In recent years the Value at Risk (VaR) concept for measuringdownside risk has been widelystudied. VaR basically is a summary statistic that quantifies theexposure of an asset or portfolio tomarket risk, or the risk that a position declines in value withadverse market price changes. Threeparties have been particularly interested: financial institutions,regulators and corporates. In this paper, we focus on VaR use for corporates. This field isrelatively unexplored. We showhow VaR can be helpful to study market value risk -- proxied by shareprice risk. We develop amethodology to decompose the overall VaR into components that areattributable to underlyingexternal risk factors and a residual idiosyncratic component.Apart from developing theoretical results, we study the airlineindustry to show what practicalresults our 'Component VaR framework' can yield. Like anymultinational company, an airlinefaces significant exposures to external risk factors, e.g. commodityprices, interest rates andexchange rates. In our opinion, Component VaR analysis can enrichdiscussions in the company onfinancial risk management and shareholder value.