In our first two articles about delta, we introduced delta as a measurement of directional risk. In “Introduction to Delta,” we made the case that we need to use a standard unit to estimate a set of assets’ overall risk. We added that it usually makes sense in grain and soybean hedging to use the most active futures contract for a given crop year as that standard unit. Our next article, “Why Physical and Futures are Different,” showed that hedging physical bushels one-to-one with futures is not always the best solution. This article presents an equation that hedgers can use to convert their physical bushels into an equivalent number of futures bushels and, ultimately, futures contracts.

The equation is relatively simple. The multiplier for converting physical bushels to futures bushels, or “hedge ratio,” is the inverse of one plus the annual interest rate (r) multiplied by the financing time in years (t), or:

one / (one + (annual interest rate * financing time in years)) = hedge ratio

Or symbolically:

1 / (1+rt) = hedge ratio

In “Why Physical and Futures are Different,” we assumed a producer is entirely confident he will have 500,000 bushels of corn to sell in six months. We also assumed he wants to hedge with futures. We also stipulated he could meet any potential margin calls and that he could freely lend or borrow at an annualized interest rate of 2.0%. In a sidebar to that article, we discussed some problems with those assumptions. For now, we will continue to look past those problems to focus on the current topic. Rest assured, there are practical ways to work around uncertain yields and limited capital (within reason). Using the example from that article and the equation above, we get the following:

1 / (1+(0.02 * 6/12)) = 0.9901

In other words, 1 bushel of physical corn equals 0.9901 corn futures bushels. In this example, the hedge ratio tells us that 500,000-bushels of physical corn requires the sale of 495,050 corn futures bushels to be accurately hedged. If we divide that last number by the 5,000 bushels in a standard CBOT corn futures contract, we get 99.01 futures contracts. Since futures do not trade in partial contracts, we round to 99. In this case, the reverse-engineering process we used in the last article produced a result that was as accurate as possible. Reverse-engineering will often yield the correct answer with enough trial and error. Still, it is generally faster to use the formula above. That is why we use it as part of the model that underpins our Quartzite Precision Marketing program for grain and soybean producers.

There are a few more things to consider. Because the delta we have calculated depends on time and interest rates, we need to be aware that if either variable changes, so will the delta. If we decrease the interest rate or the holding period, the hedge ratio will move toward 1-to-1. As time passes, it is essential to understand that a physical position’s equivalent futures delta will move toward 1-to-1. If we increase either variable, the opposite will happen. As a result, accurately calculating a physical position’s delta in futures terms becomes more critical as holding periods or interest rates increase.

Now that we have a way to calculate an equivalent futures position for a given physical position, we have taken the first step into using futures and options to manage risk. In our next article, “Option Deltas - The Basics,” we will begin the process of exploring delta in the world of options trading. There will be a lot of new information, and it will take several articles to do the topic any justice. If you are feeling a bit overwhelmed already, that is okay. You can always review what we have covered so far, or feel free to ask us a question. Remember, our primary purpose in calculating deltas is to estimate how different assets will perform in a standard unit. It may feel like we are trying to land a man on the moon sometimes, but we are not. If you are tired of tedious calculations and other finance nerdery, we would be happy to discuss if we would be a good fit for your operation. As always, thanks for taking the time to read, and we look forward to your questions and comments.