What is the One-Period YTM on US Treasury Note/Bond?

One-Period YTM (Yield To Maturity) is the YTM for a T-Note/T-Bond that is very close to its maturity and has only coupon payment left.

In this case, the YTM should be considered as the equivalent simple (not compounding) interest rate for all revenues generated during the entire investment term, since this is only 1 interest period.

So we need to include this exception in our present value expression in term of YTM as:

$\text{If n = 1, }\mathrm{PV}={\displaystyle \frac{\mathrm{Par}}{1+0.5\times \mathrm{YTM}\times f}}+{\displaystyle \frac{\mathrm{Coupon}}{1+0.5\times \mathrm{YTM}\times f}}$
$\text{If n > 1, }\mathrm{PV}={\displaystyle \frac{\mathrm{Par}}{{(1+0.5\times \mathrm{YTM})}^{n-1+f}}}+{\displaystyle \sum _{i=1}^n}{\displaystyle \frac{\mathrm{Coupon}}{{(1+0.5\times \mathrm{YTM})}^{i-1+f}}}$
$\mathrm{PV}=\text{Present Value (Investment)}$
$\mathrm{PV}=\text{Par*Price/100 + (Accrued Interest)}$
$\mathrm{Par}=\text{Par value (Face value)}$
$n=\text{Number of coupon periods}$
$f=\text{1 - Days/Period (first period fraction, 1 for full period)}$
$\mathrm{Days}=\text{Accrued days (days since the last payment date)}$
$\mathrm{Period}=\text{Days in the first period}$

Note that we have adjust the definition of "n" from the number of full periods to the number of periods, to cover both cases: with and without fractional period. If the investment term has no fractional period, the fraction value "f" becomes 1.0.

Let's look at the an example of YTM provided on a Merrill Lynch quote for T-Note 91282CEY3 that has only one coupon payment period left.

CUSIP Number: 91282CEY3
Coupon Rate: 3.00%
Maturity Date: 2025-07-15
Quote Date: 2025-05-21 
Settlement Date: 2025-05-22

Offer Price: 99.837
Yield to Worst: 4.057% (TYM - Yield To Maturity)

We can use this example to verify our present value expression for one-period T-Note:

$\mathrm{PV}={\displaystyle \frac{\mathrm{Par}}{1+0.5\times \mathrm{YTM}\times f}}+{\displaystyle \frac{\mathrm{Coupon}}{1+0.5\times \mathrm{YTM}\times f}}$
$\mathrm{PV}={\displaystyle \frac{\mathrm{100.0}}{1+0.5\times \mathrm{0.04057}\times \mathrm{0.29834254143646}}}+{\displaystyle \frac{\mathrm{1.5}}{1+0.5\times \mathrm{0.04057}\times \mathrm{0.29834254143646}}}$
$\mathrm{ }=100.88942943586$

The purchase price and other intermediary values can be calculated as:

Coupon = 0.5*Par*(Coupon Rate) = 0.5*100*0.03 = 1.5 
Days = "2025-05-22" - "2025-01-15" = 127 
Period = "2025-07-15" - "2025-01-15" = 181
f = 1 - Days/Period = 1 - 127/181 = 0.29834254143646 (first period fraction)

Accrued Interest = Coupon * Days/Period = 1.5*127/181 =  1.0524861878453
Price = PV - (Accrued Interest) = 100.88942943586 - 1.0524861878453
  = 99.836943248015

The output matches well with the offer price of 99.837 given in the Merrill Lynch quote.

References:

• PRICE function, by Microsoft.

⇒ Current Yield on US T-Note/T-Bond

⇐ YTM with Fractional Period on US T-Note/T-Bond

⇑ Performance Measurements of US Treasury Note/Bond

⇑⇑ US Treasury Securities