Synthetic long call
A protective put position — long the stock plus a long put at the same strike — whose payoff, limited loss with unlimited upside, mimics that of an outright long call option.
In plain language
Two very different-looking positions can end up with the same shape of profit and loss. A protective put — owning the stock and also buying a put on it — is one of the clearest examples.
If the stock falls, the put's gain offsets the stock's loss, capping the downside at the premium paid. If the stock rises, the stock's gains keep growing while the put simply expires worthless. That is exactly the payoff shape of an outright long call: limited loss, unlimited gain. Because of this resemblance, the workbook calls a protective put a synthetic long call.
How it works
The workbook builds the payoff with a worked position (Chapter 5): buy the stock at Rs 1,600, and buy a put with a strike of 1,600 for a premium of Rs 20.
| Stock price at expiry | Long cash P/L | Long put P/L | Net position |
|---|---|---|---|
| 1,500 | −100 | +80 | −20 |
| 1,600 | 0 | −20 | −20 |
| 1,660 | +60 | −20 | +40 |
| 1,700 | +100 | −20 | +80 |
For every fall below the strike, the net loss stays fixed at Rs 20 — the premium paid — no matter how far the stock drops, because the put's gain keeps pace with the stock's loss. Above the strike, the put is worthless and the position simply tracks the stock's gains upward, unlimited. This is the same shape as a long call struck at 1,600 costing a Rs 20 premium would produce — hence "synthetic long call."
A worked example
A mutual fund manager holding a stock at Rs 1,600 is worried about a near-term fall but does not want to give up any further upside. Instead of selling the stock or shorting futures — either of which would take her out of the market entirely — she buys a put at strike 1,600 for a Rs 20 premium, creating a synthetic long call.
If the stock falls to Rs 1,530: the stock loses Rs 70, the put gains Rs 50 (intrinsic value of 70, less the Rs 20 premium paid nets to a Rs 50 P&L on the put leg), for a net loss of Rs 20 — exactly the premium, and no worse regardless of how much further the stock might have fallen.
If the stock instead rises to Rs 1,660: the stock gains Rs 60, the put loses its full Rs 20 premium, for a net gain of Rs 40 — and that net gain keeps growing with every further rupee the stock rises.
Why NISM asks about it
Chapter 5, section 5.2, works through the protective put payoff table and states directly that "the protective put is called a synthetic long call position" because its payoff matches a long call's. Expect a question asking which combination of stock and option position is "synthetic" to which single option position.
Common exam traps
- The maximum loss on a synthetic long call (protective put) equals the put premium paid — here, Rs 20 — not the full value of the stock.
- The upside is unlimited, exactly like an outright long call, because the stock leg has no cap.
- Do not confuse this with a genuine long call: the synthetic version requires holding the actual stock plus a put, tying up far more capital than simply buying a call option outright — the payoff shape matches, but the capital required does not.
Check yourself
1.Which of the following is a hedged position?
- a)Short straddle
- b)Short strangle
- c)Covered call
- d)Protective put
Show the answer
Answer: (d) Protective put
The workbook introduces the protective put with the words "This is a hedged position." An investor long in the cash market buys a put, so losses are capped at the premium paid while gains keep rising — the payoff profile of a long call, which is why it is called a synthetic long call.
Options A and B are the opposite of hedged. A short straddle and a short strangle both have limited profit and unlimited loss, and the workbook warns the short straddle should be undertaken with significant care.
Option C is the genuinely tempting one. A covered call does combine stock with an option, but it generates income while leaving the downside wide open — its payoff is that of a short put. It caps your gains, not your losses. Only the protective put actually protects.
2.An investor holding a stock is choosing the strike for a covered call. According to the workbook, what is the effect of choosing a strike close to the prevailing stock price?
- a)It fetches a lower premium but gives a longer ride on the stock
- b)It removes the downside risk on the stock
- c)It fetches a higher premium upfront but locks the potential gain from the stock early
- d)It converts the position into a synthetic long call
Show the answer
Answer: (c) It fetches a higher premium upfront but locks the potential gain from the stock early
The workbook: the most important factor in this strategy is the strike of the sold call option. If the strike price is close to the prevailing price of the underlying stock, it would fetch higher premium upfront but would lock the potential gain from the stock early. And, if the strike price is too far from the current price of underlying, while it would fetch low upfront premium, it would provide for a longer ride of money on the underlying stock.
Option A describes a far strike. Option B is wrong whatever the strike: the covered call restricts the upside while leaving a scope for unlimited losses, which is why it is called a synthetic short put; the downside needs a long put (a collar). Option D describes the protective put, which is the synthetic long call.
3.Kiran buys a stock at ₹840 and at the same time buys a put option with a strike of ₹840 at a premium of ₹15. What is his net position at expiry if the stock falls to ₹760, and if it rises to ₹900?
- a)At ₹760: −₹80; at ₹900: +₹60
- b)At ₹760: −₹95; at ₹900: +₹45
- c)At ₹760: −₹15; at ₹900: +₹45
- d)At ₹760: +₹65; at ₹900: −₹15
Show the answer
Answer: (c) At ₹760: −₹15; at ₹900: +₹45
The workbook's protective put example (stock and strike 1600, premium 20) gives −20 at 1530 and +40 at 1660. Apply the same method.
At ₹760: long cash −80; long put −15 − 760 + 840 = +65; net −15. At ₹900: long cash +60; long put −15 (expires worthless); net +45.
For all falls, the loss is limited only to the extent of premium paid (if strikes are different, losses will be different from premium paid), while gains on a rise are unlimited. That is why a protective put payoff is similar to that of a long call — a synthetic long call.
Option A ignores the put entirely. Option B charges the premium but forgets the put's payoff on the fall. Option D reports only the put leg.
Where this is taught
Free preparation for NISM Series VIIIRelated terms
- Asymmetric payoffA payoff where gains when the underlying moves one way differ sharply from losses when it moves the other — the defining feature of options, as against the symmetric, linear payoff of futures.
- Protective putBuying a put option to protect a foreign currency receivable: it sets a floor rate (strike minus premium) while keeping the benefit if the currency rises. Suited to contingent cash flows.
- Put-call parityThe arbitrage-free relationship binding a European call and put of the same strike and expiry to the spot and the discounted strike: c + X·e^(−rt) = p + S. Deviations create risk-free profit.