riskiness of a portfolio of securities

Aims: Write a program for computing Value at Risk. Check its performance using backtesting.

Background: It is a very difficult and important problem to estimate the riskiness of a portfolio of securities. Value at Risk (VaR) is a tool for measuring financial risk. The goal of this project is to implement some of the methodologies for VaR computation (either under normal conditions or using “crash metrics”) and test it on the real financial data. Other monetary measures of risk may also be studied.

Early Deliverables

  1. You will write a simple proof-of-concept program for computing Value at Risk for a portfolio consisting of 1 or 2 stocks using two different methods: model-building and historical simulation.
  2. Different ways of computing Value at Risk will be back tested and the statistical significance of the results analyzed.
  3. The report will describe the program (software engineering, algorithms etc.,).
  4. The report will also discuss different ways of estimating the variance of returns and the covariance between returns of two different securities (using the standard formula, exponentially weighted moving average, or GARCH(1,1)).

Final Deliverables

  1. The program should be extended by allowing derivatives (such as options) in the portfolio and using Monte Carlo simulation.
  2. Allow an arbitrary number of stocks (using eigen- or Cholesky decomposition)
  3. The final program will have a full object-oriented design, with a full implementation life cycle using modern software engineering principles.
  4. Ideally, it will have a graphical user interface.
  5. The final report will describe: the theory behind the algorithms.
  6. The final report will describe: the implementation issues necessary to apply the theory.
  7. The final report will describe: the software engineering process involved in generating your software.
  8. The final report will describe: computational experiments with different data sets, methods, and parameters.

Suggested Extensions

  • Computing conditional VaR (also known as expected shortfall)
  • Explore carefully the choice of parameters for EWMA and GARCH(1,1) using a loss function such as square or log loss
  • Empirical study of the two approaches to historical simulation for n-day VaR: reducing to 1-day VaR and direct estimation
  • Complement back testing by stress testing
  • Replacing the Gaussian model for stock returns by robust models
  • Computing monetary measures of risk different from VaR

Reading

  • John C. Hull. Options, futures and other derivatives, 7th ed., Pearson, Upper Saddle River, NJ, 2009.
  • Hans Follmer and Alexander Schied. Stochastic Finance: An Introduction in Discrete Time, 3rd ed., de Gruyter, Berlin, 2011.
  • Yahoo Finance as source of data: http://finance.yahoo.com/
  • http://www.gloriamundi.org