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.
Этот курс входит в специализацию ''Специализация Financial Engineering and Risk Management'
от партнера
Специализация Financial Engineering and Risk ManagementКолумбийский университетОб этом курсе
Students should have intermediate to advanced undergraduate courses in: (i) probability and statistics, (ii) linear algebra, and (iii) calculus.
Приобретаемые навыки
Students should have intermediate to advanced undergraduate courses in: (i) probability and statistics, (ii) linear algebra, and (iii) calculus.
от партнера
Колумбийский университет
For more than 250 years, Columbia has been a leader in higher education in the nation and around the world. At the core of our wide range of academic inquiry is the commitment to attract and engage the best minds in pursuit of greater human understanding, pioneering new discoveries and service to society.
Программа курса: что вы изучите
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.
Специализация Financial Engineering and Risk Management: общие сведения
This specialization is intended for aspiring learners and professionals seeking to hone their skills in the quantitative finance area. Through a series of 5 courses, we will cover derivative pricing, asset allocation, portfolio optimization as well as other applications of financial engineering such as real options, commodity and energy derivatives and algorithmic trading. Those financial engineering topics will prepare you well for resolving related problems, both in the academic and industrial worlds.
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