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This 4 page Class Notes was uploaded by Jamie Frami on Wednesday September 23, 2015. The Class Notes belongs to FIN 6515 at University of South Florida taught by Staff in Fall. Since its upload, it has received 61 views. For similar materials see /class/212615/fin-6515-university-of-south-florida in Finance at University of South Florida.
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Date Created: 09/23/15
INTEREST RATES Price of moneyibased on the supply and demand of a nancial commodity Yield curveia graphical depiction of the relationship between the yields and the times to maturity of bonds at a particular point in time date A yield curve simply shows the relationship between shortterm and longterm rates on bonds on the date the graph is constructed The yield curve for Treasury debt on October 10 2003 was Yield 0 60 0 00llllllllllllllllllllllllllllll 2003 2007 2011 2015 2019 2023 2027 2031 Maturity Interestrate riskithe risk market rates will change 0 price riskibond prices values move opposite interest rates there exists an inverse relationship 0 reinvestment riskiinterest rate changes are positively related to the ability to reinvest at favorable rates an increase in rates means reinvestment can be made at higher rates and vice versa Term structure of interest ratesishape or behavior of the yield curve 0 Shape of the yield curve normally is upward sloping a downward sloping yield curve is said to be inverted Variability of ratesishortterm rates are more variable than longterm rates to some degree long term rates represent the average of shortterm rates Explanations for the shape of the yield curve 0 Expectations hypothesisibased on investors expectations concerning future forward interest rates investors and borrowers act according to their expectations if investors expect interest rates to increase the yield curve should be upward sloping and vice versa 0 Liquidity preference hypothesisiall else equal investors prefer liquidity thus demand a premium for investing in longerterm bonds 0 Market segmentation hypothesisibond markets are segmented by maturity categories short term and longterm the rates in each segment are determined by the supplydemand relationship that exists Forecasting interest rates 0 spot rate versus forward rate I spot rateithe yield given in the current period I forward rateia future periods yield Assuming the expectations hypothesis is a correct explanation for the shape of the yield curve the following equation can be used to compute forward rates on a compounded basis I1 fn amp10 1 y1quot 1 For example assume today is January 1 2004 and consider four zerocoupon bonds with the following characteristics time to maturity and yield Date of Years to Maturity Maturity W 123104 1 11 123105 2 17 123106 3 22 123107 4 27 The yield represents the average annual rate not the actual rate each year that will be earned by an investor who buys a zero coupon bond at the current price and holds it until maturity For instance the yield for the threeyear bond is 22 percent which implies an investor should earn an average yield of 22 percent per year for the next three yearsithis does not imply the investor will earn 11 percent in Year 1 17 percent in Year 2 and 22 percent in Year 3 The actual return in each year could be 11 percent 25 percent and 30 percent in Year 1 Year 2 and Year 3 respectively which would represent an average arithmetic rather than geometric equal to 22 percent per year for the threeyear period Based on the yields given above the forecasted rates for each year would be computed as follows f2003 110 because this is a one year bond 2 2004 10 00230 230 3 2005 10 00321 321 4 2005 10 00421 421 Bond pricing theorems 0 Bond prices are inversely related to yieldiwhen yields increase bond prices decrease Price Change 000 V5 00 710 00 715 00 720 00 Price 2000 7 n 10 years 1500 Coupon interest 10 1000 500 7 l l l l i 0 5 0 15 20 25 so Yield to Maturity The variability of bond price changes is positively related to time to maturityithat is the longer the time to maturity the greater the price change of a bond for a given change in yield For example the following table gives three bonds that are identical except for their terms to maturityithe coupon for each bond is 10 percent and interest is paid semiannually Term to Price if Price if Bond Maturity YTM 10 YTM 12 in price A 5 years 1000 92640 736 B 10 years 1000 88530 ll47 C 30 years 1000 83839 l6l6 Graphically the relationship between term to maturity and price is Price 1000 Coupon interest rate 10 Coupon interest rate 10 YTM change from 12 to 15 900 YTM 12 800 700 YTM 15 600 Terrn to Maturity years Terrn to Maturity years P ce 2000 1500 n 10years YTM 12 1000 500 7 7 1 1 1 1 1 1 5 10 15 20 25 30 Coupon Rate All else equal the lower the coupon rate for a bond the greater its price change for a particular change in interest ratesilower coupon bonds are more volatile Also bonds with higher coupon rates have higher prices Graphically these relationships are Price 2000 1500 1000 500 n10years Coupon interest rate 10 Coupon interest rate 5 Yield to Maturity