Overview

Chapter 1 defined value at risk (VaR) as the maximum potential loss that a business unit or a position can generate in a given time horizon within a defined percentage of potential scenarios (the so-called confidence level), where extremely adverse scenarios are excluded. In formal terms, if V is the value of a given portfolio, V ₀ is its initial value, and 1 ? ? is the desired confidence level (e.g., 99%), then VaR _{1 ? ?} (i.e., the amount of loss that can be exceeded only in a percentage of potential cases equal to ?) is the amount such that

or alternatively, since V ₀ ? V represents a loss whenever V < V ₀,

How can the risk manager estimate VaR in practice? Let us consider VaR for a trader dealing in UK stocks and calculated on a daily horizon at a 99% confidence level. If the trader has invested in a basket of stocks that closely resembles the FTSE100, a simple way would be to consider FTSE100 daily returns in the last 200 business days, sort them in ascending order, and then identify the percentage VaR with the third-lowest return in the sample. If, for instance, the three worst losses were ?4.1%, ?4.7% and ?6.95%, the maximum loss that can be excedeed only in 1% of cases is 4.1%. In fact, according to historical experience, the index (and therefore the trader) may lose more than VaR...