Exchange-Traded Derivatives in Practice: Margins, Expiry, Tax and Portfolio Uses

Ring: Finance-Plus (Derivatives branch) · Node DV1.05 · ~16 focused hours · Mastery gate ≥ 85%

A trader in Pune pays ₹34,200 for two lots of a ₹1,400 call on an Indian large-cap. Eight sessions later his broker blocks ₹3,54,768 of his account and tells him that on Friday he owes ₹16,80,000 in cash. The trade worked. The option finished ₹78.20 a share in the money, and he is being asked for forty-nine times the money he risked, because in India that call does not settle in cash. It settles in shares.

Every price in the derivatives branch so far has been produced by an argument: cost of carry, risk-neutral valuation, put-call parity. None of those arguments knows what a lot size is. None of them knows that an exchange collects margin four times a day, or that a securities transaction tax is charged on the strike value rather than on the premium. None of them knows that the last thirty minutes of an expiry session decide the settlement price, or that a loss you made on a Nifty option can be set against your rental income while a loss you made on an intraday equity trade cannot.

Those are the facts that decide whether a correctly priced position survives contact with the market.

This is the layer between a model and a filled order, and it is where retail money and, more often than the industry admits, institutional money actually goes. The arithmetic is not hard. Almost none of it requires anything beyond multiplication. What it requires instead is the habit of reading a contract-specification page before sizing a position, and of treating every number on that page as perishable, because the exchange changes it by circular and the tax authority changes it by Finance Act.

The other half of the node is the reason a professional bothers with any of this. Exchange-traded derivatives let an allocator move a portfolio's beta, its duration and its currency exposure without touching a single underlying holding, in an afternoon, for a fraction of the cost of trading the securities. A $250 million fund that wants ten percentage points less equity and ten more of bonds can sell 89 index futures, buy 173 bond futures and be done for about $1,179. The physical switch costs roughly $30,000 in spread and commission. The overlay is not free. It leaves rounding and basis behind, and the residual has to be measured. It is still the cheapest large decision available to most portfolios.

Two markets run through the whole node, and they disagree with each other in instructive ways. India settles single-stock derivatives physically, taxes them as business income, ramps delivery margin across expiry week, and prices index options European and cash-settled. The United States settles equity options into shares with American exercise, cash-settles broad index options, and has no securities transaction tax at all. It also taxes some of those contracts under a rule that splits every gain sixty-forty regardless of holding period. An analyst who learns one market and assumes the other will be wrong in both.

By the end you will have read a contract specification the way a professional reads it, computed a margin requirement from a scenario array rather than a rule of thumb, and priced the cost of carrying a winning option into expiry. You will also have sized three portfolio overlays, named every rupee and dollar of residual each one leaves, and written the operating note that says in advance which position must be closed regardless of view.

Learning objectives

By the end you can:

1. Read a contract specification as a primary source and extract the five parameters that must be known before sizing anything: multiplier or lot size, tick and tick value, expiry date and time, settlement style and exercise style, with a verify flag on every perishable figure.
2. State what compulsory physical settlement of Indian single-stock derivatives does to an in-the-money position, compute the delivery obligation at full contract value, and tabulate the staged delivery-margin ramp across expiry week in rupees.
3. Build a margin requirement from its parts: a SPAN-style scanned risk over a sixteen-scenario array, the exposure margin, the net option value credit, and the expiry-day add-on, then convert the total into a gross-notional and a delta-equivalent leverage figure and say which one is honest.
4. Compute the total statutory and exchange cost of an Indian derivatives round trip, including the securities transaction tax asymmetry between selling an option and letting it settle, and state the break-even move that cost implies.
5. Classify exchange-traded derivative income under the Section 43(5)(d) carve-out, compute turnover on the current guidance basis, test it against the tax-audit threshold, and apply the set-off and eight-year carry-forward rules correctly against speculative and non-speculative losses.
6. Contrast the US regime: 100-share American equity options, the early-exercise decision around a dividend computed from the put price and the interest saved, cash-settled index options, assignment mechanics, and the 60/40 treatment of Section 1256 contracts.
7. Adjust a portfolio's equity beta to a stated target with index futures, equitise a cash balance, and decompose the tracking difference into entry richness, contract rounding and unrebalanced overlay drift so that every dollar of residual has a name.
8. Move duration with bond futures and run a two-legged asset-allocation switch, comparing the overlay's cost and residual against the physical trade it replaces.
9. Set currency hedging as a policy decision rather than a trade: place a mandate on the hedge-ratio spectrum, roll a forward hedge across four quarters, and separate the knowable carry from the unknowable spot move.
10. Explain how a volatility index is built, why a constant-maturity long-volatility product decays in a static contango curve, compute that decay over one roll cycle, and say what a variance swap does differently.

The gate rewards the by-hand versions of all ten. A margin figure, a turnover figure and a contract count are exactly the outputs that a model produces fluently and gets wrong silently, so the productivity payoff at the end of this node is conditional on being able to reproduce each of them on paper first.

Prerequisites & connections

Builds on. The derivatives branch supplies the pricing. Cost of carry, futures mark-to-market and the initial-versus-maintenance margin sequence come from the forwards and futures node. Option pricing, parity and the Greeks come from the options node. Payoff construction, delta and gamma hedging, the beta-adjustment formula and the basis-point-value hedge come from the option-strategies node, which also states the minimum-variance hedge ratio used here without re-deriving it. DV1.04: Swaptions, the Black Model and Non-Rate Swaps is the immediate predecessor and owns the exchange-against-over-the-counter comparison, the central counterparty and novation, the clearing-member default waterfall, and the taxonomy that separates forward commitments from contingent claims. Read it first if you have not: this node assumes you already know what a clearing house is and starts from what it charges you. From the analyst core, market microstructure, the order book and settlement cycles come from the capital-markets node, and the Indian and US transaction-cost stacks come from the toolkit node.

Feeds forward. The allocation branch consumes these overlays directly, because a policy portfolio that rebalances with futures needs the contract counts and the residuals computed here. The alternatives branch reuses the roll-yield machinery in the volatility section, which is the same arithmetic as a commodity index's negative roll return under a different name. The personal-finance node owns capital-gains tax on securities for an individual investor and receives the business-income treatment from here as its complement.

Anywhere a fund factsheet says "the fund may use exchange-traded derivatives for efficient portfolio management", the sentence you are being asked to price is one of the three overlays below.

Several neighbouring nodes own material that borders this one, and the boundaries are deliberate. Option strategies, payoff diagrams, delta and gamma hedging and the transaction-level currency hedge belong to the option-strategies node; what this node adds is the policy layer above a transaction hedge and the settlement mechanics below it. Futures pricing, covered interest parity and the margin-call sequence belong to the forwards and futures node. Clearing, novation and the default waterfall belong to DV1.04, whose swaption and currency-swap material is a different instrument set rather than a substitute for the exchange-traded contracts here. Clearing and settlement for cash equities belong to the capital-markets node, the equity transaction-cost stack to the toolkit node, and personal capital-gains tax to the personal-finance node. Where those own a concept, this node cites the number and moves on.

Have three things in hand before starting: a calculator or spreadsheet, an exchange contract-specification page open in a browser, and the willingness to write down the date on which you read it.

Core teaching content

4.9 The United States, where almost every convention is different

Six differences matter, and an analyst who carries them can read either market's contract page without re-learning it.

Standard US equity options cover 100 shares, and there is no lot size. Every listed name uses the same multiplier, so contract counts across names are directly comparable in a way Indian stock lots never are.

They are American, exercisable at any time up to expiration. Early exercise of a put can be rational when rates are high enough that the interest on the strike exceeds the remaining option value, and early exercise of a call is rational only just before a dividend goes ex. The condition is exact and computable. Exercising early captures the dividend and forfeits the option's remaining time value, and the time value of a call, by put-call parity, equals the price of the same-strike put plus the interest saved by not paying the strike yet. So exercise just before the ex-date when the dividend exceeds P + K(1 − e^(−rT)). Worked Example 7 computes both sides for a stated case and finds the call worth exercising by $0.322663 a share, or $32.27 a contract.

Broad-based index options are European and cash-settled with a $100 multiplier, which removes the exercise question entirely and also removes the delivery problem. An index option that finishes in the money pays the difference in cash, so no shares move and no auction risk exists. The same index tracked by an exchange-traded fund gives American options on 100 fund shares, which are physically settled and can be assigned early. Two contracts on the same exposure, with opposite settlement mechanics, quoted a few clicks apart on the same screen.

Assignment is random, allocated by the clearing corporation among clearing members and then by each broker's own published method. A short option holder can compute an expected assignment rate from the exercised proportion but must be capitalised for the whole position.

There is no securities transaction tax. The US cost stack on an option is commission plus per-contract exchange and regulatory fees plus the bid-ask spread, and on a liquid contract the spread dominates everything else, which is the opposite composition from India.

And the tax treatment splits by instrument, not by holding period. Regulated futures contracts and broad-based index options are Section 1256 contracts: they are marked to market at year end whether or not the position is closed, and every gain and loss is treated as 60% long-term and 40% short-term regardless of how long it was held. Single-stock options are not 1256 contracts and follow ordinary capital-gains rules, with wash-sale rules applying to them and not to 1256 contracts. Verify flag: the 1256 rules, the 60/40 split and the definition of a broad-based index are statutory and are revised; confirm against the current Internal Revenue Code and the Internal Revenue Service's own instructions before relying on them. The structural point survives any revision: two options on almost the same exposure can carry different tax characters because of what the underlying is, which is a mirror image of India's rule that the character follows where the trade was executed.

Two contracts, one exposure, taxed on different principles.

4.11 Portfolio use II: moving duration, and switching two asset classes at once

Interest-rate exposure is sized in basis-point value, never in notional. The overlay logic is identical to the equity case with BPV where beta was:

N = (BPV_target − BPV_current) / BPV_futures, with BPV_futures = BPV_CTD / CF

The conversion factor appears because a Treasury bond future delivers a basket rather than a single bond, so the contract tracks the cheapest-to-deliver issue scaled by the factor that makes deliverables comparable. Both BPV_CTD and CF are published, both change as the cheapest-to-deliver switches, and the switch is a real risk on a large hedge.

The interesting version is two overlays at once, because that is how tactical allocation is actually done. A $250,000,000 fund that wants ten percentage points less equity and ten more of bonds sells enough index futures to remove β × $25m of market exposure and buys enough bond futures to add MD × $25m × 0.0001 of basis-point value. At a sleeve beta of 1.05 that is 89 index futures short; at a bond duration of 6.20 that is $15,500 of basis-point value, and against a futures basis-point value of $89.79 that is 173 contracts long.

Worked Example 5 runs a scenario in which equities fall 6.00% and yields fall 35 basis points. The overlay earns $2,109,873.95 against $2,117,500.00 for the physical switch, a shortfall of $7,626.05 that is entirely rounding on the two legs. Against that, the physical switch costs about $30,000 in spread and commission while the overlay costs about $1,179, a saving of $28,821 or 11.53 basis points of the amount switched. The overlay wins on cost by roughly four times the residual it leaves, which is the general shape of the trade-off and the reason overlays exist.

Two legs, one afternoon, and the portfolio's asset mix has moved ten percentage points.

Three things the overlay does not do, and each has cost somebody money. It does not change the underlying holdings, so a fund that has synthetically reduced equity still owns every stock and still reports every one of them. It does not eliminate the need for cash: futures generate daily variation margin, so a book that is synthetically long bonds in a rising-yield month pays cash out every session while the holdings it kept produce none to meet the call. And it does not survive being forgotten, because an overlay sized in January against a portfolio that has since drifted is a position rather than a hedge.

4.14 Writing the operating note before you need it

The margins, the expiry mechanics, the tax and the overlays all feed one document, and the document is short. A derivatives operating note, for a personal book or a small institutional one, answers five questions in writing, in advance, and is dated.

The first question is what may be traded. Name the instruments by contract rather than by category: the specific index future, the specific option series, with the lot size and the settlement style written out and the date the specification was read. A note that says "index derivatives" permits things the writer did not intend.

The second is the maximum notional, stated as a fraction of the book and separately as a number of contracts, because contract counts are what get typed into an order window. State it for gross notional and for delta-equivalent notional, since the two diverge sharply on any position with options in it. The covered call in Worked Example 3 carries 8.86 times gross leverage and 6.19 times delta leverage on the same margin, so a limit written against the delta figure alone permits 43.2% more gross notional than intended.

The third is the margin buffer, meaning the cash held above the requirement rather than the requirement itself, expressed both in currency and in index points of adverse move. A book with ₹3,20,000 of margin posted and ₹4,80,000 of buffer against 150 units of exposure to an index at 24,865 can absorb 3,200 index points, or 12.87%, before the buffer is gone. It can absorb 5,333 points, or 21.45%, before the margin follows it. Those two numbers state the position's survivability honestly, and they beat any value-at-risk figure for this purpose because they are computed from the account's own cash.

The fourth is the expiry-week plan. For a physically settled position: the date by which it will be closed, the funds that will be in place if it is not, and who checks. For a short option: whether it will be held into the settlement window, and what the additional expiry-day margin does to the requirement.

The fifth is the one scenario in which the position is closed regardless of view, and it is the only line in the note that does real work, because it is written when nothing is happening and executed when everything is. Make it mechanical and observable. A margin call the account cannot meet from the buffer. An underlying move past a stated level. A delivery obligation the account cannot fund. A change in the contract specification that invalidates the sizing.

A trigger that requires a judgement is not a trigger.

Common mistakes & how experts think differently

Each item below is a mistake with a number attached, which is the only kind worth listing.

1. Assuming a single-stock option settles in cash because the index option does. The two halves of the Indian derivatives segment settle differently, and the assumption is expensive in exactly one direction: a buyer discovers a ₹16.8 lakh obligation on a ₹34,200 position. Experts read the settlement style off the contract page for each underlying, every time, and treat "European" and "cash-settled" as two independent facts rather than one.

1. Quoting a margin as a percentage. A margin requirement is the output of a scenario array plus a flat exposure charge minus a premium credit, and it changes when volatility changes, when the position changes and when the clearing corporation revises the scan range. The percentage is a result, not a rule. Experts compute the array, then check the answer against the clearing corporation's own file, and reconcile any gap to a named parameter.

1. Sizing a position on initial margin and forgetting the daily cash. Initial margin is blocked; mark-to-market is spent. A position can be within its margin all week and still drain the account, and the peak-margin snapshots mean the cash needed is the cash the position needed at the worst moment of the day rather than at the close. Experts hold a buffer expressed in adverse index points, not in rupees, because points are what the market delivers.

1. Treating the securities transaction tax as a rate rather than a base. Selling an in-the-money option and letting it settle attract the same headline rates on wildly different bases, premium against settlement value, and the settlement route costs 23 times as much on the position worked here. Experts ask what a charge is levied on before they ask what the rate is.

1. Netting an intraday equity loss against a derivatives profit. Section 43(5) makes intraday equity speculative and exchange-traded derivatives non-speculative, and a speculative loss cannot reduce non-speculative income. The relief runs the other way only, which is the half people get backwards, and the mistake usually surfaces at filing when the carry-forward is already lost. Experts keep three ledgers from the first trade of the year: non-speculative derivatives, speculative intraday, and capital gains on delivery.

1. Computing derivatives turnover on notional. Turnover for the audit test is the absolute sum of favourable and unfavourable differences, not the value of contracts traded, and the two differ by orders of magnitude. A trader who reports notional turnover walks into an audit requirement that does not apply. Experts compute both the current and the previous guidance basis when a prior year is in question, because the answer changes by a factor of nearly four on the same trades.

1. Reading a futures overlay's tracking difference as an error. It is a sum of three named components: entry basis, contract rounding, and drift from a hedge ratio that was set at a different market level. An overlay whose residual has no decomposition has not been audited. Experts reconcile to the cent and can say which of the three each part came from.

1. Calling a currency hedge's carry its cost. The carry is the knowable part and can have either sign; on the four quarters worked here, hedging euros for a dollar investor earned $816,000 of carry and gave up $1,120,000 of spot move. Experts report both components separately at every roll and never let the sign of the total stand in for the sign of the decision.

1. Holding a long-volatility exchange-traded product as insurance. The product's negative carry is computable in advance, and at a normal contango it costs more than two thirds of the position a year with the volatility index unchanged. Experts either hold it for weeks with a stated exit, or use options and variance directly, and they compute the roll decay before buying rather than discovering it in the annual report.

1. Reading a derivatives disclosure in a fund factsheet as boilerplate. "The fund may use exchange-traded derivatives for efficient portfolio management" is a statement about beta, duration or currency, and it is priceable. Experts ask which of the three, at what notional, with what residual, and treat an answer that cannot be given as a finding.

Worked examples

Every input is stated. Every answer is verified by a second route where one exists. The closing note on each says what the number does not mean.

Worked example 1: The in-the-money call that becomes a delivery obligation (India, ₹)

Vindhya Cements Ltd (synthetic) trades on the Indian exchanges with a derivatives lot of 600 shares (per-stock and exchange-set). A trader is long 2 lots of the ₹1,400.00 monthly call, bought at ₹28.50 per share, so 1,200 shares of underlying and ₹34,200 of premium paid. The stock's cash-market margin rate, being value-at-risk plus extreme-loss margin, is 20.00%. Closing prices over the last five sessions are ₹1,452.00, ₹1,463.50, ₹1,441.00, ₹1,469.75 and, on expiry, a final settlement price of ₹1,478.20 computed as the volume-weighted average of the last thirty minutes. The next morning the stock opens and trades at ₹1,481.00. Brokerage is ₹20 per order.

Solution. Step 1, the delivery-margin ramp. Delivery value is the close times 1,200 shares; the full delivery margin is 20.00% of that; the blocked amount is the staged fraction.

Peak blocked margin, ₹3,54,768.00, which is 10.37 times the ₹34,200 premium outlay. The increase from the first session to the last is ₹3,19,920.00.

Step 2, the settlement obligation. Intrinsic value at settlement is 1,478.20 − 1,400.00 = ₹78.20 per share, or ₹93,840.00 on 1,200 shares. Physical settlement means paying 1,400.00 × 1,200 = ₹16,80,000.00 and receiving shares worth 1,478.20 × 1,200 = ₹17,73,840.00. The cash obligation is 49.12 times the premium paid.

Step 3, route A, sell the option on expiry day at parity. Sale value ₹93,840.00. Securities transaction tax at 0.15% of premium (the rate from 1 April 2026), ₹140.76. Exchange charge at 0.0495% of premium, ₹46.45. Regulator turnover fee at ₹10 per crore, ₹0.09. Brokerage ₹20.00. Goods and services tax at 18% on brokerage plus exchange plus regulator charges, ₹11.98. Route A exit cost, ₹219.28.

Step 4, route B, carry into settlement and sell the shares next morning. Take the settlement leg first. Securities transaction tax on the exercised option at 0.15% of intrinsic value, ₹140.76. Securities transaction tax on the delivery leg at 0.10% of the ₹16,80,000 settlement value, ₹1,680.00. Stamp duty at 0.015% on the delivery buy, ₹252.00. Exchange charge at 0.00297%, ₹49.90; regulator fee ₹1.68; goods and services tax ₹9.28. Settlement leg, ₹2,133.62. Then the sale the next morning at ₹1,481.00 on a value of ₹17,77,200.00: transaction tax ₹1,777.20, exchange charge ₹52.78, regulator fee ₹1.78, depository charge ₹13.50, brokerage ₹20.00, goods and services tax ₹15.85. Sale leg, ₹1,881.11. Route B total, ₹4,014.73.

Step 5, compare. Cost difference ₹3,795.45, a ratio of 18.31 to 1 (23.16 to 1 at the rates before April 2026). Route A nets ₹59,376.08 of profit after all charges including the ₹44.64 entry cost; route B nets ₹58,940.63 despite an overnight gain of ₹3,360.00 on the shares. The break-even overnight move that would make route B match route A is ₹3.16 per share, or 0.2140% of the settlement price, and the trader got ₹2.80.

Read it. The finding is not that settlement is expensive. It is that settlement converts a ₹34,200 position into a ₹16.80 lakh funded position for one day, charges about ₹3,819 for the privilege, and hands back an overnight price exposure the trader did not ask for and cannot control. He was lucky and still lost. Every number here moves with the rate card, which is set by Finance Act and by exchange circular. What survives a rate change is the base: the transaction tax on a sale is levied on ₹93,840 of premium, and the same tax on settlement is levied on ₹16,80,000 of shares.

Worked example 2: The same trader's tax year (India, ₹)

The trader from Worked Example 1 finishes the financial year with ₹8,42,000 of gains summed across winning derivatives trades and ₹6,15,500 of losses summed across losing ones. He received ₹41,80,000 of premium on options he sold during the year. He also lost ₹52,000 on intraday equity trades, and incurred ₹38,400 of brokerage, exchange charges, transaction tax, data and depreciation attributable to the trading business. His total tax liability for the year, computed under the slabs, is ₹3,42,000.

Solution. Step 1, character. Exchange-traded derivatives are non-speculative business income under the Section 43(5)(d) carve-out. Intraday equity, settled without delivery, is speculative business income under the main limb. Two classes of business income, one account.

Step 2, the net result. 8,42,000 − 6,15,500 = ₹2,26,500 of net derivatives profit.

Step 3, turnover. On the current guidance basis, turnover is the absolute sum of the differences: 8,42,000 + 6,15,500 = ₹14,57,500. On the older basis, which added the premium received on option sales, it is 14,57,500 + 41,80,000 = ₹56,37,500, which is 3.87 times larger on identical trades.

Step 4, the audit test. With all receipts and payments through the banking channel, the Section 44AB threshold is ₹10 crore. Turnover on the current basis is 1.46% of it; on the older basis, 5.64%. Neither triggers an audit. The second route in is the presumptive test: six percent of turnover is ₹87,450 against a declared ₹2,26,500, so the presumptive floor is cleared by ₹1,39,050.

Step 5, the deductions and the income. 2,26,500 − 38,400 = ₹1,88,100 of business income.

Step 6, the set-off that does not happen. The ₹52,000 intraday loss is speculative and cannot be set against the ₹1,88,100 of non-speculative business income. It carries forward for four years against speculative gains only. Had the year gone the other way, with a ₹4,10,000 derivatives loss and ₹1,20,000 of interest income, the loss would absorb the interest in full and ₹2,90,000 would carry forward for eight years against business income, conditional on the return being filed by the Section 139(1) due date.

Step 7, advance tax. On ₹3,42,000 of liability: ₹51,300 by 15 June, ₹1,53,900 cumulative by 15 September, ₹2,56,500 by 15 December, ₹3,42,000 by 15 March. A trader who has paid only ₹1,00,000 by 15 September is short ₹53,900 and owes ₹1,617.00 of interest under Section 234C at 1% a month for three months.

Read it. The single most valuable line here is not a number. It is that the eight-year carry-forward is conditional on filing by the due date, which converts a filing-calendar error into a permanent loss of a real asset. Every threshold above carries a verify flag: the audit limits, the presumptive rate, the instalment percentages and the guidance basis for turnover are all revised, and the guidance basis in particular changed within the last few years in a way that moves the turnover figure by nearly four times.

Worked example 3: A SPAN-style margin on one index lot, and the leverage it implies (India, ₹)

A trader holds one long Nifty future at 24,865.00 and one short 25,400 call on the same expiry, 24 days out, at an implied volatility of 15.50%, with the index at 24,800.00, a financing rate of 6.75% and a lot of 75 (the pre-2026 lot, kept for continuity; 65 from January 2026). The clearing corporation's price scan range is 6.00% of the futures price, its volatility scan range is ±1.50 volatility points, the extreme move is twice the price scan range covered at 35%, and the exposure margin is 3% of notional on both legs.

Solution. Step 1, the base valuation. Black-76 on the future gives the call at 185.972470 index points, so ₹13,947.94 of premium per lot, with a delta of 0.301679. Price scan range, 6.00% × 24,865.00 = 1,491.90 points.

Step 2, the array. Fourteen scenarios shock the future by 0, ±1/3, ±2/3 and ±1 of the scan range, each with volatility up and down; two extreme scenarios shock it by ±2 scan ranges at 35% coverage. The five that matter:

Step 3, the scanning risk. Scenario 13 binds at ₹98,803.58. It is the full down move with volatility rising rather than the extreme move, because the extreme scenario's loss is only 35%-covered and 0.35 × (−2,09,838.52) = −₹73,443.48 is smaller. That relationship is structural on a directional position: doubling the price shock roughly doubles the raw loss, and 0.35 of twice something is 0.70 of it, so the full scan range wins. The down side binds rather than the up because the short call's gain is capped at the premium while the long future's loss is not.

Step 4, the total. Futures notional 24,865.00 × 75 = ₹18,64,875.00; short-call notional 24,800.00 × 75 = ₹18,60,000.00; exposure at 3% of both, ₹1,11,746.25. Initial margin = 98,803.58 + 1,11,746.25 = ₹2,10,549.83. The premium received credits ₹13,947.94 against it, leaving ₹1,96,601.90 of net cash. On expiry day the additional 2% exposure margin on the short option adds ₹37,200.00, taking the requirement to ₹2,47,749.83, a 17.7% jump.

Step 5, leverage, two ways. Gross notional leverage is 18,64,875 / 2,10,549.83 = 8.86 times. Net position delta is 1 − 0.301679 = 0.698321, so delta-equivalent notional is ₹13,02,280.88 and delta leverage is 6.19 times. The index move that would consume the entire initial margin at constant delta is 2,10,549.83 / (0.698321 × 75) = 4,020.12 points, or 16.17% of the futures price.

Read it. Two leverage figures on one position, differing by 43%, and the honest one depends on the question. Gross notional is right for a concentration limit, because a gap move on a short option does not respect delta. Delta-equivalent is right for a risk budget, because it is what the position actually earns and loses on a small move. A policy written against the delta figure alone permits 43.2% more gross notional than it intended. And the 16.17% figure is the one to say out loud: an index fall of a sixth wipes out the margin on a position most people would describe as conservative.

Worked example 4: Beta, cash and currency on a US book (US, $ and EUR)

A US fund holds $48,000,000 of equities at a portfolio beta of 1.15 and wants 0.60. The E-mini S&P 500 future trades at 5,866.00 with a $50 multiplier. Separately, the fund holds $12,000,000 of cash it wants exposed to the index for one quarter; the index spot is 5,820.00, the financing rate 4.30%, the dividend yield 1.30%, and at the horizon the index is 6,110.10. And separately again, it hedges a €40,000,000 European sleeve with rolling three-month forwards over four quarters.

Solution. Step 1, the beta trade. Contract value 5,866.00 × 50 = $293,300.00. N = (0.60 − 1.15) × 48,000,000 / 293,300 = −90.010228, so short 90 contracts. Effective beta = 1.15 + (−90 × 293,300 / 48,000,000) = 0.600062, an error of 0.000062.

Step 2, the beta trade under a shock. On an 8.00% index fall, the portfolio loses 1.15 × −8.00% × 48,000,000 = −$4,416,000.00 and the futures gain 90 × 293,300 × 8.00% = +$2,111,760.00, netting −$2,304,240.00, or −4.8005%. Cross-check: 0.600062 × −8.00% = −4.8005%. The two routes agree to six decimals, which is the test that the contract count and the multiplier were both applied once.

Step 3, equitising the cash. Fair futures price = 5,820.00 × (1 + (4.30% − 1.30%) × 0.25) = 5,863.65, so the market's 5,866.00 is 2.35 points rich. N = 12,000,000 / 293,300 = 40.913740, so 41 contracts long. At the horizon the future converges to 6,110.10, so futures P&L = 41 × 50 × (6,110.10 − 5,866.00) = $500,405.00, cash interest = 12,000,000 × 4.30% × 0.25 = $129,000.00, total $629,405.00 or 5.2450%.

Step 4, the alternative and the gap. Fully invested, the index returns 6,110.10 / 5,820.00 − 1 = 4.9845% of price plus 0.3250% of dividend, so $637,144.33 or 5.3095%. Tracking difference, −$7,739.33, or −6.45 basis points.

The rounding row measures the whole 41 contracts against 40.930138, being the count the same cash buys at the fair price of 5,863.65 rather than at the 5,866.00 actually paid. Splitting it that way keeps the cost of the rich entry in its own row and makes the three components sum to the total exactly.

The third row has a closed form and it reproduces the numerical residual to the cent, which is the independent check.

Step 5, the currency roll. Each quarter the fund sells €40,000,000 forward at spot plus the points and settles against spot at the next roll.

Decomposed: carry = (0.0058 + 0.0055 + 0.0049 + 0.0042) × 40,000,000 = +$816,000; spot = (1.0850 − 1.1020) + (1.1020 − 1.0940) + (1.0940 − 1.0805) + (1.0805 − 1.1130), all times 40,000,000 = −$1,120,000. The two sum to −$304,000 exactly. Unhedged, the euro's move from 1.0850 to 1.1130 would have been worth +$1,120,000. Across the ratio spectrum on the same path: unhedged +$1,120,000, half-hedged +$968,000, fully hedged +$816,000, and a 150% hedge +$664,000.

Read it. The hedge did not cost $304,000. It earned $816,000 of carry that was knowable at each roll and surrendered $1,120,000 of currency move that was not, and a review that reports only the net has thrown away the only part of the decision that was ever forecastable. Note also what the spectrum table does not say: the fully hedged outcome is the worst of the four on this path, and on the opposite path it would be the best. The ratio is a policy about which regret you prefer, and it should be set when no position is open.

Worked example 5: Switching equity into bonds with two futures legs (US, $)

A $250,000,000 fund holds 70% equities at a sleeve beta of 1.05 and 30% bonds at a modified duration of 6.20. It wants ten percentage points, $25,000,000, moved from equities to bonds for one quarter. The E-mini trades at 5,866.00 with a $50 multiplier. The bond future's cheapest-to-deliver has a basis-point value of $71.20 and a conversion factor of 0.7930. Equity round trips cost 8 basis points and bond round trips 4; futures cost $4.50 per contract round turn.

Solution. Step 1, the equity leg. Exposure to remove = 1.05 × 25,000,000 = $26,250,000 of index-equivalent. N = −26,250,000 / 293,300 = −89.498807, so short 89 contracts.

Step 2, the bond leg. Basis-point value to add = 6.20 × 25,000,000 × 0.0001 = $15,500.00 per bp. Futures basis-point value = 71.20 / 0.7930 = $89.785624 per bp. N = 15,500 / 89.785624 = 172.633427, so long 173 contracts.

Step 3, the scenario. Equities fall 6.00%, yields fall 35 basis points. Equity futures gain 89 × 293,300 × 6.00% = $1,566,222.00. Bond futures gain 173 × 89.785624 × 35 = $543,651.95. Overlay total, $2,109,873.95.

Step 4, the physical comparison. Selling $25m of equities avoids 1.05 × 6.00% × 25,000,000 = $1,575,000.00 of loss; buying $25m of the bond sleeve earns 6.20 × 0.35% × 25,000,000 = $542,500.00. Physical total, $2,117,500.00. The overlay is short by $7,626.05, which is 0.36% of the move and is entirely the two rounding residuals: 0.498807 of an equity contract not sold and 0.366573 of a bond contract over-bought.

Step 5, the costs. Physical: 25,000,000 × (0.0008 + 0.0004) = $30,000.00. Synthetic: 262 contracts × $4.50 = $1,179.00. Saving, $28,821.00, or 11.53 basis points of the amount switched, against a $7,626.05 tracking residual. The overlay wins by roughly four to one.

Read it. The saving is real and it is not the whole comparison. The overlay leaves the fund still owning every share it decided to own less of, still reporting them, and now posting margin, roughly $2.17 million at a 5% requirement across both legs with the bond contract taken at $100,000 of face, and paying daily variation margin in cash against an unrealised position. If the fund's tactical view is right for two years rather than one quarter, the physical trade is the better one, because the overlay has to be rolled, re-sized and explained every quarter and each roll pays the basis again. Overlays are cheap per unit of time and expensive per unit of duration.

Worked example 6: What a long-volatility product costs when nothing happens (US, $)

A constant-maturity long-volatility index holds front-month and second-month volatility futures, rolling a 1/21 fraction of the front into the second each session. The term structure is static for the whole path: spot 15.00, and a future maturing in d business days priced at 15.00 + 0.075d. So the front future starts at 16.575 with 21 days to run and the second at 18.150 with 42.

Solution. Step 1, the curve. Contango front to second is 1.575 points, or 9.5023%. The front future itself sits 10.50% above spot and the second 21.00% above.

Step 2, the daily arithmetic. On each session the weights are the previous day's, and the index return is the weighted change in the two contract prices. With a linear curve, that return is the same every day: −0.075 / 16.575 = −0.45249%. The daily bleed on a linear term structure is exactly the slope divided by the front level.

Step 3, the cycle. Compounding 21 sessions: (1 − 0.0045249)^21 − 1 = −9.0844%. The index starts at 100.000000 and ends at 90.915629.

Step 4, the year. Twelve cycles compound to −68.1094%. At the end of that year the volatility index reads 15.00, exactly where it started, and the product tracking it has lost more than two thirds of its value. To be flat, the constant-maturity futures level would have to be 3.14 times higher.

Step 5, the clean instrument. A variance swap on a $250,000 vega notional struck at 18.00 has a variance notional of 250,000 / (2 × 18) = $6,944.44 per variance point. Realised volatility of 15.50 pays 6,944.44 × (15.50² − 18.00²) = −$581,597.22, where the naive vega-times-difference estimate says −$625,000.00; the convexity is worth $43,402.78 to the buyer. Realised of 22.00 pays +$1,111,111.11 against a linear estimate of $1,000,000.00, a convexity gain of $111,111.11.

Read it. The 68.11% is not a forecast and not a historical average; it is what a static curve of this shape mechanically does, and a real curve moves, sometimes flipping into backwardation in a crisis and paying the holder handsomely for a few weeks. The instrument's problem is not that it is badly built. It tracks its index faithfully. The problem is that the index it tracks has a large, computable negative carry, and anyone holding it for a year is paying an insurance premium of that size whether or not they wrote the number down. The same arithmetic, under the name roll return, prices a long-only commodity index in contango.

Worked example 7: Early exercise around a dividend, and its Indian mirror (US, $ / India, ₹)

Harborline Industries (synthetic) trades at $86.40. A holder is long 20 American call contracts, strike $80.00, 38 days to expiry, covering 2,000 shares. A dividend of $1.10 per share goes ex tomorrow. The risk-free rate is 4.30%, and the same-strike, same-expiry put trades at $0.42.

Solution. Step 1, the test. Exercising early captures the dividend and forfeits the call's remaining time value. By put-call parity that time value equals the put price plus the interest saved by not paying the strike yet: P + K(1 − e^(−rT)).

Step 2, the arithmetic. K(1 − e^(−rT)) = 80 × (1 − e^(−0.043 × 38/365)) = $0.357337. Add the put at $0.42: the threshold is $0.777337. The dividend of $1.10 exceeds it by $0.322663 per share, so exercise.

Step 3, the size of the decision. $0.322663 × 100 = $32.27 per contract, or $645.33 on 20 contracts. Exercising requires $160,000.00 of cash and delivers shares worth $172,800.00 plus $2,200.00 of dividend.

Step 4, the sensitivity. At a dividend of $0.55 instead, the gain is −$0.227337 per share and the correct action is to hold. The break-even dividend is the threshold itself, $0.777337, so the decision turns on a number that is roughly 0.9% of the share price and moves with the put's implied volatility.

Step 5, the other side. If 1,850 of 6,000 open contracts at this strike are exercised, a holder short 40 lots faces an assignment probability of 30.83% and should expect 12.33 contracts assigned, while holding stock or cash for all 40.

Step 6, the Indian mirror. An Indian single-stock option cannot be exercised early, so this decision does not exist there. What exists instead is the strike-adjustment rule: the exchange adjusts strikes only for dividends it classifies as extraordinary, at a threshold of 2% of the underlying's market value (check against the current circular). This dividend is 1.10 / 86.40 = 1.2731% of the price, so on the Indian rule no adjustment would be made and the option holder would simply absorb the ex-date drop. Same economics, opposite mechanism: the American market lets you act, the Indian market decides whether to compensate you.

Read it. The early-exercise decision is worth $645.33 here, which is small, exactly computable, and forgone by almost everyone who holds American calls through an ex-date, because the calculation requires the put price and nobody looks it up. Note also what the test does not say. It says nothing about whether the position should be held at all, only about whether exercising beats holding. On a liquid contract, selling the option is usually better than either, because a sale captures the whole remaining time value rather than forfeiting it.

Verify. Every figure in this node at full precision, so any of it can be checked against your own recomputation. Worked Example 1: peak delivery margin 354,768.000000; settlement obligation 1,680,000.000000; route A cost 219.282675; route B cost 4,014.730527; ratio 18.308471; break-even overnight move 3.163250, the sale-leg charges being rescaled to the break-even price rather than held at the ₹1,481.00 case. Worked Example 2: turnover on the current basis 1,457,500.000000 and on the older basis 5,637,500.000000; business income 188,100.000000. Worked Example 3: scanning risk 98,803.584324; exposure margin 111,746.250000; initial margin 210,549.834324; gross leverage 8.857167; delta leverage 6.185143. Worked Example 4: exact contracts −90.010228; effective beta 0.600062; net return −0.048005; tracking difference −7,739.329897, being −4,817.500000 of richness, +860.882236 of rounding and −3,782.712133 of drift; four-quarter hedge P&L −304,000.000000 as +816,000.000000 of carry and −1,120,000.000000 of spot. Worked Example 5: equity leg −89.498807; bond leg 172.633427; overlay P&L 2,109,873.954603; cost saved 28,821.000000. Worked Example 6: one-cycle return −0.090844; twelve cycles −0.681094; variance payoff −581,597.222222. Worked Example 7: threshold 0.777337; exercise gain 0.322663 per share. Auction close-out: price 1,802.400000, cost 194,520.000000.

Practice set

Work each one before reading the solution. A calculator is assumed. Numeric answers within 0.5% of the stated figure count as correct, except where a rounding decision is the point of the question, in which case the integer must match. Markets alternate deliberately: if one currency's conventions feel automatic and the other's do not, that is the gap the practice is for.

P1 (guided). Read the specification. An index contract has a lot of 75 units and a tick of 0.05 index points, with the index at 25,120.00. Compute (a) the notional value of one lot, (b) the value of one tick, (c) how many lots are needed to carry at least ₹50,00,000 of exposure, and (d) the exposure that many lots actually carry. Then state the one thing on the specification page you would check before trading that has nothing to do with price.

Solution. (a) 25,120.00 × 75 = ₹18,84,000. (b) 0.05 × 75 = ₹3.75. (c) 50,00,000 / 18,84,000 = 2.6539, so 3 lots. (d) 3 × 18,84,000 = ₹56,52,000, which overshoots the target by ₹6,52,000 or 13.0%, and there is no way to trade a fraction of a lot. The non-price check: the expiry date and time, because a position sized correctly in the wrong series is not a position in the exposure you wanted. Second answer accepted: the settlement style, cash or physical.

P2 (guided). The ramp. A trader is long 3 lots of a stock future with a lot of 1,250 shares. The underlying's cash-market margin rate is 17.50%, and the closes over the last five sessions are ₹842.00, ₹851.50, ₹838.25, ₹860.00 and ₹866.40. Tabulate the delivery margin blocked on each session at stages 10%, 25%, 45%, 70% and 100%, and state the settlement obligation.

Solution. Deliverable quantity 3,750 shares.

Settlement obligation on a long future is the full contract value at the settlement price: 866.40 × 3,750 = ₹32,49,000. Blocked margin rises ₹5,13,318.75 across four sessions. Note the E−2 dip: the stock fell that day, so the blocked amount rose less than the stage increase alone implies, because the base fell while the percentage rose.

P3 (guided). The two bases. A holder is long a call on 900 shares at a strike of ₹2,600, and the underlying settles at ₹2,688. Compute the securities transaction tax under (a) selling the option at parity, (b) exercising it, and (c) the delivery leg of physical settlement, and state the ratio of the settlement route to the sale route. Use 0.10% of premium on an option sale, 0.125% of intrinsic on an exercised option, and 0.10% of settlement value on the delivery leg.

Solution. Intrinsic = 2,688 − 2,600 = ₹88 per share, ₹79,200 in total. (a) 0.10% × 79,200 = ₹79.20. (b) 0.125% × 79,200 = ₹99.00. (c) 0.10% × 2,600 × 900 = 0.10% × 23,40,000 = ₹2,340.00. Settlement route total = 99.00 + 2,340.00 = ₹2,439.00, a ratio of 30.80 to 1 against the sale. The rates are perishable and the ratio is not: it is driven by the base, and the base for a delivery is the whole contract value.

P4. Levering up rather than down. A $62,500,000 portfolio has a beta of 0.92 and the manager wants 1.20. The index future is at 5,720.00 with a $50 multiplier. Compute the contract count, the effective beta after rounding, and the portfolio's profit on a +5.00% index move both with and without the overlay.

Solution. Contract value 5,720 × 50 = $286,000. N = (1.20 − 0.92) × 62,500,000 / 286,000 = 61.188811, so long 61. Effective beta = 0.92 + 61 × 286,000 / 62,500,000 = 1.199136. With the overlay, 1.199136 × 5.00% × 62,500,000 = $3,747,300.00; without it, 0.92 × 5.00% × 62,500,000 = $2,875,000.00. The overlay adds $872,300.00 of gain on the move and would have added the same magnitude of loss on the mirror move, which is what "levering market exposure without buying a share" actually means.

P5. Equitising, with the market falling. A fund equitises $8,000,000 of cash with an index future at 4,338.00 ($50 multiplier) when the index spot is 4,310.00. Over the quarter the index falls to 4,166.00. The cash earns 4.50% and the index yields 1.40%. Compute the equitised outcome, the fully invested outcome and the tracking difference.

Solution. N = 8,000,000 / (4,338 × 50) = 36.883356, so 37 contracts. Futures P&L = 37 × 50 × (4,166 − 4,338) = −$318,200.00. Cash interest = 8,000,000 × 4.50% × 0.25 = +$90,000.00. Equitised total, −$228,200.00. Fully invested = 8,000,000 × [(4,166 / 4,310 − 1) + 1.40% × 0.25] = −$239,285.38. Tracking difference, +$11,085.38. Decomposed against a fair futures price of 4,343.4025: entry cheapness +$9,994.63, because the contract was bought 5.4025 points below fair; rounding −$1,441.58; drift +$2,532.34. The overlay beat the physical position, and 90% of the reason was that the future was cheap when it was bought, which is a piece of luck rather than a property of overlays. Say which component did the work before congratulating the overlay.

P6. Margin from a supplied array. A clearing corporation's risk array for a one-lot position returns these sixteen net outcomes in rupees: −18,400, +12,250, −41,300, +33,100, −52,750, +44,900, −66,100, +51,800, −78,450, +58,200, −91,200, +62,400, −104,900, +66,100, −73,150, +47,600. The position's notional is ₹19,80,000 and the exposure rate is 3%. Compute the scanning risk, the initial margin, the margin as a percentage of notional, and the leverage.

Solution. Worst cell −₹1,04,900, so scanning risk = ₹1,04,900. Exposure = 3% × 19,80,000 = ₹59,400. Initial margin = ₹1,64,300, which is 8.30% of notional, and the leverage is 19,80,000 / 1,64,300 = 12.05 times. The array's worst cell is the thirteenth rather than the fifteenth or sixteenth, because the extreme scenarios are only 35%-covered and on this position they do not bind.

P7. Two turnover bases on a losing year. A trader's derivatives year shows ₹21,40,000 of gains and ₹26,65,000 of losses across trades, with ₹93,50,000 of premium received on options sold. Compute the net result, turnover on both bases, the ratio, and whether either turnover figure triggers a Section 44AB audit at the ₹10 crore threshold.

Solution. Net result = 21,40,000 − 26,65,000 = −₹5,25,000, a loss. Turnover on the current basis = 21,40,000 + 26,65,000 = ₹48,05,000. On the older basis = 48,05,000 + 93,50,000 = ₹1,41,55,000, a ratio of 2.95 to 1. Neither triggers the ₹10 crore threshold; the larger figure is 14.16% of it. But this is a loss year, so the second route matters: if this taxpayer had previously opted into the presumptive scheme and now declares a loss with total income above the basic exemption limit, an audit is required regardless of turnover.

P8. Where a loss can and cannot go. In the same year the trader has ₹14,50,000 of salary, ₹2,10,000 of interest income, ₹1,68,000 of rental income, and a ₹90,000 intraday equity gain, alongside the ₹5,25,000 derivatives loss from P7. Allocate the loss and state what carries forward and for how long.

Solution. Set-off runs in two stages and the order matters. Within the business head first: the non-speculative loss absorbs the ₹90,000 speculative intraday gain, because speculative income is still business income and the restriction runs only in the other direction. That leaves ₹4,35,000. Then across heads: against interest, ₹2,10,000; against rent, ₹1,68,000; against salary, ₹0, because salary is the one head a business loss cannot reach. Total absorbed, ₹4,68,000, leaving ₹57,000 to carry forward for eight assessment years, against business income only, and only if the return is filed by the Section 139(1) due date. The ₹14,50,000 of salary is taxed in full. The asymmetry to hold in your head: a non-speculative loss can absorb a speculative gain, and a speculative loss cannot absorb a non-speculative gain.

P9. Duration up. A $40,000,000 bond sleeve at a modified duration of 2.10 is to be moved to 7.40 with a future whose cheapest-to-deliver has a basis-point value of $68.40 and a conversion factor of 0.8455. Compute the basis-point value to add, the futures basis-point value, the contract count, the profit on a 40 basis-point rally, and the residual against a perfect hedge.

Solution. BPV to add = (7.40 − 2.10) × 40,000,000 × 0.0001 = $21,200.00 per bp. Futures BPV = 68.40 / 0.8455 = $80.898876. N = 21,200 / 80.898876 = 262.055556, so 262 contracts long. On a 40 bp rally, 262 × 80.898876 × 40 = $847,820.22. A perfect hedge would earn 21,200 × 40 = $848,000.00, so the residual is −$179.78, being 0.055556 of a contract not bought. The residual is 0.02% of the move, which is the general shape of rounding error on a large rate overlay and the reason rate overlays are more precise than equity ones: the contract is smaller relative to the exposure.

P10. A hedge that earned less carry. A US fund hedges a £25,000,000 sterling sleeve over four quarters. The spot at each roll, the three-month forward points, and the spot at each settlement are: (1.2650, +0.0031, 1.2820), (1.2820, +0.0028, 1.2705), (1.2705, +0.0024, 1.2960), (1.2960, +0.0019, 1.2540). Compute the total hedge P&L, its carry and spot components, and the unhedged outcome.

Solution. Forwards struck at 1.2681, 1.2848, 1.2729, 1.2979. Hedge P&L per quarter = (forward − settle) × 25,000,000: −$347,500, +$357,500, −$577,500, +$1,097,500, total +$530,000. Carry = (0.0031 + 0.0028 + 0.0024 + 0.0019) × 25,000,000 = +$255,000. Spot component = +$275,000. The two sum to $530,000. Unhedged, sterling moved 1.2650 to 1.2540, worth −$275,000. The hedge outperformed the unhedged position by $805,000, and only $255,000 of that was foreseeable.

P11. A shallower curve. A constant-maturity long-volatility index rolls 1/21 daily between a front future at 21 business days and a second at 42, on a static curve 17.00 + 0.050d. Compute the front and second futures prices, the contango, the one-cycle return and the twelve-cycle compounded return.

Solution. Front = 17.00 + 0.050 × 21 = 18.050; second = 17.00 + 0.050 × 42 = 19.100; contango = 5.8172%. Daily bleed = −0.050 / 18.050 = −0.27701%, and over 21 sessions the index falls from 100 to 94.341174, a −5.6588% cycle. Twelve cycles compound to −50.2933%. Half the slope and a higher level, and the annual decay falls from 68.11% to 50.29%: still catastrophic as a buy-and-hold, and the difference between the two shows that the decay is driven by the ratio of slope to level rather than by the slope alone.

P12. When not to exercise. A holder is long 15 American calls, strike $135.00, on a stock at $142.60 with 26 days to expiry. A $0.68 dividend goes ex tomorrow, the risk-free rate is 4.30%, and the same-strike put trades at $0.31. Should the calls be exercised, and what is the decision worth?

Solution. Interest saved = 135 × (1 − e^(−0.043 × 26/365)) = $0.412874. Threshold = 0.412874 + 0.31 = $0.722874. The dividend of $0.68 is below it, so do not exercise. Exercising would cost 0.68 − 0.722874 = −$0.042874 per share, or −$64.31 across 15 contracts. The decision is close, which is the honest answer: at a dividend a nickel higher, or a put a nickel cheaper, it flips. Anyone using a rule of thumb rather than the arithmetic gets this one wrong about half the time.

P13. What a failed delivery costs. A seller fails to deliver 1,100 shares settled at ₹968.00. The highest price from the trade day to the auction day is ₹1,010.00, and the closing price on the day before the auction is ₹992.00. Compute the close-out price and the cost to the defaulter.

Solution. Candidate one, the highest price, ₹1,010.00. Candidate two, 20% above the prior close, 1.20 × 992.00 = ₹1,190.40. The formula takes the higher, so the close-out is ₹1,190.40. Cost = (1,190.40 − 968.00) × 1,100 = ₹2,44,640, which is 22.98% of the settlement value. The 20% rule binds here even though the stock never traded anywhere near ₹1,190. The penalty is deliberately punitive, because the system's alternative to punishing a failure is tolerating one.

P14. The trigger, written in points. An account holds 2 lots of an index future (lot 75, index 24,865.00) with ₹3,20,000 of initial margin posted and ₹4,80,000 of cash buffer above it. Compute the adverse index move in points and in percent that (a) exhausts the buffer and (b) exhausts the buffer and the margin together, and write the closing trigger in one sentence.

Solution. Exposure is 150 units. (a) 4,80,000 / 150 = 3,200 points, or 12.87% of the index. (b) (4,80,000 + 3,20,000) / 150 = 5,333.33 points, or 21.45%. Notional is 150 × 24,865.00 = ₹37,29,750, so buffer plus margin is 21.45% of notional, which is the same number arrived at another way and therefore the arithmetic check. A workable trigger: close the position if the index falls more than 2,400 points from entry, being three quarters of the buffer, so that the closing trade happens with cash still in hand. Any mechanical, observable threshold below 3,200 points is acceptable. A trigger stated as "if things look bad" is not.

Applied mini-project

Write the derivatives operating note for one real account, and make every number in it reproducible.

Pick an account you actually have or could plausibly open, in either market. Five artefacts, each with a stated test it must pass before it counts. Use a spreadsheet or Python. Label any invented entity synthetic, and trace every rate, lot size and threshold to the exchange's or the tax authority's own page with the date you read it recorded beside it.

Artefact 1 is the specification sheet. For every instrument the account would use, copy from the exchange's own contract-specification page: underlying, lot size or multiplier, tick and tick value, expiry date and time, settlement style, exercise style, the last trading day, and the settlement-price convention. Test 1: each row carries the source and the date read, and at least one row is a physically settled instrument if you are in the Indian market. Test 2: compute the notional of one contract at today's level and confirm it clears the market's minimum contract size.

Artefact 2 is the margin build. Take one position of at least two legs and build its requirement from the parts: a sixteen-scenario risk array with the price and volatility scan ranges named and sourced, the exposure margin, the net option value credit, and the expiry-day add-on where one applies. Test 3: identify the binding scenario before you compute the array, then check whether you were right, and explain any disagreement. Test 4: reconcile your total against the clearing corporation's own margin calculator for the same position, to within 5%, and attribute any residual to a named parameter rather than calling it approximation.

Artefact 3 is the expiry-week plan. For the same position, tabulate the delivery-margin ramp across the last five sessions if it is physically settled, or the expiry-day margin change if it is not. Test 5: state the date and time by which the position will be closed and the funded amount that must be available if it is not, and show that the account has it.

Artefact 4 is the tax and cost note. Build the all-in round-trip cost stack for one typical trade, with each charge's base named, and compute the break-even move in the instrument's own units. Then state the tax treatment. For India: the head under Section 43(5), the turnover on the current guidance basis, the audit threshold it is tested against, the set-off and carry-forward rules that would apply to a loss, and the advance-tax instalment dates. For the United States: whether the instrument is a Section 1256 contract and what that does to the character of the gain. Test 6: every rate and threshold carries a verify flag with a primary source and a date. Test 7: the cost stack reconciles against a real contract note, or against the exchange's own charges calculator if you have not traded, and any gap is explained.

Artefact 5 is the closing trigger: one sentence, mechanical and observable, stating the condition under which the position is closed regardless of view. Test 8: the trigger is expressed in units the market produces, such as index points, a price level or a margin shortfall against the buffer, and you have computed what it is in currency.

The deliverable is a two-page note plus the workbook behind it. The note carries the specification table, the margin figure with both leverage measures, the expiry-week plan, the cost and tax summary, and the closing trigger. The workbook carries the eight test results with their residuals.

Rubric (20 points; pass at 16 with no zero on any row).

Any artefact whose test fails scores zero for that row regardless of how well it is written. A margin figure you cannot reconcile is not a conservative estimate. It is a number you do not have.

Reading & resources

Each entry here is a place to verify against, never a place to copy a number from without tracing it yourself. The rates and specifications in this node all live in the first four entries, and they change.

Primary sources for the specifications and the margins:

• NSE contract-specification pages and circulars (nseindia.com), for lot sizes, expiry days, settlement styles, physical-settlement rules and the delivery-margin staging. The circulars archive is where a change is announced before it appears anywhere else. [Free] [Beginner to Advanced]
• NSE Clearing / Indian Clearing Corporation margin files and the SPAN parameter file, the actual scan ranges, volatility scan ranges and exposure rates used to compute the number your broker shows you. Reading one of these once changes how you read a margin forever. [Free] [Advanced]
• SEBI circulars on index derivatives (sebi.gov.in), including the October 2024 measures that reset the minimum contract size, the weekly-expiry count, the expiry-day short-option margin and the upfront premium collection. [Free] [Intermediate]
• CME Group and Cboe contract specifications, for the E-mini and Micro E-mini equity index futures, Treasury futures with their conversion-factor tables and cheapest-to-deliver data, and the index option settlement conventions including the special opening quotation. [Free] [Beginner to Advanced]

Tax:

• Income-tax Act, Sections 43(5), 44AB, 44AD, 70, 71, 72, 73, 139(1), 208 and 234C, read at incometaxindia.gov.in. The carve-out that makes exchange-traded derivatives non-speculative is a single proviso clause and is worth reading in the original. [Free] [Intermediate]
• The Institute of Chartered Accountants of India's Guidance Note on Tax Audit, current edition, for the turnover computation. The 2022 revision changed the treatment of option premium and the change is material. [Free] [Intermediate]
• Internal Revenue Service Publication 550 and the Section 1256 rules, for the US mark-to-market and 60/40 treatment, and for how wash sales apply to equity options and not to 1256 contracts. [Free] [Intermediate]

Mechanics and craft:

• Options Clearing Corporation, "Characteristics and Risks of Standardized Options", the disclosure document every US options account receives and almost nobody reads. Its assignment and exercise-by-exception sections are the clearest short statement of those mechanics anywhere. [Free] [Beginner to Intermediate]
• John C. Hull, Options, Futures, and Other Derivatives, for the early-exercise conditions, the conversion-factor and cheapest-to-deliver arithmetic, and the variance-swap replication. The reference text for everything this node computes. [Paid] [Intermediate to Advanced]
• Cboe's VIX white paper, the primary statement of the model-free variance calculation, including the strike weighting and the interpolation to a constant 30-day horizon. [Free] [Advanced]
• Zerodha Varsity, "Markets and Taxation" and the brokerage calculator (zerodha.com/varsity), the clearest free walk-through of the Indian charge stack with a live calculator that reproduces the cost tables here. Rates change, so use it to verify the current figures rather than to learn them. [Free] [Beginner]

Portfolio use:

• CFA Institute Level III, the derivatives and currency-management readings, for beta and duration adjustment, the hedge-ratio spectrum, and the strategic-versus-tactical currency decision in examinable form. [Paid] [Intermediate]
• A large multi-asset fund's own annual report, the derivatives note, read as a primary document: which contracts, what notional, what the overlay was for, and whether the fund tells you the residual. Sovereign wealth funds and large public pension plans publish these and they are the best free examples of the overlays here at institutional scale. [Free] [Intermediate]

Do this rather than only reading. Open the contract-specification page for one instrument you could trade, and copy the five lines into a note with today's date. Then find the same instrument's specification as it stood two years ago, in the circulars archive, and list what changed. Fifteen minutes of that teaches the lesson better than any of the arithmetic above, because it puts the point beyond argument: the parameters are a feed rather than a fact.

Teach it back & journal

Feynman prompt. Explain to someone who trades Indian options on a phone app why a winning trade can cost more than a losing one. Start with the ₹34,200 of premium and walk them to the ₹16,80,000 of cash, showing the delivery-margin ramp session by session so they watch the blocked amount climb while the position is going their way. Then put the two cost stacks side by side, ₹219.28 against ₹4,014.73, and make them say out loud what the securities transaction tax is charged on in each case. If they interrupt to ask what happens on the day they are short of funds, you have installed the mechanism, and the answer is that their broker closes something, probably not the position they would have chosen.

Then the second half, and it is a harder audience. Explain to a colleague who runs a portfolio why selling 89 index futures and buying 173 bond futures is not the same thing as selling $25 million of stock and buying $25 million of bonds, even though the scenario arithmetic comes out within $7,626 of each other. Have them name the three residuals before you name them. Then ask what happens to the overlay if nobody looks at it for a year, and see whether they get to the answer on their own: a hedge sized at a market level that has moved is a position.

Journal prompt. For two weeks, before any derivatives trade you make or any fund derivatives disclosure you read, write down five lines on paper: multiplier or lot, tick, expiry date and time, settlement style, exercise style, with the source and the date beside each. Then write the single number that follows from them, being the notional of one contract. At the end of the two weeks, count how many of the five you would have got wrong from memory, and how many you had never actually looked up. Expect the count to be greater than zero, and expect the ones you got wrong to be the two that cost money: settlement style first, lot size second.

Then write a paragraph on this. The whole node argues that the layer between a model and a filled order is where money is actually lost, and that the layer is made of parameters somebody else changes without telling you. Which of your own positions or recommendations currently rests on a parameter you learned once and have not re-read? Name it, look it up, write down the date, and record whether it had changed. Then decide what you will re-read on a schedule rather than on a surprise, and write down when.

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.