MATHEMATICS FOR ECONOMICS AND FINANCE

Degree course: 
Corso di First cycle degree in ECONOMICS AND MANAGEMENT
Academic year when starting the degree: 
2016/2017
Year: 
3
Academic year in which the course will be held: 
2018/2019
Language: 
Italian
Credits: 
9
Period: 
Second semester
Standard lectures hours: 
78
Requirements: 

Both math courses offered in the first two years of the program

Final Examination: 
Orale

Written exam

Assessment: 
Voto Finale

The aim of this course is to offer participants the basic notions required to understand financial markets and to pick the right decision when dealing with risk.

Further details and skills will be discussed during classes

1 Preliminaries on Financial Markets
1.1 A Primer on Banks and Rates
1.1.1 Banks and the Federal Funds Rate
1.1.2 Short-Term and Long-Term Rates and Yield Curves
1.2 A Primer on Securities Markets
2 The Time Value of Money
2.1 Time
2.2 Interest Rate and Return Rate
2.2.1 Interest Rate
2.2.2 Required Return Rate and the Risk-Free Rate
2.2.3 Total Return Rate
2.3 Simple Interest
2.4 Compound Interest
2.4.4 Continuous Compounding
2.5 Generalized Compound Interest
2.5.1 Varying Interest and Varying Compounding Periods
2.6 The Net Present Value and Internal Rate of Return
2.6.1 Present Value and NPV of a Sequence of Net Cash Flows
2.6.2 The Internal Return Rate
2.6.3 NPV and IRR for General Net Cash Flows
2.7 Annuity Theory
2.7.1 Future and Present Values of Simple Ordinary Annuities
2.7.2 Amortization Theory
2.7.3 Annuities with Varying Payments and Interest Rates
2.8 Applications of Annuities
2.8.1 Saving, Borrowing, and Spending
2.9 Applications to Stock Valuation
2.9.1 The Dividend Discount Model
2.9.2 Present Value of Preferred and Common Stocks
2.10 Applications to Bond Valuation
2.10.1 Bond Terminologies
2.10.2 Bond Prices Versus Interest Rates and Yield to Maturity

3.1 Markowitz Portfolio Model: The Setup
3.1.1 Security Return Rates
3.1.2 What About Multivariate Normality of Security Return Rates?
3.1.3 Investors and the Efficient Frontier
3.1.4 The One-Period Assumption,Weights, and Short Selling
3.1.5 Expected Portfolio Return Rate
3.1.6 Portfolio Risk
3.1.7 Risks and Covariances of the Portfolio’s Securities
3.1.8 Expectation and Volatility of Portfolio Log Return
3.2 Two-Security Portfolio Theory
3.2.1 Preliminaries
3.2.2 Efficient Frontier of a Two-Security Portfolio
3.2.3 Reducing Risk Through Diversification

4 Capital Market Theory and Portfolio Risk Measures
4.1 The Capital Market Theory
4.1.1 The Capital Market Line (CML)
4.1.2 Expected Return and Risk of the Market Portfolio
4.1.3 The Capital Asset Pricing Model (CAPM)
4.1.4 The Security Market Line (SML)
4.1.5 CAPM Security Risk Decomposition
4.2 Portfolio Risk Measures
4.2.1 The Sharpe Ratio

A.O. Petters, X.Dong
An Introduction to Mathematical Finance with Applications
Understanding and Building Financial Intuition
Springer, 2016

Convenzionale

Class lectures
Additional material available on the esse3 teaching platform

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