# HEDGING: CLOSING INTEREST RATE GAPS

Hedging aims at reducing the net interest income volatility by setting limits on gaps. We address the issue in two steps: the first step considers a single period starting at a future date, and, in the second step, we consider several periods ahead. In general, ALM policies tend to reduce the risk for the immediate horizon, while keeping open gaps of increasing value when the horizon extends, for taking advantage of beneficial variations of interest rates.

## Single Period

The example of a single period allows differentiating the steps for constructing hedging programs. It would apply, notably, for the short-term horizon, say the current year. For illustrating gap management, we use the simple example of the previous chapter on interest rate gaps (Table 24.1). The liquidity gap shows a deficit of 12. The variable rate gap before funding is +8, but the deficit of 12 counts as a variable rate liability as long as its rate is not locked in advance, so that the post-funding variable interest rate gap is -4 (Table 24.2).

TABLE 24.1 **Balance sheet projections for the banking portfolio**

TABLE 24.2 **Liquidity and interest rate gaps**

Liquidity gaps are algebraic differences between assets and liabilities, interest rate gaps are interest-sensitive assets minus interest-sensitive liabilities, or' Variable rate" interest rate gaps.

'Funding is assumed to be variable rate before any hedging decision is made.

TABLE 24.3 **Hedging the liquidity and the interest rate gaps**

The liquidity gap is -12. The variable rate gap is +4 before funding and -4 post-funding, considering that the interest rate of funds to be raised at a future date is unknown. Let us assume that we wish to close both liquidity and interest rate gaps simultaneously. We assume that the above gaps calculated at a point in time are valid for some period after the date of the above projection (for example 1 year).

In order to close the liquidity gap, we need to raise funds for an amount of 12 at the starting date of above gaps. The positive variable rate gap of existing assets and liabilities means that the Nil of existing assets and liabilities increases when interest rates shift upward. In reality this is not so because 12 have to be raised, at a rate unknown today. Post-financing, the variable rate gap becomes -4, which shows that a rise of interest rates would actually make the Nil decline.

In order to obtain immunization, the post-funding gap should be zero. In other words, the funding and hedging policies should generate a gap offsetting the commercial portfolio positive gap. The incremental variable rate gap due to funding is equal to the fraction of debt remaining variable rate after hedging, with a minus sign. Since the gap is +8 before funding, the variable rate debt should be set at 8 to offset this gap. This implies that the remaining fraction of debt, 12 — 8=4 should have an interest rate fixed as of today. An equivalent approach is to start directly from the post-funding gap. This gap is +8 - 12 — -4. Setting this gap to zero requires reducing the amount of variable rate debt from 12 to 8. We find again that we need to fix the rate today for the same fraction of debt raised, or 4, leaving the remaining fraction of debt, 8, with a floating rate. The solution "variable rate for 8 and locked rate for 4" neutralizes both the liquidity gap and the interest rate gap (Table 24.3).

In order to lock in the rate for an amount of debt of 4, various hedges apply. In this case, we have too much variable rate liabilities, or not enough variable rate assets. A forward swap converting 4 of the floating rate debt into a fixed rate debt is a solution. The swap would pay the fixed rate and receive the floating rate. Alternatively, we could increase the variable rate fraction of assets by 4. A swap paying the fixed rate and receiving the variable rate would "transform" 4 of fixed rate assets into 4 of variable rate assets. This is the same swap.