Writing Calendar Spreads as a Percentage of Full Carry

1 Introduction

Full carry is achieved when the price of a later dated contract can be expressed as the price of the near contract plus the full cost of carrying the underlying commodity between the months. Carrying costs include interest, insurance and storage. Carry costs change over time. For example, storage costs in a warehouse may increase while interest rates to finance the underlying may increase or decrease. Changes in these variable affect the theoretical limit of the degree of cantango that the futures curve can achieve. Having a good idea where the current spread is as a percentage of full carry is an important part of curve management.

Greater interest rates lead to higher storage costs. The plot below shows the evolution of the LIBOR rate since January 2001. Notice that we are currently in a rate hiking regime. If this trend continues the theoretical full carry numbers will increase, i.e. larger contangoes are possible.

The plot below shows the evolution of Corn storage costs. Here too, we see a big increase in the cost of storage. This will further increase the full carry of the corn calendar spreads.

The equation below shows how to determine the theoretical full carry.

\[ \text{Full Carry} = - \left( \frac{\text{LIBOR} + 2}{360 \times 100} \times \text{Front Price} + \text{Storage} \right) \times ( \text{Deferred Expiry} - \text{Front Expiry} ) \]

2 Corn ZH Example

Given the historical Libor and storage data we can represent each of the historical spreads as a percentage of full carry. The evolution of this percentage is shown in the plot below. By eye there seems to be some seasonality in the evolution of the data. This is explored in the next plot.

In the plot below we show the statistics of the corn ZH spread starting in December and ending in November of the following year. The outer gray lines show the 5th and 95th percentiles. Dashed black lines show the 25th and 75th percentiles. The mean and median are represented by the solid blue and black lines respectively. The last data we we for the C ZH spread is shown in red.

Notice that the current spread is on the lower end of the range with respect to the theoretical full carries. If the corn crop is of average size we should see the current percentage of full carry number increase toward expiry.

3 Shiny

The percentage of full carry calculations have been included in shiny for corn and soybeans. You can select this option by changing the view of the calendar spread. This option is contained in the same radio button selection box as the absolute change from start option.

Mauritz van den Worm
Portfolio Manager and Quantitative Researcher

My research interests include the use of artificial intelligence in managing commodity portfolios