Session 3- The yield curve.pdf

# 21117 fixed income s 55 the forward rates logic q1

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2/11/17 Fixed Income Securities 24 5.25% ?% 5.5%

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The Forward Rates: Logic Q1: What is the future rate that will make the investor indifferent between the two alternatives? The breakeven rate for which the investor is indifferent between the two alternatives is: A1: The breakeven rate is 5.75% and that is the forward rate. 2/11/17 Fixed Income Securities 25 % 75 . 5 1 2 % 25 . 5 1 2 % 5 . 5 1 2 2 % 5 . 5 1 100 2 1 2 % 25 . 5 1 100 1 5 . 0 2 1 5 . 0 2 1 5 . 0 = Υ Υ Υ Υ Φ Τ ΢ ΢ ΢ ΢ Σ Ρ Ο Π Ξ Μ Ν Λ + Ο Π Ξ Μ Ν Λ + × = Ο Π Ξ Μ Ν Λ + × = Ο Π Ξ Μ Ν Λ + Ο Π Ξ Μ Ν Λ + × × × × f f f
The Forward Rates: Logic o Q2: What if his view is that the future forward rates will be higher than current rates? o A2: The view that the future market is higher than the current market is not suﬃcient. The future rate has to be higher than the forward rate for the investor to be bias on alternative 2. 2/11/17 Fixed Income Securities 26

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The Forward Rates: Usage 2/11/17 Fixed Income Securities 27
Where to get Forward Rates? 2/11/17 Fixed Income Securities 28 The forward rate Dec Contract = 100-­‑98.48=1.52%

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Constructing the Term Structure of Interest Rates The relationship between the spot and forward rates Term structure theories 2/11/17 29 Fixed Income Securities
The Interest Rate Rela6onship How to calculate the spot rates from the forward rates? o …where r n is the n-­‐period spot rate, r 1 is the first period spot rate, f i-­‐1,i is the one period forward rate starting at period i-­‐1 and ending at i, where i =( 1, …n ) Forward rate can be 1week, 3months, 6month, 1 year etc. 2/11/17 Fixed Income Securities 30 1 + r n ( ) n = 1 + r 1 ( ) 1 + f 1 × 2 ( ) 1 + f 2 × 3 ( ) ... 1 + f n 1 × n ( ) r n = 1 + r 1 ( ) 1 + f 1 × 2 ( ) 1 + f 2 × 3 ( ) ... 1 + f n 1 × n ( ) n 1

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Deriving Spot Rates Investor A can either invest 100\$; For 1 year deposit at current rate r 1 =5.25% and then reinvest all proceed for one more year at f t i -1xt i =5.75% , or Choose a 2 year deposit rate set t r 2 . What is the 2year spot rate, for there to be no arbitrage ? 2/11/17 Fixed Income Securities 31
Deriving Spot Rates 2/11/17 Fixed Income Securities 32 By arbitrage condition the spot rate is: ( ) ( )( ) % 5 . 5 % 75 . 5 1 % 25 . 5 1 1 2 2 2 = + + = + r r

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Deriving Spot Rates 2/11/17 Fixed Income Securities 33 Find the spot rates/ the term structure of interest rates. Year 1 2 3 4 5 Forward 5.25% 5.75% 6% 6.25% 6.75% Spot 5.25% 5.5% 5.66% 5.81% 5.99% Disc. fact 0.9501 0.8985 0.8478 0.7978 0.7214
The Term Structure of Interest Rate 2/11/17 Fixed Income Securities 34 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00% 1 2 3 4 5 6 7 Forward Rates Spot Rates

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Deriving Spot Rates 2/11/17 Fixed Income Securities 35 Price the 2 year UST bond that pays 3% coupon rate? Year 1 2 3 4 5 Forward 5.25% 5.75% 6% 6.25% 6.75% Spot 5.25% 5.5% 5.66% 5.81% 5.99% Disc. fact 0.9501 0.8985 0.8478 0.7978 0.7214 P = c × 100 1 + r 1 ( ) + c × 100 1 + r 2 ( ) 2 + ... + c × 100 + 100 1 + r n ( ) n
The Term Structure Theories 2/11/17 Fixed Income Securities 36

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The Term Structure Theories 2/11/17 Fixed Income Securities 37
Expectation theory o Pure Expectation theory The forward rates represents purely the expected future short term rates. It fails to recognize the uncertainty

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