0

I've been building a unit & rate library for a forex trading algorithm and I realized I didn't have an answer to this question:

Can currencies be taken to the Nth power?

Unlike physical units, such as length or distance, the square of a currency doesn't occupy a space (I don't have much finance training so there may be theoretical properties that do).

Context:

My library is overloading operators such as $10\text{ USD } \times .98 \frac{\text{Euro}}{\text{USD}}=9.8 \text{ Euro}$. It offers currency and rate classes. If the user wants to square the true value (non unit) they can retrieve the value itself then square that. However, this library is trying to capitalize on relationships between currencies and rates. I plan on expanding it in the future, so I want a strong base. Is there a theoretical and meaningful use of a currency squared?

DominicTarro
  • 46
  • This is too vague. Since the number of dollars, let's say, is a number, then of course you can square it. It's not immediately clear what that new figure would represent. Can you supply some context for it? – lulu May 29 '20 at 19:44
  • Should say: there are some bizarre financial instruments out there. I've seem options on the square of some interest rate or other, for example. There, of course, the squared number is just a reference which figures into a pre-agreed payout formula. – lulu May 29 '20 at 19:46
  • 1
    Any units can be multiplied and taken to any power. Whether this composite unit has a meaningful interpretation in a given context is another story – Ben Grossmann May 29 '20 at 19:46
  • 2
    As for your statement about physical units, note that it is not only length that can be taken to a power. For example, $\text{[length]}/[\text{time}]^2$ measures acceleration – Ben Grossmann May 29 '20 at 19:47

1 Answers1

1

You can take any value with units (physical such as meters or conventional such as dollars) and raise them to any power--positive, negative, non-integer. It is perfectly legitimate to have a result such as "dollars to the two-thirds." This might be useful for describing some subtle attribute of an economy, say.

However, there is no way you can invest "100 dollars to the two-thirds." In short, the question of what is interpretable or actionable for such non-integer and non-standard units is separate from the mathematical permission to use them.

David G. Stork
  • 30,409