A portfolio of sold options often looks steady in calm markets. Time value works in the seller's favour in principle, but price moves and changes in implied volatility can change the value of the positions considerably at any time. The profit and loss of the open positions therefore says little about how much risk the portfolio carries in a strong market move.
Four figures are the starting point: the sold premium against the net liquidation value, the max loss from the payoff profile of the open positions, each trade's contribution to the account margin and the ratio of premium to margin. Together with the hedge budget, the margin reserve and the Greeks they give a more comprehensive picture of portfolio risk.
This guide explains what each of these figures measures, how they relate and where they are easily misread. At the end it describes how Foliograph assembles them from the journal and from Interactive Brokers' TWS.
Why option sellers need different figures
Selling premium often comes with a high win rate. Many positions end with a small gain, single losses can be a multiple of it. As long as no strong move comes, profit and loss therefore show a steady picture that says little about the size of the risks taken.
For a portfolio of short options, other questions matter than for a stock portfolio:
- How much premium is open? Sold premium against the account value describes the size of the book, not its risk.
- What would be lost in the worst case? Max loss from the payoff profile describes the upper bound per position, if there is one.
- How much collateral is tied up? Margin and the reserve above it determine how much room the account has for further moves.
- How much premium value is still open? Remaining premium against margin shows how much potential premium profit, if the options expire worthless, is still set against the collateral tied up today.
None of these figures replaces the others. A put sold far out of the money brings in little premium and still has a max loss close to the full strike value. An uncovered short call can tie up little margin although its loss has no upper bound.
Sold premium against the account value
Sold premium is the sum of the net opening premiums of all open short premium strategies, counted on the contracts still open. If nine of ten sold puts have already been bought back, only the premium of the last one counts. Against the net liquidation value it describes how large the premium book is compared with the account. A share of 3% means the open premiums equal three percent of the account value. The figure measures the size of the book, not its risk: 3% from far out-of-the-money short puts, from uncovered (naked) short calls or from spreads with defined risk are not the same. How much risk stands behind the premium can only be judged together with max loss, margin, time to expiration and the structure of the positions.
How strongly an option reacts to changes in implied volatility depends, among other things, on its moneyness, that is how far in or out of the money it is, and on time to expiration and the volatility level. For the same expiration, vega per contract is typically highest near the money. Relative to the premium collected, however, options far out of the money can react much more sensitively. The simplified example uses an underlying at 100, 30 days to expiration and no interest or dividends. The strikes are at about 93.26 and 99.01, so the two puts have a delta of -0.05 and -0.40 respectively at 15% IV. The table shows what happens with the price of the underlying unchanged when implied volatility doubles from 15% to 30%:
| Short put | Premium at 15% IV | Value at 30% IV | Factor | |Delta| at 30% IV | Loss normalized to 1.26 premium |
|---|---|---|---|---|---|
| Delta -0.05 | 0.09 | 0.98 | x11 | 0.20 | 12.20 |
| Delta -0.40 | 1.26 | 2.94 | x2.3 | 0.44 | 1.68 |
To collect, on paper, the same premium of 1.26, this example takes 13.8 puts with delta -0.05 instead of one put with delta -0.40, about 14 contracts when traded. The last column uses these 13.8 contracts and the unrounded model values, the option prices shown are rounded. This clearly raises the aggregate vega and the nominal max loss of the overall position. At the same time, when volatility rises the absolute delta of the puts far out of the money grows, so they become more sensitive to direction. In sell-offs the volatility skew also often shifts, so the implied volatility of puts far out of the money can rise more than that of options near the money. The example is based on the Black-Scholes model and assumes the same rise in implied volatility for both options.
The breakdown often says more than the total. Options on single stocks, indices, futures and ETFs behave differently. Many index options, such as those on SPX and NDX, are cash-settled. When a short put on a stock is assigned, a stock position at the strike results. The purchase amount is strike times number of contracts times contract multiplier and usually a multiple of the premium. An assigned short call requires shares to be delivered. If none are in the account, a short stock position results.
The spread across underlyings matters as well. Ten short puts on ten different stocks are not ten independent bets: in a broad decline many stocks move in the same direction at the same time. A large share of a single underlying or category is therefore information of its own next to the total. Besides the spread across underlyings, the expiration structure matters. Many short options close to expiration at the same time can concentrate the gamma risk of the portfolio strongly. With single stocks, events such as quarterly results come on top. They can change price and implied volatility abruptly and hit all positions on the same stock at once. Whether such a date falls before the expiration of a position is therefore part of its risk profile. In earnings season the dates of many companies also fall within a few weeks and one company's results often move stocks of the same industry as well.
From payoff profile to maximum loss
The max loss of a position follows from its payoff profile at expiration. For a short put it lies at an underlying price of zero, for a vertical credit spread with the same number of contracts and a common expiration it equals, in the expiration profile, the strike difference less the net credit. An uncovered short call has no upper bound. In a fully covered call the shares held offset the rising loss on the short call above the strike. The unlimited call risk disappears, the downside price risk of the shares remains.
For a portfolio, the simple sum of these values is not an attainable loss. The worst cases of different positions require different or even opposite moves: a short put loses most at a price of zero, a short call on the same underlying when prices rise. Both cannot happen at once. The sum is therefore an upper bound built from single values, not a scenario. As soon as an uncovered short call is included, the portfolio has no theoretical loss limit either.
Separating by direction says more. Short puts and put spreads lose when prices fall, short calls and call spreads when prices rise. The down tail sums the bounded max-loss values of the positions whose loss side lies in falling prices, the up tail the same for rising prices. These sums are not joint scenarios either but a summary of single positions by direction. The positions reach their max loss at different prices, on different underlyings and at different expirations. With different underlyings, opposite moves can also happen at the same time, such as falling stock prices and a rising VIX. For the overall risk, joint stress scenarios that value all positions under a consistent set of market assumptions are therefore useful, such as falling stock prices with implied volatility rising at the same time.
Max loss is a property of the position, not a forecast. It says nothing about how likely a loss is but describes the loss limit of the payoff profile at the expiration considered. For strategies with several expirations the profile is also only an approximation, because the value of the later options at the first expiration is still open.
How much margin a trade ties up
Margin is the collateral the broker requires for open positions. Under Reg T it follows fixed rules for single positions and recognized option combinations, plus the broker's own requirements. Portfolio margin instead values related positions together in risk-based stress scenarios, so hedges and offsetting positions count for more. Under both regimes margin can change over the life of a position, for example through price moves, changing option values, new positions or offsets within the portfolio. For uncovered short options margin can rise considerably when the underlying moves against the position. For spreads with defined risk the structure of the position sets tighter limits on margin.
How much margin a single trade ties up depends on the other positions. It can be described as a margin contribution: the change in the account's maintenance margin if only this trade were closed. This means the minimum margin required on an ongoing basis for existing positions, not the initial margin that applies when opening new positions. A positive value means margin would be released. The contribution is not an independent margin of the trade. If a long put held separately hedges a short put, closing the short put releases little margin. Closing the long put can even raise the account margin, its margin contribution is then negative. Under Reg T such offsets follow fixed rules and are therefore easier to trace. With few offsets between trades, the sum of the contributions can be close to the account margin. Under portfolio margin, portfolio effects weigh more and the sum can differ more clearly from the account margin.
Premium, remaining premium and margin side by side
With margin per trade, premium can be related to the collateral tied up. Premium/margin at opening describes how much premium was collected per unit of margin. Margin at opening means the margin contribution shortly after opening, also measured as maintenance margin. 500 premium on 2'500 margin is 20%. This is not a return in the classic sense, since margin is not invested capital but a changing collateral requirement. The figure describes how much of the margin was used at opening, not the quality or the risk of the trade. An uncovered short put can show a high value while carrying a large loss risk. If the margin contribution is zero or negative, as with a hedge, no meaningful ratio can be formed.
Over the life of a position both premium and margin change. Remaining premium is the current net buyback value of the strategy still open, the amount it would take to close its remaining option legs. For a credit spread with a short put at 5.00 and a long put at 3.00 that is 2.00 (5.00 - 3.00), not the 5.00 of the short put alone. The premium itself was collected in full at opening. How much of it has been earned at today's market value follows approximately from opening premium minus remaining premium: with 500 premium and a buyback value of 100, the trade is 400 in profit before fees, that is 80% of the premium. This profit is only realized when the trade is closed or the options expire. If the buyback value rises to 800 instead, the trade is 300 in the red. The remaining premium only adds fully to the profit if all options of the position expire worthless. Remaining premium against margin answers a different question, namely how much premium is still set against the margin tied up today. With margin unchanged at 2'500 that is 4%, if margin has risen to 5'000 only 2%. The values at opening and today can therefore only be compared directly when margin is the same.
To compare positions with different time to expiration, the remaining premium can be annualized. 100 left with 3 days to go gives a different annual rate than 100 left with 40 days. The annualized figure is a theoretical rate under two assumptions: the options expire worthless and margin stays unchanged until expiration. For short options both assumptions are strong. With only a few days left, annualizing quickly produces very high values. The figure is a mathematical conversion, neither a return on the account nor an expected annual return or a forecast.
Hedges in the same picture
Many option sellers hold hedges next to their short positions, such as bought puts on a stock index or calls on volatility products. Their cost can be related to the open short premium as a hedge budget. This means the premium paid for the hedges still open, not their current market value. A value of 20% means the open hedges cost 20% of the premium collected on the open short positions. Since short positions and hedges may have been opened at different times, the hedge budget only describes the positions open today. It does not say how much hedging cost over a month or a year and it is not a return.
The hedge budget describes cost, not protection. Whether a hedge absorbs the max loss of the short positions in a stress phase depends on underlying, strike, expiration and size. Hedges are usually trades of their own. They can lower the margin of the whole account, but whether and how much of that shows at the individual trade depends on which positions the broker offsets them against.
What these figures do not show
Premium, max loss and margin describe size, loss limits and capital tied up. How sensitively the portfolio reacts to the next move they do not show. That is what the Greeks show. They describe how much the value of an option changes when price or volatility change or time passes.
Delta shows how much the option value changes on a small price change of the underlying. Gamma shows how much delta itself changes along the way. Vega describes the reaction to changes in implied volatility and theta the effect of time passing. Absolute vega is typically largest near the money. Relative to the option premium, however, a rise in volatility can weigh much more for options far out of the money. With short time to expiration, high gamma can make delta change strongly even on small price moves.
For the whole account the reserve above the margin matters as well, at Interactive Brokers the excess liquidity. The cushion relates the excess liquidity to the net liquidation value. The smaller the cushion, the less reserve remains against rising margin requirements. In strong market moves the net liquidation value can fall while margin requirements rise at the same time. A cushion that looks comfortable today can then deteriorate quickly.
Vega and theta in relation
For a short option, vega and theta work against each other. If implied volatility rises, the option value rises and the position loses value. As time passes, the option value falls again. This raises the question of how many days of time decay roughly offset the price effect of one more IV point. In the simplified Black-Scholes model without interest or dividends, small changes give an approximation that is the same for every strike: days per IV point = 2 x days to expiration / implied volatility in percent.
| Time to expiration | IV 15% | IV 20% | IV 30% |
|---|---|---|---|
| 30 days | 4 | 3 | 2 |
| 45 days | 6 | 4.5 | 3 |
| 60 days | 8 | 6 | 4 |
With 30 days to expiration and 15% IV, one more IV point therefore equals roughly four days of theta, provided the price does not change. Relative to the premium, the same IV point weighs much more for puts far out of the money. For the delta -0.05 put from the example above it equals about a third of the premium, for the delta -0.40 put about 9%. The rule of thumb only describes the local effect of a single IV point. For larger changes it cannot be scaled up linearly, since vega and theta change themselves. If, in the same simplified model, the implied volatility of a put with 30 days to expiration rises from 15% to 20% and stays there, the put roughly returns to its original model value after about 13 days with the price unchanged. Linear scaling with 4 days per point would give 20 days. In reality price, volatility skew and interest rates, among other things, change at the same time. The example is therefore not a forecast for an actual trade.
Limits of the figures
All of these figures are snapshots. Max loss describes the payoff profile at expiration, not today's market value. Margin can change with every market move and a measurement through a trading platform captures it only at certain times. The net liquidation value comes from the last account snapshot. The figures therefore show only partially how the portfolio develops during a fast move.
Price gaps, rising implied volatility, early assignments, upcoming dividend dates and higher margin requirements can raise the short-term risk or change the position structure before the payoff profile at expiration is reached. Liquidity comes on top: in stress phases the bid-ask spreads of options often widen considerably, especially for illiquid options or options far out of the money. The buyback price actually achievable can then lie well above the displayed mid or mark price that remaining premium and profit and loss are based on. With several currencies, all ratios also depend on the exchange rate used to convert premium and margin into a common base currency.
The figures describe the state of the portfolio. How someone responds to it depends on their own strategy, time horizon and risk capacity.
Frequently asked questions
Is the margin contribution a margin of its own for the trade?
No. An account's margin is more than the sum of single positions. Positions on the same underlying offset each other, under portfolio margin even in joint stress scenarios. Per trade, Foliograph uses a what-if order to determine how much margin closing the whole trade would release, for a spread all legs together. That is its contribution in today's portfolio, not an independent margin.
Does the sum of the margin contributions match the account margin?
Under Reg T the sum of the margin contributions can come very close to the account margin. In internal tests on three accounts it was within about 0.1% in Foliograph. That is merely an observation from these tests. Differences arise when positions from different trades offset each other, such as a short put and a long put held separately. Under portfolio margin positions offset more, so the sum can differ considerably.
What does unlimited mean for max loss?
For an uncovered short call the loss grows with the underlying's price without an upper bound. There is no number for the maximum loss then, not for the portfolio as a whole either. In max loss (limited) Foliograph counts only the bounded values, including the put side of such positions, shows the number of unlimited positions next to it and marks the figure red. If the call is covered by stock, the position is listed separately with the covered positions.
Do I have to switch off the read-only API in TWS?
Only for margin per trade. TWS does not evaluate what-if orders while Read-Only API is switched on. Over this connection Foliograph sends only what-if requests, which TWS calculates and never executes. With the option off, however, TWS would accept orders from API programs on this computer. If you prefer not to, leave the measurement off, all other features keep working.
Why does a debit trade have no premium/margin?
Premium/margin relates collected premium to margin. In a debit trade, such as a bought put, a bought call or a debit spread, premium was paid instead of collected. For a bought put or call the maximum loss equals the premium paid, for a vertical debit spread with the same number of contracts and a common expiration the net debit paid. No further margin therefore has to be posted for this loss risk. Foliograph therefore shows the ratios only for net-credit trades. A margin contribution reported by TWS can still appear in the Margin column regardless.
How often does Foliograph measure margin?
Four times a day while TWS is running. One value per trade and day is kept, which builds the history on the trade page. A greyed-out value in the portfolio is from an earlier day, for example when TWS was closed in between. Under Settings > Connections, Measure now starts a measurement right away.
Are my positions uploaded to the cloud?
No. Foliograph is a desktop application, trades, account snapshots and margin measurements stay in a local database on your computer. The data comes straight from Interactive Brokers, via TWS, a Flex Query or a CSV account statement.
Terms on this page
- Assignment (Option assignment)
- Base currency (Reporting currency)
- Contract Multiplier (Multiplier)
- DTE (Days to Expiry)
- Excess Liquidity and Cushion (Margin reserve, margin cushion)
- Hedge Budget (Hedge cost ratio, hedge budget share)
- Implied Volatility (IV)
- Margin (Initial and maintenance margin, margin requirement, collateral)
- Max Loss (Maximum loss, max loss (limited), option max loss)
- Net Liquidation Value (NLV, account value, net liquidation)
- Premium/Margin (Return on margin, remaining/margin p.a., remaining yield)
- Sold Premium (Short premium, sold option premiums)
- VIX (CBOE Volatility Index)
- Win rate (Hit rate, percent profitable)
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All market and analytical information is provided for educational and analytical purposes only and does not constitute investment advice or a trading recommendation.