Strategies for sellers

OpeningTwo years of premium, given back in a day

The stock is at $100, IV 30%. You sell one put with a strike of 90 that expires in 30 days, and collect $40.

This option's Delta is −0.096, and the market-implied probability that it finishes in the money is about 11%. About nine times out of ten it expires worthless and the $40 is yours. It sounds like a steady monthly income.

Now look at the other side. One day earnings disappoint and the stock gaps down to 80 at the open. At expiry you have to buy, at 90, a stock worth 80, a loss of $10 per share. Subtract the $0.40 you collected and each contract loses $960, the equivalent of 24 months of premium.

A seller's problem is never “will I win?” The real questions are: how big is the loss when you do lose, how often does it come, and can you survive long enough to see the next one? Every tool in this chapter is built around those three questions.

8.1What selling really is: selling insurance

Selling options earns two things: time value, and the premium by which implied volatility usually exceeds realized volatility. The cost is negative convexity: as the stock rises you make money more and more slowly, and as it falls you lose money faster and faster.

Premiums, claims and the loss ratio

An insurer's profit is premiums minus claims, and the same is true for an option seller. Sell a 30-day put with a 95 strike and you collect $1.33; at expiry you pay out max(95 − S_T, 0). The expected size of that payout depends on how much the stock actually moves over the next 30 days, not on the IV at which you sold.

The table shows three things. First, when realized volatility equals implied volatility, the expected value is zero: the option is fairly priced and the seller has no edge. Second, the seller's entire edge comes from the gap between IV and realized volatility, which is the volatility risk premium from Chapter 6. Third, that edge as a share of the premium grows the further OTM you go: at 25% realized volatility, the expected profit on the 95 put is 33% of the premium and on the 90 put 52%, but in dollars it is only $21. In insurance terms, deep OTM policies have a lower loss ratio, but each one brings in only a few tens of dollars.

Most of the time, implied volatility on index options is higher than the volatility that is later realized, and that is why selling strategies can survive over the long run. The gap reverses in a few periods, and when it does it often reverses by a lot at once. The rightmost column of the table is that kind of period.

Negative convexity: a drop hurts more than a rise of the same size helps

A 10% rise adds only $120, because the most you can ever make is $133; a 10% drop loses $468, and a 20% drop loses $1,343, nearly three times the Delta estimate. That is negative Gamma: the position automatically gets bigger as the stock falls and smaller as it rises (Chapter 4, Section 4.4).

8.2Covered calls

A covered call sells part of the stock's future upside for cash today. On the way down, it gives you only the small cushion of the premium.

Structure: hold 100 shares and sell one call. If the stock is below the strike at expiry, the call expires worthless and you keep both the shares and the premium; if it is above, your shares are called away at the strike. By put–call parity (Chapter 3), a covered call has exactly the same payoff at expiry as a cash-secured put at the same strike. They are the same risk, and the covered call is not more “conservative.”

Choosing the strike and expiration

* Risk-neutral probability of finishing in the money at expiry, N(d₂).

Choosing a strike means dividing among three things: how much you collect now, how much upside you keep, and how likely you are to lose the shares. Practical rules:

• You want to keep the shares for the long run: sell Delta 0.15–0.25. The chance of being called away is 10%–20%, and you keep plenty of upside.
• You don't mind the shares being called away and want to turn them into cash income: sell ATM or Delta 0.40 and above. The premium is rich, and being called away is the norm.
• Expiration: 30–45 days is the usual compromise. A 45-day 105 call brings in 2.42, or 1.61 per 30 days, slightly less than the 1.66 of the 30-day call. Shorter options have higher daily Theta, but you have to trade more often, and Gamma is bigger too.
• Earnings and ex-dividend dates: earnings can carry the stock past the strike in one jump; when there is a dividend, an ITM call may be exercised early on the day before the ex-dividend date. This chapter's examples pay no dividends.

The real cost of “selling the upside”

When the stock moves a little up or down, the covered call makes an extra $1.66 a month; when the stock rises 20%, it makes $13.34 less, the equivalent of eight months of premium. A covered call cuts off the right tail of the return distribution, and a stock's long-run return happens to be concentrated in a handful of big up months. Case 2 shows this over a full year's path.

Handling assignment

When the stock rises above the strike, you have three choices.

1. Accept assignment. You sell at 105; add the 1.66 premium and you have effectively sold at 106.66. If that was a price you were happy to sell at anyway, do nothing.
2. Roll up and out. With 5 days left and the stock at 108, the 105 call is worth 3.49, of which only 0.49 is time value. Buy it back and sell a 35-day 110 call for 3.29: you pay a net 0.20 and lift your cap from 105 to 110. Sell a 63-day 110 call for 4.80 instead and you take in a net 1.31, but your shares are locked up for two more months. Rolling isn't free: you are trading more time for a higher cap.
3. Buy back after being called away. If you still want to own the stock, buy it back after assignment; that is the second half of the wheel (Section 8.4). The buyback price is usually higher than the price you sold at, and that difference is the real cost of the covered call.

Without dividends, American-style calls are rarely exercised early, because the holder would throw away the remaining time value. Only when time value is close to zero (deep ITM, near expiry) or the stock goes ex-dividend the next day does the chance of early assignment rise noticeably.

Selling ITM calls to “lower your cost”: keep the books separate

Some traders repeatedly sell ITM calls against a stock they hold at a very low cost, and call it “lowering their cost basis.” Break it down: the stock is at 15 and you sell an 18-day 14 call (IV 80%, hypothetical) for 1.62. Of that, 1.00 is intrinsic value and 0.62 is time value. Your cost on paper really does fall by 1.62, but the 1.00 of intrinsic value is just the money for selling your stock at 14 ahead of time. Your real income is only 0.62.

This option's Delta is 0.69, so after you sell it only about 30% of your directional exposure is left. What it really amounts to is “cut the position by 70% + collect time value,” which suits someone who was planning to trim near 14 anyway. If you want to keep a full position, selling ITM calls quietly sells most of it.

8.3Cash-secured puts

A cash-secured put is like a “limit buy order with cash back,” but in the worst case it does worse than a real limit order.

Structure: sell one put and keep enough cash in the account to buy 100 shares at the strike. With the stock at 100, sell a 30-day 95 put for $133 and set aside $9,500. If the stock is below 95 at expiry, you buy at 95, for an effective cost of 95 − 1.33 = 93.67; otherwise you keep the premium and the cash is released.

“Buy at a price you'd be happy to own it at” sounds reasonable: you wanted to buy at 95 anyway, so why not sell a put and get paid first? Put it side by side with simply placing a limit buy order at 95:

The first two rows are the put seller's “cash back”: as long as the stock is above 95 at expiry, you collect an extra 1.33. The last row is the trap: when the stock gaps to 80, the limit order fills at an opening price near 80 (your order said “95 or lower”), but the put seller has to buy at 95. The bigger the gap, the worse the short put does compared with the limit order. The third row shows that a short put only cares about the moment of expiration: it can't catch any low along the way.

Four common traps

1. “Happy to own it at 95” comes with conditions. You are picturing a normal pullback to 95, but assignment usually comes after bad news, and by then 95 may no longer be a price you like. Before you trade, ask yourself: if it drops to 80 on disastrous earnings, would I still want to buy at 95?
2. The annualized-return illusion. $133 ÷ $9,500 = 1.4% a month, about 17% a year in simple terms. That number assumes nothing goes wrong in any month. It is a premium yield, not a return.
3. “Secured” means actually setting the cash aside. In a margin account, selling a 95 put naked requires only about $1,633 (formula in Section 8.6), so it is easy to sell five times as many by accident, and the position goes from “secured” to “naked.”
4. Selling because the premium is high. A high premium means high IV, which means the market expects a big move. High-IV stocks are more likely to fall through the strike.

There is just one rule: only sell puts on stocks you would be willing to own in full, and set the number of contracts by “the market value of the position after assignment,” not by margin.

8.4The wheel

The wheel does best in flat and gently rising markets. In a sustained decline it gets stuck holding a losing stock and collects less and less premium.

Below is a simulation over three hypothetical 12-month paths. Rules: start with $10,000 in cash; with no shares, sell a 30-day put at about Delta 0.30 (strike rounded to a whole number); with shares, sell a 30-day call at about Delta 0.30, but with the strike no lower than the price you were assigned at, so a sale never locks in a loss. IV is constant at 30%; no interest on cash and no commissions.

The down path exposes the wheel's core flaw. Once you've been assigned, you face two bad choices:

• Insist on a strike no lower than your cost: once the stock has fallen far, the 96 call is worth almost nothing and the wheel stops turning. You become an ordinary stockholder, taking the −35% decline with only $770 of premium as a cushion, and end the year at −23.3%.
• Keep selling Delta 0.30 calls anyway: on the same path you collect more premium and end the year at $8,492. But as soon as the stock bounces off its lows through a strike below your cost—say you are called away at 74—you have sold stock bought at 96 for 74, locking in −22 per share, and you miss the rest of the rebound.

At its core, the wheel is a continuous sale of put risk: you sell puts when you have no shares and sell calls when you do (shares + short call = synthetic short put). Throughout the cycle you are a seller of puts, and a different path doesn't change that. It suits underlyings you would be happy to own for the long run anyway, with moderate volatility and no risk of a trending decline.

Four rules to keep the wheel out of trouble

• Only start the wheel on stocks you would be willing to hold for more than a year, and set aside the full cost of buying one contract's worth of shares.
• After assignment, first ask: if I had no position today, would I buy this? If the answer is no, sell it right away; don't let the covered call make the decision for you.
• In a decline, set the strike of the call you sell at “the price you'd be willing to sell at,” not mechanically by cost or Delta.
• Skip a cycle before earnings, or switch from selling puts to a put spread, so you don't get assigned in a gap.

8.5Credit spreads

A credit spread sells one option and at the same time buys a further OTM option of the same type, limiting the maximum loss from “almost all your capital” to “the width minus the premium.”

Example: stock at 100, sell a 45-day 91 put and buy an 86 put for a net credit of 0.631. The maximum loss is 5 − 0.631 = 4.369, or $437 per contract; you make money if the stock is above 90.37 at expiry.

Choosing the Delta: 0.10, 0.16, 0.30

* Computed at IV 30% with drift equal to the risk-free rate. The probability of touch uses the reflection formula for geometric Brownian motion and is roughly twice the probability of finishing in the money (Table 4-1 in Chapter 4).

• Delta 0.10: the highest win rate, but each win brings in only $36, while a loss can cost up to $464. It rarely needs managing, but once it is hit it is often already close to max loss, with no room to adjust. It is the most sensitive to estimation error: if the true win rate is just a point or two below 89.4%, the expected value turns negative (Section 8.9).
• Delta 0.16: about one standard deviation away, and the most common compromise. It has the highest Theta and less than a 40% chance of being touched.
• Delta 0.30: more credit, a better payoff ratio and the highest expected value per unit of risk. The cost is a 70% chance of being touched while you hold it, which means frequent management, and Gamma risk shows up sooner.

In a model with flat IV, the expected value of all three depends only on the gap between realized volatility and IV, and the closer to the money, the higher the expected value per unit of risk. In reality puts have skew (Chapter 6): the further OTM, the higher the IV. That lets the 0.10 spread collect more than the table shows, but the high IV on deep OTM options is itself the market's price for gaps, and not all of it is premium you get to keep.

Defined risk has surprises too: early assignment

A spread's short leg is an American-style option and can be assigned before expiration. When the short leg of a put spread is deep in the money and its time value is close to zero, exercising early is a rational choice for the holder (Case 3 has the full numbers). After assignment you hold 100 shares per contract, the protective leg is still in place, and the final loss is still limited by the width. The trouble is capital: the shares have to be paid for in full or on margin, and the account may get a margin call the same day.

8.6Naked selling: margin and unlimited risk

The margin on a naked option covers only “normal” moves. In a gap the loss can exceed the margin itself, and the loss on a naked call has no theoretical limit.

Example: stock at 100, sell a 30-day 90 put naked for 0.40. Margin is 0.40 + max(20 − 10, 9) = 10.40, or $1,040 per contract. If the put expires worthless, the return on margin is 3.85%, or 47% a year in simple terms. That number makes naked selling look very tempting.

On a 20% drop, each contract loses $1,038, already wiping out all of the original margin; meanwhile the margin requirement climbs to $2,679. Suppose a $20,000 account sold 10 contracts, using half its capital as margin: the next day equity is down to $9,620, but the margin requirement is $26,790. The broker will force the position closed, and at the worst prices.

Naked calls are even more extreme. Sell a 30-day 110 call for 0.66, with $1,066 of margin. A takeover announcement sends the stock to 140 (assume IV rises to 50%): the call is worth 30.64 and each contract loses $2,999; at 150, the loss is $3,978. The stock has no ceiling, and neither does the loss.

Why institutions can do it and individuals shouldn't

• Diversification: an institution's book of short options is spread across thousands of strikes and underlyings, so a single gap hurts only a small part of it; individuals tend to concentrate in a few familiar stocks.
• Hedging: market makers hedge Delta continuously and buy OTM wings to control the tails; individuals usually can't hedge overnight.
• Margin and risk control: institutions use scenario-based portfolio margin and independent risk management, and know in advance how much they would lose at −20%; most individuals do that math for the first time after the gap.
• Survival: institutions earn the market-making spread plus the volatility premium, a business with a capital cushion behind it; for an individual, one blown-up account means there is no next time.

An individual seller's default choice should be a defined-risk structure (credit spreads, iron condors; see Chapter 9) or a truly cash-secured position. Naked selling is suitable only in small size, on liquid index products, and after running the stress test in Section 8.8.

8.7Three rules of thumb for management

“Take profits at 50%, act at 21 days to expiration, stop out when the loss reaches twice the premium” are rules of thumb. They change the shape of the return distribution; they don't create expected value out of nothing.

These three rules are widely repeated. They come mainly from backtests of US index options and from the trader education published by options brokers, and the backtests mostly cover short puts, strangles and iron condors opened at around 45 days. The specific numbers aren't stable across years or underlyings. Below we first explain the mechanism behind each rule, then test them with a simulation.

50% profit target: the second half isn't worth waiting for

With the stock unchanged, it takes about 21 days to earn half. At that point only 0.315 is left to earn, yet you still carry up to 4.685 of potential loss. At entry the profit-to-loss ratio was 0.631 : 4.369 ≈ 1 : 6.9; after earning half it becomes 0.315 : 4.685 ≈ 1 : 14.9. Holding on is like opening a new trade on terms twice as bad. Close it, put the capital into a new 45-day position, and you get 1 : 6.9 back.

21 days: avoid the last three weeks “going binary”

The same −3% move costs $56 at 45 days and $191 at 2 days. Theta grows in step; this is the Gamma–Theta trade-off from Chapter 4, Section 4.6. In a model with no gaps, the “risk versus income” of the last few days doesn't become unfair. What really changes is two things:

• The position turns binary. With 2 days left and the stock at 95, the spread's Delta is only 0.025; at 91, Delta becomes 0.486. A 4% move in the stock takes the position from “almost no risk” to “close to full exposure,” too fast for you to react.
• A gap doesn't let you collect Theta day by day. Theta comes in one day at a time; a gap's loss arrives all at once. The closer to expiration, the bigger the share of the premium a single gap eats.

What the 21-day rule means: get out before Gamma climbs steeply, and leave the last three weeks of “collect Theta and bet nothing happens” to someone else. By then there isn't much premium left anyway (only 0.245 in Table 8-8, while the maximum loss is still 4.76).

2× stop: pin each trade's loss to a known number

Set the stop at “loss = 2 × premium,” that is, close when the spread's value rises to 3 × 0.631 = 1.89. The most you lose on a trade is then about $126 instead of $437. Combined with the 50% profit target, a win makes 0.315 and a loss costs 1.262, so the breakeven win rate is 1.262 ÷ (1.262 + 0.315) = 80%, regardless of the size of the premium.

The rule comes from naked strangles, which have no maximum loss, so you have to draw a line yourself. On a spread, it has to be converted for the structure. The 0.30 96/91 spread collects 1.321; a 2× stop corresponds to a loss of 2.64, while the maximum loss is only 3.68 to begin with. The stop saves little, yet it is easily knocked out by back-and-forth chop. Also, an overnight gap jumps right over a stop order, and the actual fill can be far worse than the stop level.

Testing the three rules with a simulation

Read this table on three levels.

1. Without a volatility premium, rules can't save you. At 30% realized volatility, the four rules average −$1.3, −$4.9, −$1.2 and −$2.2 per trade, all within random error (standard error about $2–5). Management rules can't turn a zero-expectancy trade into a positive one.
2. With a premium and no gaps, holding to expiry makes the most per trade. The rules cut the expected value per trade from $20 to $5–7, and in exchange the holding period drops from 45 days to 14 and the worst 5% improves from −$368 to −$141. Per day held, A and C are about the same.
3. Only with gaps do the rules show their value. B and C earn more than 60% more per day held ($0.71 and $0.61) than A ($0.37), with much smaller tails. This is exactly the world the rules were designed for: real markets have gaps; Black-Scholes doesn't.

8.8Position size: size by maximum loss, run a −20% gap test

A seller's position size is set by “how much could I lose in the worst case,” not by how much premium you collect.

The same $50,000 account, the same $100 stock, three ways to sell puts; the next day the stock gaps −20% and IV rises to 45%:

The premium the three approaches collect differs by less than a factor of two ($560 to $961), but their gap losses differ twelvefold. After the gap, the naked row's margin requirement is $64,285; the account can no longer support it, and the broker will close the position for you.

A workable set of sizing rules

1. Per-trade cap: for defined-risk positions, the maximum loss is no more than 2%–5% of the account. For positions without defined risk (naked selling, cash-secured puts), use “the loss in a −20% gap” in place of the maximum loss.
2. Portfolio stress test: run all your short option positions through one scenario (every underlying −20% at once, IV up to 45% across the board), and keep the combined loss within 15%–20% of the account. Underlyings in the same sector, or ones that are all high-Beta, count as a single position in a gap.
3. Work back to the number of contracts: allowed loss ÷ loss per contract under stress. With a 10% budget ($5,000), the cash-secured 95 put allows at most 3 contracts (5,000 ÷ 1,384 = 3.6), and the naked 90 put at most 4 (5,000 ÷ 1,038 = 4.8).
4. Stress-test the margin too: you must be able to meet the margin requirement under the stress scenario (not just today's), or you will be forced out at the worst possible moment.

These percentages are common starting points, not theoretical optimums. The principle: after the worst day has passed, you still have enough money and nerve to keep trading. −20% is the usual scenario for single stocks; for indexes you can use −10%; for a stock held through earnings, use its largest historical earnings-day move.

8.9A “90% win rate” can mean negative expectancy

A win rate on its own tells you nothing. The only thing that decides whether a strategy makes money over the long run is its expectancy.

A strategy wins 90% of the time, makes $50 on average when it wins and loses $500 on average when it loses: E = 0.9 × 50 − 0.1 × 500 = −$5. It needs a win rate of 500 ÷ 550 = 90.9% just to break even.

Go back to the 0.10 spread from Section 8.5. At market prices, its probability of profit at expiry is 89.4%; it makes $35.7 on average when it wins and loses $299.7 on average when it loses, so its breakeven win rate is 299.7 ÷ (35.7 + 299.7) = 89.4%, exactly equal to the win rate itself. That is no coincidence: under fair pricing every option strategy has an expected value of zero, and “win rate” and “payoff ratio” are just two ways of slicing the same zero.

The edge is thin. If the true win rate is 88%: 0.88 × 35.7 − 0.12 × 299.7 = −$4.6. If commissions plus slippage add up to $3 per round trip (an assumption), the breakeven win rate rises to (299.7 + 3) ÷ (35.7 + 299.7) = 90.2%. One or two percentage points of win rate decide whether a high-win-rate strategy is positive or negative.

Can you trust your win-rate estimate?

• Your sample has to cover different market conditions: a win rate measured only in calm years has never seen a gap.
• Pull out your single biggest loss and look at it on its own; it is often several times the average loss. Recompute the expectancy with it.
• Compare it with the probability implied by Delta. If your actual win rate stays clearly above what the market implies, the most likely explanation is that your sample hasn't hit that gap yet.

CasesThree cases

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