bondEquivalentYield¶

Evaluates the bond-equivalent yield of a Treasury bill.

Synopsis¶

bondEquivalentYield (settlement, maturity, discountRate)

Required Arguments¶

date settlement (Input): The date on which payment is made to settle a trade. For a more detailed discussion on dates see the Usage Notess ection of this chapter.
date maturity (Input): The date on which the bond comes due, and principal and accrued interest are paid. For a more detailed discussion on dates see the Usage Notes section of this chapter.
float discountRate (Input): The interest rate implied when a security is sold for less than its value at maturity in lieu of interest payments.

Return Value¶

The bond-equivalent yield of a Treasury bill. If no result can be computed, NaN is returned.

Description¶

Function bondEquivalentYield computes the bond-equivalent yield for a Treasury bill.

It is computed using the following:

if \(\mathit{DSM}\leq 182\)

\[\frac{365 * \mathit{discountRate}}{360 - \mathit{discountRate} * \mathit{DSM}}\]

otherwise,

\[\frac {- \frac{\mathit{DSM}}{365} + \sqrt{\left(\frac{\mathrm{DSM}}{365}\right)^2 - \left(2 * \frac{\mathit{DSM}}{365} - 1\right) * \frac {\mathit{discountRate} * \mathit{DSM}} {\mathit{discountRate} * \mathit{DSM} - 360}}} {\frac{\mathit{DSM}}{365} - 0.5}\]

In the above equation, DSM represents the number of days starting at settlement date to maturity date.

Example¶

In this example, bondEquivalentYield computes the bond-equivalent yield for a Treasury bill with the settlement date of July 1, 1999, the maturity date of July 1, 2000, and discount rate of 5% at the issue date.

from __future__ import print_function
from numpy import *
from datetime import date
from pyimsl.math.bondEquivalentYield import bondEquivalentYield

discount = .05

settlement = date(1999, 7, 1)
maturity = date(2000, 7, 1)

equiv_yield = bondEquivalentYield(settlement, maturity, discount)
print("The bond-equivalent yield for the T-bill is %.2f%%."
      % (equiv_yield * 100))

Output¶

The bond-equivalent yield for the T-bill is 5.29%.