Comparing Forward-Starting Interest Rate Swap Hedges
Summary
The document compares two ways to hedge future ten-year interest rate exposures: using separate forward-starting swaps for the two target dates, or using a single longer forward-starting swap spanning both periods. The response says the strategies can produce very similar delta exposure when notionals match, but are not exactly equivalent. The difference depends on the fixed-leg annuities embedded in the swaps.
It illustrates the distinction by decomposing an arbitrary swap into a mid-market swap and a fixed-leg annuity component. The floating legs of the structures line up, while the annuity components in the single-swap construction broadly offset but leave small residual curve exposures. These risks can shift as the trades age. The discussion is qualitative and uses illustrative rates; it does not provide a full valuation, hedge ratio calculation, or detailed assumptions about discounting and conventions. Its equivalence claim is therefore approximate and conditional on the stated setup.
Key ideas
- Separate forward-starting swaps and one longer swap can create similar, but not identical, rate exposure.
- The comparison assumes matching notionals and relies on a discounting tolerance.
- Fixed-leg annuities account for residual differences between the structures.
- Residual curve risks may change over the life of the swaps.
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Full text
# Are these two hedging strategies equivalent? # Are these two hedging strategies equivalent? I am looking at two strategies for hedging interest rate risk, and I need some help to show whether they are equivalent or not. The aim of the hedging programme is to hegde the 10yr risk free rate in 10yr's time and 20yr's time. Strategy 1: I enter into a 10yr starting 10yr IR swap to hedge the 10yr rate in 10yr's time. I enter into a 20yr starting 10yr IR swap to hedge the 10yr rate in 20yr's time. Strategy 2: I enter into a 10yr starting 20yr IR swap to hedge both the 10yr risk free rate in 10yr's time and 20yr's time. Are these strategies equivalent? Is the only difference between these the sizing of the swap nominal? ## Answer by Attack68 (score 1) https://quant.stackexchange.com/a/78410 TLDR The two strategies are essentially the same within a discounting tolerance, assuming all have the same nominals. Practically, you will acheive very similar delta exposure. Although technically they are not identical. When you think of an interest rate swap you can always consider it as two parts: Abitrary IRS = Mid-Market IRS + Annuity on the fixed leg You are considering 3 swaps: - 10y10y, lets say the mid-market rate is 2.0%. - 20y10y, lets say the mid-market rate is 2.2%. - 10y20y, lets say the mid-market rate is the average i.e. 2.1%. When you trade 100m nominal of 10y10y@2.0% and 20y10y@2.2% you will have two arbitrary swaps both at mid-market. There is no annuity component on either of these. However, If you were to trade 100m of 10y20y@2.1% you have the following synethetic: - 10y10y at 2.0% plus 0.1% annuity. - 20y10y at 2.2% minus 0.1% annuity. Your floating legs completely match. It is only the presence of these fixed annuities that differ. They broadly net out, however, so it just leaves some small curve risks, and risks that will change slightly throughout the life of the trades.
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