Analytic Finance

This PhD-level course is concerned with models for portfolio decisions by investors and the pricing of securities in capital markets. It is meant to be difficult, but accessible to the motivated MBA student.

This quantitative course presents advanced material relevant for portfolio managers, extending the material covered in Investments. Topics include the money management industry (mutual funds, pension funds, hedge funds), modern techniques for optimal portfolio selection, liquidity and transaction costs, properties of asset returns, and investment strategies designed to exploit apparent violations of market efficiency.

The course has one central theme. Asset pricing has undergone a sea of change in the last 20 years or so, with the realization that expected returns do vary across time, and across assets in ways that the static CAPM and random-walk view does not recognize. We will cover a range of topics, including 1) how stock and bond returns can be predicted over time, 2) understanding the volatility of stock and bond returns, 3) multi-factor models for understanding the cross-sectional pattern of average returns, such as value, growth and momentum effects, 4) the size of the average market return and its relation to fundamental risks, 5) optimal portfolios that reflect multifactor models, return predictability and hedging motives, 6) advanced trading strategies used by trading desks and hedge funds, 7) performance evaluation and benchmarks for funds, 8) liquidity effects and "bubbles" in stock and bonds.

This course covers state-of-the art models and techniques required to analyze fixed income instruments, and their derivatives, in modern financial markets. By the end of the course, students will learn (i) the basic concepts of fixed income instruments, such as yield, duration, convexity; (ii) the modern empirical methodologies to describe Treasury and corporate bond data, such as "curve fitting," factor analysis, and default probabilities; (iii) the most recent modeling techniques for fixed income derivative products used in the Street, such as the models of Vasicek, Cox Ingersoll and Ross, Ho and Lee, Hull and White, Black-Derman-Toy, and Heath-Jarrow-Morton; and, importantly, (iv) how to use these models in practice to value both traditional derivative instruments, such as Swaps, Bond Options, Caps and Floors, as well as the more recent products, such as Inverse Floaters, Range Notes, Mortgage Backed Securities and Credit Derivatives. The key feature of Fixed Income Asset Pricing is that it strongly emphasizes the applications of these models to value real world fixed income products, and their derivatives, by focusing both on the practical difficulties of applying models to the data, as well as on the necessity to use computers to compute prices.

Financial risk management is reported to be the main reason for the use of financial derivatives by non-financial institutions. The course has two main objectives. The first is to cover techniques to identify, measure and manage corporate financial risk, as modern financial markets and regulation require. Specifically, topics of discussion will include dynamic hedging and portfolio replication, the development of Value-at-Risk, the management of exchange rate risk, interest rate risk, credit risk and operation risk. The second main objective is to build a framework to integrate financial risk management solutions with long-term corporate strategy. We will discuss cases where the use of financial engineering was vital for the success of a business strategy. Typical applications in this case include privatizations, mergers and acquisitions, and financing strategies, among others. However, the course will focus more on the uses of derivative securities rather than their technical aspects.