A hedge is a contract that offsets adverse changes in the value of another exposure. The hedge pays out when we’re losing money on our other exposure. So we’re hedged by the contingent cash receipt.
Let’s say we’re a seller of a commodity. We have an operational exposure to its market price. If the market price falls, our revenues will suffer. Two ways to hedge this exposure using options are to:
Say we buy a put option with a strike price of $100, for a premium paid of $6. If the price of our commodity falls below the $100 strike price, perhaps to $80, we receive a cash payout based on the difference. (This is known as ‘cash settlement’. It gives exactly the same result as physical sale and delivery of the commodity, but saves transport and storage.) In this case, the payout we receive would be: $100 – $80 = $20.
Ignoring timing differences, our net gain on the put strategy would be the payout received of $20 LESS the $6 premium paid = $14.
The receipt from the put offsets our lost revenues on selling our commodity more cheaply in the market, to provide an effective hedge.
But if the commodity price ends up equal to, or even higher than, the $100 strike price of the put, there is no payout. In these cases, we’d suffer a net hedging loss of the $6 premium we’d paid, as set out in table 1. All amounts are in $.
Note three key features in Table 1:
An alternative, and recently examined, hedge structure is a synthetic forward contract. Here we use two options in combination, to build the synthetic forward contract. We still buy a put option, exactly as we did before. But now we also sell a call option, with the same strike price as the put.
The key to understanding this structure is that the individual results from each option simply add up. This is where investing time in our consistent sign convention and narrative labels pays off handsomely. Let’s see how it works using an extract from a recent exam.
Your company, SuperHero Inc (SHI), wants to remove any price risk from its sale of a commodity, Kryptonite, which is a major revenue item.
Until recently, you have been able to fix the future price using a forward contract. The counterparty that you have normally dealt with has exited the business, however, leaving no credible market maker for a forward price. But there are option prices available for three-month expiry. Option price data for Kryptonite:
Describe how a synthetic forward contract appropriate for SHI can be constructed using the options quoted above. (Financial Maths & Modelling (FMM), October 2013, Q6 extracts)
We buy a put option for a premium payable of $6, with results as before:
We also sell a call option for a premium received of $7. When the Kryptonite price exceeds the call strike price of $100, we have to make a payment, for example: $120 – $100 = $20. But we always get to keep our premium received of $7.
Following our ‘receipt/(payment)’ sign convention consistently, the net results from the call sold are:
Now it’s very easy to combine the results from each individual option. The individual results simply add up or net off. And our explicit sign convention makes it easy to get each item the right way round in the combination:
The relationships between the net gains and losses on the put (blue), the call (red) and the synthetic forward (green) are summarised in the following chart:
[Image:chart_bi.gif align=”center” alt=”Synthetic forward contract to sell kryptonite chart”]
Many candidates found this exam case difficult. The examiner said: “There were relatively easy marks to be gained by describing how to create a synthetic forward contract using options, but some candidates did not take advantage of that.”
“It is possible that the source of difficulty here is the application of option knowledge to corporate hedging rather than to option trading strategies. This is an important part of the syllabus and the topic of hedging will be covered on a more regular basis.” (Examiner’s report, FMM, October 2013).
Understanding hedge construction and passing your exams doesn’t need extraordinary powers. It just needs study and lots of question practice, both of which you can achieve.
Apply the ‘mostly positive’ sign convention consistently with explicit labels and you will master many challenging topics in finance. Some of your colleagues may even think that you have developed superhuman abilities.
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Doug Williamson FCT is a writer, tutor, coach and former chief examiner. He is uniquely qualified to help you pass your ACT exams, having read and marked thousands of students’ exam answers, carefully noting where you can gain many easy marks