In our introduction to the Greek known as delta, we state that delta is a measurement of directional risk. In that article, we discussed the need to convert individual exposures into standard units to compare them. We used the example of measuring distances to highlight that idea. In this article, we will explain why physical bushels and futures bushels are not the same units. They are close, like meters and yards, but at scale, the difference matters. In the next article, we will teach you one way to convert physical bushels into futures bushels. For now, we will spend our time showing why the two are different.

In the case of a physical position hedged with futures, the timing of cash flows differs. With futures positions, hedgers realize gains and losses each day. Cash moves into or out of the hedger’s trading account when the market moves up or down. If these moves are large and persistent, they can result in a significant interest cost or benefit. With physical positions, traders only realize gains and losses at the end, so there is no interest cost or benefit from the daily changes in value. An extreme example might help at this point.

Assume a producer is entirely confident he’ll have 500,000 bushels of corn to sell in six months and wants to hedge with futures. Also, assume he has unlimited access to capital to meet any potential margin calls,* and that he can freely lend or borrow at an annualized interest rate of 2.0%.** The producer believes physical bushels and futures bushels are the same. He knows there are 5,000 bushels in a standard corn futures contract. He sells 100 futures to hedge his exposure. The next day, the market rises by $1.00/bushel. The producer now has a $500,000 loss in his trading account. The value of his production has increased by $500,000, so his equity should be the same as on day one, correct?

Close, but not quite. The futures loss settles in cash, and the producer needs to source it from somewhere. He might fund the account himself, with money on which he can no longer earn interest. He might also borrow the funds from a lender and pay interest. Either way, there is a cost (opportunity or actual) associated with funding the margin call in his trading account. If the price remains a dollar higher for six months; we can calculate the cost of financing the futures account with the following formula:

annualized interest rate * financing time in years * amount financed = cost of financing

Or in this example:

0.02 * 6/12 * $500,000 = $5,000

At the end of the term, the hedge will have cost $505,000 (including the financing cost), while the physical position will have only gained $500,000. We can flip the example as well. If the market drops a $1.00/bushel the day after the producer makes the trade, the producer will have $500,000 of cash in his account on which he can now earn (or not pay) interest. Over six months, he’ll accrue a $5,000 benefit from this cash infusion, for a total gain of $505,000 from the hedge.

Assuming a producer’s goal is to, as accurately as possible, offset the change in the hedged asset’s value (i.e., to be market-neutral), could he have done better? Yes, he could have. If we run the same scenarios with only 99 futures, total hedge gains or losses (including interest and depending on market direction) would be $499,950. This amount almost perfectly offsets the physical’s corresponding $500,000 change in value. A mere one-percent change in the hedge’s size results in a hundred-fold increase in hedge accuracy.***

In our next article, “Converting Physical to Futures,” we will introduce a formula to calculate the number of futures needed to hedge a physical position. If you’ve already figured that out on your own, that’s even better. Let us leave you with a few warnings before we wrap up. Because interest rates are constantly changing and time is always passing, the ideal number of futures to hedge is physical position is changing all the time. Usually, these changes are small, but they can add up. So it’s essential to keep an eye on things and regularly check and adjust hedges if needed. We’ll get more into that idea in a future article on Dynamic Hedging. If you’re feeling overwhelmed by this, that’s okay. Feel free to reach out with any questions or comments - we’re here to help. Or, feel free to read more about Quartzite Precision Marketing, our flagship risk management program for grain and soybean producers. As always, thanks for taking the time to read, and we look forward to your feedback.

About those assumptions:

*If you are balking at these assumptions, that is fair. Handling production uncertainty and margin limitations are essential parts of managing risk. We understand these issues (that is one of the reasons our clients hire us), and we want to discuss them, but there is a lot of ground to cover between here and there.

**For the time being, we will mostly ignore that the interest rates producers earn and pay are usually different. Ultimately, an average of a producer’s lending and borrowing rates is typically close enough for practical purposes. There are slightly more accurate solutions, though they require an individual approach.

The Details Matter:

***It is normal in finance for seemingly small and boring details like this to meaningfully impact final results. At Quartzite, we think it is crucial to get the details right because getting them right is often the difference between a job well done and a sloppy mess.