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Lecture 8: Forward RatesFNCE90056:Investment ManagementDr. Minsoo KimDepartment of FinanceFaculty of Business and EconomicsUniversity of MelbourneUniversity of MelbourneDr. Minsoo Kim1 / 35
Lecture 8: Forward RatesIntroductionIntroductionUniversity of MelbourneDr. Minsoo Kim2 / 35
Lecture 8: Forward RatesIntroductionTodayIn the 1970s, the Chicago Board of Trade (CBOT) and theChicago Mercantile Exchange (CME) pioneered the trading ofinterest rate futures. Pictured is the Roman goddess of grain,Ceres, atop the CBOT building.In this lecture, we will see thatmany transactions can beconstructed using only theinformation in today’s termstructure.Forward ratesForward discount factorExpectation HypothesisModern theories of termstructureThe notation can get messy.University of MelbourneDr. Minsoo Kim3 / 35
Lecture 8: Forward RatesForward RatesForward RatesUniversity of MelbourneDr. Minsoo Kim4 / 35
Lecture 8: Forward RatesForward RatesZero rates vs Forward ratesZero rates from today to year T:z0TForward rates from year t to year T:ftTUniversity of MelbourneDr. Minsoo Kim5 / 35
Lecture 8: Forward RatesForward RatesZero rates vs Forward rates vs Actual (future) rateZero rates from today to year T:z0TForward rates from year t to year T:ftTActual (future) rates from year t to year T:rtTActual (future) rate = Spot rate.By definition,z0T=r0TUniversity of MelbourneDr. Minsoo Kim6 / 35
Lecture 8: Forward RatesForward RatesForward ratesForward rates are the borrowing/lending rates for futuretransactionsimplied by today’s term structure.From today’s term structure, we can generate a family of forwardcurves — and vice versa.Forward rate agreements (FRAs) are essentially forward contracts1written on interest rates. They allow borrowers and lenders to lock infuture interest rates.1Forwards are the simplest form of derivative contract. In a typical “spot”transaction, the terms of the transaction are set — and the transaction is executed —today. In a forward contract, the terms are set today, but the actual transaction occurson some pre-specified future date.University of MelbourneDr. Minsoo Kim7 / 35
Lecture 8: Forward RatesForward RatesA motivating exampleA firm wishes to borrow $100 from year 1 until year 2.They can structure this transaction in (at least) two ways:1wait until year 1, and then borrow at the futurespot rate,r12There is nothing wrong with this, but it involves interest rate risk.The future spot rate (at year 1) is random from the perspective ofsomeone today.2lock in a rate (today) for the future transaction.This is the forward rate,f12.That is, the rate for borrowing year 1 to year 2 that you can lock intoday. The forward rate is not random (in year 0), so this approachbears no interest rate risk.University of MelbourneDr. Minsoo Kim8 / 35
Lecture 8: Forward RatesForward RatesNo-arbitrage determination of forward ratesWe will invoke no-arbitrage to show how spot rates are linked to forwardrates. To do so, let’s consider a different example than the one on slide 8.

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Term
Fall
Professor
NoProfessor
Tags
Inflation, Monetary Policy, Spot price, Dr Minsoo Kim

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