Spring 2022 Instructor
高等投資科學 Advanced Investment Science (QF 444800)
Course Description & Audience: The course concentrates on fundamental principles and the application of scientific tools, mainly mathematical, to investment problems. One of the goals of this course is to illustrate how these principles can be transformed into practical solutions to actual investment problems. Coverage of the material will be suitable for upper-level undergraduate and graduate students (who majored in Quantitative Finance, Engineering, Mathematics, Economics, or Management) interested in advanced investment sciences and quantitative finance. The intended topics of the courses to cover are listed as follows:
Part 1: Single-Period Random Cash Flows
Mean-Variance Portfolio Theory
Capital Asset Pricing Model Theory
Factor Models & Arbitrage Pricing Theory
Utility Theory
Part 2: Derivative Securities
Forwards and Futures
Model of Asset Dynamics
Elementary Stochastic Calculus
Basic Options Theory
Part 3: General Multi-Period Cash Flow Streams
Optimal Portfolio Growth
Special Topic: General Investment Evaluation
Special Topic: Algorithmic Trading Systems
Prerequisites: Students planning to take this course should have some background in calculus, linear algebra, basic probability theory, and statistics. Familiarity with numerical software such as Matlab or Python is also required. If in doubt about the background, the student should consult with the instructor.
Time and Place: Lectures are at T2T3T4, in Room 206 of the TSMC Building. The instructor's office hours are Wednesdays from 13:00 to 15:00 in Room 608. Meetings are also possible at other times by appointment.
Textbooks: While students will receive significant handout material to support the lectures, we reference some great textbooks below:
D. G. Luenberger, Investment Science, Oxford University Press, 2013.
J. C. Hull, Options, Futures, and Other Derivatives, Pearson, 2021.
J. Cvitanic and F. Zapatero, Introduction to the Economics and Mathematics of Financial Markets, MIT Press, 2003.
G. Campolieti and R. N. Makarov, Financial Mathematics: A Comprehensive Treatment, CRC Press, 2014.
J. A. Primbs, A Factor Model Approach to Derivative Pricing, 2016
E. A. Ok, Real Analysis with Economic Applications, Princeton University Press, 2007.
Teaching Method: Lecture.
Homework: Approximately weekly.
Grading: The grade will be based on two midterm tests (25% for each), homework (20%), and a special project (30%). The instructor may exercise discretion up to 10% in each grading category.
Course Material
02/15: Introduction and Some Preliminaries
02/22: Markowitz's Portfolio Theory
03/01: The Two Funds Theorem and the One Fund Theorem
03/08: Captial Asset Pricing Model
03/15: Factor Model Theory & APT
03/22: APT II & Utility Theory
03/29: Utility Theory II
03/31:
Midterm 1
04/05: Spring Break. No Class.
04/12: Forwards and Futures I
Final Project Research Topic Due.
04/19: Forwards and Futures II & Model of Asset Dynamics
04/26: Model of Asset Dynamics
05/03: Model of Asset Dynamics II: Ito lemma and Elementary Stochastic Differential Equation
05/10: Model of Asset Dynamics & Basic Option Theory
05/17: Basic Option Theory II: Binominal Lattice Model & Black-Scholes PDE
Remote Class.
05/24: Black-Scholes PDE and European Call Option Pricing Theorem
Remote Class.
05/31: Basic Option Theory III: Greeks
06/07: (Last Class!) Algorithmic Trading
Remote Class.
Discuss the final project proposal.
06/11:
Take-Home Midterm 2
06/17: Last day of the final exam week.
Looking for good writing tips? See Writing Tips for PhD Students by Prof. John H. Cochrane.
Final Project Report Due. Your final project should include the following ingredients.
Title
Abstract
Introduction
Provide a literature survey explaining what has been done, then point out what is missing in the literature (For example, say there is some weakness of the existing approach, so you want to fix it by providing your approach. As another example, say there is an issue that no one has noticed, so you jump in. As the last example, you found a phenomenon from your experiment/simulation/dataset, so you formed your hypothesis and wish to test it). This should provide enough ground to motivate your work. Then, provide the difference between your approach and others, and compare and contrast.
Problem formulation or Preliminaries
If your work involves a theoretical setting, provide them in this section. Define every notion and the corresponding notations in a consistent and precise way. You should tell the reader exactly the main problem you want to tackle and the methodologies you adopted.
Main results or Empirical studies
The main claim or findings go first. Then, provide supporting evidence. For empirical studies, provide a detailed explanation about your data; e.g., where did you get the data? why did you choose this dataset, not others? what do you see from the result? Are there any good or bad findings? If you run a simulation, describe how you conducted it precisely and concisely.
Concluding Remarks or/and Future Work
References
Your final project should be no more than 10 pages of A4 papers.
You are encouraged to use LaTeX to write your project report; e. g., overleaf might be a handy editor.
Assignments
Assignment 01: Mean-Variance Portfolio Theory I
Assignment 02: Mean-Variance Portfolio Theory II (Due 03/08)
Assignment 03: CAPM Theory (Due 03/22)
Assignment 04: Factor Models and APT (Due 03/29)
Assignment 05: Utility Theory (Due 04/12)
Assignment 06: Forwards and Futures (Due 04/26)
Assignment 07: Model of Asset Dynamics (Due 05/03)
Assignment 08: Model of Asset Dynamics II (Due 05/17)
Assignment 09: Basic Option Theory I (Due 05/24)
Assignment 10: Basic Option Theory II (Due 05/31)
Lecture Handouts
Chapter 07: Elementary Pricing Theory
Chapter 10: Elementary Stochastic Calculus
Chapter 14: Optimal Portfolio Growth I: Discrete-Time Approach
Chapter 15: Optimal Portfolio Growth II: Continuous-Time Approach
Exams (and the Topics Covered)
Midterm 1
Basic Probability Theory, Mean-Variance Theory, One-Fund/Two-Fund Theorem, CAPM, Factor Models Theory, Arbitrage Theory, and Elementary Utility Theory.
Midterm 2
Forwards and Futures, Model of Asset Dynamics, Elementary Stochastic Calculus (Ito Calculus and Martingales), Basic Option Theory (Binomial Lattice Model, Risk-Neutral Measures, and Black-Scholes Theory), Greeks.
Relevant References
Karl Sigman, IEOR4700: Notes on Financial Engineering, Columbia University, 2006.
J. H. Cochrane, Investments Notes, Stanford University, 2006.
傅承德, 財務統計, 數學傳播 26卷2期, 2002.
陳宏, 郭震坤, 財務數學(上) ,數學傳播 26卷1期, 2002.
陳宏, 郭震坤, 財務數學(下) ,數學傳播 26卷2期, 2002.
韓傳祥, 金融中波動率的數學問題, 數學傳播 37卷1期, 2013.
C. H. Hsieh, Note on Strictly Increasing Function.
C. H. Hsieh, Note on Arithmetic Mean and Geometric Mean.
Final Project Proposed by Students.
Spring 2022
吳珮妤, Optimizing Asset Allocation with ETFs Under Different Macroeconomics Scenario
林雅琪, On Performance Evaluation for Trading Strategies Portfolio: A Mean-Variance Approach
陳德才, 自組虛擬貨幣ETF與現行市場上虛擬貨幣ETF之成效分析
戴晟恩, Factor Model Approach on ETF Trend Trading
黃俊踴, On Portfolio Optimization Using Dow Jones Sustainability Indices (DJSI)
莊博雅, Social Media Sentiment Analysis for Predicting TSLA's Stock Price and Revenue
呂嘉芸, PCA and Deep Learning Model on Asset Pricing
簡立昀, On Optimal Algorithmic Trading Strategy: Technical Indicators Approach
Spring 2021
翁翊珊, On Bond Portfolio Optimization: A Minimum Duration Strategy
余品薇, Portfolio Management: Cryptocurrency, Derivatives, and Asset Using Markowitz Optimization Subject to Variance, VaR, and CVaR
李育霖, The Uselessness of the Hurst Exponent on S&P 500 Stocks
鄭宇宏, Cryptocurrency Portfolio Optimization under CVaR
簡家豪, 由0050中精煉出數隻股票來組成新的投資組合盼其能超過原本之報酬率