Reporting a Non-Linear Hedge

There is nothing more difficult than going into a meeting and saying: if market goes up, we are 50% hedged, but if it goes down, we are only 10% hedged. If you say this, it is likely your portfolio is made up of derivatives with non-linear payoffs.

Linear payoffs

Futures are always in the money for better or worse. If you sold a future for $500 and it expires at $510, you pay $10 per bushel. If it expires at $490, you pay $10 per bushel. The future has a linear payoff regardless of the price movement.

Listed options have linear payoffs when they are in the money. This means that the change in payout is directly proportional to the change in the underlying asset. For example, if you have a Wheat option against the March contract at a strike of $500, and the price expires at $501, the call option will pay you $1 per bushel. If the price expires at $510, the call option will pay you $10 per bushel. The option has a linear payoff when it expires in the money.

Non-linear payoffs

Listed options have non linear payoffs when they are out of the money, because they pay nothing when the underlying futures price expires out of the money. Out of the money means:

• For a call option, the futures price expires below the strike price and no payout occurs
  • For example, if you sell a call option with a strike price of $500 and the futures price expires at $490, you receive no payout. If it expires at $300, you receive no payout either, you are always at zero at any price below strike, it is not linear.
• For a put option, the futures price expires above the strike price and no payout occurs
  • For example, if you sell a put option with a strike price of $500 and the futures price expires at $510, you receive no payout. If it expires at $700, you receive no payout either, you are always at zero at any price above strike, it is not linear.

Options, options combinations, and over the counter exotic options can have non-linear payoffs. If you have them in your portfolio, you are having to explain a potentially complex payoff structure to your stakeholders that may not always follow, at least, at the same speed.

How to report non-linear hedges

There is no short cut. You'll need to report the delta of your portfolio at different price levels to show how your hedge performs under different market conditions. This can be done manually, but it is time consuming and error prone. It is best if you have a way to aggregate your portfolio and in a platform that reports the delta at different price levels.

Your portfolio delta takes the place of the nominal volume. Here is what to expect:

• If you are a producer hedging the downside, your delta will most likely increase at higher levels and approach a value equal to the nominal volume as price goes deep in the money. Your delta will be lower as prices go lower. Why? Because your portfolio is likely made up of sold call options and you have also likely sold some downside in order to lift your hedged price with premium received.

• If you are a consumer hedging the upside, your delta will most likely increase at lower levels and approach a value equal to the nominal volume as price goes deep in the money. Your delta will be lower as prices go higher. Why? Because as prices go higher, your options are more likely to be out of the money and therefore have a lower delta. Why? Because you likely sold some upside in order to lower your hedging price with the premium received.

All this is normal, you are not doing anything wrong. The entire organization will likely grow if they are open to learning new things about hedging through your explanations, discussions and reporting.

If you need help with this, you can always reach out.