Value at Risk (VaR) provides an estimate of the greatest likely loss if a known risk were to occur. It may represent the loss in value of a portfolio of shares if a market slump occurred. In practice the analyst calculates the greatest loss that could arise in 99 percent of all cases. This means that in 1 percent of cases the loss would actually exceed the amount of the calculated VaR, which is effectively a boundary value. It is a probabilistic statement; if a VaR is estimated to be £1 million with a confidence of 99 percent (probability of 0.99) then a loss of more than £1 million might be expected on one day in every 100. A slightly more mathematical definition is given by P. Jorion: “VaR measures the worst expected loss over a given time interval under normal market conditions at a given confidence level”.
There are several factors underlying the growth of VaR as a risk-management tool. Firms increasingly hedge their exposure to sources of market risk. Financial market volatility can dramatically impact the profitability of firms, particularly those firms that improperly hedge market risks. The experience of Enron, Orange County, Long-Term Capital Management, Metallgesellschaft, and Barings Bank illustrates the magnitude of large unanticipated events that are not going to be captured by standard VaR forecasts.
The VaR approach offers an appealing summary statistic of portfolio risk embodied within a single statistic. Specifically, VaR is a powerful operational tool to establish position limits for traders, but also enables managers and regulators to control to some extent the firm’s overall margin between risk and return.
But while the concept of VaR is straightforward, its implementation is not. There are a variety of models and model implementations that produce very different estimates of the risk for the same portfolio. These difficulties were highlighted when regulators presented some of the largest banks in the world with the same test portfolio and asked them to compute the VaR. The answers varied widely, causing regulators to adjust their thinking on how the measure may be used to manage market risk. The difficulties in model based evaluation were considered in a Bank of England study on valuation practices in banks. Another important point is the divergence in a model’s implementation within software and how it, too, affects the establishment of a risk measurement standard. Discrepancies arise because of the VaR’s extreme sensitivity to the modeler’s choice of parameters.
- Jon Danielsson, The Value-at-Risk Reference: Key Issues in the Implementation of Market Risk (Risk Books, 2007);
- Jorion, Value at Risk: The New Benchmark for Managing Financial Risk (McGraw-Hill, 2007);
- Francesco Saita, Value at Risk and Bank Capital Management (Elsevier Academic Press, 2007);
- Martin Scheicher and Burkhard Raunig, A Value at Risk Analysis of Credit Default Swaps (Dt. Bundesbank, 2008);
- Value-at-Risk Theory and Practice (Chapman & Hall, 2009).
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