Understanding Spread and Interest Rate Sensitivity in Total Return Swaps

Summary

The document raises a valuation question about total return swaps (TRS). Its author describes deriving risk neutral survival and default probabilities from risk free and spread adjusted rates, then using those probabilities to adjust swap cash flows, including financing payments and the reference asset’s coupons and price changes. They ask why the resulting spread sensitivity may be larger than the interest rate sensitivity, even though they expected the sensitivities to resemble those of the reference asset.

The comparison is with a corporate bond, for which the author expects equal percentage sensitivities to interest rates and credit spreads. The text presents this as a conceptual puzzle rather than resolving it: it gives no derivation, numerical example, or answer explaining the difference. It may help readers identify which cash flows and credit adjustments to examine in a TRS valuation, but it does not establish that the observed sensitivity relationship holds generally. The result would depend on the contract, valuation assumptions, and cash flow treatment.

Key ideas

• The author models TRS cash flows using risk neutral survival and default probabilities derived from risk free and spread adjusted rates.
• TRS cash flows include financing payments and the reference asset’s coupons and price changes.
• The document asks why spread sensitivity may exceed interest rate sensitivity in a TRS.
• It poses the sensitivity comparison but provides no derivation or answer.

Tags

# Spread sensitivity of TRS


# Spread sensitivity of TRS












I am about to understand the valuation of a TRS. The approach I am applying derives risk neutral survival / default probabilities from the ratio between risk free and spread adjusted rates and uses them to adjust the respective TRS cash flows like interest rate payments made by the TRS receiver and the cash flow from the reference asset, i.e. coupons and appreciation / depreciation of the reference asset.

Naively I would have expected that the TRS sensitivities to interest rates and spreads are the same as they would be for the reference asset itself (at least if we ignore the interest payments from the TRS receiver). However, I observe that for a TRS the spread sensitivity is usually bigger than the interest rate sensitivity, whereas for a common corporate bond the x% IR sensitivities is equal to the x% spread sensitivity. Technically it is obvious but economically it's not...

Could anyone help me solving this puzzle?

Thank you!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.