Buying an option is simple: you pay the price, and the most you can lose is what you paid. Selling one is different. You take in cash today and promise to buy or deliver shares later, so your broker wants a deposit against that promise. That deposit is margin, and it decides how many trades you can hold at once and what happens to your account when the market turns.
Margin and buying power
Margin here means collateral: money your broker sets aside to cover what a position might lose. Buying power is what is left over for new trades. Open a trade that needs $1,600 of margin and your buying power drops by $1,600: nothing has been spent, but the money is committed while the trade is open. Long options and debit spreads are paid for in full, so their price is their whole requirement.
Defined risk and undefined risk
A position has defined risk when its worst loss is fixed the moment you open it, and for those trades the margin is simply that worst loss. A short option with nothing behind it, called naked or uncovered, has undefined risk: a short put loses more the further the stock falls, all the way to zero, and a short call has no ceiling at all. Here is a $95 put sold for $1.33 on a $100 stock, 30 days out.
One $95 put sold on a $100 stock with 30 days left at 30% volatility. The credit caps the gain on the right; on the left the loss keeps growing all the way down. Raise volatility to see how the position marks against you before expiry.
On the right is the $133 you keep if the stock stays above $95. On the left the loss grows a dollar for every dollar below the breakeven, and at a stock price of zero it would be $9,367. Now buy the $90 put for about 40 cents as well. That makes a put credit spread, and the line stops falling.
Short the $95 put, long the $90 put. Below $90 the line goes flat: the most you can lose is the $5 width less the credit, and that is also the margin. Compare the left edge with the chart above.
The spread gives up 40 cents of credit to put a floor under the loss: the worst case falls from $9,367 to $407, the $5 between the strikes less the 93 cents collected, and the margin falls with it.
The exchange minimum for a short put
For an uncovered stock put, the exchanges set a minimum, and brokers can ask for more on top, called a house requirement. The minimum is the larger of two numbers, per share, times 100:
- 20% of the stock price, minus the amount the put is out of the money, plus the premium; or
- 10% of the strike, plus the premium.
With the stock at $100 and the $95 put sold for $1.33, the first test gives $20 − $5 + $1.33 = $16.33 and the second $9.50 + $1.33 = $10.83. The larger wins: $1,633 a contract. A short call uses the same first test with 10% of the stock price as its floor, and broad index options use a lower percentage, because an index moves less than a single stock.
Cash-secured instead
You can also sell the same put cash-secured: the account holds all the cash needed to buy the shares if assigned. That is the strike times 100, less the premium collected: ($95 − $1.33) × 100 = $9,367. It ties up nearly six times the margin minimum, but it can never be called for more money. Module 14 will build the cash-secured put into a strategy of its own.
Portfolio margin in outline
Everything above is strategy-based margin: a fixed formula per position. Larger accounts can apply for portfolio margin, which works the other way round. The broker reprices the whole account across a range of moves in each underlying, for a single stock up and down about 15%, and requires the worst loss it finds. Hedges count, so for hedged books it is usually far less than the formula, and because each scenario reprices at current implied volatility, it rises when volatility does.
Why margin grows in a selloff
Walk the stock down through the short put formula. As it falls toward the strike, the out-of-the-money amount you subtract shrinks to zero. The premium, which you add, rises twice over: from the fall itself, and from implied volatility jumping, as it usually does in a selloff.
Value of the $95 put you are short, against the stock price, with 25 days left. Moving left along a line is the stock falling; jumping to the upper line is volatility rising, which in a selloff happens at the same time. Hover at $100 on the lower line and $92 on the upper one.
Take the stock from $100 to $92 with 25 days left and volatility up from 30% to 45%. The put is now worth about $5.89, so the requirement is 20% of $92 plus $5.89: $24.29 a share, $2,429 a contract, nearly half as much again as the $1,633 you started with, just as the position shows a $456 loss. If your account falls below what is required, you get a margin call: deposit cash or cut positions, or the broker closes positions for you, usually at the worst prices of the move. Premium sellers leave a large share of buying power unused for exactly this day.
The maths: three requirements side by side
For one short put with stock price S, strike K and premium P, all per share:
- Exchange minimum:
100 × max(0.20 S − max(S − K, 0) + P, 0.10 K + P) - Cash-secured:
100 × (K − P) - Put credit spread with a long put at
K2belowKand net creditC:100 × (K − K2 − C), which is also its maximum loss.
Worked example at S = 100, K = 95, P = 1.33, K2 = 90, C = 0.93: the minimum is 100 × max(20 − 5 + 1.33, 9.5 + 1.33) = $1,633; cash-secured is 100 × 93.67 = $9,367; the spread is 100 × (5 − 0.93) = $407.
The two tests cross once the put is far enough out of the money: the 10% floor takes over when S − K exceeds 0.20 S − 0.10 K, which works out to S above 1.125 K, about $106.88 for the $95 put.
Your turn
Open AMZN on the Options Chain at the monthly expiration. Take the put about 5% below the stock price, read its Mid, then work out the exchange minimum and the cash-secured amount for selling one.