Quick Answer
A speculator who is short a future but fears an unlimited-loss rally can buy a call at the futures level. The call caps the short's upside risk while the short keeps its downside profit. The combined payoff is a long put, so short futures plus a long call equals a synthetic long put.
The last three strategies each add one option to an existing futures position so the combined payoff replicates a different single option. This section builds the first of them. The direction is everything: get it right and the synthetic is reasoning, flip it and the answer is wrong.
The Synthetic Map (What Each Combination Replicates)
Three combinations show up on the exam. Each pairs a futures position with one option, and the combined payoff equals a different single option.
| Futures position held | Option added | Synthetic result | Why you would do it |
|---|---|---|---|
| Short futures | Buy a call | Synthetic long put | Cap the short's unlimited upside risk; keep the downside profit |
| Long futures | Buy a put | Synthetic long call | Floor the long's downside (protective put); keep the upside profit |
| Long futures | Sell (write) a call | Covered call (payoff of a synthetic short put) | Collect premium, cushion small declines, cap the upside at the strike |
Read each row two ways, and both must agree. First, the option added must fix the risk the futures position is worried about (a short fears a rally, so it adds a call; a long fears a decline, so it adds a put). Second, the resulting synthetic must match that fix. A row that passes only one direction is a flipped, wrong answer.
Memory Aid: Ask which move each futures leg fears. A short fears the rally up, so it buys a call as a ceiling. A long fears the drop down, so it buys a put as a floor. The option you add is insurance against the direction that hurts.
Short Future Plus Long Call
Start with a speculator who is short futures (bearish) but wants to cap the position's otherwise-unlimited upside risk. The fix is to buy a call at, or near, the futures level.
- If the market rallies, the long call's gains offset the short future's losses above the strike. The runaway loss is capped; the call is the insurance.
- If the market falls, the short future profits and the call simply expires. The premium paid is the cost of having carried that insurance.
- The call is bought against a short future, so it is the ceiling on a position whose loss would otherwise have no ceiling.
Trace the combined outcomes and the shape is unmistakable:
- Market rises → short future loses, long call gains above the strike → loss is limited.
- Market falls → short future gains, call expires → substantial profit on the decline.
Limited loss on a rally, profit on a decline: that is exactly the payoff of a long put. So short futures plus a long call equals a synthetic long put. The call converts the open-ended short into a defined-risk bearish position.
Think of it this way: the naked short is a bearish bet with no roof. Buying the call nails a roof over it. Once the roof is on, the position wins when prices fall and loses only a limited amount when they rise, which is the same thing a long put does from the start.
Exam Tip: Gotchas
- Short future plus long call is a synthetic long PUT, not a synthetic long call. The speculator is bearish, so the synthetic must be the bearish single option (the put). Naming it a synthetic long call inverts the whole position and is a critical error.
- The call is the fix because a short fears a RALLY. A short future's unlimited risk is to the upside, so the insurance is the right to buy (a call), which gains as price rises. Adding a put here would double down on the bearish side, not cap the risk.
- This is put-call parity in words. A long call and a short put at the same strike equal a long future, so any two of {long future, long call, long put} rearrange into the third. That is why adding a call to a short future manufactures a put.