financial-risk-measurement

This repo contains the source code where I implement the topics of the Risk Econometrics exam that I studied during my academic experience at the University of Bologna.

The textbook from which I studied the theory is "Elements of Financial Risk Management", and the implementation was conducted in R, using the rugarch, rmgarch and quarks packages.

Goal

The goal of the project is to measure the portfolio risk using Value at Risk and the Expected Shortfall, comparing the different methods for their calculation and modeling the conditional volatility of log returns.

The methods used are applied separately considering both a univariate and a multivariate portfolio.

Univariate analysis

In the first part of the project, univariate-financial-risk-measurement, is considered a portfolio with a single asset, the SP500 from January 1st 2001 to December 31st 2010.

The methods used are:

Case with unconditional (static) volatility over time:

• Non-parametric methods (no assumptions on the distribution of returns)

  • Historical Simulation (HS)
  • Age-Weighted Historical Simulation (WHS)

• Parametric methods (hypothesis on the distribution of returns)

  • Normal Distribution
  • Stundent-t distribution
  • Cornish-Fisher expansion

VaR and ES are calculated both on the entire portfolio and using rolling windows of 250 and 1000 trading days.

Case with conditional (dynamic) volatility over time:

Different methods for modeling conditional volatility are compared:

• The RiskMetrics EWMA model
• Different specifications of GARCH (Standard GARCH, Integrated-GARH, GJR-GARCH, Nonlinear-GARCH and Exponential-GARCH).

For each of these models, different distributional assumptions of returns have been evaluated:

• Normal distribution
• Stundent-t distribution
• Empirical distribution using the Cornish-Fisher expansion method
• Empirical distribution using the Filtered Historical Simulation (FHS) method
• Empirical distribution using the Extreme Value Theory (EVT) method (Hill estimator)

The best specification was chosen using backtesting.

Multivariate analysis

In the second part of the project, multivariate-financial-risk-measurement, is considered a portfolio with two assets, one equity (SP500) and one bond (U.S. 10 Year Treasury Note).

By maintaining a similar scheme of the univariate analysis, the focus is only on modeling portfolio volatility and covariance/correlation between assets over time using Dynamic Conditional Correlation models (DCC-EWMA and DCC-GARCH).