Statistics for Financial Practitioners

This is a first course on probability and statistics that has been designed for financial market practitioners. The aim of this course is to establish a level of knowledge in inferential statistics and econometric modelling that would be useful for a user of financial and econometric models.

A look at the broad outline is in the [Syllabus].

Books

There are two main textbooks for the course.

1. Investment science by David Luenberger
2. Introduction to Probability and Statistics by Sheldon Ross

Other supplementary textbooks are:

1. Statistics for business and economics by James McClave and George Benson.

Other fun books to read are:

1. The Economics of Financial Markets by Houthakker and Williamson.
2. Capital Ideas by Peter Bernstein.

Software

The statistical software used in this class is the freeware package called R. This is available for both Linux as well as Windoze. The R project is at http://www.r-project.org. You can find a good introduction to the package and programs in R at Ajay Shah's R by example website link.

Course sesssions

1. Motivation for this course[Slideshow][Printable version]
2. An introduction to principles of probability [Slideshow][Printable version]
• Defining events and event spaces
• Mutually exclusive events
• Defining probability
• Basic features of probability
• Unconditional and conditional probability
• Independent events
3. Probability distributions and density functions [Slideshow][Printable version]
• Discrete and continuous random variables
• Probability distributions
• Probability density functions
• Cumulative distributions and density functions
4. Summarising probability distributions and density functions [Slideshow][Printable version]
• Expectation of RVs
• Expectation of functions of RVs
• Moment generating functions
• Describing data: Histograms, kernel density plots
• Describing data: Mean, median, mode, centiles, quartiles
5. Samples and sampling distributions [Slideshow][Printable version]
• Samples and populations
• Parameters vs. statistics
• Sampling distribution of a statistic
• Central Limit Theorem
6. Applying CLT to understand sample means[Slideshow][Printable version]
• Properties of the sampling distribution of the sample mean
• Inference about the sample mean: confidence levels and confidence intervals
• Questions about the sample vis-a-vis a given population
• Questions about the population mean, given a sample
• Difference in inference for large samples vs. small samples
• Estimating the difference in means of two populations
• Estimating the difference in proportions of two populations
7. Financial market returns[Slideshow][Printable version]
• The importance of returns
• The distribution of returns
• Value at Risk
8. Jointly distributed random variables[Slideshow][Printable version]
• Joint probabilities
• Marginal probabilities
• Conditional probabilities
• Independance
• Covariance
• Conditional mean and variance
9. The Markowitz problem[Slideshow][Printable version]
• Portfolio optimisation
• Defining a two-asset portfolio
• Matrix notation
• Generalising to an n-asset portfolio
• Diversification
• The efficient portfolio frontier
10. The expected utility framework[Slideshow][Printable version]
• Decision making under uncertainty
• History
• Expected utility hypothesis (EUH)
• Risk aversion
• Using the EUH
11. Lessons from the Markowitz framework[Slideshow][Printable version]
• The two-fund separation theorem
• The efficient portfolio frontier including the risk-free asset
• The one-fund theorem
• Asset pricing
• The securities market line
• The Capital Asset Pricing Model
12. Estimating inputs to the pricing models[Slideshow][Printable version]
• E(r) for a security
• Variance and covariances
• E(r) for the market
• Beta of a security

Mechanics

• The classes will be two hour sessions followed by half an hour of problem solving in class.

• There will be problem sets at the end of every class, which are expected to be done before the next class.

• There can be a 15 minute quiz at the start of a class. There is an exam at the end of every 13 sessions (on average). A pass in the exam is required to continue in the course.

Useful links

• Ajay Shah's website

Back up to Susan Thomas' teaching page