emphasis is on the mechanics of the foreign exchange market, reviewing spot, forwards, futures, swaps and options markets: the main tools used to hedge exchange rate risk. The course constructs the building blocks of international finance, and then introduces corporate aspects of international finance, especially hedging techniques. • Econ XX: Principles of Corporate Finance. Instructor: Staff. Pre-reqs: financial economics core courses. This course examines issues in corporate finance from the perspective of financial managers who are responsible for making significant investment and financing decisions. The concepts of net present value, uncertainty, and strategic concerns, are used to analyze how investment and financing decisions interact to affect firm value. • Econ XX: Microfinance in Developing Economies Instructor: Staff. Pre-reqs: financial economics core courses This course addresses the financial, legal and ethical issues of microfinance in developing economies. The course begins with lessons from informal markets, the role of women, the place of subsidies, impact measurement, and management incentives. Issues of asymmetric information, principal-agent theory, and household decision making in the context of microfinance will be discussed. • Econ XX: Global Asset Allocation. Instructor: Staff. Pre-reqs: financial economics core courses The course begins with an overview of global economies and global financial market risks and returns. Theoretical and practical issues in active asset allocation are examined, including the Black-Litterman approach to using mean-variance analysis 13 for global portfolio optimization. Both long-term, strategic asset allocation and short-term, tactical asset allocation issues and strategies are presented, simulated and critiqued. Econ XX: Asset Pricing under Asymmetric Information. Instructor: Staff. Prereqs: financial economics core courses, Econ 55 This course builds on information economics and decision theory. The first building blocks covered include decision making under uncertainty; von Neuman and Morgenstern expected utility functions, concept and measures of risk aversion, Jensen's inequality, certainty equivalents, risk premia and stochastic dominance. Principal-Agent problems, including adverse selection and moral hazard, are examined and basic signaling and screening models are introduced. • Econ XX: Fixed Income Securities. Instructor: Staff. Pre-reqs: financial economics core courses This course explores key issues in fixed income, financial engineering, and risk management. It develops tools for valuing and modeling the risk exposures of fixed income securities and their derivatives, with the ultimate goal of deploying these instruments in a corporate or financial risk management setting. • Econ XX: Corporate Restructuring Instructor: Staff. Pre-reqs: Principles of Corporate Finance This interdisciplinary course examines the finance, economics, law and business strategies that underlie major corporate restructuring transactions. These transactions include: mergers, acquisitions, tender offers, bankruptcy, leveraged buyouts, leveraged cash-outs, sell-offs, spin-offs, equity carve-outs, share repurchases, and liquidations. • Econ XX: Global Asset Allocation. Instructor: Staff. Pre-reqs: financial economics core courses The course begins with an overview of global economies and global financial market risks and returns. Theoretical and practical issues in active asset allocation are examined, including the Black-Litterman approach to using mean-variance analysis for global portfolio optimization. Both long-term, strategic asset allocation and shortterm, tactical asset allocation issues and strategies are presented, simulated and critiqued. • Econ XX: Venture Capital and Private Equity. Instructor: Rasiel, staff. Pre-reqs: financial economics core courses The financial, legal, and economic issues relating to financial contracts between venture capitalists and their limited partners, as well as the firms they invest in. The course addresses not only how venture capitalists provide capital to start-up firms in growing industries, but also how private equity markets provide capital to help established medium-sized firms (often family businesses) grow and restructure. 14 Proposal for new Concentration in Financial Economics, offered by the Economics Department. October 1, 2009 Dr. Patrick Bayer, Chair, Department of Economics. I. Cover Letter We articulated in our proposal for the creation of a Minor in Financial Economics (as well as our 2008 Self Study) (1) the need for a greater set of undergraduate opportunities to study financial economics at Duke, (2) a vision for how to integrate such opportunities into a broader liberal arts curriculum and (3) an explanation for the unique opportunity that our department has to accomplish this given its faculty and infrastructure resources. With the proposed creation of a Minor in Financial Economics, all Duke undergraduates with sufficient quantitative training will have the opportunity to combine their chosen major field of study with a minor field in financial economics. While the course offerings for this minor will also be available to economics majors, the Minor degree will not itself be available for economics majors. The current proposal for a Concentration in Financial Economics therefore emerges from this asymmetry created by the formation of the Minor in Financial Economics; i.e. the fact that only non-economics majors would be able to pursue a formalized degree focused on how the financial sector operates within the broader economy. The creation of a similar formalized track within the economics major in the form of a Concentration in Financial Economics would remedy this asymmetry – offering majors the same opportunity to formally focus on the financial sector in their studies. We therefore view the proposed Minor degree and the proposed Concentration within the economics major as complementary and built around a similar rationale and infrastructure. The difference between the two paths lies primarily in the different types of preparation that those pursuing a Minor and those pursuing a Concentration bring to their studies. Due to the more stringent quantitative requirements for the Minor, the students who pursue a Minor in Financial Economics would enter the program with strong technical and quantitative skills but less economic intuition. Due to the greater number of intermediate level economics requirements that economics Majors will have taken, those who enter the Concentration would be more prepared in terms of economic intuition. Through a common gateway course, both Majors and Minors will have an opportunity to build on their respective strengths before entering the elective course work for their respective paths focused on Financial Economics. 15 II. New Listing in the Undergraduate Bulletin For the BS Degree with Concentration in Financial Economics For the B.S. Degree The Bachelor of Science degree in economics signifies achievement of proficiency in quantitative skills and experience in applying these to economics. Students who contemplate graduate study in economics are urged to develop skills in intermediate calculus (Mathematics 103), linear algebra (Mathematics 104), differential equations (Mathematics 131), and advanced calculus (Mathematics 139). Students interested in graduate work in business administration may wish to focus less on mathematics and more on computer science, statistics, and quantitative economics. Prerequisites: Economics 1A and 2A; or 1D or 51D. Economics 55D. Mathematics 32 and 102; or 103 or any higher-level mathematics course with Mathematics 103 as a prerequisite. Statistics 103, Statistics 104/Mathematics 135, Statistics 112, Statistics 113 or Statistics 114/Mathematics 136. Statistics is a prerequisite for Economics 139D and many 100-level economics courses and therefore should be taken by the fall of sophomore year. Prerequisites for the major, as well as requirements, may not be taken pass/fail. Requirements: Three core courses: Economics 105D, Economics 110D and Economics 139D. Economics 139D should be completed no later than the spring of sophomore year since most 100level economics courses have Economics 139D as a prerequisite. Five electives chosen from any additional non-core economics courses at the 100 level or above, with the exception of Economics 151, Economics 182, and Economics 888. Substitution of similar courses in other departments at Duke for courses in the Department of Economics used toward major requirements is not permitted. A maximum of two transfer and/or study abroad credits may be counted toward major requirements. (The only exception applies to study abroad credit from the full year program at the London School of Economics, from which a maximum of four transfer and/or study abroad credits may be counted toward major requirements.) The Department of Economics maintains online resources to guide economics majors and minors: http://www.econ.duke.edu/ecoteach/undergrad/ For the B.S. Degree with Concentration in Financial Economics The Economics department also offers a B.S. Degree with a concentration in financial economics. Certification of this concentration is designated on the official transcript. Students who wish to pursue this designation must complete the requirements for the B.S. Degree with the addition of the following requirements. Requirements: Economics XXX: Intermediate Economics for Finance. 2 Three electives chosen from among the following 100 level economics courses: Economics 157, 166, 168, 181, 183, 187, 200ES, 220, 225/Math 215 and others with approval of DUS. III Current Listing in the Undergraduate Bulletin For the B.S. Degree The Bachelor of Science degree in economics signifies achievement of proficiency in quantitative skills and experience in applying these to economics. Students who contemplate graduate study in economics are urged to develop skills in intermediate calculus (Mathematics 103), linear algebra (Mathematics 104), differential equations (Mathematics 131), and advanced calculus (Mathematics 139). Students interested in graduate work in business administration may wish to focus less on mathematics and more on computer science, statistics, and quantitative economics. Prerequisites: Economics 1A and 2A; or 1D or 51D. Economics 55D. Mathematics 32 and 102; or 103 or any higher-level mathematics course with Mathematics 103 as a prerequisite. Statistics 103, Statistics 104/Mathematics 135, Statistics 112, Statistics 113 or Statistics 114/Mathematics 136. Statistics is a prerequisite for Economics 139D and many 100-level 2 A full description of this course is included in the Proposal for a Minor in Economics submission. 16 economics courses and therefore should be taken by the fall of sophomore year. Prerequisites for the major, as well as requirements, may not be taken pass/fail. Requirements: Three core courses: Economics 105D, Economics 110D and Economics 139D. Economics 139D should be completed no later than the spring of sophomore year since most 100level economics courses have Economics 139D as a prerequisite. Five electives chosen from any additional non-core economics courses at the 100 level or above, with the exception of Economics 151, Economics 182, and Economics 888. Substitution of similar courses in other departments at Duke for courses in the Department of Economics used toward major requirements is not permitted. A maximum of two transfer and/or study abroad credits may be counted toward major requirements. (The only exception applies to study abroad credit from the full year program at the London School of Economics, from which a maximum of four transfer and/or study abroad credits may be counted toward major requirements.) The Department of Economics maintains online resources to guide economics majors and minors: http://www.econ.duke.edu/ecoteach/undergrad/