9.6 Derivatives Case Lab
Key Takeaways
- Case questions usually combine position direction, contract type, payoff, and risk-management objective.
- Start by identifying the exposure, then select the derivative position that offsets or expresses that exposure.
- Distinguish payoff from profit and price from value before doing calculations.
- No-arbitrage answers depend on equivalent cash flows, not on broad opinions about market direction.
- Strong derivative analysis connects contract mechanics to business purpose, cash flow timing, and residual risks.
How to work a derivatives case
A derivatives case is usually a translation problem. The stem describes a company, investor, or trader with an exposure. Your job is to convert that exposure into a contract position, payoff, hedge effect, or arbitrage relation.
Start by asking what can go wrong for the decision maker. If a firm will buy euros in 90 days, it is harmed by a stronger euro. If a pension plan owns equities, it is harmed by a falling equity market. If a borrower pays floating interest, it is harmed by rising short-term rates.
Then choose the derivative that gains when the exposure loses value. A future buyer usually uses a long forward or futures hedge. A future seller usually uses a short forward or futures hedge. A floating-rate borrower usually wants pay-fixed swap exposure. A stockholder who wants downside protection may buy puts.
Mini case 1: importer currency hedge
A US importer must pay EUR 5 million in three months. The firm is worried that the euro will appreciate against the US dollar. The natural exposure is a future euro purchase. The hedge should gain when the euro rises, so the firm can buy euros forward or take a long euro futures position.
If the euro rises, the firm pays more in the spot market but gains on the derivative. If the euro falls, the firm pays less in the spot market but loses on the derivative or forgoes the lower price if the forward is locked. The hedge reduces uncertainty, not every cost.
Mini case 2: equity investor option choice
An investor owns a diversified equity portfolio and wants to reduce downside risk for six months while preserving upside. A short futures hedge would reduce downside, but it would also reduce upside because gains on the portfolio would be offset by losses on the short futures position.
A protective put is more aligned with the objective. The put gains when the portfolio or index falls below the exercise price, while the investor keeps upside above the insured level. The cost is the option premium and any mismatch between the portfolio and the index used for the put.
Mini case 3: swap transformation
A company has floating-rate debt and expects interest rates to increase. The company wants predictable borrowing costs. A pay-fixed, receive-floating swap can transform the liability. Floating receipts on the swap offset floating payments on the debt, leaving the fixed swap payments as the main net cost.
The company has reduced interest rate uncertainty, but it has not eliminated all risk. It still faces counterparty risk, collateral or settlement obligations, documentation risk, and the possibility that rates fall, making fixed payments unattractive relative to floating rates.
Mini case 4: arbitrage framing
Suppose a forward price is far above the no-arbitrage level implied by spot price, financing cost, and income. The cash-and-carry idea is to buy the underlying now, finance the purchase, and sell it forward. The future sale through the forward repays the financing and locks in the spread if costs and assumptions hold.
If the forward price is far below fair value, reverse cash-and-carry is the intuition. Short the underlying, invest the proceeds, and buy the forward. At maturity, use the forward purchase to close the short. Real markets add short-sale constraints, bid-ask spreads, collateral, and execution risk.
Structured aid: integrated answer grid
| Stem clue | Likely classification | Candidate action |
|---|---|---|
| Fixed future purchase price | Forward commitment | Long if buying, short if selling |
| Standardized contract with margin | Futures | Track daily settlement and margin calls |
| Exchange fixed and floating cash flows | Swap | Identify pay side and receive side |
| Right to buy | Call option | Use max(0, S - X) |
| Right to sell | Put option | Use max(0, X - S) |
| Same future payoff, different current cost | Arbitrage relation | Buy cheap package and sell expensive package |
| Hedge does not perfectly offset exposure | Basis risk | Explain mismatch source |
Final exam workflow
- Name the underlying and time horizon.
- Identify the existing exposure and whether the party is a future buyer or seller.
- Classify the derivative as forward commitment or contingent claim.
- Determine long or short position.
- Calculate payoff first, then profit if a premium or cost is given.
- Check moneyness for options.
- Explain residual risk: basis, liquidity, credit, margin, opportunity cost, or model risk.
Exam focus
Level I derivatives questions reward clean mechanics. Avoid jumping to a memorized answer before labeling the position. A long call, long forward, and pay-fixed swap can all benefit from certain market moves, but their cash flows, downside, and obligations differ.
The strongest answer states the economic reason. A farmer shorts futures because the farmer will sell the crop and is harmed by lower prices. A protective put preserves upside because the investor owns the asset and buys a right to sell. A no-arbitrage trade works because two strategies have equivalent future payoffs.
A US company that must buy euros in three months and wants protection against euro appreciation would most likely:
An equity investor wants downside protection while retaining upside potential. The most suitable basic derivative strategy is:
In an arbitrage question, the key condition that supports a riskless profit is most likely: