Derivative Benefits, Risks, and Issuer and Investor Uses: formula sheet

Key formulas

Exchange-traded features

Standardized terms + exchange trading + clearinghouse guarantee + daily mark-to-market + margin

Use this as a checklist. If a question describes customized terms, think OTC.

OTC features

Customized terms + private negotiation + less transparency + counterparty credit risk (unless centrally cleared)

Mostly forwards, swaps and many options. Typically less regulated and less liquid, though regulation of OTC is increasing.

Clearinghouse/CCP role (novation)

Original buyer–seller contract → buyer–CCP and CCP–seller

The CCP becomes counterparty to both sides, so each side faces the CCP, not each other.

Daily settlement

Gain or loss for the day = change in contract price × contract size × number of contracts

Margin accounts are adjusted every day, which limits the build-up of unpaid losses.

Leverage effect on return

Return on margin ≈ Change in position value ÷ Margin posted

Same price move gives a larger percentage result when margin is small. Gains and losses are both magnified.

Basis

Basis = Spot price − Futures price

This is a common convention, but the sign convention can vary, so check how a question defines it. Basis risk is the risk that this difference changes unexpectedly. It also arises when the hedged asset differs from the contract's underlying (a cross-hedge), or when maturity or location differ.

Maximum loss by position

Long option: premium paid. Short call: potentially unlimited. Long forward or futures: limited to the contract price (the underlying falling to zero), but can exceed margin. Short forward or futures: theoretically unlimited.

Use this to check any statement about 'limited' or 'unlimited' loss. A long forward or futures loss is capped by the price falling to zero, yet it can still be far larger than the margin posted.

Hedge logic

Gain/loss on derivative ≈ −(gain/loss on exposure)

A good hedge makes the net position close to fixed. It is rarely perfect because of basis risk.

Floating-rate borrower using a pay-fixed swap

Net cost = floating loan rate + fixed swap rate − floating swap rate received

If the swap floating rate equals the loan rate, the net cost is the fixed swap rate (plus any loan spread).

Exposure-to-hedge direction

Hurt by a price fall → short hedge; hurt by a price rise → long hedge

A producer of a commodity is exposed to falling prices, so it goes short futures. A buyer of a commodity is exposed to rising prices, so it goes long futures.

Synthetic long asset

Long underlying ≈ Long forward + risk-free bond

The bond is worth the present value of the forward price, so it funds delivery at expiry.

Synthetic risk-free asset

Long underlying + short forward ≈ risk-free bond

A full hedge locks in the risk-free return, so the hedged position earns the risk-free rate if there is no arbitrage.

Futures contracts to change duration

Number of contracts = (target MD − current MD) ÷ futures MD × (portfolio value ÷ futures price)

MD is modified duration. Futures MD is the modified duration of the futures contract (for bond futures, based on the cheapest-to-deliver bond). A positive result means buy, a negative result means sell. Treat as an approximation and match each duration to the same units.

Futures contracts to change equity exposure

Contracts = (target beta − current beta) ÷ futures beta × (portfolio value ÷ futures contract value)

Futures on an index have beta of about 1. Positive means buy, negative means sell.

Covered call payoff and profit at expiry

Payoff = S_T − max(0, S_T − X); Profit = S_T − S_0 − max(0, S_T − X) + c_0

S_T is the stock price at expiry, S_0 the purchase price, X the strike and c_0 the call premium received. Upside is capped at the strike, and the premium is added to profit as a small cushion.

Quick revision

• A derivative's value depends on the performance of an underlying asset, rate or index.
• 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.
• Derivatives can help price discovery and improve market efficiency.
• Derivatives often allow risk to be transferred at lower transaction cost than trading the underlying.
• Leverage means a small outlay gives large exposure, so gains and losses are both magnified.
• Common criticisms are speculation, complexity, and the risk that losses spread through the financial system.
• Hedging reduces an existing exposure; speculating takes on new risk for expected gain.
• Issuers use derivatives to manage risks in cash flows, funding costs and input or output prices.
• Investors use derivatives to change exposure, take views, and manage portfolio risk efficiently.
• Derivatives can give access to exposures that are hard or costly to hold directly.
• In a question, identify who the user is and what the goal is before reading the options.

Common mistakes

• Saying exchange-traded derivatives have no credit risk at all. Fix: Say credit risk is greatly reduced, not eliminated. The clearinghouse can in theory fail, which is why margin and default funds exist.
• Assuming all OTC derivatives are bilateral and uncleared. Fix: Remember that standardized OTC trades such as many swaps can be centrally cleared through a CCP, which takes on the counterparty role.
• Saying derivatives eliminate risk. Fix: Remember that derivatives transfer risk between parties. The hedger gives up risk and the counterparty takes it.
• Confusing price discovery with price setting by the derivative. Fix: Think of price discovery as information. Derivative prices reveal expectations, and they often react to news quickly.
• Saying leverage means derivatives always lose more than they gain. Fix: Leverage magnifies both gains and losses. The risk is the larger swing relative to cash invested.
• Thinking a long option can lose more than the premium. Fix: A buyer's maximum loss is the premium. The writer of a call faces potentially unlimited loss.
• Taking the same side as the exposure, such as a floating-rate borrower receiving fixed in a swap. Fix: A floating-rate borrower wants fixed cost, so it pays fixed and receives floating.
• Claiming a forward hedge keeps the upside. Fix: Forwards, futures and swaps lock in the outcome both ways. Only bought options keep the favourable side, for a premium.
• Calling every derivatives trade a hedge. Fix: A hedge offsets an existing exposure. If there is no underlying exposure, the trade is speculation or exposure gain.
• Choosing the wrong direction when changing duration. Fix: Longer duration means more sensitivity to rates, so you add rate exposure (buy bond futures, or receive fixed and pay floating). If you expect rates to rise, shorten duration (sell bond futures, or pay fixed and receive floating).

Exam tips

• Identify the market from the clue words first: standardized means exchange, customized means OTC.
• Expect distractors that claim a clearinghouse removes all risk. Prefer wording like reduces or mitigates.
• Remember that a CCP can clear OTC trades, so do not link OTC only to bilateral credit risk.
• Read the question stem for who is the counterparty after the trade is cleared.
• With no penalty for wrong answers, always answer. Eliminate the option that mismatches the market type, then choose between the other two.
• Questions usually ask you to name the benefit from a short scenario, so practise matching keywords to benefits.
• Watch for absolute words such as 'always', 'eliminates' and 'guarantees'. They usually mark wrong options.
• Read whether the stem asks about benefits or risks. Leverage and opacity can appear as tempting wrong options.