Week 5 Bond Prices and Yields PDF

Week 5 Bond prices and yields BANK2011 Banking and the Financial System The University of Sydney Page 1  Learning Objectives 1. Explain the relationship between bond pricing and present value. 2. Define the relationship among a bond’s price and its coupon rat...

Week 5 Bond prices and yields BANK2011 Banking and the Financial System The University of Sydney Page 1  Learning Objectives 1. Explain the relationship between bond pricing and present value. 2. Define the relationship among a bond’s price and its coupon rate, yield to maturity, and holding period return. 3. Explain the links between credit risk, bond ratings, and bond yields. 4. Define the yield curve and interpret it using the expectations hypothesis and liquidity premium theory. The University of Sydney Page 2  Zero-Coupon Bonds – U.S. Treasury bills (T-bills) are the most straightforward type of bond. – Each T-bill represents a promise by the U.S. government to pay $100 on a fixed future date. – No coupon payments - zero-coupon bonds – Also called pure discount bonds (or discount bonds) since the price is less than face value - they sell at a discount. – Price of $100 face value zero-coupon bond $100 = (1+ i)n The University of Sydney Page 3  Zero-Coupon Bonds Assume i = 5% Price of a One-Year Treasury Bill 100 = = $95.24 (1+ 0.05) Price of a Six-Month Treasury Bill 100 = = $97.59 (1+ 0.05)1/2 The University of Sydney Page 4  Zero-Coupon Bonds – For a zero-coupon bond, the relationship between the price and the interest rate is the same as we saw on present value calculations. – When the price moves, the interest rate moves with it, in the opposite direction. – We can compute the interest rate from the price using the present value formula. The price of a one-year T-bill is $95. i = ($100/$95) - 1 = 0.0526 = 5.26% The University of Sydney Page 5  Coupon Bonds – The issuer of a coupon bond promises to make a series of periodic interest payments (coupon payments), plus a principal payment at maturity. Price of Coupon Bond =  Coupon payment Coupon payment Coupon payment  PCB =  + +...... +   (1+ i)1 (1+ i)2 (1+ i)n  Face value + (1+ i)n The University of Sydney Page 6  Consols – Consols or perpetuities, are like coupon bonds whose payments last forever. – The borrower pays only interest, never repaying the principal. – The U.S. government sold consols once in 1900, but the Treasury has bought them all back. – The price of a consol is the present value of all future interest payments. Yearly Coupon Payment PConsol = i The University of Sydney Page 7  Yield to Maturity – The most useful measure of the return on holding a bond is called the yield to maturity: – The yield bondholders receive if they hold the bond to its maturity when the final principal payment is made. $5 $100 Price of one-year 5 percent coupon bond = + (1+ i) (1+ i) – The value of i that solves the equation is the yield to maturity. The University of Sydney Page 8  Yield to Maturity – If Bond Price = $100, Yield to maturity = the coupon rate – If Bond Price > $100, Yield to maturity < the coupon rate – If Bond Price < $100, Yield to maturity > the coupon rate Bond Price   Yield to maturity  The University of Sydney Page 9  Yield to Maturity – This relationship should make sense. – If you pay $95 for a $100 face value bond, you will receive both the interest payments and the increase in value from $95 to $100. – This rise in value is referred to as a capital gain and is part of the return on your investment. – When the price of a bond is higher than face value, the bondholder incurs a capital loss. The University of Sydney Page 10  Holding Period Returns – The holding period return is the return to holding a bond and selling it before maturity. – The holding period return can differ from the yield to maturity. The University of Sydney Page 11  Holding Period Returns – The one-year holding period return is the sum of the yearly coupon payment divided by the price paid for the bond and the change in the price divided by the price paid. Yearly coupon payment Change in price of bond Holding period return = + Price paid Price paid Holding period return = Current yield + Capital gain The University of Sydney Page 12  Holding Period Returns – Whenever the price of a bond changes, there is a capital gain or loss. – The greater the price change, the more important that part of the holding period return becomes. – The longer the term of the bond, the greater those price movements and associated risk can be. The University of Sydney Page 13  Bond Ratings – The best-known bond rating services are – Moody’s – Standard & Poor’s – They monitor the status of individual bond issuers and assess the likelihood a lender will be repaid by the bond issuer. – A high rating suggests that a bond issuer will have little problem meeting a bond’s payment obligations. The University of Sydney Page 14  Bond Ratings – Firms or governments with an exceptionally strong financial position carry the highest ratings and are able to issue the highest-rated bonds, Triple A. – The top four categories are considered investment-grade bonds. – These bonds have a very low risk of default. – Reserved for most government issuers and corporations that are among the most financially sound. The University of Sydney Page 15  Bond Ratings – The distinction between investment-grade and speculative, noninvestment- grade is important. – A number of regulated institutional investors are not allowed to invest in bonds rated below investment grade, which is Baa on Moody’s scale or BBB on Standard & Poor’s scale. The University of Sydney Page 16 The University of Sydney Page 17  Bond Ratings – Speculative grade bonds are bonds issued by companies and countries that may have difficulty meeting their bond payments but are not at risk of immediate default. – Highly speculative bonds consist of debts that are in serious risk of default. – All bonds with grades below investment grade are often referred to as junk bonds or high-yield bonds. The University of Sydney Page 18  Bond Ratings – Types of junk bonds: – Fallen angels are bonds that were once investment-grade, but their issuers fell on hard times. – Bonds issued by issuers about which there is little known. – Material changes in a firm’s or government’s financial condition precipitate changes in its debt ratings. – Ratings downgrade - lower an issuer’s bond rating. – Ratings upgrade - upgrade an issuer’s bond rating. The University of Sydney Page 19  The Impact of Ratings on Yields – Bond ratings are designed to reflect default risk. – The lower the rating – The higher the risk of default. – The lower its price and the higher its yield. – To understand quantitative ratings, it is easier to compare them to a benchmark. The University of Sydney Page 20  The Impact of Ratings on Yields – U.S. Treasury issues are viewed as having little default risk, so they are used as benchmark bonds. – Yields on other bonds are measured in terms of the spread over Treasuries. – Bond yield is the sum of two parts: = U.S. Treasury yield + Default risk premium The University of Sydney Page 21  The Impact of Ratings on Yields – If bond ratings properly reflect risk, then the lower the rating of the issuer, the higher the default-risk premium. – When Treasury yields move, all other yields move with them. – We can see this from Figure 7.2 showing a plot of the risk structure of interest rates. The University of Sydney Page 22 The University of Sydney Page 23  The Impact of Ratings on Yields – Changes in the U.S. Treasury yields account for most of the movement in the Aaa and Baa bond yields. – From 1979-2016, the 10-year U.S. Treasury bond yield has averaged almost a full percentage point below the average yield on Aaa bonds and two percentage points below the average yield on Baa bonds. The University of Sydney Page 24  The Impact of Ratings on Yields – A two-percentage point increase in the yield, from 4 to 6 percent, lowers the value of the promise of $100 in 10 years by $11.72, or 17 percent. – Clearly ratings are crucial to corporations’ ability to raise financing. – A lower rating increases the costs of funds. – Investors clearly must be compensated for assuming risk. The University of Sydney Page 25  Term Structure of Interest Rates – Why do bonds with the same default rate but different maturity dates have different yields? – Long-term bonds are like a composite of a series of short-term bonds. – Their yield depends on what people expect to happen in the future. The University of Sydney Page 26  Term Structure of Interest Rates – The relationship among bonds with the same risk characteristics but different maturities is called the term structure of interest rates. – Comparing 3-month and 10-year Treasury yields we can see: 1. Interest rates of different maturities tend to move together. 2. Yields on short-term bonds are more volatile than yields on long-term bonds. 3. Long-term yields tend to be higher than short-term yields. The University of Sydney Page 27  Term Structure of Interest Rates The University of Sydney Page 28  The Expectations Hypothesis – The expectations hypothesis of the term structure focuses on the risk-free interest rate. – The risk-free interest rate can be computed, assuming there is not uncertainty about the future. The University of Sydney Page 29  The Expectations Hypothesis – If there is no uncertainty, then an investor will be indifferent between holding a two-year bond or a series of two one-year bonds. – Certainty means that the bonds of different maturities are perfect substitutes for each other. – The expectations hypothesis implied that the current two-year interest rate should equal the average of current one-year rate and the one-year interest rate one year in the future. The University of Sydney Page 30  The Expectations Hypothesis – When interest rates are expected to rise, long-term interest rates will be higher than short-term interest rates. – The yield curve which plots the yield to maturity on the vertical axis and the time to maturity on the horizontal axis, will slope up. – This also means: – If interest rates are expected to fall, the yield curve will slope down. – If expected to stay the same, the yield curve will be flat. The University of Sydney Page 31  The Expectations Hypothesis The University of Sydney Page 32  The Expectations Hypothesis The University of Sydney Page 33  The Expectations Hypothesis – If bonds of different maturities are perfect substitutes for each other, then we can construct investment strategies that must have the same yields. 1. Invest in a two-year bond and hold it to maturity 2. Invest in two one-year bonds, one today and one when the first matures. The University of Sydney Page 34  The Expectations Hypothesis – The expectations hypothesis tells us investors will be indifferent between the two options. – This means they must have the same return: (1 + i2t)(1 + i2t) = (1 + i1t)(1 + ie1t+1) – We can now write the two-year interest rate as the average of the current and future expected one-year interest rates: i1t + i1et +1 i2t = 2 The University of Sydney Page 35  The Expectations Hypothesis Source: Cecchetti and Schoenholtz (2021: 171) The University of Sydney Page 36  The Expectations Hypothesis – We can generalise this: a bond with n years to maturity is the average of n expected future one-year interest rates: i1t + i1et +1 + i1et +2 +... + i1et + n −1 int = n The University of Sydney Page 37  The Expectations Hypothesis Does this hypothesis explain the three observations we started with? 1. Interest rates of different maturities will move together. – We can see this holds from the previous equation. 2. Yields on short-term bonds will be more volatile than yields on long- term bonds. – Long-term rates are averages of short-term rates, so changing one short-term rate has little effect on the long-term rate. 3. The expectation hypothesis cannot explain why long-term yields are normally higher than short-term yields – It implies that the yield curve slopes upward when the interest rates are expected to rise. The University of Sydney Page 38  The Liquidity Premium Theory – Risk is the key to understanding the upward slope of the yield curve. – Bondholders face both inflation and interest-rate risk. – The longer the term of the bond, the greater both types of risk. – Computing real return from nominal return requires a forecast of expected future inflation. – A bond’s inflation risk increases with its time to maturity. The University of Sydney Page 39  The Liquidity Premium Theory – Interest-rate risk arises from the mismatch between the investor’s investment horizon and a bond’s time to maturity. – If a bondholder plans to sell a bond prior to maturity, changes in the interest rate generate capital gains or losses. – The longer the term of the bond, the greater the price changes for a given change in interest rates and the larger the potential for capital losses. – Investors require compensation for the increase in risk they take for buying longer term bonds. The University of Sydney Page 40  The Liquidity Premium Theory – We can think about bond yields as having two parts: – One that is risk free: explained by the expectations hypothesis. – One that is a risk premium: explained by inflation and interest-rate risk. – Together this forms the liquidity premium theory of the term structure of interest rates. i1t + i1et +1 + i1et +2 +.... + i1et + n −1 int = rpn + n The University of Sydney Page 41  Information in the Risk Structure of Interest Rates – The immediate impact of a pending recession is to raise the risk premium on privately issued bonds. – Note that an economic slowdown or recession does not affect the risk of holding government bonds. – The impact of a recession on companies with high bond ratings is also usually quite small. – The lower the initial grade of the bond, the more the default-risk premium rises as general economic conditions deteriorate. The University of Sydney Page 42  Information in the Risk Structure of Interest Rates – Panel A of Figure 7.6 shows the annual GDP growth over four decades superimposed on shading that shows the dates of recessions. – During shaded periods growth is usually negative. – Panel B of Figure 7.6 shows GDP growth against the spread between yields on Baa-rated bonds and U.S. Treasury bonds. – When risk spread rises, output falls. The University of Sydney Page 43 The University of Sydney Page 44  Information in the Term Structure of Interest Rates – Information on the term structure, particularly the slope of the yield curve helps to forecast general economic conditions. – The yield curve usually slopes upward. – On rare occasions, short-term interest rates exceed long-term yields leading to an inverted yield curve. – An inverted yield curve is a valuable forecasting tool because it predicts a general economic slowdown. The University of Sydney Page 45  Information in the Term Structure of Interest Rates – Figure 7.7 shows GDP growth and the slope of the yield curve, measured as the difference between the 10-year and 3-month yields: term spread. – Panel A shows GDP growth together with the growth and term spread at the same time. – Panel B shows GDP growth in the current year against the slope of the yield curve one year earlier. – The two lines clearly move together. – When the term spread falls, GDP growth tends to fall one year later, suggesting that the term spread is a leading financial indicator of output growth The University of Sydney Page 46 The University of Sydney Page 47  Homework problems – CS chapter 6 – Problems 1, 3, 4, 6, 7, 23 – CS chapter 7 – Problems 4, 6, 7, 19 – Data exploration problem 3 The University of Sydney Page 48