9.6 Derivatives Case Lab

How to work a derivatives case

A derivatives case is a translation problem. The stem describes a company, investor, or trader with an exposure, and 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: a firm buying euros in 90 days is harmed by a stronger euro; a pension owning equities is harmed by a falling market; a floating-rate borrower is harmed by rising short-term rates. Then pick the derivative that gains when the exposure loses value.

A future buyer uses a long forward/futures hedge; a future seller uses a short hedge; a floating-rate borrower wants pay-fixed swap exposure; a stockholder seeking downside protection buys puts.

Mini case 1: importer currency hedge

A US importer must pay EUR 5 million in three months and fears euro appreciation. The exposure is a future euro purchase, so the hedge must gain when the euro rises: 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 it falls, the firm pays less in spot but loses on the forward (or forgoes the lower price). The hedge reduces uncertainty, not every cost, and a forward leaves no upside while a long call on the euro would preserve the benefit of a falling euro at the cost of a premium.

Mini case 2: equity investor option choice

An investor owns a diversified portfolio and wants to limit downside for six months while keeping upside. A short index-futures hedge would cut downside but also surrender upside, because portfolio gains would be offset by futures losses. A protective put fits the objective: the put gains when the index falls below the strike, while the investor keeps upside above the insured level. The costs are the premium and any basis risk between the portfolio and the index underlying the put.

Mini case 3: swap transformation

A company has floating-rate debt and expects rates to rise; it wants predictable costs. A pay-fixed, receive-floating swap transforms the liability: floating receipts offset floating debt payments, leaving the fixed swap leg as the net cost. The company has cut rate uncertainty but not all risk: it retains counterparty risk, collateral and settlement obligations, documentation risk, and the chance that rates fall, making the fixed payments costly relative to floating.

Mini case 4: arbitrage framing

Suppose a forward price sits far above the no-arbitrage level implied by spot, financing cost, and income. The cash-and-carry trade is to buy the underlying now, finance it, and sell it forward; the forward sale repays the financing and locks the spread if costs hold. If the forward is far below fair value, reverse cash-and-carry: short the underlying, invest the proceeds, and buy the forward to close the short at maturity. Real markets add short-sale constraints, bid-ask spreads, collateral, and execution risk, so the textbook profit shrinks.

Structured aid: integrated answer grid

Final exam workflow

1. Name the underlying and time horizon.
2. Identify the exposure and whether the party is a future buyer or seller.
3. Classify as forward commitment or contingent claim.
4. Determine long or short.
5. Compute payoff first, then profit if a premium is given.
6. Check moneyness for options.
7. State the residual risk: basis, liquidity, credit, margin, opportunity cost, or model risk.

Mini case 5: covered call income with a view

A portfolio manager holds a stock at 80, expects it to drift sideways for a quarter, and wants incremental income. Writing a covered call with strike 88 for a premium of 2 produces income now and obligates the manager to sell at 88 if the stock rallies. If the stock ends at 84, the call expires worthless and the manager keeps the 2 premium plus the 4 appreciation. If it ends at 92, the call is exercised, the manager delivers at 88, and the upside above 88 is forgone, though the realized outcome of 88 plus 2 still beats the starting 80.

If the stock falls to 70, the premium of 2 cushions only part of the 10 loss, illustrating that a covered call is a mildly bullish, income-oriented strategy, not downside protection. Contrast this with mini case 2, where the investor wanting genuine downside insurance bought a put instead.

Exam focus

Level I derivatives items reward clean mechanics. Do not jump to a memorized answer before labeling the position: a long call, a long forward, and a pay-fixed swap can all benefit from certain moves, yet their cash flows, downside, and obligations differ. The strongest answer states the economic reason, for example a farmer shorts futures because the farmer will sell the crop and is harmed by lower prices, or a no-arbitrage trade works because two strategies share equivalent future payoffs at different current costs.

When a case gives numbers, compute the payoff with the relevant max() expression first, then net any premium for profit, and only then comment on residual risks such as basis, counterparty, liquidity, or opportunity cost.