How to Use the DOLLARDE and DOLLARFR Functions in Microsoft Excel to Convert Fractional Security Prices

In global financial markets—particularly when trading government debt securities, agricultural commodities, interest rate futures, and sovereign Treasury bonds—prices are historically quoted in fractional increments (such as 1/8ths, 1/16ths, 1/32nds, or 1/64ths) rather than standard decimals. For example, a bond quote of 102.16 in traditional market notation does not represent 102 and 16/100ths, but rather 102 and 16/32nds (which equals 102.50 in decimal). Trying to calculate cash flows, yields, or returns on raw fractional notation leads to severe mathematical errors. Microsoft Excel provides two specialized companion functions to handle these conversions: DOLLARDE (converts fractional dollar quotes to decimals) and DOLLARFR (converts decimal prices back to fractional quotes).

Understanding Fractional Market Quotations

Financial exchanges use standard integer denominators for specific asset classes:

• 32nds: Standard for US Treasury Notes and Bonds (e.g. 100.16 = \(100 + \frac{16}{32}\) = 100.5).
• 16ths: Common in agricultural and commodity futures (e.g. 5.08 = \(5 + \frac{8}{16}\) = 5.5).
• 8ths: Used in traditional equity and bond fractions (e.g. 25.04 = \(25 + \frac{4}{8}\) = 25.5).

Because the digits after the decimal point represent the numerator of the fraction rather than a decimal fraction, standard division or multiplication fails. DOLLARDE and DOLLARFR parse the integer denominator and perform exact base transformations.

Function Syntax and Arguments

1. DOLLARDE Syntax

=DOLLARDE(fractional_dollar, fraction)

• fractional_dollar: The price expressed as an integer followed by a decimal point and the fractional numerator (e.g. 1.02 for \(1 + \frac{2}{16}\)).
• fraction: The integer denominator used in the fraction (e.g. 16, 32, or 8).

2. DOLLARFR Syntax

=DOLLARFR(decimal_dollar, fraction)

• decimal_dollar: The true decimal price you wish to format into fractional notation.
• fraction: The target integer denominator.

Step-by-Step Practical Examples

Example 1: Converting a 32nd Treasury Quote to Decimal (DOLLARDE)

Suppose a Treasury bond is quoted on trading screens at 102.16 with a denominator of 32 (meaning 102 and 16/32):

=DOLLARDE(102.16, 32)

Excel parses the numerator 16, divides by 32 (\(16 / 32 = 0.5\)), and outputs the true decimal price:

102.5

Consider a quote of 100.08 with denominator 32 (meaning \(100 + \frac{8}{32}\)):

=DOLLARDE(100.08, 32)

Excel returns:

100.25

Example 2: Converting Decimal Prices Back to Market Fractions (DOLLARFR)

Suppose your quantitative model computes an optimal fair market value of 105.75 for a bond quoted in 32nds:

=DOLLARFR(105.75, 32)

Because \(0.75 = \frac{24}{32}\), Excel formats the output as:

105.24

For a commodity contract priced at 12.125 using 16ths as the denominator:

=DOLLARFR(12.125, 16)

Because \(0.125 \times 16 = 2\), Excel outputs:

12.02

Formatting Note on Leading Zeros

A crucial formatting pitfall in fractional quotes involves single-digit numerators. When working with 16ths or 32nds:

• One thirty-second (\(\frac{1}{32}\)) is written as 0.01, not 0.1. Entering =DOLLARDE(100.1, 32) interprets the numerator as 10 (\(\frac{10}{32}\)), returning 100.3125 instead of 100.03125.
• Always ensure single-digit numerators include a leading zero after the decimal (e.g. .01, .02, .03).

Troubleshooting Common Errors

• #NUM! Error: Occurs if fraction < 0. If fraction is not an integer, Excel truncates it to an integer. If fraction = 0, Excel returns a #DIV/0! error.
• #VALUE! Error: Occurs if either argument contains non-numeric text or symbols that cannot be parsed as numbers.