A contract that moves risk
A derivative is a contract whose value depends on something else: a commodity, a currency, a share, or an interest rate. It does not create the underlying exposure, it transfers it from one party to another.
A producer wants a known price before harvest. A buyer wants a known cost before the season. A derivative lets them agree today on a price for later, and both sleep better even though the total risk in the world is unchanged.
Derivatives are neither safe nor dangerous on their own. What matters is whether the user is reducing an exposure they already have, or taking on a new one for the chance of a profit.
Key points
- Derivatives transfer risk rather than remove it.
- Hedging offsets an exposure you already hold.
- Speculation creates an exposure you did not have.
Pricing a forward
F = S × (1 + r)ᵀ
The price that makes carrying the asset and agreeing to buy it later equivalent.
If an asset costs 100 today and money costs 8% a year, agreeing to buy it in one year should cost 108. Anything else invites arbitrage: borrow, buy, store, and deliver at a higher forward price for a riskless gain.
The same logic explains why a forward price is not a forecast. It is the spot price grown at the cost of carry, and it will only match the future spot price if the market's expectations happen to be right.
Storage costs, dividends, and convenience yield adjust the relationship, but the anchor stays the same: today's price plus the cost of waiting.
Key points
- A forward price is a no-arbitrage price, not a prediction.
- Higher rates or carrying costs raise the forward price.
- If the forward looks cheap, check what you are assuming about carry.
Locking in a price
A farmer expects 1,000 tonnes of wheat and fears a price fall. Selling futures at 32,000 a tonne locks in the price before the crop is harvested.
At harvest the spot price is 29,000. The crop sells for 29,000,000, but the futures position gains 3,000 a tonne, or 3,000,000. Total proceeds are 32,000,000, exactly the locked-in price.
Margin is the deposit that makes the contract credible. At 10% of a 32,000,000 notional, the farmer posts 3,200,000, and daily settlement means cash moves before the crop is even sold.
A hedge is not a way to make money. It is a way to make the future predictable, and it costs the upside you would have had if prices moved your way.
Key points
- A hedge fixes the price; it does not improve it.
- Margin calls can arrive before the underlying cash flow.
- Basis risk remains even when the hedge is in place.
Options: paying for the upside
Payoff = max(S − K, 0)
The value of the right to buy at the strike.
Profit = max(S − K, 0) − Premium
Payoff after the cost of the option.
A futures contract removes both the downside and the upside. An option removes the downside and keeps the upside, and the premium is what you pay for that asymmetry.
A call with a strike of 600 bought for a premium of 25 is worth 80 when the underlying finishes at 680, a net profit of 55. If the underlying finishes at 540 the option expires worthless and the loss is the 25 premium, no more.
The break-even is the strike plus the premium, 625. Below that the option loses money even if it finishes in the money; above it the position profits one for one.
Key points
- Options cost a premium in exchange for asymmetry.
- The maximum loss on a bought option is the premium.
- Break-even includes the premium, not just the strike.
Interactive experiment
Beta, Sharpe, and Jensen's alpha
One asset, one market. Measure how much systematic risk the asset carries (beta), how well it is paid for total risk (Sharpe), and whether it beat what CAPM says it should earn (alpha).
Sharpe = (E(R) - Rf) / SD . B = Cov(Ra, Rm) / Var(Rm)
Your inputs
Return available with no risk.
Result
- Beta
- 2.00×
- Sharpe ratio
- 0.32×
- Jensen's alpha
- 1.0%
- Correlation with the market
- 1.00×
- Asset mean return
- 2.0%
- Asset volatility
- 3.2%
- Market mean return
- 1.0%
- Treynor ratio
- 0.00×
Beta of 2.00 means the asset moves 2.00x with the market. Sharpe is 0.32 and the result shows positive alpha: it beat its CAPM benchmark.
03 / Apply
An airline hedges its fuel bill
An airline expects to buy fuel every month for a year. It hedges part of the requirement with futures and leaves the rest exposed, balancing the certainty it needs against the flexibility it wants.
The assumptions
- Fuel is a large share of operating cost.
- Hedging the full requirement would lock in the upside too.
- Margin calls must be funded from working capital.
What to take away
01
Partial hedges keep some flexibility and some risk.
02
The hedge protects the budget, not the trading desk.
03
Funding margin is part of the cost of hedging.
Your turn
0 of 4 answered
01Question
An asset costs ৳100 today and the one-year rate is 8%. Ignoring storage, what is the no-arbitrage forward price?
02Question
A call has a strike of ৳600 and a premium of ৳25. The underlying finishes at ৳680. What is the net profit per unit?
03Question
A farmer sells futures on 1,000 tonnes at ৳32,000. The spot price at harvest is ৳29,000. What are total proceeds, including the futures gain?
04Question
Which best describes the difference between a future and a forward?
Take it into the Lab
Experiment with the same idea.
The Lab turns this topic into a workspace: change the drivers, watch the statements move, and see the consequence before you commit to a decision.
What-if analysis
Change price, cost, and working capital. Watch margins, return, and risk move together.
Open the labFormula lab
Understand, manipulate, observe, solve, then apply the formula to a decision.
Walk the formulaStatement playground
See how one driver propagates through the income statement, balance sheet, and cash flow.
Open the playgroundSources & further reading
CFA Institute · Derivatives and risk management ↗OpenStax · Principles of Finance (free textbook) ↗Educational sample content. Worked examples use hypothetical figures. Dates refer to the note's latest content update.