7Intforw_futures

7Intforw_futures - Interest Rate Forwards and Futures...

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Slide 7-1 Interest Rate Forwards and Futures Chapter 7 Chapter 7 Slide 7-2 Today’s Agenda Hedging future borrowing and lending rates: – Forward Rate Agreements – Eurodollar Futures Hedging the value of bonds / bond portfolios: – Measuring the interest rate sensitivity of bonds (Duration) – Duration matching
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Slide 7-3 Bond Basics U.S. Treasury Securities – Bills (maturity < 1 year), no coupons, sell at discount – Notes (maturity: 1-10 years), coupons, sell at par – Bonds (maturity: 10-30 years), coupons, sell at par – STRIPS: Claim to a single coupon or the principal of a government bond. (Don´t confuse this with the “forward strip”.) U.S. Treasury yield curve: Constructed from STRIPS – The yield of a bond equals the expected/actual return only for zero-coupon bonds Notation: r t ( t 1 , t 2 ): Interest rate from time t 1 to t 2 prevailing at time t . P t ( t 1 , t 2 ): Price of a bond quoted at time t, to be purchased at t = t 1 maturing at t = t 2 Slide 7-4 Yield to Maturity (YTM) Section 7.1 Yield-to-Maturity, y (0, T ), also called the internal rate of return (IRR), is the rate of return of a zero-coupon bond if the bond is held until maturity. P (0, T ) is the price you would pay to receive $1 at time T = the present value of $1 received at time T = discount factor for discounting at the YTM. Example: Coupon bond that pays an annual coupon of c. The bond will sell at par if B(0,T,c)=$1 . The par coupon is: T ,T y ,T P )] 0 ( 1 [ 1 $ ) 0 ( + = B (0, T , c ) = $ c (1 + y ) t t = 1 T + $1 (1 + y ) T = $ c × P (0, t ) t = 1 T + P (0, T ) c = 1 P(0,T) P(0,t) t = 1 T
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Slide 7-5 Given the above yield curve, what must be the coupon of a 3- year coupon bond price if it is to sell at par? c = 1 P(0,T) P(0,t) t = 1 T % 95 6 816298 0 881659 0 943396 0 816298 0 1 . . . . . c = + + = Slide 7-6 Interest rate derivatives Consider the following problem: A construction company plans to start a new project 6 months from now. At the start of the project, the company will have uncovered borrowing needs of $ 20 million. The company will be able to repay the loan once the project is completed and the customer has paid. How can the company hedge its exposure to interest rate risk?
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Slide 7-7 Forward rate agreements (FRAs) Section 7.2 FRAs are over-the-counter contracts that guarantee a future borrowing or a lending rate on a given notional principal amount. FRAs can be settled at maturity (“in arrears”), or at the initiation of the borrowing or lending transaction – FRA settlement in arrears: ( r t (t,t+s) - r FRA ) * notional principal – At the time of borrowing: ( r t (t,t+s) - r FRA )/(1 + r t (t,t+s) ) * notional principal t 0 t t+s time Duration of loan Slide 7-8 Hedging interest rate risk with FRAs Back to the last hedging example. Suppose you want to borrow $20 million for 3 months, 6 months from now. Let
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7Intforw_futures - Interest Rate Forwards and Futures...

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