By Rupert Kuveke
Given a portfolio of assets, VaR assesses the assets comprising the portfolio, and produces a single figure which represents the value of the portfolio which is at risk of being lost, for a specific probability, over a specific future period of time. For example, the 1% Daily VaR of a portfolio may be $10,000,000. This means that the portfolio has a 1% chance of losing at least $10,000,000 tomorrow.
Companies can utilise VaR to assess and manage their risk levels. VaR can also be used by regulatory committees such as the Basel Committee on Banking Supervision to set margin requirements for banks.
For my project, I assessed three methods for utilising VaR. These were:
- Historical Simulation,
- Filtered Historical Simulation, and,
- Fitting a GARCH(1,1) model combined with a standardised t distribution to a data set
For all my VaR calculations, I used S&P 500 Index data from 1988 to 2013. The S&P 500 Index, or Standard & Poors 500 Index, is an American stock market index which consists of 500 leading American companies from various industries.
If we deposit money in a bank, we are assured of a fixed, known rate of return. This is not the case with assets such as shares. Shares are volatile financial instruments, and there is an inherent uncertainty as to the distribution of share returns. With respect to financial markets, we may define volatility as the conditional standard deviation of the underlying asset return.
VaR calculations need to be able to account for the volatile nature of the individual shares comprising the portfolio being assessed. A sophisticated model should also be able to take into consideration the effect of volatility clustering, whereby small fluctuations in returns tend to be followed by more small changes, and conversely large fluctuations in returns tend to be followed by more large fluctuations, as experienced during the Global Financial Crisis.
Of the three methods assessed in this project, the third method, that of combining a GARCH(1,1) model with a nonnormal distribution, was most successful in generating sophisticated VaR values.
A GARCH model is a generalised autoregressive conditional heteroskedastic model. We may combine a GARCH model with a nonnormal distribution, allowing us to more accurately account for the nonnormality of asset returns.
GARCH models can model volatility fluctuations accurately, and can react quickly to spikes in volatility.
As a result, calculating VaR using a GARCH model produces more sophisticated, accurate values than using Historical Simulation, which is a model-free method. Filtered Historical Simulation also performed better than Historical Simulation, but was unable to accommodate daily fluctuations in volatility levels as well as the GARCH(1,1) model with a nonnormal distribution.
I thoroughly enjoyed the experience of attending and presenting my work at the Big Day In.
I would like to thank AMSI and CSIRO for the opportunity to participate in the Vacation Research Scholarship program. I would also like to thank my supervisor, Associate Professor Paul Kabaila, for his support and guidance.
Rupert Kuveke was one of the recipients of a 2013/14 AMSI Vacation Research Scholarship.