Value at Risk (VaR)

Value at Risk (VaR) is a measure of the potential risk in value of investments. It attempts to answer the question like, “How much could I loss?” It is quantified in three variables: a confidence level (normally either 95% or 99%), an estimate of loss (expressed either in currency or percentage terms) and the time frame.

The Idea behind Value at Risk (VaR)

The volatility method is also used for risk measurement. However, it does not consider the investments’ movements. For example, stocks’ prices are highly volatile which changes suddenly. They are measured by using Value at Risk method.

How it Works (Example)

Suppose a UK company expects to receive \$ 14 million from a US customer. The value in pounds will depend on the exchange rate between the dollar and pounds resulting in gains or loss as the exchange rate change. Assume that the exchange rate today is \$ 1.75/Pound and the daily volatility of pound/dollar exchange is 0.5%.

Calculate the 1-day 95% Value at Risk of receivable.

Solution

The value of the \$ 14 million today is 8 million (\$ 14 million / \$ 1.75/Pound) with a daily standard deviation of 40,000 (0.5% * 8 million pound).

Value at Risk method is calculated as standard deviation * Z-score (from normal distribution table). The standard normal value associated with one-tail 95% confidence level is 1.645 (see normal distribution tables).

Hence, the 1-day 95% VaR is 1.645*40,000 = 65,800 Pound

It means that we are 95 % confident that the maximum daily loss will not exceed 65,800 pound. Alternatively, we could also say that there is a 5% chance that loss will exceed 65,800 pound.

Why it Matters

The result of VaR summarizes the exposure to risk and probability of an adverse move. If the result is negative, the process that led to computation of VaR can be used to decide where to trim the risk. For example, derivatives can be added to hedge and risky securities can be sold.