Risk management for options

OpeningOnly $100 per contract

Your account holds $100,000. You pick ten stocks, all trading around $100, and on each one you sell a 30-day put with a 90 strike (IV 40%). Each brings in $99.8, $998 for all ten, less than 1% of the account. It looks as if you are risking only 1%.

The premium is the most you can make, and it says almost nothing about how much you can lose. The stress loss is 12.6 times the premium; even with IV unchanged, a plain 20% drop in the stocks costs $9,517. Ten stocks look diversified, but on the day the market falls, they mostly fall together.

This chapter does three things: it measures position size the right way; it gives buyers and sellers each a set of sizing rules; and it uses stress tests to turn those rules into a weekly routine. At the end you will have your own position rule card.

13.1Three ways to measure a position

Measure an options position with three rulers: notional exposure, max loss and Greek risk. Premium is a fit measure only for buyers.

• Notional exposure: shares covered by the contracts × stock price. It tells you how much stock you could have to take on or owe in the worst case, and it is the base for assignment and margin.
• Max loss: the worst outcome at expiry. Spreads and iron condors have a hard cap; a naked short put is capped at “strike − premium” (the stock goes to zero); a naked short call has no cap.
• Greek risk: Delta dollars (Δ × 100 × stock price) tell you how much stock the position is equivalent to; Vega tells you how much you make or lose for each point of IV. Put them through a realistic shock (a price gap plus an IV spike) and you get the stress loss.

The stress-loss column assumes “stock instantly −20%, IV doubles.” How to read the table:

• Buyers: the premium is the max loss, so measuring by premium is right. Under the same shock the long call loses only $289, less than the premium: the doubling of IV wins part of it back.
• Sellers: the premium is the smallest number on the three rulers. The short 90 put collects $100; its stress loss is 12.6 times that, and its max loss 89 times.
• Spreads: the $435 max loss is the position’s size. With 30 days left, one shock doesn’t reach the cap ($278), but the closer to expiry, the closer it gets.
• Strangles: Delta dollars are only −$706, which looks neutral, but its Vega is the largest in the table (−$15.6), and a 20% move up loses $956 as well. A neutral position’s risk lives in Vega and in gaps.

13.2Rules for buyers

A buyer’s worst enemy is a losing streak. Keep each trade small enough that even the worst run of losses is a drawdown you can recover from.

Size per trade: the Kelly ceiling

Let the win rate be p; a win makes b times the premium on average, and a loss costs the whole premium. The bet size that compounds fastest over the long run is:

The Kelly fraction is a ceiling, not a target. It assumes you know your win rate and payoff exactly, and a buyer’s win-rate estimate is often off by several percentage points. In practice you take half of it or less, which is why the common rule is premium per trade no more than 1%–2% of the account. If you set a −50% stop-loss on every trade, you could count the risk per trade as half the premium; but IV crush and gaps often make stops fail, so to be safe, count the full premium.

How long losing streaks run

How long a losing streak will a buyer with a 35% win rate run into over 100 trades? It can be computed exactly:

How many trades at once

2% per trade only works if the trades are uncorrelated. Five calls on tech stocks get knocked down by the same macro headline on the same day; in effect they are one 10% bet. So buyers need two aggregate rules as well: no more than 5 trades open at once, and total premium no more than 10% of the account; positions on the same theme (same sector, same direction, same event) count together and are capped at 6% combined.

13.3Rules for sellers

Size a short-option position by “how much can this lose”: max loss for defined risk, the stress test for undefined risk, plus one cap on the total and one on concentration.

Defined risk: size by max loss

Spreads and iron condors have a known max loss, so use it directly to set the number of contracts: max loss per trade no more than 3% of the account (1%–2% when you are new to selling). The 90/85 put spread in Table 13-1 has a max loss of $435 per spread, so a $100,000 account can open 3,000 ÷ 435 = 6.9; round down to 6, for a max loss of $2,610.

Add one aggregate rule: defined-risk positions in the same direction may lose no more than 20% in combined max loss. The reason is simple: when the market drops hard, all your bullish put spreads hit their caps together, and “each one’s max loss” is realized on the same day.

Undefined risk: size by stress test

The max loss on naked puts and strangles is too large to be a useful guide, so use stress loss instead: stress loss per trade (−20%, IV doubles) no more than 5% of the account. The short 90 put has a stress loss of $1,254 per contract, so the most you can sell is 5,000 ÷ 1,254 = 4.0; 3 contracts is safer.

Same account, same contract, three approaches, three completely different numbers:

• By premium (“it’s only $100 each”): no limit
• By cash secured: 100,000 ÷ 9,000 = 11 contracts
• By 5% stress loss: 3 to 4 contracts

Total exposure and concentration

• Total stress loss no more than 20% of the account. A 20% drawdown needs a 25% gain to recover; a 50% drawdown needs a double. 20% is a drawdown you can still trade through normally, without your judgment getting bent out of shape.
• Total notional exposure on short puts (strike × 100 × contracts) no more than 1–1.5 times the account. That is how much stock you may be forced to take on in a market-wide decline.
• No single underlying above 25% of total stress loss, no single sector above 40%. Concentration caps guard against single-stock gaps: one earnings report or one regulatory headline is enough.

Why −20%

For a broad index, −20% is roughly the worst single day in modern history: on October 19, 1987, the S&P 500 fell about 20% in one day. Using it as a weekly stress scenario is conservative enough. For single stocks, a 20%–30% gap after earnings is not rare, so −20% is only a starting point; binary events such as biotech trial results or a failed merger should be tested at −50% or worse. For leveraged ETFs, multiply in the leverage: a 3× long ETF falls about 30% when the index falls 10%. The same goes for IV doubling: for an index that normally trades at 15% IV, doubling in a sharp selloff is no exaggeration; for a wild stock already at 80%, doubling is less realistic, and the price gap is what matters.

13.4Stress tests: three scenarios, once a week

A stress test is only worth something if you run it on a fixed schedule. Same time every week, same scenarios; if a limit is breached, you cut, whatever you feel that day.

1. Export positions: after the close every Friday, list all option and stock positions.
2. Run three scenarios: A, all underlyings −20% at once; B, prices unchanged, IV doubles; C, both together. If you have short calls, add a +10% or +15% scenario.
3. Check the limits: stress loss per trade ≤ 5%, total ≤ 20%, single underlying ≤ 25%.
4. Cut what’s over: cut the biggest contributor first. Don’t open a new opposing position to “offset” it; a new position has risks of its own.
5. Write it down: record the numbers and what you did in your trading journal (Chapter 14), and after a month check whether the rules need adjusting.

Line by line: every trade is within 5%, and the 15.8% total is within 20%. But the SPY spreads contribute 31% of total stress loss, above the 25% concentration cap. After closing 1 spread, SPY’s share drops to 22.7% and total stress loss becomes $14,232. The other thing to watch is C: it is the only position that loses money on a rally, $1,393 at +15%, so this account also needs a weekly up-move scenario.

Three common mistakes

• Extrapolating linearly from Delta. The ten 90 puts from the opening have a combined Delta of about +157.5 shares. A Delta estimate says −20% loses only 157.5 × 20 = $3,150; adding the Gamma term gives $7,350; full repricing gives $9,517. The Delta estimate misses two-thirds of the loss. A seller’s stress test has to reprice the options; the approximations can only be trusted for small moves (Chapter 4).
• Testing positions one at a time. Every trade being within 5% doesn’t mean the total is within 20%; positions that get run over on the same day have to be counted together.
• Forgetting IV and liquidity. Testing price without IV misses about a quarter of the loss: the same ten puts lose $9,517 at −20%, and $12,541 once IV doubles as well. And when you trade, you pay the bid–ask spread on top (Section 13.7).

13.5The illusion of diversification

Short puts on ten stocks are mostly one bet: that the market won’t fall. You diversified tickers, not risk.

Every stock’s move can be split into two parts: the part that follows the market (β × the market’s move) and its own part. A short put has positive Delta, so ten of them add up to a long market position. The ten puts in the opening each have a Delta of −0.1575, so together they are like holding about 157.5 shares, or $15,750 of stock; if the stocks’ average β is 1.2, that is equivalent to $18,900 long SPY (beta weighting, Chapter 12).

Normally, stocks go their own way and correlation is low: now and then one or two of the ten puts get run over, the rest expire worthless, and the portfolio is smooth. On a day of sharp selling, everyone is selling, correlations between stocks rush toward 1, and all ten get run over together. The simple one-factor model below shows this: each stock’s return = √ρ × common shock + √(1 − ρ) × own shock, with true volatility assumed at 35% (below the 40% IV, so sellers make money on average), 4,000 scenarios, and the same random numbers for every correlation.

Three findings:

• The average return barely changes. Each stock’s own distribution is the same, so the expectancy is the same. A backtest that looks only at average return can’t see the danger of correlation.
• Higher correlation actually means fewer losing outcomes. At ρ = 0.9 only 14.7% of scenarios lose money, fewer than at ρ = 0. That is exactly why these accounts feel reassuring: there are more quiet months.
• But when they lose, they lose together. The worst 1% widens from −$2,038 to −$9,706, nearly five times as much. Real markets have fatter tails than the normal distribution, and correlations rise in selloffs and fall back in rallies, so if anything this model is optimistic.

13.6The margin spiral

When sellers exit at the worst moment, it is often because they ran out of margin first, not because their view changed. A drop and an IV spike do two things at once: they shrink your equity and raise the margin your broker requires.

Walking through the numbers

Under common Reg T rules, the margin on each naked short put is the option’s market value plus the greater of “20% of the stock price minus the out-of-the-money amount” and “10% of the strike,” times 100. Scale the opening account up to 3 contracts per stock (30 short 90 puts in all):

The stocks fall 20%, the account loses 36%, and the margin requirement grows to 2.6 times its starting level. By the third row, even if you are sure the stocks will come back, your broker will demand $23,625 more or close you out, and it closes you out at prices set by 80% IV.

If the same account follows the Section 13.3 rule “total stress loss ≤ 20%,” at $1,254 of stress loss per contract it can sell at most 15. Margin at the open is $16,497 (16.5% of equity); after the same shock it loses $18,158 and margin is $43,655, only 53.3% of equity, so the account gets through. The real job of sizing rules is to leave you choices on bad days. That is also where the rule card’s “margin used no more than 35% of equity” comes from.

Two real spirals

February 2018. The market had been unusually calm for more than a year, and shorting volatility had become “steady income” in many people’s eyes. On February 5, the VIX more than doubled in a single day, its largest one-day percentage gain on record, and the Dow posted what was then its largest one-day point drop ever. Exchange-traded products that were short VIX futures had to buy futures around the close to rebalance, and that buying itself pushed futures prices higher. One of these products lost most of its net asset value overnight and was then terminated early by its issuer. Accounts that were short index puts faced falling prices, soaring IV and higher margin all at once.

March 2020. Under the shock of the pandemic, US stocks plunged within a few weeks; market-wide circuit breakers were triggered several times in March, and the VIX set a record closing high, above its peak in the 2008 financial crisis. Even the US Treasury market briefly ran into liquidity strains. Many brokers raised margin requirements, and option bid–ask spreads widened sharply. Many sellers turned out to be right in the end, as the market won back its losses over the following months, but they didn’t last until that day.

13.7Liquidity, early assignment and pin risk

Stress tests use mid prices, but in reality you fill at the far side of the quote; models settle at expiry, but in reality American-style options can be exercised at any time. These three risks don’t show up in the Greeks, yet they often decide the final loss.

Liquidity: spreads are widest on bad days

The option value shown in your account is usually the mid price. On a normal day a $1.00 put might be quoted $0.95 × $1.05; in a selloff the same contract rises to $13.10 and the quote might become $12.40 × $13.80 (both quotes are hypothetical). Buying back 30 contracts at the ask instead of the mid costs extra: 0.05 × 100 × 30 = $150 on a normal day, 0.70 × 100 × 30 = $2,100 in a selloff.

• Trade only contracts whose bid–ask spread is no more than 10% of the premium; on cheap, deep OTM options the spread is often half the premium
• Don’t use stop-market orders on options: in a fast market they fill at absurd prices. Use limit orders or alerts triggered by the underlying’s price instead
• Multiply stress-test results by 1.1–1.2 to leave room for slippage

Early assignment: deep ITM short legs

The holder of an American-style option can exercise at any time. When a put is deep in the money with little time value left, the holder does better exercising early and earning interest on the strike proceeds than holding on. In the model, for a 95 put with 14 days left and IV 38%, the European price drops below intrinsic value (negative time value) once the stock is below $84.05; at $88 the time value is still $0.41, and at $85 only $0.06 is left.

With the 95/90 put spread from Chapter 12, if the stock falls to 85 the short leg is likely to be assigned early. You receive 1,000 shares worth $95,000. In a Reg T account, stock usually carries 50% initial margin, or $47,500, while the spread’s max loss is only (5 − 1.021) × 1,000 = $3,979. Economically your risk is still capped by the 90 put, but many brokers don’t count that long put as protection when computing margin, so the account may get a margin call.

For short calls, the danger point is just before the ex-dividend date. If a call’s time value is less than the upcoming dividend, the holder will exercise the day before the ex-dividend date to collect the dividend. For a 100-strike call with 10 days left and IV 25%, the time value at stock prices of 102, 103, 104, 105 and 108 is $0.93, $0.67, $0.48, $0.35 and $0.16. With a $0.50 dividend, expect assignment once the stock is above 104.

Pin risk: closing right at the strike

On expiration day the stock closes at $100.10, and you are short 10 of the 100 calls. Whether you get exercised won’t be known until the weekend: holders can still decide after the close, based on after-hours prices. If you are assigned, you start Monday’s open short 1,000 shares; if Monday opens 3% higher, you lose 1,000 × 100.10 × 3% = $3,003. Spreads are no different: if at the close only the short leg is just in the money and the long leg expires worthless, you can be assigned with no protection. The rule is simple: before the close on expiration day, close every short leg within 1% of the current price.

13.8Options position rule card

Write the rules before you lose money. The card below is one of this course’s deliverables: the numbers are suggested starting points. You can tighten them based on your own experience, but loosening them is not recommended. A check means you have written that rule into your own trading plan.

Tighten the numbers in a few situations. If your account is under $25,000 and can hold only three to five positions, the concentration rules are nearly impossible to meet: trade only defined-risk structures and cut max loss per trade to 2%. In a portfolio margin account the broker allows more leverage, so lower the cap on margin used accordingly; the total stress-test cap stays the same. In your first three months as a beginner, halve every limit.

Use this card together with the adjustment rules in Chapter 12: before adjusting, ask “if I had no position, would I open this one?”; before opening, run through this card. Only once both checks are passed do you get to your view on direction.

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