# How to measure contango?

Is there any unit of measure for the magnitude of the contango (or backwardation) for futures, so you can compare the contango of many symbols.

• Could you use the percent difference between the futures price and the spot? – chrisaycock Apr 27 '13 at 1:20
• In some paper I've seen these ways: 1) $log(f_{10})-log(f_{3})$, where $f_{t}$ stands for the future value at time $t$; 2) the value of the 2nd principal component of the term structure. – Lisa Ann Apr 27 '13 at 19:12
• See e.g. VIX Central for an example of percentage difference, which yes, is a common numeraire. – franktheshark Apr 28 '13 at 23:31

## 1 Answer

Just take something like

$$\frac{\log{\frac{F_j}{F_i}}}{t_j - t_i} \times 365$$

where $t_i$ denotes the expiry (or alternatively delivery) date of future $i$. The annualization is so you can compare different futures.

• I've edited your post to typeset the mathematical notation with $\LaTeX$. Please make sure I got it right. – chrisaycock Apr 27 '13 at 22:06