Calculation of Risk

To measure unexpected losses which occur, there are two methodologies commonly used (i) Value-at-Risk analyses and (ii) Scenario techniques. Both methods are used to calculate the risk as accurately as possible. Below, we see the calculation process of each of the different approaches.

Value-at-Risk Concept

VaR (value at risk) was invented by JP Morgan in 1994 as a general risk management tool and has now become the industry standard for risk. It has become a popular and important risk measure primarily because of the Basel Committee, which standardises international banking regulations and practises. The value-at-risk analysis offers the advantage that it allows the comparison of different risks not only across different portfolios, but also across different types of risks such as credit, market, and operational risks.

VaR lets an investor know in monetary terms how much one’s portfolio can expect to lose, for a given cumulative probability and for a given time horizon. To calculate the credit VaR, it is necessary to determine the distribution of potential losses in the credit portfolio. For this purpose, assumptions are made in terms of the future development of the default rate and the exposure at default (credit amount outstanding at the time of default, minus proceeds from collateral and estate).

For example, for a cumulative probability of 99% over a period of 1 day, the VaR amount would tell us the amount by which one would expect the portfolio to lose e.g. $100. Mathematically we express this as:

Pr[portfolio loss · VaR]= 0.95%

Pr[portfolio loss · $100]= 0.95%

Note that Pr[. . . ] denotes “cumulative probability of [. . . ]” and is measured over the same time period as the loss.

VaR can be calculated by simulation using historical data or some mathematical formula. VaR can also be calculated by the “variance-covariance method” (also known as the delta-normal method) but makes unrealistic assumptions about portfolio returns e.g. returns are normally distributed.

The VaR is the maximum loss that will occur with a certain probability i.e. “confidence level” at a given time period. To determine the value at risk, a confidence level is determined that indicates the probability of the maximum calculated loss not exceeding the level during holding period. This confidence level is generally between 95% and 99.95%, which means that higher losses are possible, but it will only occur with a probability of between 5% and 0.05%. The holding period presents the horizon during which the losses can take place, and is derived from the liquidity of the assets.

Limitations of VaR: The value-at-risk analysis has limited descriptive ability. Even though it showcases the figure of losses within the confidence level chosen, it does not indicate any prediction about the probability distribution of losses beyond that confidence level. Going further, the VaR misses to take into account any extreme events in an economic crisis with extremely high default rates. Because of this reason, a stress tests should also be carried out as it calculates the value fluctuations based on the assumption of extreme market movements. The VaR relies on certain assumptions and estimates which can lead to misinterpretations of the risk. There are constraints to the comparability and aggregation of different types of risks caused by the different distribution of the risk types. Lastly, the historical data used for calculations are often not available to a sufficient extent (e.g. on probabilities of default, exposure at default, and correlations).

Scenario analysis

In the scenario analysis approach, the available historical market data and/or internal company data are used to create scenarios pertaining to the possible development of default rates. Like in VaR analysis, the assumptions taken here are,

• loss developments are assumed to have already occurred in a certain historical period under review.
• worst case scenarios are assumed to have incurred leading of extreme losses.

These scenarios are applied to ascertain the extent of the fluctuations in the portfolio’s value if the negative event occurs. Value fluctuations may pertain to the amount losses from lending, or variances in the value of the collateral. The highest possible risk is calculated on the basis of the scenario analysis.

Limitations of scenario analysis: Compared to the VaR method, the results of the scenario analysis is inferior in quality as the scenarios applied are subject to a small number of historical events. The same diversity of the parameters use in the VaR method cannot be achieved. Therefore, the scenario analysis is limited in its explanatory power as it takes into account only a few changes in parameters. When banks and other companies use this approach towards gauging risk, they generally receive less accurate results compared to the VaR approach. It is important to determine what additional cost would be incurred in implementing the concept, and what additional benefit would be derived from more effective management that would result from the execution.