Subject 2. Position Equivalencies

Derivatives can be combined to create a particular investment product with the desired risk exposure.

Synthetic Long Asset

This is an options strategy used to stimulate the payoff of a long asset position. It is entered by buying at-the-money calls and selling an equal number of at-the-money puts of the same underlying asset and expiration date.

This is an unlimited-profit, unlimited-risk-options trading strategy that is used when the options trader is bullish on the underlying asset but seeks a low-cost alternative to purchasing the asset outright.

Synthetic Short Asset

A synthetic short asset is an options strategy used to simulate the payoff of a short asset position. It is entered into by selling at-the-money calls and buying an equal number of at-the-money puts of the same underlying asset and expiration date.

This is an unlimited-profit, unlimited-risk-options trading strategy that is used when the options trader is bearish on the underlying asset but seeks an alternative to short selling the asset. Compared to actual short selling of a stock, there is no need to borrow to short sell, and there is no need to pay dividends on the short stock (if it is a dividend-paying stock).

Synthetic Assets with Futures/Forwards

Long stock + short futures = risk-free rate

This strategy generates the risk-free (cash) rate.

Synthetic Put

This strategy combines the short sale of a security with a long-call position on the same security. It effectively creates a position that has the same risk-reward attributes as a straightforward put position.

Synthetic Call

Synthetic call = long stock + long put

This is similar to the protective put strategy. It has unlimited profit potential and limited risk.

Foreign Currency Options

The important point to note is that a foreign currency call option always has a put option that is an identical twin. For example, assume the spot exchange rate is US$:euro = 0.8:1. That is, a euro is worth US$0.8. The following two options are identical in terms of payoff with the same expiration.

  • Buy a call option to buy US$ with a strike price of 1.25 euro per US$ (1/0.8).
  • Buy a put option to sell euros with a strike price of US$0.8 per euro.

If you need 10 US dollars at option expiry time and:

  • the exchange rate becomes 1.3 euro per US$, you can exercise the call option and pay 12.5 euros for 10 US dollars, or you can exercise the put option to sell 12.5 euros for 10 US dollars.
  • the exchange rate becomes 1.1 euro per US$, you will simply pay 11 euros for 10 US dollars on the spot market and let the options expire.

Practice Question 1

For the synthetic long stock strategy, ______

I. there is no maximum profit.
II. heavy losses can occur.
Correct Answer: I and II

The payoff is similar to that of a long stock position. The options trader stands to profit as long as the underlying stock price goes up. If the underlying stock price takes a dive, heavy losses can occur.

Practice Question 2

If you are bearish about a stock, you can ______

I. synthetic short the stock
II. write a call
III. write a put
Correct Answer: I and II

Practice Question 3

How would you create a synthetic put?

A. Short stock + long call
B. Long stock + short futures
C. Short call + long stock
Correct Answer: A

Practice Question 4

Which option portfolio with the same exercise price for both options is most similar to a short stock option?

A. Short put + long call
B. Long put + short call
C. Short put + short call
Correct Answer: B

Practice Question 5

Suppose XYZ stock is trading at $50 in September. An options trader sets up a synthetic long stock position by selling an October 50 put for $100 and buying an October 50 call for $150. One option contract covers 100 shares. If the XYZ stock rallies and is trading at $55 on expiration in July, the trader will make ______.

A. $450
B. $500
C. $0 (the position is perfectly hedged)
Correct Answer: A

The short October 50 put will expire worthless but the long October 50 call expires in the money and has an intrinsic value of $500 ($5 x 100). Subtracting the initial cost of $50, the options trader's profit comes to $450.

Practice Question 6

Consider the foreign exchange market for JPY and EUR. To hedge your risk exposure to JPY you can buy a call option on JPY. Alternatively, you can ______ to get the same payoff, no matter how the JPY/EUR exchange rate fluctuates.

A. sell a call option on EUR
B. buy a put option on EUR
C. buy a put option on JPY
Correct Answer: B

The payoffs will be identical.

Practice Question 7

A "synthetic cash" position can be created by ______.

A. long stock + short put
B. long stock + short futures
C. short stock + long call
Correct Answer: B

Practice Question 8

A synthetic long asset position can be created by ______.

I. long call + short put
II. long put + short call
III. risk-free rate + long futures
Correct Answer: I and III

Practice Question 9

Which one is an unlimited-profit, unlimited-risk-options trading strategy?

A. Synthetic long asset
B. Long call
C. Short put
Correct Answer: A

A long call has limited risk (losing the call premium), and a short put has limited profit (making the put premium). However, the synthetic long asset strategy replicates a long position in the underlying: the loss will be unlimited if the underlying asset price goes down (until it goes to zero), and the profit will also be unlimited if the underlying asset price shoots upwards.

Practice Question 10

A stock is trading at $30 per share. Your strategy involves a short sale on the stock, with the purchase of calls on the stock with the strike price of $30. This combination trade is referred to as a ______.

A. synthetic stock futures trade
B. synthetic put
C. covered put
Correct Answer: B

If the stock price declines to $10 by the time the calls expire, the net profit on the synthetic put position would be $10 ( i.e., the short sale position would have a profit of $10 while the calls will expire worthless). If a straight put with a strike price of $30 had been purchased instead, the profit on it would also be $10.

Practice Question 11

How would you create a synthetic call?

A. Short stock + long put
B. Long stock + short put
C. Long put + long stock
Correct Answer: C

The long put position eliminates much of the downside risk, whereas the long stock position leaves the profit potential unlimited.

Practice Question 12

Which strategy does NOT have unlimited profit potential?

A. Synthetic long asset
B. Synthetic short call
C. Synthetic long put
Correct Answer: B

The maximum profit for selling a (synthetic) call is the premium.

Practice Question 13

Which strategy has unlimited risk potential?

A. Synthetic long asset
B. Synthetic long call
C. Synthetic long put
Correct Answer: A

If the asset price becomes zero, the value of synthetic long asset will be zero too.