Quantitative Finance
Treasury 32nds Fractional Bond Quote Conversion (DOLLARDE & DOLLARFR Formula)
Convert US Treasury fractional handle-and-ticks quotes (such as 99.16 = 99 and 16/32 = 99.50) to exact decimal prices and back using closed-form INT, LEN, and power-of-10 arithmetic.
Decode 32nds and 64ths bond quotes without mispricing 99.16 as $99.16!
US Treasury notes and bonds quote fractional ticks in 32nds of a point: a screen quote written as 99.16 (or 99-16) means a handle of 99 plus 16/32 = 99.5000 per $100 par—NOT $99.16! For a positive fractional quote Q with integer denominator F (such as 32 or 16, having d = LEN(F) digits), the exact decimal price is Handle + Ticks / F = INT(Q) + ((Q - INT(Q)) * (10 ^ LEN(F))) / F.
Conversely, converting a decimal price D back into F-ths fractional notation computes INT(D) + ((D - INT(D)) * F) / (10 ^ LEN(F)), turning 99.50 back into 99.16 for F = 32!
| Fractional Quote (F = 32) | Extracted Ticks (/32) | True Decimal Price | $1M Par Clean Value |
|---|---|---|---|
| 99.08 (99-08) | 8 / 32 | 99.25000 | $992,500.00 |
| 99.16 (99-16) | 16 / 32 | 99.50000 | $995,000.00 |
| 101.24 (101-24) | 24 / 32 | 101.75000 | $1,017,500.00 |
Fractional Quote to Decimal Price (Closed-Form DOLLARDE)
Converts non-negative fractional quote B2 under denominator B3 (e.g., 32) into exact decimal price per 100 par.
=IF(OR(B2 < 0, B3 <= 0), "Invalid Quote or Denominator", ROUND(INT(B2) + ((B2 - INT(B2)) * (10 ^ LEN(B3))) / B3, 5))Decimal Price to Fractional Quote (Closed-Form DOLLARFR)
Converts decimal price B4 back into F-ths handle.ticks notation under denominator B3.
=IF(OR(B4 < 0, B3 <= 0), "Invalid Quote or Denominator", ROUND(INT(B4) + ((B4 - INT(B4)) * B3) / (10 ^ LEN(B3)), 5))Try the example
Use the original values or change them to test your understanding.