Financial Risk Management: Models, History, and Institutions

CHAPTER 5

Portfolio VaR for Market Risk

The previous chapter took one step in the direction of addressing the real-world complexities of many assets, namely, the nonlinearity of their returns with respect to some underlying risk factor. This chapter deals with another source of complexity, the dependence of returns jointly on several risk factors. With these two enhancements, the simple VaR techniques we studied in Chapter 3 become applicable to a far wider range of real-world portfolios.

A simple example of a security with several risk factors, which we mentioned in Chapter 3, is foreign exchange, which is typically held either in the cash form of an interest-bearing foreign-currency bank deposit, or the over-the-counter (OTC) derivatives form of a foreign exchange forward contract. In either form, foreign exchange is generally exposed not only to an exchange rate, but to several money-market rates as well. Another example is a foreign equity. If you are, say, a dollar-based investor holding the common stock of a foreign company, you are exposed to at least two risk factors: the local currency price of the stock and the exchange rate. As yet another example, if a long domestic equity position is hedged by a short index futures position, in an effort to neutralize exposure to the stock market, a small exposure to risk-free interest rates as well as the risk of poor hedging performance are introduced. Similar issues arise for most commodity and stock index positions, which are ...