FINC6010 Cheatsheet · Derivative Securities

0 · Exam Mapcourse.json + brief

“This is a restricted exam, with only one A4 single-sided page of printed or handwritten notes permitted.” (FINC6010 Assessment Information, Semester 2 2026)

1 · Contract ClassifierCh 1 · method

Hedge offsets a separately identified exposure; speculation creates or retains a view; arbitrage compares complete equivalent strategies. Long/short says position direction, not purpose.

1b · Unknown Contract DrillCh 1 · classify

A producer and a speculator can hold the same short futures position; only the producer may be offsetting an expected sale. Likewise, an importer can choose a long forward to fix the domestic-currency cost or a call to cap adverse movement while retaining favourable movement after premium.

2 · Futures SettlementCh 2 · ledger

Initial margin is collateral, not a down payment. Maintenance margin is the trigger threshold. The stated restoration rule sets the deposit after a breach.

daily variation marginLong: VMₜ = n × Q × (Fₜ − Fₜ₋₁)
Short: VMₜ = −n × Q × (Fₜ − Fₜ₋₁)
Balanceₜ = Balanceₜ₋₁ + VMₜ + depositₜ

Market mechanics

Novation: the clearing house becomes counterparty to both sides. It manages default resources; market and liquidity risks remain. Settlement price is the exchange reference for daily gains and losses, not every trader’s execution price.

Convergence: near delivery, spot and futures must meet closely enough to remove an executable buy-cheap/sell-dear package. Open interest counts outstanding positions; volume counts trades.

Orders are separate from valuation: a limit protects price but may not execute; a market order prioritises execution, not price. A stop-limit has both an activation trigger and a worst acceptable price.

2b · Futures SpecificationCh 2 · mechanics

3 · Hedge Direction & BasisCh 3 · core

basis and effective pricebₜ = Sₜ − Fₜ
Long purchase: S₂ − (F₂−F₁) = F₁ + b₂
Short sale: S₂ + (F₁−F₂) = F₁ + b₂

The hedge locks an approximate result because closing basis is uncertain. Basis risk comes from spot and futures moving differently; timing, location, grade and use of a related asset can all matter.

3b · Minimum-Variance SizeCh 3 · calculation

cross-hedge ratioh* = ρ × σS / σF
N* = h* × QA / QF

Report continuous N* before whole-contract rounding. High positive correlation supports a larger risk-reducing hedge; weak correlation limits attainable variance reduction. Minimum variance is an objective, not a promised price.

3c · Contract Choice & GovernanceCh 3 · limits

4 · Forward PricingCh 4 · replication

A forward price is a no-arbitrage benchmark, not a forecast. For an investment asset that can be bought and stored, compare forward delivery with borrowing, buying and carrying the asset to T.

continuous compoundingNo income: F₀ = S₀eʳᵀ
Known cash income: F₀ = (S₀ − I)eʳᵀ
Known proportional yield: F₀ = S₀e⁽ʳ⁻q⁾ᵀ
Currency: domestic financing; foreign rate acts as yield

Arbitrage decision

If market forward is above replicating cost: borrow, buy and carry the asset, and short the dear forward. If it is below, reverse cash-and-carry only when borrowing the asset and short selling are feasible.

Check bid–ask spreads, financing, storage, asset borrowing, quantity, timing and contract specifications. Frictions create a no-arbitrage band. For consumption assets, convenience benefits can weaken simple equality.

Delivery price is fixed in an existing contract. Its later forward value is the discounted advantage or disadvantage versus current market terms—do not overwrite the fixed K with today’s new forward quote.

4b · Replication ProofCh 4 · full-credit form

A complete arbitrage answer shows a non-negative package and why the unknown Sₜ cancels. “Cash-and-carry” alone is not the trade. Keep the same quotation, compounding convention, maturity and quantity across the market forward and replicating package.

5 · Swap Cash-Flow LedgerCh 5 · method

write before cancellingNet cost = original financing
+ swap payment − swap receipt

Cancel floating terms only when benchmark, notional, reset date and day-count basis match. The original borrowing stays outstanding. Notional normally sets payment size and is not exchanged in a single-currency rate swap.

5b · Comparative AdvantageCh 5 · QSD

quality-spread differentialQSD = fixed-rate spread − floating-rate spread

QSD is the total potential gain ceiling. Benefits assigned to both firms plus any intermediary spread cannot exceed it. Compute both market spreads, subtract, design directions, then rebuild both complete cash-flow ledgers.

Value each currency leg with its own yield curve, then convert into one reporting currency at current spot. Attach a currency unit to every arrow. Replacement value creates counterparty risk after market rates or exchange rates move.

5c · Prove the TransformationCh 5 · checks

For each party, keep original financing, swap payment and swap receipt separate until the signs are visible.

6 · Option Position MapCh 6 · rights

6b · Payoff → ProfitCh 6 · formulas

terminal payoffLong call = max(Sₜ − K, 0)
Long put = max(K − Sₜ, 0)
Short payoff = − corresponding long payoff

simplified terminal profitLong call = max(Sₜ−K,0) − c
Short call = c − max(Sₜ−K,0)
Long put = max(K−Sₜ,0) − p
Short put = p − max(K−Sₜ,0)

Strike controls exercise; premium controls profit break-even. An in-the-money option can still lose after premium. Long-call loss is limited to premium; short-call loss can keep expanding as Sₜ rises.

6c · Graph & Exercise AuditCh 6 · geometry

7 · Worked: Daily MarginCh 2 · supplied numbers

Given: long 3 contracts; 100 units each; entry F=$52.40; initial margin $2,400/contract; maintenance $1,800/contract. Settlements: $51.90, $53.10, $50.80.

opening balancesInitial = 3×$2,400 = $7,200
Maintenance = 3×$1,800 = $5,400

Threshold: all balances exceed $5,400, so no margin call under these data. Reconcile: cumulative VM = −150+360−690 = −$480.

3×100×($50.80−$52.40) = 300×(−$1.60) = −$480 ✓

Margin traps

7b · Ledger Under PressureCh 2 · drill

Build columns in this order: date; previous settlement; new settlement; ΔF; position sign; n×Q; variation transfer; pre-deposit balance; maintenance test; deposit; closing balance. Keeping the pre- and post-deposit balances separate prevents an untraceable call amount.

8 · Worked: Cross-Hedgecourse example

Given: processor will buy 900 tonnes; futures contract covers 50 tonnes; σS=1.8%, σF=2.0%, ρ=0.80.

1. Future purchase → price rise is adverse → long futures.
2. Compute the minimum-variance ratio.
3. Scale the exposure by contract quantity.
4. Report the continuous count before rounding.

ratioh* = 0.80 × 0.018 / 0.020 = 0.72

contract countN* = 0.72 × 900 / 50 = 12.96

Answer: 13 long contracts is a defensible whole-contract hedge. State that rounding leaves a small mismatch. Long futures fit because gains when the input price rises can offset the higher physical purchase cost.

8b · Hedge Answer AuditCh 3 · marks

Do not call a losing futures leg a failed hedge. If a long hedge loses after the input price falls, the physical purchase becomes cheaper. Evaluate against the protected effective price or variance objective.

8c · Basis Reconciliation DrillCh 3 · no new data

For a purchase hedge, lay out spot paid and subtract a futures gain (or add a futures loss). For a sale hedge, lay out spot proceeds and add a futures gain (or subtract a loss). Only then compress to F₁+b₂.

9 · Worked: Cash-and-CarryCh 4 · supplied numbers

Given: asset spot price $100; no income; one year; 5% effective financing.

discrete one-year carryTheoretical delivery price = $100×(1.05) = $105

If the market delivery price exceeds $105 by more than executable frictions, buy the replicating package and short the dear forward. If market K is below $105, reverse cash-and-carry requires an executable short sale.

9b · Carry Variant ChooserCh 4 · assumptions

Compounding must match the question. Label T in years. Known cash income enters as present value; proportional yield enters the exponent. Explain practical no-arbitrage bands when spreads, storage, funding or short-sale restrictions are supplied.

9c · Arbitrage Answer TemplateCh 4 · drill

1. Compute the theoretical delivery price using the stated compounding and carry inputs.
2. Compare it with the market delivery price in the same units and maturity.
3. Buy the cheaper complete route; sell the dearer complete route.

10 · Worked: QSDCh 5 · supplied quotes

spreadsFixed spread = 7.0% − 5.2% = 1.8%
Floating spread = 0.75% − 0.35% = 0.40%
QSD = 1.8% − 0.40% = 1.40%

Interpretation: 1.40% is the total potential gain ceiling before transaction costs. Savings allocated to North + South + intermediary cannot exceed 1.40%. A complete answer must still give each firm its desired exposure and prove its claimed cost from a ledger.

10b · Swap Ledger CheckCh 5 · method

Given: debt costs Reference + 1.1%; swap pays 4.4% fixed and receives matching Reference.

three-line ledgerOriginal debt: + Reference + 1.1%
Swap payment: + 4.4% fixed
Swap receipt: − Reference
Net synthetic fixed cost = 5.5%

Cancellation is valid only because the reference terms match. If notional, benchmark, reset date or day-count differs, a basis exposure remains.

10c · Structure VerificationCh 5 · drill

11 · Worked: Call PayoffCh 6 · supplied figure

Given: long call, strike K=$60, premium c=$4.

Break-even: K+c=$64. At Sₜ=$60 the option has no intrinsic value and expires worthless; the holder loses the premium. At Sₜ=$64 the $4 payoff exactly recovers the $4 premium.

Holder/writer paired profits sum to zero when financing and transaction costs are ignored. Writer profit is $4−max(Sₜ−$60,0).

11b · Option Fast TableCh 6 · recall

Label the vertical axis payoff or profit before drawing. Then mark K, break-even, slopes and bounds. Short positions are negatives of long payoffs, with premium sign reversed for profit.

11c · Option Trap BankCh 6 · drill

12 · Method Chooserall chapters

13 · Error Sweeplast 90 seconds

Cash-flow map before formula. Show continuous quantities before rounding. Separate payoff from profit, delivery price from current value, margin trigger from restoration target, and position direction from economic purpose.

14 · Fast Recall Termsglossary

Attach every term to the requested calculation or decision.