CFA Level I · CFA Level I Exam

Derivative Instrument and Derivative Market Features: formula sheet

Full chapter guide

Key formulas

Definition: Derivative value = f(underlying value); The derivative's value is derived from the underlying and has a finite life.
Long forward/futures payoff at expiry: Payoff = S(T) − F0; Symmetric. The short position gets the opposite: F0 − S(T).
Long call payoff at expiry: Payoff = max(0, S(T) − X); Profit = payoff − premium. Maximum loss for the buyer is the premium.
Long put payoff at expiry: Payoff = max(0, X − S(T)); Profit = payoff − premium. Asymmetric payoff.
Main purposes: Risk management; price discovery; operational efficiency; market efficiency; Know each purpose and be able to recognize it in a stem.
Exchange-traded profile: Standardized terms + clearinghouse + daily margin + public prices + high regulation; Typical of futures and many listed options. Lower counterparty risk, higher liquidity and transparency.
OTC profile: Customized terms + bilateral credit risk + private prices + lighter (but growing) regulation; Typical of forwards and swaps. Flexible, but more counterparty risk and less transparency.
Typical instrument mapping: Futures → exchange; Forwards, swaps → OTC; Options → either; Use this to classify an instrument quickly when a question does not state the market.
Daily gain or loss on a futures position: Long: (Settlement price today − Settlement price yesterday) × Contract size × Number of contracts. Short: the negative of this.; On the day of trade, use the trade price instead of yesterday's settlement price.
Margin account balance: Ending balance = Beginning balance + Gains − Losses + Deposits − Withdrawals; Do the arithmetic every day; a margin call depends on the ending balance.
Margin call trigger: Margin call if balance < Maintenance margin; Equal to maintenance is not below it. The call is only triggered below.
Variation margin required: Variation margin = Initial margin − Current balance; Under the CFA curriculum convention, the deposit restores the account to initial margin, not to maintenance margin. Exchange practice can differ.
Margin ordering: Maintenance margin < Initial margin; Initial margin is the higher figure; the gap is the cushion before a call.
Long forward payoff at expiration: Payoff (long) = ST − F0; ST is the spot price of the underlying at expiry. F0 is the forward price agreed at initiation. It can be positive or negative.
Short forward payoff at expiration: Payoff (short) = F0 − ST; Exactly the negative of the long payoff. Applies per unit; multiply by contract size.
Forward payoff, total: Total payoff = (ST − F0) × units (long); Always multiply by the number of units, such as barrels, ounces or shares.
Fixed-for-floating swap net payment: Net payment = (fixed rate − floating rate) × notional × period fraction; Positive means the fixed payer pays. Negative means the fixed payer receives. Check the day-count period, such as 0.5 for semiannual or 0.25 for quarterly.
Futures daily settlement: Daily gain (long) = settlement price today − settlement price yesterday; The short gets the opposite. The result is added to or taken from the margin account.
Call payoff at expiration (buyer): max(0, S_T − X); S_T is the underlying price at expiration, X is the strike. Never negative.
Put payoff at expiration (buyer): max(0, X − S_T); Never negative for the buyer.
Buyer profit: Profit = Payoff − Premium; Ignores financing cost and transaction costs unless the question includes them.
Seller (writer) profit: Profit = Premium − Payoff; Seller's profit is the exact negative of the buyer's.
Breakeven price: Call: X + premium. Put: X − premium; The same for buyer and seller.
Maximum loss and gain: Long call: loss = premium, gain unlimited. Long put: loss = premium, gain = X − premium. Short call: gain = premium, loss unlimited. Short put: gain = premium, loss = X − premium; Put gain/loss assumes the underlying can fall to zero.
Moneyness: Call in the money if S > X; put in the money if S < X; at the money if S = X; Out of the money has zero exercise value now.
CDS payout on credit event: Payout = Notional × (1 − Recovery rate); Equals loss given default on the notional covered.

Quick revision

A derivative's value depends on an underlying asset, rate, index or other variable.
Forward commitments (forwards, futures, swaps) obligate both sides; contingent claims pay off on a specified future event, and options give the holder a right.
Exchange-traded derivatives are standardised and centrally cleared; OTC derivatives are customised and private.
OTC contracts carry more counterparty credit risk unless they are centrally cleared or collateralised.
A clearinghouse becomes the counterparty to both sides of a cleared trade.
Initial margin is the deposit made when a futures position opens.
Variation margin settles daily gains and losses through marking to market.
When the account balance falls below maintenance margin, a margin call typically requires a variation margin deposit large enough to restore the account to the initial margin level, as the CFA curriculum treats it.
A forward is customised and typically settles at expiry; a future is standardised and marked to market daily.
A swap exchanges a series of cash flows, such as fixed for floating interest payments.
An option buyer pays a premium and holds the right; the writer holds the obligation.
A credit default swap gives protection against default of a reference entity; the protection buyer pays a periodic premium.

Common mistakes

Saying a derivative has its own intrinsic value independent of the underlying. Fix: Remember its value is derived from the underlying. No underlying movement, no reason for value to change.
Thinking the underlying must be a physical asset. Fix: Underlyings include rates, indexes, currencies, credit events and weather. Many settle in cash.
Saying all OTC derivatives are unregulated. Fix: Remember that OTC regulation has increased since the 2008 crisis, with reporting and central clearing for many standard contracts. Say 'generally less regulated', not 'unregulated'.
Assuming exchange-traded derivatives carry no counterparty risk at all. Fix: Say counterparty risk is greatly reduced, not eliminated. Margin and daily settlement limit it, but the clearinghouse itself still matters.
Calling initial margin a down payment on the contract. Fix: Remember that futures margin is a performance bond. No loan is made and no ownership is purchased.
Restoring the account only to maintenance margin after a call. Fix: Variation margin brings the balance back up to initial margin.
Calling a futures contract customized and OTC, or a forward exchange-traded. Fix: Remember: forward = private, customized, credit risk; futures = exchange, standardized, clearinghouse, daily marking to market.
Reversing the payoff: using F0 − ST for the long. Fix: The long buys, so the long gains when the price rises. Long = ST − F0. Short is the opposite.
Treating the buyer's payoff as negative when the option expires worthless. Fix: Payoff is never below zero for the buyer. The loss shows up only after subtracting the premium.
Forgetting the premium when asked for profit. Fix: Read whether the question asks for payoff or profit. Profit always includes the premium.

Exam tips

Expect conceptual questions that test one feature: underlying, payoff, leverage or purpose. Read the key phrase carefully.
Words such as 'eliminate' or 'always' can signal an overstated claim, but do not rely on keywords alone. Check each option against the concept.
Know that options are asymmetric and forwards, futures and swaps are symmetric.
Do the simple payoff arithmetic carefully and include the contract size.
Questions are standalone, so spend little time here and bank the easy marks.
Questions are three-option and conceptual. Look for one option that attaches a feature to the wrong market and eliminate it.
Watch absolute words such as 'no', 'all' and 'always'. Counterparty risk is reduced, not eliminated, on exchanges.
Know the instrument map: futures on exchanges, forwards and swaps OTC, options in both.