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Chapter 2

5.3 Value at risk (VaR)

 VaR assesses the scale of the likely loss in value of a portfolio in a specified
time period at a defined level of probability.

 'There is a 95% chance that the value of the portfolio will fall by less than
$10 million over the next week'.

 VaR = standard deviation × appropriate Z score from Normal distribution tables.

 Regulators require banks to use VaR as a measure of risk.

Example 2

Risky Co, a UK based company, has sold goods on credit to a European
customer. They have invoiced in Euros for 12 million.

The exchange rate is currently 1.1996 EUR to the £.

The daily volatility of the pound/euro exchange rate is 0.5%.

Calculate to the nearest £, the 1-day 95% VAR.

Solution

€12,000,000/1.1996 = £10,003,334.44

Std Dev = £10,003,334 × 0.5% = £50,016.67

Z score for 95% = 1.645 (from tables)

VAR = £50,016.67 × 1.645 = £82,277

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