Value at risk: a sophisticated tool to assess market riskby Saidul Islam
IN THE post financial crisis era, the issue of risk management in banks has drawn attention of all stakeholders, especially the regulators. In the context of Bangladesh, concerted efforts are being taken to address the issue from all concerned. All scheduled banks operating in Bangladesh have started to comply with the core risk management guidelines issued by the Bangladesh Bank. Despite having these guidelines, the Bangladesh Bank also has issued comprehensive risk management guidelines for banks very recently. In the said guidelines, the scheduled banks are asked to utilise some sophisticated techniques to measure different risks. Value at risk is one such technique or tool that is widely used to measure market risk in general and equity price risk and foreign exchange risk in particular. The central bank is making the commercial banks aware regarding fortuitous losses, which might be resulted from advertent or inadvertent or both business undertakings.
Banking business lines mainly comprise three types from the risk management point of view. The types are banking book, trading book and off-balance sheet exposures. The major risk that trading book portfolio confront is the market risk. Two very crucial components of market risk are equity price risk and foreign exchange risk.
Equity price risk is the risk of loss of market value of equity portfolio resulting from adverse movement in the market value of shares. The resultant losses enervate the capital base of investing company. It is an arduous task for a particular entity to accurately measure the losses derived from equity price fluctuation. Banks generally use stress testing to reflect the probable losses on the capital position.
On the other hand, foreign exchange risk is the current or prospective risk to earnings and capital arising from adverse movements in currency exchange rates. The banks usually take foreign exchange position from some activities like trading in foreign currencies through spot, forward and option transactions, holding foreign currency positions in the banking book and engaging in derivative transactions that are denominated in foreign currency for trading or hedging purposes. Whatever be the sources, the banks run the risks of loss originated from foreign exchange positions. Foreign exchange risk can most accurately measured by value at risk.
Value at risk, commonly referred to by its acronym VaR, is a statistical measure of the worst probable loss on a position or portfolio of positions that can be expected over a specified period of time to a given level of confidence. It is the maximum loss which with X% confidence over a holding period of n days. Value at risk itself is an accepted methodology for quantifying market risks. VaR measures the potential loss in market value of a portfolio using estimated volatility and correlation. The ‘correlation’ referred to the relationship that exists between the market prices of different instruments in a bank’s portfolio. VaR is calculated within a given confidence interval, typically 95 or 99 per cent; it seeks to measure the possible losses from a position or portfolio under normal circumstances.
There are three basic approaches that are used to compute value at risk, though there are numerous variations within each approach. The measure can be computed analytically by making assumptions about return distributions for market risks, and by using the variances in and co-variances across these risks. It can also be estimated by running hypothetical portfolios through historical data or from Monte Carlo simulations.
Since value at risk measures the probability that the value of an asset or portfolio will drop below a specified value in a particular time period, it should be relatively simple to compute if we can derive a probability distribution of potential values. That is basically what we do in the variance-covariance method, an approach that has the benefit of simplicity but is limited by the difficulties associated with deriving probability distributions.
Historical simulations represent the simplest way of estimating the value at risk for many portfolios. In this approach, the VaR for a portfolio is estimated by creating a hypothetical time series of returns on that portfolio, obtained by running the portfolio through actual historical data and computing the changes that would have occurred in each period.
Monte Carlo simulation is also as a risk assessment tool. This simulation is useful in assessing value at risk, with the focus on the probabilities of losses exceeding a specified value rather than on the entire distribution.
The variance-covariance method is based on the assumption that the underlying market factor has a normal distribution. Under this assumption, it is possible to determine the distribution of mark-to-market portfolio profits and losses, which is also normal. Besides using statistical tools and techniques, we use matrix representation of market factors in our VaR calculation under this approach.
The approach comprises of four steps that are described below:
At the very first step, data on market factor to be obtained from relevant sources. To calculate VaR on equity position, we need data on market prices of shares. Data on market prices are quite available at the DSE website. Volatility in the market prices is seen to occur when analysis is done by taking a large number of data. A large pool of data makes the estimate more realistic and reliable. Another reason behind of gathering a large number of data is that the underlying assumption is market risk factors are normally distributed which requires large number of samples. The important determinant of VaR is distribution in the change of the market factors.
In the second step, data so gathered are analysed with the aid of statistical tools and techniques. We need to estimate the variance of each of the instruments in case of calculating VaR for the equity position. Covariance across the instruments also to be estimated owing to movement of market factors of two different instruments are more or less related to each other. Covariance is the measure of the relationship between market factors of two instruments. Variance-covariance so estimated will be presented by using matrix notation.
Third step consists of determining weight of each instrument of the portfolio. This weight measures the proportion of a particular instrument relative to the whole portfolio. The relative weight of each instrument in the portfolio is tabulated in matrix form. Once the relative weight matrix is determined, the transpose relative weight matrix can be developed with little effort.
In the fourth and final step portfolio variance is calculated using matrix multiplication of relative weight matrix, variance-covariance matrix and the transpose matrix and relative weight. The resultant matrix produces portfolio standard deviation by squaring root the resultant matrix. The underlying assumption of this approach is the market factors are normally distributed. We use here Standard normal distribution as the numbers of normal distributions is too many. As stated earlier, the VaR is calculated by considering certain per cent confidence interval. In our calculation, we use 95, 98, 99 per cent confidence interval. The confidence level indicates the probability at which the maximum loss will be within the calculated VaR over a certain period of time. The VaR calculated using different confidence interval carry same qualitative meaning with a different quantitative meaning.
Saidul Islam is an assistant director at the Bangladesh Bank.
comments powered by Disqus
IN THE post financial crisis era, the issue of risk management in banks has drawn attention of all stakeholders, especially the regulators. In the context of Bangladesh, concerted efforts are being taken to address the issue from all... Full story
Rowhani’s win reveals that the majority of Iranians seek moderate policies at home and abroad. How far he and the Supreme Leader will follow the people’s lead remains to be tested. Washington — the administration... Full story