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Computing the US Treasury Equivalent Yield

The US treasury yield is computed by assuming that bond value is based on the ISMA formula, with an adjustment made to the first period discount factor to incorporate simple interest discounting in the first period. That is, bond prices under the US Treasury convention are determined as:

 

Equation Template

 

P = dirty price (clean price plus accrued interest) of the bond per 100 units (PPH) face value.

r = number of days from the settlement date to the next nominal coupon payment date (based on the appropriate accrual convention).

s = number of days in the relevant coupon payment period (based on the appropriate accrual convention).

d1 = the first/next coupon payment. For an odd first period, this amount may differ from the standard coupon payment. It may also equal zero if the bond is trading ex-dividend.

d2 = the coupon payment due on the next nominal payment date. For bonds with an odd first period, this amount may differ from the standard coupon payment.

c = annual coupon payment per 100 units of face value.

h = number of coupon periods in a year.

n = number of full coupon periods remaining until redemption. The number of remaining coupon payments is therefore equal to

v = the discount factor for one period,

y = the required annual nominal redemption yield, expressed as a decimal.

 

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