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CFA Level I · CFA Level I Exam

Pricing and Valuation of Forward Contracts for CFA Level I

Forward pricing sets the forward price so that no arbitrage is possible: F₀ = S₀ × (1 + r)^T for an asset with no cash flows. Valuation is different: it measures the gain or loss on an existing contract at a later date. Learn the price formula first, then adjust for income, costs, currencies and rates.

What this chapter covers

This chapter shows how to set the price of a forward contract and how to value one after it has been created. The core idea is no arbitrage. You can buy the asset today and carry it to the delivery date, or you can enter a forward and pay later. Both routes must cost the same. If they do not, a risk-free profit exists, and trading removes it.

You start with an asset that has no cash flows, where the forward price is the spot price compounded at the risk-free rate. Then you adjust for benefits such as dividends, coupons or convenience yield, and for costs such as storage. Next you value a forward during its life, which is the present value of the difference between the new forward price and the original contract price. The chapter then applies the same logic to forward rate agreements, currency forwards with interest rate parity, and forwards across varying maturities.

This chapter is the base for the rest of the derivatives topic. Futures, swaps and options all reuse the same no-arbitrage thinking. It also links to fixed income through spot and forward rates, and to economics through exchange rates and interest rate parity. Learn it well and later derivatives chapters become easier.

Derivatives and Risk Management carries a modest weight in the curriculum, but the pricing logic here is reused across forwards, futures, swaps and options, so one clear method earns marks in several places. Questions are short, standalone, numerical and often solved in under 90 seconds once the formula is automatic. They also tempt you with plausible wrong options, such as a price instead of a value or the wrong sign on income. With no penalty for wrong answers, a solid method lets you eliminate two options fast and pick the right one.

Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities: topics in the order to study them

  1. 1Forward Contract Pricing PrinciplesStart with no arbitrage, the cost-of-carry idea and the difference between price and value, because every later formula rests on them.
  2. 2Forward Pricing for Assets with No Cash FlowsThis is the simplest case, F₀ = S₀ × (1 + r)^T, and it gives you the base formula to adjust later.
  3. 3Forwards on Assets with Income or Carry CostsOnce the base formula is clear, you subtract the future value of benefits and add the future value of costs.
  4. 4Valuing Forward Contracts During Their LifeValuation needs the pricing formula, so you learn it after pricing and before applying it to rates and currencies.
  5. 5Forward Rate Agreements (FRAs) Pricing and ValuationFRAs apply the same price-versus-value logic to interest rates, so they come after the asset forwards.
  6. 6Forwards on Currencies and Interest Rate ParityCurrency forwards use two interest rates, and covered interest rate parity is a direct extension of the carry formula.
  7. 7Forward Pricing Across Varying MaturitiesFinish with different maturities and the term structure, which pull together spot rates, forward rates and the earlier formulas.

How to prepare Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

Aim to understand one idea, no arbitrage, and then practise it in each setting until you can set up the calculation in seconds.

  1. Write the no-arbitrage argument in your own words: buy and carry versus forward. Check that you can explain why a mispriced forward creates a risk-free profit.
  2. Learn the base formula F₀ = S₀ × (1 + r)^T and then add the adjustments in one consistent form: F₀ = S₀(1 + r)^T − FV(benefits) + FV(costs). This is the same as (S₀ − PV of benefits + PV of costs) × (1 + r)^T. Practise each variant until you can write it without notes.
  3. Separate price from value. The forward price is fixed at inception so that the contract value is zero. The value later is the present value of the difference between the current forward price and the contract price, with the sign depending on whether you are long or short.
  4. Practise FRAs with a fixed layout: identify the rates for the two periods, compute the forward rate from (1 + S_B × t_B) = (1 + S_A × t_A) × (1 + F × (t_B − t_A)), then value the FRA as the present value of (new forward rate − contract rate) × notional × period length. Take care with day-count and the payment date.
  5. Work currency questions with a clear quote convention. Quote as price currency per 1 unit of base currency, note which is which, then apply covered interest rate parity with the price currency rate in the numerator.
  6. Use your TI BA II Plus or HP 12C for compounding. On the BA II Plus, use the y^x key for powers, and clear the memory between questions. Keep rates as decimals and keep full precision until the final answer.
  7. Finish with timed sets of standalone three-option questions. Use the options, which are listed from smallest to largest, to check the sign and size of your answer before you commit.

Common mistakes in Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

    Last-day revision: Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities

    • Forward price comes from no arbitrage, not from expected spot price.
    • No cash flows: F₀ = S₀ × (1 + r)^T.
    • Income or benefits lower the forward price; costs raise it.
    • With discrete income and costs: F₀ = S₀(1 + r)^T − FV(benefits) + FV(costs), which equals (S₀ − PV of benefits + PV of costs) × (1 + r)^T. Here FV and PV are taken to the delivery date and to today at rate r.
    • A forward has zero value at inception when the price is set fairly.
    • Long forward value at time t = PV of (new forward price − original contract price).
    • The short position value is the negative of the long position value, ignoring credit risk.
    • An FRA locks in a rate for a future borrowing or lending period.
    • The FRA forward rate F is implied by spot rates: (1 + S_B × t_B) = (1 + S_A × t_A) × (1 + F × (t_B − t_A)), where A is the earlier date and B the later one, with times in years under the stated day-count.
    • Long FRA (the party that pays fixed and gains when rates rise) value at time t has two steps. Step 1: value at the FRA settlement date = [(new forward rate − contract rate) × notional × (days ÷ 360)] ÷ [1 + new forward rate × (days ÷ 360)], where days is the length of the underlying period from settlement to the end of the period. Step 2: discount that amount back from the settlement date to the valuation date at the spot rate for the time remaining to settlement. The short FRA has the opposite sign.
    • Covered interest rate parity, for a quote of price currency per 1 unit of base currency: F = S × (1 + r_price)^T ÷ (1 + r_base)^T, with the price currency rate in the numerator.
    • The currency with the higher interest rate trades at a forward discount.
    • Check that your answer fits the smallest-to-largest option order and the sign logic.

    Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities practice questions

    Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities in other exams

    The same ground in other exams, if you are preparing for more than one or want another angle on it.

    Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities: frequently asked questions