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Work out and contrast the payoffs of hedging strategies built on forward contracts versus those built on options.

FRM® Part I · Financial Markets and Products · Introduction to Derivatives · FRM1.FM.4.f

The idea

A hedger with a future sale can sell a forward, which fixes the price. Gains and losses on the exposure are offset and nothing is paid upfront, but the favourable move is given up and the forward itself can show a loss. Buying a put instead sets a floor, like an insurance policy: the downside is protected at the strike and the upside is kept, but the premium must be paid. An importer is the mirror image, using a long forward to fix the purchase cost or a call to cap it. Here K is the strike and S the price at maturity, and interest is ignored. With a put, the effective revenue per unit is: Put revenue = max(S, K) − premium. With a forward, the effective revenue is simply the forward price F, whatever S turns out to be. Options also suit contingent exposures, because a forward can leave an unwanted position if the underlying deal fails.

Formulas

Effective sale revenue hedged with a put

Put-hedged revenue = max(S, K) − p

S
the price at maturity
K
the put's strike price
p
the put premium paid

Ignores interest on the premium. A forward hedge gives the forward price whatever S turns out to be.

A practice question

From the question bank, with the reason each wrong option is wrong.

Compared with a hedge using a forward contract, what is the principal drawback of hedging with a purchased option?

  1. Gains on the underlying exposure are given upWhy not: This is the drawback of a forward hedge; the option retains the favourable move.
  2. The hedger is obliged to transact even when the market moves favourablyWhy not: An option holder has a right, not an obligation; the obligation belongs to a forward.
  3. The hedger's loss on the option is unlimited if the market moves againstWhy not: The most a purchased option can lose is the premium.
  4. The premium must be paid upfront - correct

A forward costs nothing at inception but fixes the outcome; an option keeps the favourable side of the market but costs a premium.

A harder one

A producer will sell oil in three months. One hedge is a short forward at 80. The other is a put with a strike of 80 costing 3.50 per barrel. The spot price at maturity is 90. Ignoring interest, what is the effective revenue per barrel under the forward hedge and under the put hedge respectively?

  1. 90.00 and 90.00Why not: Ignores the hedge on the forward and the premium on the put.
  2. 80.00 and 83.50Why not: Adds the premium to the strike instead of deducting it from spot revenue.
  3. 80.00 and 86.50 - correct
  4. 86.50 and 80.00Why not: Swaps the two: the forward fixes the revenue at 80, and the put keeps the upside.

Forward: revenue is 80 whatever the spot. Put: expires worthless at 90, so revenue = 90 - 3.50 = 86.50. The put keeps the upside net of its cost.

The hardest tier

A producer will sell oil in six months. Alternative A: sell a forward at 80. Alternative B: buy a put with a strike of 78 for a premium of 2 (ignore interest). Above what final spot price does B give higher net revenue per barrel than A?

  1. 80Why not: Compares spot with the forward price and ignores the premium paid for the put.
  2. 78Why not: Uses the strike of the put as the cross-over point.
  3. 76Why not: Uses the revenue floor under the put (78 - 2), which is not the cross-over price.
  4. 82 - correct

Under B revenue is max(S, 78) - 2; above 78 this is S - 2. Setting S - 2 = 80 gives S = 82. Below 82 the forward is better, above 82 the put is.

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