What it means
A call option gives the right to buy a share at a fixed price, so it gains value when the share price rises and can only lose the amount paid for it. A put option gives the right to sell at a fixed price, so it gains value when the price falls.
If you own the share and also own a put, you have a position that profits from a rise and is protected from a big fall. Put those two pieces together and the result looks just like a call.
If the share climbs, you gain nearly all of the rise, minus the cost of the put, and if it collapses, the put lets you sell at the agreed strike price so your loss is capped. That is exactly the shape of a call option payoff.
The link between the two comes from put-call parity, which says that a call, a put, the share and a risk-free loan are tied together by price. Because of this relationship, owning the share plus a put is equivalent to owning a call plus cash.
Traders use the equivalence to spot cases where one route is cheaper than the other. In practice people build a synthetic call when a direct call is hard to buy, too expensive or unavailable on a given share.
Someone who already owns the share can simply add a put, and that creates the position at once. The cost is the premium paid for the put, which acts like an insurance premium.
There are trade-offs. The put premium reduces returns every time protection is bought, so a continuous programme of protective puts can be a drag in calm markets.
The put also expires, so the protection must be renewed or it stops, and the strike price and expiry should be chosen to fit how much loss the investor can tolerate. A mirror image exists in the synthetic put, which is built by short selling the share and buying a call.
Both structures show that options and shares can be mixed to produce any payoff pattern an investor wants.
In practice
Real-world examples.
Example
A founder holds shares in her listed company and cannot sell them for another year. She buys puts to cap her downside, which creates the same exposure as owning calls on the shares.
Example
A retail investor buys 100 shares at $80 and a put with a strike of $75 for $3 a share. His worst loss is $5 a share on the fall to the strike plus $3 for the put, which is $8 a share or $800 in total.
Example
A fund manager with a large holding in a bank share wants to stay invested through an uncertain earnings season. She adds put protection for three months and plans to review the strike level once the results are out.
Formula
Calculation
Synthetic long call = Long share + Long put (same strike and expiry)
Suppose an investor buys a share at $50 and buys a put with a strike of $50 for a premium of $2.
If the share rises to $60: the share gains $60 - $50 = $10, the put expires worthless and costs $2. Net gain = $10 - $2 = $8.
If the share falls to $45: the share loses $50 - $45 = $5, the put gains $50 - $45 = $5. Net result = -$5 + $5 - $2 = -$2.
If the share falls to $30: the share loses $20, the put gains $20. Net result = -$20 + $20 - $2 = -$2.
The loss is capped at the $2 premium, and the gain is unlimited minus $2. This matches a call with a strike of $50 bought for $2.Case study
Seen in the real world.
Hollis Engineering is an illustrative, fictional business whose treasury held 20,000 shares of a supplier worth $40 each, or $800,000, that it wanted to keep for strategic reasons. The finance director worried about a drop after the supplier's results.
She bought 20,000 puts with a strike of $38 for $1.50 each, a total cost of 20,000 x $1.50 = $30,000. This created a synthetic call: the company kept all the upside above $38, while the downside was limited to $2 a share on the fall to the strike plus the $1.50 premium.
In the illustrative result the supplier's share price fell to $30. The shares lost $10 each, or $200,000, but the puts paid out $8 each, or $160,000, so the net loss was $200,000 - $160,000 + $30,000 = $70,000 instead of $200,000.
Watch out
Common mistakes.
- Forgetting the cost of the put, which reduces profit in every scenario.
- Assuming the protection lasts for ever, when the put expires and must be renewed at the then-current price.
- Choosing a strike far below the share price to save money, which leaves a large uninsured loss.
Questions
People also ask.
Is a synthetic call the same as a protective put?
The payoff is the same, and the term protective put emphasises the insurance purpose, while synthetic call emphasises that the position copies a call.
Why not just buy a call?
You might already own the shares, or calls might be too expensive or unavailable, so adding a put is simpler.
What is the maximum loss on a synthetic call?
The difference between the share price paid and the put strike, plus the put premium.
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