Interpreting Eurodollar Futures as Compounded Forward Rates and Tenor Basis
Summary
The document explains what a strip of Eurodollar futures can imply when its quarterly rates are compounded over a one-year period. The resulting rate represents a December-starting one-year compounded three-month LIBOR forward, and is closely related to a forward swap rate against three-month LIBOR. It should not be compared directly with a one-year LIBOR rate as though both represented the same tenor exposure.
The difference reflects tenor basis: longer-term LIBOR could include a different credit-risk premium than three-month LIBOR. A tenor basis swap exchanges payments based on the two indices, with a spread that helps connect their rates. The response gives an illustrative market quote and an example valuation, but those figures are specific to the time and curve cited; the document does not provide a general pricing derivation. Its central lesson is to distinguish compounded short-tenor forwards from longer-tenor rates and account for basis when comparing them.
Key ideas
- Compounding quarterly futures-implied rates gives a forward rate for compounded three-month LIBOR over the period.
- That rate is comparable to a forward swap rate against three-month LIBOR.
- A compounded three-month forward should not be equated directly with a one-year LIBOR rate.
- Tenor basis reflects differences between rates for different LIBOR maturities, including credit-risk premia.
- Basis swaps exchange payments across tenors and quote a spread between them.
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# Calculating Implied Forward Rates from Eurodollar Futures Quotes
# Calculating Implied Forward Rates from Eurodollar Futures Quotes
I'm trying to calculate the implied forward rates of the Eurodollar (USD) curve, knowing that the Eurodollar curve is supposed to be a mirror of the yield curve (else arb).
I have this formula for the value of the strip:
$Strip = \displaystyle \frac{\prod_{i= 1}^{n}\bigg(1 + R_i \cdot \big(\frac{days_i}{360} \big) \bigg) - 1}{\frac{term}{360}}$
Using this for current values of LIBOR, I have /GEZ6, /GEH7, /GEM7, /GEU7 to replicate a 1-year forward curve. The rates are $R_1 = 93.5bp$, $R_2 = 95bp$, $R_3 = 98bp$, $R_4 = 101bp$. Using this formula gives me the value of the strip at 97.2 basis points, which I'm confident is wrong.
How do I value the 1-year interest rate forward at December?
## Answer by atkins (score 2)
https://quant.stackexchange.com/a/29816
What you have calculated, correctly as far as I can tell, is a December-starting 1-year compounded Libor 3m forward rate. That's a weird-sounding thing, but it is essentially equivalent to a December-starting 1-year forward swap rate vs Libor 3m. (I've just priced exactly this against a live USD Libor 3m yield curve and I get 97.3 bp.)
However, this should not be expected to be comparable to the 1y Libor rate over the same period. There is a systematic "basis spread" between 1y and 3m Libor rates, primarily driven by the greater credit risk premium demanded for longer-term lending (thus 1y Libor rates are systematically higher than 3m Libor rates over the same period). That basis is traded through tenor basis swaps, which allow (for example) a stream of 1y Libor payments to be swapped into a stream of 3m Libor payments plus a fixed spread.
Currently, for a 1-year spot-starting basis swap paying 1y Libor vs 3m Libor, that spread is quoted at around 60 bp. Add that on to your compounded 3m rate, and you're in the ballpark of the current level of 1y Libor.
The tenor basis is a subtle subject. Try this paper which includes a literature review of the topic:
http://www.qfrc.uts.edu.au/research/research_papers/rp348.pdfShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.