In this section, we show how to combine the various measures of risk for defining market risk VaR in the case of a very simple position as a percentile of the P & L of the position.

Consider an asset that depends on a single risk factor. There are not many such assets. An example would be a zero-coupon bond whose value depends on the single interest rate applicable at maturity of the bond. For assets which depend on several risk factors and portfolios, we need to fully expand the VaR model, as in the market risk section 10. The single risk factor position is "elementary" because there is no need to go through all technicalities of VaR calculations and we can focus on the three major steps required for deriving market risk VaR.

FIGURE 17.2

The three steps combine the previous measures of risk, sensitivity and volatility, for deriving the "value-at-risk," VaR, a measure of potential loss, or "downside risk" (Figure 17.2). VaR or downside risk is the most "comprehensive" measure of risk. It integrates sensitivity and volatility with the adverse effect of uncertainty, but it also relies on assumptions with respect to the distribution of values. The three main steps for an "elementary" position are:

1 measure the sensitivity of the position with respect to the risk factor

2 measure the volatility of the risk factor, and combine the sensitivity of the position and the volatility of the risk factor for deriving the volatility of the position

3 determine a loss percentile at confidence level a, based on an assumption with respect to the distribution of value.

The loss percentile at a is the VaR at the confidence level selected.

This presentation is a prerequisite, starting with an elementary position and using basic assumptions. It is extended to multiple factors positions or portfolios of position in the chapter on delta-normal VaR (Chapter 35).

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