Converting Short-Term Treasury CMT Quotes into Discount Factors

Summary

The document asks how to interpret one-, two-, and three-month US Treasury Constant Maturity (CMT) par yields when converting them into discount factors. It contrasts treating each quote as a discount bond with treating it as a hypothetical coupon security, and situates the calculation in applications such as comparing money-market rates, deriving forward rates, and changing day-count conventions.

The brief answer treats a short-maturity quote as a single-payment bond: it assumes a semiannual coupon convention, places the coupon and principal together at maturity, then discounts that payment using a semiannual compounding expression scaled by the Actual/365 year fraction. This is a stated answer rather than a derivation or comparison with official Treasury methodology. The document supplies no validation, data, or discussion of conventions and limitations, so users should verify that the assumed interpretation matches their intended curve construction.

Key ideas

• The document concerns converting short-maturity Treasury CMT par yields into discount factors.
• The answer models the short CMT instrument as a single payment of principal and coupon at maturity.
• Its present-value calculation uses semiannual compounding adjusted for the Actual/365 year fraction.
• The answer gives no derivation or validation against official Treasury conventions.

Tags

# Converting US Treasury CMT to Discount Yields


# Converting US Treasury CMT to Discount Yields












I'd like to convert the US Treasury Constant Maturity series (par, semi-annual coupon, Actual/365 daycount convention) into Discount Factors (for appropriate comparison for certain money-market series, calculation of forward rates, conversion to alternative daycounts, etc.).

The "hypothetical security" reflecting the CMT quote is straightforward for 6 months to 30 years: $PV=FaceValue$ that pays $FaceValue * CMT Rate/2$ every 6 months before maturity, $FaceValue*(1+CMTRate/2)$ at maturity (even on weekends/holidays, since it's an interpolated curve).

What is the hypothetical security for the 1, 2, and 3 month CMT quotes? Is it a discount bond (and, if so, what's the discount formula to arrive at $PV$)? Or is it a coupon bond with $PV=FaceValue$ that pays $FaceValue*(1+CMTRate * YearFrac365)$ at maturity?

## Answer by dm63 (score 0)

https://quant.stackexchange.com/a/57804

I think it is a coupon bond with semiannual coupons of $CMTRate$, thus a payment of $FaceValue*(1+CMTRate/2)$ at maturity and no other payments due. The $PV$ of this bond is $FaceValue*CashflowatMaturity/(1+CMTRate/2)^{2*YearFrac365}$

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