18.3.1 Process Bonds and T-bill based on the YTM parameters

While processing a Bond, if the Price quote is not by ‘Yield to Maturity’, the YTM is computed based on the formula given below:

Where:

• P0 is the Purchase price of the Bond
• N is the Total number of coupons
• Ci is the Coupon payment for coupon i
• y0 is the Periodic YTM
• Y0 is the Annualized YTM
• A is the Day Count Method – Denominator
• n is the Coupons in a Year
• P is the Period of Reinvestment. If Null, defaulted to A/n
• R.P. is the Redemption Price
• AI is the Accrued Interest
• di is the Coupon Date ¡V Value Date
• d_N is the Redemption Date – Value Date

The formula used to calculate the yield given price – for T-Bills (provided you have enabled the Use Bond Formula option), will be

Where

• P0 is the Purchase price of the T-Bill
• R.P. is the Redemption Price
• y0 is the Periodic YTM
• d is the Redemption Date ¡V Value Date
• A is the Day Count Method – Denominator

The following example explains the computation of YTM for T-Bills, using the formula mentioned above.

Table 18-8 Price Table

Purchase Price	USD 90
Redemption Price	USD 100
Day count method Numerator	Actual
Day count method Denominator	365
Reinvestment Period	183 days
Redemption Date	30-June-2003
Purchase Value Date	31-Jan-2003
Annualizing Method	Simple

Applying the formula the periodic YTM is calculated as follows:

90 = (100/((1+y0)^(((30-June-2003)-(31-Jan-2003))/183)))

y0 = ((100/90)^ (183/((30-June-2003)-(31-Jan-2003)))) – 1

y0 = 0.1372 or 13.72%

Annual YTM is computed using the relationship given above.

Y0 = 0.14*(365/183)

Y0 = 0.2736 or 27.36%

Refer to the Batch Processing Chapter of this manual for detailed information on End-of-Day processing for Securities with YTM as the as method of accruing Discount or Premium