Question

A synthetic short sale is created with a long put and a short call with the...

A synthetic short sale is created with a long put and a short call with the same strike price and expiration dates. Bank of America stock is currently trading at $21.71 per share. A May $25 call is trading at $2.75 and a May $25 put is currently trading at $2.25.

  1. Evaluate the payoffs of a short sale of BOA and the synthetic short sale at prices of $18, $25 and $28. Don’t forget the premiums on the options in your calculations and that each contract is for 100 shares. Assume your short sale is 100 shares also.
  2. Draw a payoff profile for each strategy.
  3. Compare the payoffs of each strategy in terms of monetary outlay and payoff at each price.
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Answer #1

Solution:

Payoff of short sell = Selling price - spot price

Payoff of synthetic short = Payoff of short call + payoff of long put

Payoff of synthetic short = MIN(Strike price- Spot price,0) + Premium received + MAX (Strike price - Spot price) - Premium Paid

Monetary outlay will be

For short sale = 21.71 *100 = 2171

For synthetic short = Net premium (Premium received from short call - premium paid in long put ) *100 = (+2.75 - 2.25) *100 = 50

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