Charta is on Google Play: practise on the go. Get the app
Charta

State what derivatives are, outline their features and uses, and contrast linear derivatives with non-linear ones.

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

The idea

A derivative is a contract whose value is derived from the price or level of an underlying asset, rate, index or event, such as a stock, a currency, an interest rate or a commodity. Its main features are that it is settled in the future, needs little or no initial outlay relative to the exposure it creates, which is leverage, and is zero-sum between the two parties before costs. Derivatives are used to hedge risk, to speculate, to arbitrage and to change exposure cheaply. Linear derivatives, namely forwards, futures and swaps, have payoffs that move one-for-one with the underlying, so they can be valued from the spot price and financing rates alone. Non-linear derivatives, namely options, have kinked payoffs and need a volatility input. Leverage magnifies gains and losses equally, so it is not the same as higher expected return.

A practice question

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

Which of the following has a payoff at maturity that is a linear function of the underlying price?

  1. A long position in a European call optionWhy not: The call payoff max(S - K, 0) is kinked at the strike, so it is non-linear.
  2. A short position in a European put optionWhy not: The short put payoff -max(K - S, 0) is also kinked and therefore non-linear.
  3. A long position in a forward contract - correct
  4. A long straddle (a call plus a put at the same strike)Why not: The straddle payoff is V-shaped, so it is non-linear in the underlying price.

A forward pays S - K, a straight line in the final price S. Forwards, futures and swaps are linear derivatives, while options have kinked payoffs and are non-linear.

A harder one

A trader posts initial margin of USD 5,000 on a futures position with a notional value of USD 100,000. The futures price rises by 2 percent in the trader's favour. The return on the margin posted is closest to:

  1. 2%Why not: Reports the return on the underlying and ignores the leverage created by the small margin.
  2. 5%Why not: Confuses the margin-to-notional ratio (5%) with the return earned.
  3. 250%Why not: Inverts the ratio: margin divided by gain (5,000 / 2,000) instead of gain divided by margin.
  4. 40% - correct

Gain = 2% x 100,000 = USD 2,000. Return on margin = 2,000 / 5,000 = 40%. Leverage multiplies the 2% move by the notional-to-margin ratio of 20.

The hardest tier

A trader buys a European call at a premium of 6.50 and sells a European put at a premium of 4.00, both on the same stock with a strike of 100 and the same expiry. The stock ends at 92. Ignoring financing, the trader's profit per share is closest to:

  1. -10.50 - correct
  2. -8.00Why not: Ignores the net premium of 2.50 paid and reports the payoff only.
  3. -5.50Why not: Adds the net premium instead of deducting it (-8.00 + 2.50): wrong sign on the premium.
  4. -6.50Why not: Counts only the long call (premium lost) and forgets the loss on the short put.

Call payoff = 0. Short put payoff = -(100 - 92) = -8. Net premium paid = 6.50 - 4.00 = 2.50. Profit = -8 - 2.50 = -10.50. The pair replicates a forward with delivery price 100, a linear payoff.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

Start free →

More in Introduction to Derivatives