Why Six-Month Loan Risk Differs from Compounded Three-Month Rates

Summary

The document clarifies a basis swap pricing question about why a six-month forward rate can differ from the rate implied by two consecutive three-month periods. The key distinction is between the underlying reference index and the loan exposure: a three-month Libor fixing represents the rate on an interbank loan with a three-month term, while a six-month loan remains exposed to its counterparty for six months even if its interest is linked to compounded three-month rates.

This means that matching the total calendar period does not automatically make the credit and liquidity risks equivalent. A six-month loan bears counterparty risk over the full six-month term, whereas a sequence of three-month reference periods reflects shorter-tenor lending rates. The answer offers this conceptual explanation but does not derive basis swap pricing, quantify the spread, or address other market drivers such as collateral, funding, or index transition. It therefore explains a tenor-risk distinction rather than providing a full pricing framework.

Key ideas

• A three-month reference fixing describes a three-month interbank lending rate.
• A six-month loan has counterparty exposure lasting six months, even if interest compounds from shorter-period rates.
• Equal calendar coverage does not imply equal credit or liquidity risk across contract structures.
• The explanation distinguishes loan tenor from the frequency of the rate used to calculate interest.

Tags

# Basis swap pricing dynamics


# Basis swap pricing dynamics












The existence of basis spreads leads to that e.g. a 6M forward rate has a different price than two after each other following 3M forward rates. This due to that the 6M forward rate has a higher credit and liquidity premium.

Can someone explain why? As I see it, the money is locked in 6 months in both contracts and therefore should have equal credit and liquidity risk. Is this because the demand and supply of 3M contracts is higher than the 6M?

## Answer by Antoine Conze (score 1)

https://quant.stackexchange.com/a/34160

You are confusing the underlying index 3M Libor and a 6M loan that pays a compounded 3M interest. A 3M Libor is by definition the (average) rate on an interbank 3M loan. A 6M loan, regardless of its reference interest rate, is subject to counterparty risk up to 6M.

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