Quantitative Finance and Economics Lecture 9: Portfolio Theory

This lecture of quantitative finance and economics covers portfolio theory.

1  Lecture Slides 

Download PDF slides: Introduction to portfolio theory

Download PDF slides: Portfolio Theory with Matrix

Portfolio Theory Examples

Portfolio Theory with Matrices Examples

R Portfolio Functions

IntroPortfolioTheory.xls

R codes: portfolio.r , testport.r

 

2  Introduction (2:57)

 

3  Introduction to Portfolio Theory (14:35)

 

4  Portfolio Examples (6:08)

 

5  Portfolio Value-at-Risk (6:11)

 

6  Portfolio Frontier (10:28)

 

7  Efficient Portfolios (10:00)

 

8  Minimum Variance Portfolio (12:43)

 

9  Portfolios with a Risk Free Asset, Part_1 (7:24)

 

10  Portfolios with a Risk Free Asset, Part_2 (18:32)

 

11  Tangency Portfolio (17:33)

 

12  Examples (10:11)

 

13  Portfolio Theory with Matrix Algebra, Part 1 (15:26)

 

14  Portfolio Theory with Matrix Algebra, Part 2 (15:54)

 

15  Portfolio Theory with Matrix Algebra, Part 3 (16:34)

 

16  Brief Comment about Excel Solver Add-in (2:12)

 

 

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Quantitative Finance and Economics Lecture 8: Hypothtesis Testing

This lecture of quantitative finance and economics covers hypothesis testing.

1  Lecture Slides 

Download PDF slides

R Hypothesis Testing Examples

R codes: hypothesisTestingCER.r

 

2  Hypothesis testing: Introduction (8:29)

 

3  Hypothesis testing: Overview (9:06)

 

4  Hypothesis testing: CER Model (10:47)

 

5  Chi-square and Student’s t distributions (5:16)

 

6  Test of Specific Coefficient Value (26:07)

 

7  Test for Normal Distribution (8:36)

 

8  Test for No Autocorrelation (5:36)

 

9  Diagnostics for Constant Parameters (22:21)

 

 

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Quantitative Finance and Economics Lecture 7: Bootstrapping

This lecture of quantitative finance and economics covers bootstrapping.

1  Lecture Slides 

Download PDF slides

R Bootstrap Examples

R codes: bootStrap.r

 

2  Introduction (2:43)

 

3  Bootstrap (26:06)

 

4  Performing Bootstrapping in R (18:10)

 

5  Bootstrapping VaR (8:44)

 

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Quantitative Finance and Economics Lecture 6: Constant Expected Return Model and Estimation

This lecture of quantitative finance and economics covers constant expected return model and estimation.

1  Lecture Slides 

Download PDF slides

R CER Model Examples

cerExample.csv

R codes: cerModelExamples.r

 

2  Introduction (11:28)

 

3  Constant Expected Return Model (14:07)

 

4  Simulating Data (12:14)

 

5  Random Walk Model (5:38)

 

6  Estimateing Parameters of CER (18:59)

 

 

7  Bias and Precision (13:02)

 

8  Mean Squared Error (1:22)

 

9  Standard Error (22:12)

 

10  Asymptotic Properties of Estimators (14:11)

 

11  Confidence Intervals (12:47)

 

12  Monte Carlo Simulation (15:27)

 

13  Value at Risk in CER Model (7:36)

 

 

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Quantitative Finance and Economics Lecture 5: Descriptive Statistics

This lecture of quantitative finance and economics covers descriptive statistics.

1  Lecture Slides 

Download PDF slides

R Descriptive Statistics Examples

R Examples: Descriptive Statistics Examples for Daily Dataownload PDF slides

R codes: descriptiveStatistics.r

 

2  Covariance Stationarity (11:28)

 

3  Histograms (11:33)

 

4  Sample Statistics (15:24)

 

5  Empirical CDF and QQ plots (12:00)

 

6  Outliers Part 1 (7:15)

 

7  Outliers Part 2 (7:39)

 

8  Descriptive Statistics for Daily Data (24:17)

 

 

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Quantitative Finance and Economics Lecture 4: Time Series Conceipts

This lecture of quantitative finance and economics covers some basic conceipts of time series.

1  Lecture Slides 

Download PDF slides

R Time Series Examples

R codes: timeSeriesConcepts.r

 

2  Time Series Concepts (16:48)

 

3  Autocorrelation (9:14)

 

4  White Noise Processes (12:31)

 

5  Nonstationary Processes (17:29)

 

6  Moving Average Processes (25:45)

 

7  Autoregressive Processes Part 1 (3:19)

 

8  Autoregressive Processes Part 2 (28:19)

 

 

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Quantitative Finance and Economics Lecture 3: Matrix Algebra

This lecture of quantitative finance and economics covers matrix algebra.

1  Lecture Slides 

Download PDF slides

R Matrix Examples

matrixReview.xlsx

R codes: matrixReview.r

 

2  Matrix Algebra: Review Part 1 (17:02)

 

3  Matrix Algebra: Review Part 2 (20:10)

 

4  Further Instruction (2:11)

 

5  Matrix Algebra: Portfolio Math (21:14)

 

6  Matrix Algebra: Bivariate Normal (7:26)

 

 

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Quantitative Finance and Economics Lecture 2: Probability Review

This lecture of quantitative finance and economics presents some basic reviews of probability.

1  Lecture Slides

Lecture slides, Part 1

Lecture slides, Part 2

R Probability Examples

probReview.xls

R codes: probReview.r

 

2  Introduction-1 (1:06)

In this lecture we begin our review of probability theory. We will learn about random variables and distribution functions for discrete and continuous random variables. Particular attention will be paid to the normal distribution and its use in financial modeling. We will also discuss the shape characteristics of distributions such as expected value, standard deviation, skewness and kurtosis. Finally, we define the risk concept, Value-at-Risk, and how it relates to the quantiles of a distribution. These probability concepts will serve as a foundation for the rest of the course.

 

3  Univariate Random Variables (20:11)

 

4  Cumulative Distribution Function (8:42)

 

5  Quantiles (7:50)

 

6  Standard Normal Distribution (16:02)

 

7  Expected Value and Standard Deviation (19:58)

 

8  General Normal Distribution (6:23)

 

9  Standard Deviation as a Measure of Risk (4:34)

 

10  Normal Distribution: Appropriate for simple returns? (14:22)

 

11  Skewness and Kurtosis (15:39)

 

12  Student’s-t Distribution (5:52)

 

13  Linear Functions of Random Variables (11:13)

 

14  Value at Risk (19:48)

 

15  Introduction-2 (1:04)

 

16  Location-scale Model (12:15)

 

17  Bivariate Discrete Distributions (14:18)

 

18  Bivariate Continuous Distributions (14:15)

 

19  Covariance (19:16)

 

20  Correlation and the Bivariate Normal Distribution (11:59)

 

21  Linear Combination of 2 Random Variables (11:09)

 

22  Portfolio Example (19:20)

 

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Quantitative Finance and Economics Lecture 1: Simple Returns

This lecture of quantitative finance and economics covers simple returns.

Download ODF slides

Return Calculations Examples

 

 

1  Introduction(0:58)

 

2  Simple Returns

2.1  Future Value, Present Value and Compounding (17:02)

 

2.2  Asset Returns (16.53)

 

2.3  Portfolio Returns (9:12)

 

2.4 Dividends (4:00)

 

2.5  Inflation (4:57)

 

2.6  Annualizing Returns (5:32)

 

3  Continuously Compounded Returns

3.1  Continuously Compounded Returns (15:55)

 

3.2  Continuously Compounded Portfolio Returns and Inflation (5:50)

 

4  Excel Examples

Excel file used here

4.1  Simple Returns (4:01)

 

4.2  Getting Financial Data from Yahoo! (10:26)

 

4.3  Return Calculations (6:21)

 

4.4  Growth of $1 (6:58)

 

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Quantitative Finance and Economics: Syllabus

This is the syllabus of the course of quantitative finance and economics.

1  About the Course

This course is an introduction to data analysis and econometric modeling using applications in finance. Equivalently, this course is an introduction to computational finance and financial econometrics. As such, the course uses concepts from microeconomics, finance, mathematical optimization, data analysis, probability models, statistical analysis, and econometrics.

The course will be 10 weeks long . Each week consists of roughly two and a half hours of recorded video lecture, broken up into five- to 20-minute segments. Finance topics include asset return calculations, risk and performance measures, portfolio theory, index models, and if time permits, the capital asset pricing model. Mathematical topics include optimization methods involving equality and inequality constraints and basic matrix algebra. Statistical topics include probability and statistics (expectation, joint distributions, covariance, normal distribution, sampling distributions, estimation and hypothesis testing, and so on) with the use of calculus, descriptive statistics and data analysis, linear regression, basic time series methods, the simulation of random data, and resampling methods. Read more Quantitative Finance and Economics: Syllabus