A unit of measure is an agreed reference used to express how much of a quantity there is. A quantity value combines a numerical value with that reference: a position worth 200 USD has numerical value 200 when expressed in USD. In quant work, carrying units through a calculation helps distinguish a plausible number from a meaningful valuation. The formal measurement-unit definition is given in JCGM's vocabulary of metrology.
A data type such as a floating-point number does not, by itself, say whether its value represents shares, USD, years or a return. A model needs that meaning as well as the number.
Let the labels do some work
Suppose a fictional equity position holds 2 shares, with each share marked at 100 USD. Ignoring fees, its value is
The share labels cancel. The result has the currency unit expected for a position value. Adding the share count to the quoted price would have no meaningful financial interpretation, even if software accepted the arithmetic.
This reasoning also helps read a currency pair: multiplying a currency amount by a quote expressed as the target currency per source currency produces an amount in the target currency. Reversing the quote requires taking its reciprocal before using that multiplication.
Units, dimensions and economic labels
A dimension describes a quantity's dependence on the base quantities in a chosen system; a unit supplies a reference for expressing its value. Seconds and hours describe the same time dimension while giving different numerical values for the same interval. The distinction and its limits are set out in JCGM VIM 1.7.
Finance also needs semantic labels beyond physical dimensions. USD and EUR must stay distinct in a valuation until an exchange conversion is supplied; they are financial currency units, not SI base dimensions. A share count refers to a particular instrument. Writing “shares” in the cancellation above is useful bookkeeping, even though counts have dimension one in the metrological sense. JCGM VIM 1.8 makes clear that such quantities still carry meaning beyond a bare number.
Two prices can have matching currency labels and still refer to different instruments, valuation times or quote conventions. Unit consistency is one necessary check, alongside checking what each field means.
Percent is a scale that must survive ingestion
A percentage expresses a fraction on a scale of one hundred:
NIST describes the percent symbol as the number 0.01 in SP 811, section 7.10.2. A percent quote and its decimal fraction describe the same proportion, but their stored numerical values differ.
For a fictional deposit, assume annual simple interest, principal , and an accrual interval defined to have year fraction . Let be the decimal numerical value of the annual interest rate. Under this convention,
If the percent quote
5 is mistakenly used as the decimal rate, the same calculation returns 500 USD of interest: 100 times too much. Both results carry USD. Unit cancellation alone cannot catch this representation error.
Units check the kind of result. A separate scale check catches the factor-of-100 error between a percent quote and its decimal fraction.
Here is a dimensionless year fraction. For actual dates it must come from a stated day-count convention, consistent with the rate quote. Compounding also needs to be specified: the simple-interest formula above is a chosen convention, not a universal interest formula.
In a data contract, record the quantity's meaning, currency or other unit, numerical scale and time convention. Names such as
price_usd_per_share and annual_rate_decimal make intended use easier to inspect; names alone do not enforce it. Convert at a defined input boundary and retain a small expected-value example that exposes a wrong conversion.Continue with market conventions
Instrument Data Conventions applies this discipline to day-count, compounding and contract data. It has a public preview; the full lesson requires membership. The FX lesson follows currency units through executable quotes and cross rates and is free with sign-in.
Practice
A fictional deposit has principal 250 USD and an annual simple rate quoted as 4%. For this exercise, define a three-month interval to have year fraction . What interest is earned?
Answer. Convert the quote to and use the specified year fraction:
Using 3 directly for the time input would treat three months as three years. The stipulated convention is what makes this exercise determinate; an actual dated instrument needs its contractual day-count rule.
Sources
- JCGM VIM3, 1.9: Measurement unit — the conventional reference used to express quantities.
- JCGM VIM3, 1.7: Quantity dimension — dimensions and the distinction between dimension and kind of quantity.
- JCGM VIM3, 1.8: Quantity of dimension one — ratios, counts and their retained meaning.
- NIST SP 811, Chapter 7 — sections 7.1, 7.10 and 7.10.2 on quantity values, unit one and percent.