# HEDGING BUSINESS RISK AND INTEREST RATE RISK

Business scenarios are required whenever there is too much uncertainty with respect to the behavior of clients, resulting in static gaps that are varying significantly across scenarios, as well as when dealing with projections of new business, for which several scenarios need to be considered. Using multiple scenarios for business volume allows dealing with business risk. This section presents the "matrix" methodology for cross-tabulating business scenarios and interest rate scenarios, and identifying the best hedging solutions. The methodology relies on discrete scenarios, but can accommodate any number of such scenarios.

It is illustrated with a simple example combining two simple interest rate scenarios with two business scenarios only, for illustrating the principle, but the methodology is easily extended to higher numbers, except that the volume of calculations increases.

The process involves the calculation of interest income, and of its summary statistics, expectation and volatility, across the matrix cross-tabulating interest rate scenarios with business scenarios. The next step simulates the effect of hedging solutions for optimizing the hedging policy. Again, the example is limited to the comparisons of two hedging solutions, which is enough to understand how to extend the same process to a larger number of hedging scenarios. The last paragraph summarizes the process and shows how the concept of "efficient frontier" can be used for optimization purposes.

## Multiple Business and Interest Rate Scenarios

The gap methodology assumes that the gap value is known for a given time point. This implies that we consider a unique business scenario as if it were certain, since the unique value of the gap results directly from asset and liability volumes. Ignoring business risk is not realistic, and results in hiding risks rather than revealing them.

Gap volume depends on clients' behavior for static gaps and on business projections for dynamic gaps. The ALCO deals with business issues and cannot ignore business uncertainty. Multiple business scenarios address the issue and are materialized by several projections of the balance sheet, at various dates, plus liquidity and interest rate gaps profiles.

Risk management becomes more complex, with interest income volatility resulting from both interest rate risk and business risk. Still, it is possible to characterize the risk-return trade-off, where return refers here to the Nil of the banking portfolio. Hedging policies now depend on how both interest rate and business risks influence the interest income. It is interesting to note that financial instruments can help hedging some of the business risk as it will be explained.

The starting point of the method is made up of several interest rate scenarios and business scenarios. The principle of this methodology consists in simulating all values of the target variable, the interest income, across all combinations of interest rate and business scenarios. Because we cross-tabulate interest rate scenarios and business scenarios, the methodology is called the "matrix" methodology.

The values of Nil in each cell of the matrix depend on any existing hedge that generates its own interest costs and revenues. When hedging solutions change, the entire set of value changes. Hedging adds a third dimension. If we have two business scenarios and two interest rate scenarios, we need to consider four combinations and calculate the Nil for each one of them. If we consider two hedging solutions, we need to consider two sets of four values of Nil, or eight cases.

The first step sets up the matrix cross-tabulating interest rate and business scenarios. For each pair of such scenarios, the value of the target variable is determined. For turning around the complexity generated by considering a large number of combinations, the basic idea is to summarize the entire set of values of the target variable within the matrix, whatever their numbers, by a couple of values. One is the expected value of the target variable and the second is its volatility across the entire matrix. For each hedging solution, the values within the matrix changes, and there is a new pair of expected Nil and volatility of Nil across the matrix. The third step consists of changing hedging solutions and recalculating accordingly the values of expected Nil and the volatility across each matrix matching a hedging program.

When hedging changes, the pair of values changes and moves in the "risk-return" space. The last step consists of selecting the hedging solutions that best suit the goals of the ALCO, such as minimizing the volatility, or targeting a higher expected profitability by increasing the exposure to interest rate risk. Those solutions that maximize expected profitability at constant risk or minimize risk at constant expected profitability make up a set of hedging solutions called the "efficient frontier." All other hedging solutions are discarded. It is up to the management to decide which level of risk is acceptable.

The technique allows investigating the impact on the risk-return profile of the balance sheet under a variety of assumptions. For example:

• what is the impact on the risk-return profile of assumptions on volumes of demand deposits, of loans with prepayment risk, or of committed lines of which usage depends upon customers' initiatives?

• which funding and hedging solutions minimize the risk when only interest rate risk exists, when there is business risk only, and when both interact?

• how can the hedging solutions help to optimize the risk-return combination?

The ALM simulations also capture optional risks to the extent that we embed in balance sheet scenarios the effect of options transforming fixed rates into variables rates and vice versa. The gaps will change accordingly. However, this makes the calculation overly complex and other techniques such as valuing the embedded options of optional gaps might be preferable (see Chapter 27).