- Mathematics for Economics I - Mathematics for Economics II

At the end of the course students should be able to: - Compute present and future values of cash-flow streams to compute the net present values of different real and financial investments. - Have a basic knowledge of the functioning of financial markets and of the way in which investment decisions are made. - Understand the risk-return tradeoff. Understand how diversification affects risk. - Have a clear understanding of the difference between systematic and diversifiable risk and know how to measure each. - Understand how interest rates are set and the principles of valuation of fixed income securities. - Know the basic types of derivatives and understand why and how they are used in risk management.

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Financial Economics -1. Introduction to Financial Markets a.Financing investment in the economy b.Financial markets and trading financial assets -2. Financial Mathematics a.Introduction: The time value of money b.Simple and compound interest. Equivalent interest rates. c.Present and Future Values. d.Annuities -3. Investment Appraisal a.Cash flows b.Determining current and future values c.Net present value of an investment project d.Internal rate of return e.Other valuation techniques -4. Risk and Return a.Mathematical representation of a portfolio b.Expected portfolio returns c.Variance and standard deviation d.Finding the minimum variance portfolio e.Graphical representation of expected return and standard deviation of a portfolio -5. Portfolio Theory a.Diversification Effect b.Assumptions of the Mean-Variance Analysis c.The Efficient Frontier d.The tangency portfolio -6. The Capital Asset Pricing Model (CAPM) a.Relationship between risk and expected return b.The CAPM model c.The CML and The SML d.Portfolio Beta -7. Fixed Income Securities a.Valuation of fixed income b.The term structure of Interest Rates c.Forward interest rates d.Default risk e.Risk Management -8. Derivatives Products a.Types of derivatives b.Pricing Principles

Learning activities in year 2020/2021 str based on a bimodal system: lectures will be given on an online basis, onsite teaching when it comes to the reduced groups. 1.- Theory (online)- Sessions. The instructor of the course teach the basic concepts of the topic. Classnotes are provided to the students. 2.- Solution to exercises. The student must solve the test to assess his/her degree of knowledge of the different concepts. This part comprises the individual work of the student at home. 3.- Exercises - Sessions (onsite). The instructor of these sessions solves the exercise sets provided to the students.