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Work out and contrast the payoffs of speculative positions taken with futures versus those taken with options.

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

The idea

Speculators use derivatives to take a view with little capital. With a bullish view they buy futures or calls, and with a bearish view they sell futures or buy puts. A futures position has a payoff that is linear in the price move, requires only margin, and can lose more than the margin posted because variation margin must be paid. A purchased option has a maximum loss equal to the premium, but the price must move beyond the strike plus the premium before it profits. Written options and short futures can lose very large amounts. Compare positions on equal capital: futures are usually more levered when right, while options lose the whole premium when the view is wrong. Always deduct the premium when computing option profit.

Formulas

Breakeven price of a long call at expiry

Breakeven = K + c

K
the strike price
c
the call premium paid

Ignores interest on the premium. Between K and the breakeven the call is exercised but still loses part of the premium.

A practice question

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

Which statement correctly contrasts a long futures position with a long call, both used to speculate on a price rise?

  1. The call loses one-for-one as the price falls, while the futures loss is limitedWhy not: Reverses the two: the futures position has the linear, open-ended loss.
  2. Both positions have a loss limited to the amount initially paidWhy not: A futures holder can lose more than the margin posted, since variation margin must be paid.
  3. The futures loss grows as the price falls, while the call's loss is limited to the premium paid - correct
  4. Both positions profit only after the price rises by more than a premiumWhy not: Only the call has a premium; futures profit as soon as the price exceeds the entry price.

A long futures payoff is linear in the price move and can lose more than the initial margin. A long call has a maximum loss equal to the premium and needs a rise beyond strike plus premium to profit.

A harder one

A stock trades at 100. A speculator has 5,000 to invest. Option A is to buy 500 stock futures at 100, with margin of 10 per unit. Option B is to buy 1,000 calls with a strike of 100 at a premium of 5. The stock rises to 108 at expiry. Ignoring interest, which option is more profitable and by how much?

  1. Calls, by 4,000Why not: Counts the call payoff of 8,000 and forgets to deduct the premium of 5,000.
  2. Futures, by 1,000 - correct
  3. Calls, by 2,600Why not: Buys only 50 futures units by treating the 5,000 as the full price, understating the futures profit.
  4. Futures, by 2,500Why not: Compares the futures with only 500 calls (profit 1,500) instead of 1,000 calls.

Futures profit = 8 x 500 = 4,000. Call profit = (8 - 5) x 1,000 = 3,000. The futures are ahead by 1,000. If the stock falls, the call loss is capped at 5,000 while the futures loss grows.

The hardest tier

A speculator expects a price fall from 40. Position A is short one futures at 40. Position B is long one put with a strike of 40 for a premium of 2.50. For final prices above 40, at what final price do A and B show the same profit per unit?

  1. 40.00Why not: Equates the payoffs and ignores the premium on the put.
  2. 37.50Why not: Uses the put's breakeven, 40 - 2.50, which is not where the two profits cross.
  3. 42.50 - correct
  4. 45.00Why not: Adds the premium twice (40 + 2 x 2.50).

Above 40, A earns 40 - S and B loses the premium, -2.50. Setting 40 - S = -2.50 gives S = 42.50. Above 42.50 the put loses less, while below 40 the futures earn 2.50 more per unit.

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