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Optionsbeginner

Long Put

A long put is created by buying a put option. The buyer pays premium PP for the right to sell the underlying at strike KK on or before expiry. Maximum loss equals PP and is incurred when ST≥KS_T \geq K. Maximum profit equals K−PK - P and is reached only if ST=0S_T = 0. The expiry profit curve is the mirror of a long call, sloping down to K−PK - P to the left of the strike and sitting flat at −P-P to the right.

Why it matters

A long put is defined-risk insurance against a price drop. Hold the stock and add a put to cap downside, the textbook protective put. Or hold the put alone as a bearish bet, profiting if the stock collapses. Either way, the most you can lose is the premium. The trade-off is that the cost of insurance eats into returns when nothing bad happens. Just as not claiming on car insurance does not refund the premium, the put expires worthless if the share stays above KK.

Formulas

Payoff at expiry
Payoff=max⁡(K−ST,0)\text{Payoff} = \max(K - S_T, 0)
Equal to K−STK - S_T below the strike, zero above it.
Profit at expiry
Profit=max⁡(K−ST,0)−P\text{Profit} = \max(K - S_T, 0) - P
Break-even at ST=K−PS_T = K - P. Maximum profit =K−P= K - P when ST=0S_T = 0. Maximum loss =−P= -P.

Worked examples

Scenario

Buy a 3-month CSL put with K=K = 300$ at premium P=P = 8$. At expiry CSL trades at ST=S_T = 280$.

Solution

Payoff =max⁡(300−280,0)== \max(300 - 280, 0) = 20$. Profit =20−8== 20 - 8 = 12$ per share. On an ASX contract of 100 shares, that is $1200 of profit on $800 of premium, a 150\% return on the option layout.

Scenario

An ETF manager holds 10 000 SPY-equivalent units at $480 and buys 100 protective put contracts (each over 100 units) with K=K = 460$ at P=P = 5$. The market crashes to $400.

Solution

Total insurance cost =10000×5== 10000 \times 5 = 50000$. Put payoff =10000×max⁡(460−400,0)== 10000 \times \max(460 - 400, 0) = 600000$. Stock loss =10000×(480−400)== 10000 \times (480 - 400) = 800000$. Net loss with hedge =800000−600000+50000== 800000 - 600000 + 50000 = 250000,versus, versus 800000 unhedged. The put has built a floor near $460 that protects against the tail.

Common mistakes

  • ✗You need to own the underlying to buy a put. Speculative puts can be bought without any underlying position. A bearish trader can hold puts alone, hoping to profit from a fall without ever owning the stock.
  • ✗A long put has unlimited profit potential. Maximum payoff is KK, achieved if the stock falls to zero. After subtracting the premium, max profit is K−PK - P.
  • ✗Buying a put is the same as shorting the stock. A put caps loss at the premium, while a short sale has theoretically unlimited loss as the stock rises. Puts also avoid the borrowing fees and recall risk of stock shorting.

Revision bullets

  • •Buy a put to pay PP for the right to sell at KK
  • •Max loss =P= P when ST≥KS_T \geq K
  • •Max gain =K−P= K - P (only if ST=0S_T = 0)
  • •Break-even at ST=K−PS_T = K - P
  • •Bearish bet or portfolio insurance

Quick check

Maximum profit on a long put position is:

Buy a put with K=K = 60$ and P=P = 4$. Stock closes at ST=S_T = 48$. Profit per share is:

Connected topics

Short PutLong StraddleSynth. Call

In learning paths

Options Path

Sources

  1. Hull (2022), §10.4, §12.1
    Hull, John C. Options, Futures, and Other Derivatives. 11th ed. Pearson, 2022. ISBN 978-0-13-693997-9.
    Standard textbook reference for the long put payoff diagram, profit profile, and protective put strategy.
  2. McMillan (2012), Ch. 5
    McMillan, Lawrence G. Options as a Strategic Investment. 5th ed. Prentice Hall Press, 2012. ISBN 978-0-7352-0466-2.
    Strategy reference on long puts as a bearish speculation tool and as portfolio insurance.
  3. OIC Long Put Strategy
    Options Industry Council. Strategy Guide: Long Put. Options Education, accessed 2026.
    Industry guide with explicit profit and loss profile and break-even formula for the long put.
  4. ASX Protective Put Education
    Australian Securities Exchange. ASX Options Strategies: Protective Puts. ASX Investor Education, accessed 2026.
    Local reference explaining the protective put as portfolio insurance for ASX-listed shareholdings.
How to cite this page
Dr. Phil's Quant Lab. (2026). Long Put. Derivatives Atlas. https://phucnguyenvan.com/concept/long-put
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