## Units of measurement

Recently I had to familiarise myself with commodity futures. One thing that surprised me was the common unit of measurement for natural gas. It is used in MMBtu, which is a short for a million of British thermal units. It is perfectly logical to measure gas in the amount of heat that it can produce (rather than weight or volume), for obvious reasons. What surprised me was the definition of the Btu: it is defined as amount of heat required to raise the temperature of 1 pound (0.454 kg) of liquid water by 1 °F (0.56 °C) at a constant pressure of one atmosphere. I thought that most people had switched to SI long ago, and measures like pounds, cups and Fahrenheits remained only in grandmothers’ cookbooks. I was wrong, apparently.

By all means there can be reasons to stick to good old measures. One is convenience. It might be that the usual SI units are inconvenient for being used in finance. It took me some time to come up with an example of a SI measure that is utterly unfit for everyday use in our trade.

Consider interest rate. It has the dimension of frequency (1/time). Let me see if the SI unit of frequency, hertz (Hz), is convenient for expressing commonly used rates.

Take the interest rate of 1% per annum, simply compounded, quoted according to the Actual/365 day counting convention. How much is it in SI?

1 year = 365 days (by the day count convention) = 365*24*3600 seconds.
$\frac{0.01}{365*24*3600}\approx 3.1709792*10^{-10}$
Imagine yourself quoting a rate of .317 nanohertz to a customer.

Originally I planned to post this on 1 April, but something distracted me… Late is better than never, anyway.