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FI 478 Investment Strategies and Speculative Markets Professor Fan Yu Lecture 4 Term Structure of Interest Rates Swaps This Version: February 8, 2008 c ° 2008 Fan Yu. All Rights Reserved. 1

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Term Structure of Interest Rates As we will see later, an interest rate swap is the exchange of a fi xed rate payment with a fl oating rate payment, and it can be e ff ectively treated as a portfolio of bonds or forward rate agreements. Therefore we must deal with a term structure of interest rates where the rate might be di ff erent for loans with di ff erent maturities. We will introduce several important concepts. These are zero rates and forward rates. They help us understand the pricing of coupon bonds and forward rate agreements. Once we understand these then swaps are straightforward to price. Zero rates The n -year zero rate R ( n ) is the annualized c.c. interest rate earned on an investment that starts today and lasts for n years. p 0 = 100 e R ( n ) n No intermediate payments. Useful as a discount function for discounting future cash fl ows. Yield curve The curve constructed by plotting the zero rates as a function of n . What you see in the newspaper as the yield curve is not as useful. Why? US Treasury securities 3-month and 6-month T-Bills auctioned every Thursday, 1-year T- Bills auctioned every 4th Thursday. These are zero-coupon bonds and their yields are the correct zero rates. T-Notes and T-Bonds have coupons, some of the T-Bonds are even callable, so their yields are not the correct zero rates. Correct zero rates have to be extracted using the bootstrap method. T-Strips are synthetic zero-coupon bonds created from notes and bonds, so a yield curve can be created from them directly. 2
LIBOR rates London Interbank O ff er Rate. Has a variety of maturities. Repre- sents lending rates between large international banks. Most swaps agreements use LIBOR as a reference rate. Repo rates Repo stands for “repurchase agreement.” It is how investment banks borrow from or lend to each other. In an overnight repo, you agree to sell securities (usually Treasury securities) to another party and buy them back the next day. You pay a slightly higher price to buy them back. This implicit interest rate is called the repo rate. Relatively riskless. If you agree to buy securities today and sell them back at some future date, you are entering to a “reverse repo.” Sometimes repos are “on special,” meaning that the repo rate is particularly low. This can happens when a T-Bond issue is in short supply and there is a convenience yield to holding them. If you happen to have them, then you can borrow money at cheaper rates. 3

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Given a collection of zero rates one can price any coupon bonds.
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