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Columbia University

Optimization Methods in Asset Management

Columbia University via Coursera

Overview

This course focuses on applications of optimization methods in portfolio construction and risk management. The first module discusses portfolio construction via Mean-Variance Analysis and Capital Asset Pricing Model (CAPM) in an arbitrage-free setting. Next, it demonstrates the application of the security market line and sharpe optimal portfolio in the exercises. The second module involves the difficulties in implementing Mean-Variance techniques in a real-world setting and the potential methods to deal with it. We will introduce Value at Risk (VaR) and Conditional Value at Risk (CVaR) as risk measurements, and Exchange Traded Funds (ETFs), which play an important role in trading and asset management. Typical statistical biases, pitfalls, and their underlying reasons are also discussed, in order to achieve better results when completing  real statistical estimation. The final module looks directly at real-world transaction costs modeling. It includes the basic market micro-structures including order book, bid-ask spread, measurement of liquidity, and their effects on transaction costs. Then we enrich Mean-Variance portfolio strategies by considering transaction costs.

Syllabus

  • Course Overview
  • Mean-Variance Analysis and CAPM
    • In this module, we will cover topics related to Mean-Variance Analysis and Capital Asset Pricing Model (CAPM), which is a fundamental theory in portfolio selection. CAPM can be used to price risky assets in the market. We will start by utilizing Mean-Variance Analysis to construct an optimal portfolio in an arbitrage-free market. Then we will introduce the efficient frontier and capital market line. Finally, we use excel to implement Mean-Variance optimization and construct a portfolio with the highest Sharpe ratio. In practice, Mean-Variance Analysis and CAPM can also be extended in other pricing techniques such as factor model. In the assignment, you will be required to apply Mean-Variance Analysis to do portfolio selection, Sharpe ratio computation, and risky asset pricing, etc.
  • Assignment week
  • Practical Issues in Implementing Mean Variance
    • In this module, we show the difficulties in implementing Mean-Variance and provide possible methods to improve the estimated frontier by revising constraints and amending parameter estimation. VaR and CVaR are introduced as different measurements about risk beyond variance. In the second lesson, we will also learn common ETFs and their returns and volatility. ETFs play an important role in trading and asset management because of their features at low costs, tax efficiency, and stock-like behaviors. In the last lesson, we will introduce some facts about typical statistical biases and pitfalls, as well as underlying reasons. This can remind us to be more careful when doing the statistical estimation. If you have any questions, you should reach out to us on the discussion forum.
  • Assignment Week
  • Other Applications of Financial Engineering
    • In the real world, transaction costs are charged when we buy or sell assets in the market. How to model transaction cost is a key question in portfolio execution. In this module, we learn about the basic market micro-structures, including order book, bid-ask spread, measurement of liquidity and their effects on transaction costs. Then we enrich Mean-Variance portfolio strategies by taking transaction costs into consideration. By learning this module, you will be better prepared to deal with real-world investment problems.

Taught by

Martin Haugh and Garud Iyengar

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