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How a Two-Year Spot Rate Discounts Year-Two Cash Flows

Article Quant Q&A · Author: kgui
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Summary

The note clarifies what a two-year spot rate represents when valuing fixed-income cash flows. It is the rate used to discount cash flows occurring at the two-year horizon, such as the second annual coupon payment on a coupon-bearing bond. The same horizon-specific interpretation applies to other maturities, such as a three-year spot rate and year-three cash flows.

The response distinguishes this discounting role from a bond’s yield to maturity. For a fairly priced, zero-coupon bond maturing in two years, the two-year spot rate coincides with that bond’s yield to maturity because there is only one payment, at maturity. A coupon bond has cash flows at multiple dates, so the relevant spot rates are applied to the separate cash flows; the short answer does not develop the full pricing calculation or discuss compounding conventions.

Key ideas

  • A two-year spot rate discounts cash flows due at the two-year point.
  • A three-year spot rate similarly applies to cash flows at the three-year point.
  • For a fairly priced two-year zero-coupon bond, the two-year spot rate equals its yield to maturity.
  • Coupon-bond cash flows occur at multiple horizons, so maturity-specific rates are relevant to their discounting.

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Fixed incomeDerivatives pricing
Full text
# Two year spot rate meaning


# Two year spot rate meaning












I am trying to understand the concept of spot rates better.

Does a 2-year spot rate indicate the rate you get for a two year bond or the rate you should discount the second year cash flow for an annual coupon bond? Same for a 3-year spot rate.

## Answer by phdstudent (score 4)

https://quant.stackexchange.com/a/55017

The 2-year spot rate is the rate at which you discount the year 2 cashflows. If the bond has no coupon, has a two year maturity, and is fairly priced then the 2-year spot rate is the yield to maturity of the bond (or as you say 'the rate you get').

Shown 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.