R GLENN HUBBARD ANTHONY PATRICK O’BRIEN Money, Banking, and the Financial System © 2012 Pearson Education, Inc Publishing as Prentice Hall CHAPTER Interest Rates and Rates of Return LEARNING OBJECTIVES After studying this chapter, you should be able to: 3.1 Explain how the interest rate links present value with future value 3.2 Distinguish among different debt instruments and understand how their prices are determined 3.3 Explain the relationship between the yield to maturity on a bond and its price 3.4 Understand the inverse relationship between bond prices and bond yields 3.5 Explain the difference between interest rates and rates of return 3.6 Explain the difference between nominal interest rates and real interest rates © 2012 Pearson Education, Inc Publishing as Prentice Hall CHAPTER Interest Rates and Rates of Return BANKS IN TROUBLE • During the financial crisis, the number of insolvent banks increased sharply • With the collapse of the housing market, increasing numbers of homeowners had stopped making payments on their mortgage loans Banks that held these loans saw their value drop • Mortgage loans that were turned into mortgage-backed securities, similar to bonds, declined by 50% or more during 2008 and 2009 • Banks had badly misjudged both the default risk and the interest-rate risk on these bonds • An Inside Look at Policy on page 78 discusses the performance of the bond market through 2010 © 2012 Pearson Education, Inc Publishing as Prentice Hall of 53 Key Issue and Question Issue: During the financial crisis, soaring interest rates on assets such as mortgage-backed securities caused their prices to plummet Question: Why interest rates and the prices of financial securities move in opposite directions? © 2012 Pearson Education, Inc Publishing as Prentice Hall of 53 3.1 Learning Objective Explain how the interest rate links present value with future value © 2012 Pearson Education, Inc Publishing as Prentice Hall of 53 Why Do Lenders Charge Interest on Loans? The interest rate on a loan should cover the opportunity cost of supplying credit, particularly, the costs associated with three factors: • Compensation for inflation: if prices rise, the payments received will buy fewer goods and services • Compensation for default risk: the borrower might default on the loan • Compensation for the opportunity cost of waiting for the money to be paid back The Interest Rate, Present Value, and Future Value © 2012 Pearson Education, Inc Publishing as Prentice Hall of 53 Most Financial Transactions Involve Payments in the Future The importance of the interest rate comes from the fact that most financial transactions involve payments in the future; the interest rate provides a link between the financial present and the financial future The Interest Rate, Present Value, and Future Value © 2012 Pearson Education, Inc Publishing as Prentice Hall of 53 Compounding and Discounting Future value The value at some future time of an investment made today If: i = the interest rate Principal = the amount of your investment (your original $1,000) FV = the future value (what your $1,000 will have grown to in one year) then we can rewrite the expression as:   Compounding for More Than One Period Compounding The process of earning interest on interest as savings accumulate over time If you invest $1,000 for n years, where n can be any number of years, at an interest rate of 5%, then at the end of n years, you will have:   The Interest Rate, Present Value, and Future Value © 2012 Pearson Education, Inc Publishing as Prentice Hall of 53 Solved Problem 3.1A Comparing Investments Suppose you are considering investing $1,000 in one of the following bank CDs: • First CD, which will pay an interest rate of 4% per year for three years • Second CD, which will pay an interest rate of 10% the first year, 1% the second year, and 1% the third year Which CD should you choose? The Interest Rate, Present Value, and Future Value © 2012 Pearson Education, Inc Publishing as Prentice Hall of 53 Solved Problem 3.1A Comparing Investments Solving the Problem Step Review the chapter material Step Calculate the future value of your investment with the first CD Principal = $1,000, i = 4%, n = years FV = $1,000 x (1 + 0.04) = $1,124.86 Step Calculate the future value of your investment with the second CD and decide which CD you should choose Principal = $1,000, i1 = 10%, i2 = 1%, i3 = 1%, n = years FV = $1,000 x (1 + 0.10) x (1 + 0.01) x (1 + 0.01) = $1,122.11 Decision: You should choose the investment with the highest future value, so you should choose the first CD The Interest Rate, Present Value, and Future Value © 2012 Pearson Education, Inc Publishing as Prentice Hall 10 of 53 Making the Connection Reading the Bond Tables in the Wall Street Journal Treasury Bonds and Notes • The current yield equals the coupon divided by the price: $42.50/$1,122.50, or 3.79% for Bond A • The current yield of Bond A is well above the yield to maturity of 1.7066% • This illustrates that the current yield is not a good substitute for the yield to maturity for instruments with a short time to maturity because it ignores the effect of expected capital gains or losses The Inverse Relationship between Bond Prices and Bond Yields © 2012 Pearson Education, Inc Publishing as Prentice Hall 39 of 53 Making the Connection Reading the Bond Tables in the Wall Street Journal Treasury Bills • Treasury bills are discount bonds, not coupon bonds • Treasury notes and bonds quote prices, while Treasury bills quote yields • The bid yield is the discount yield for sellers The asked yield is for buyers • The dealers’ profit margin is the difference between the asked bid yields • The yield to maturity, in the last column, is useful for comparing investments The Inverse Relationship between Bond Prices and Bond Yields © 2012 Pearson Education, Inc Publishing as Prentice Hall 40 of 53 Making the Connection Reading the Bond Tables in the Wall Street Journal New York Stock Exchange Corporation Bonds • A bond’s rating shows the likelihood that the firm will default on the bond • Prices are quoted in decimals • The last time this Goldman Sachs bond was traded that day, it sold for a price of $1,048.68 The Inverse Relationship between Bond Prices and Bond Yields © 2012 Pearson Education, Inc Publishing as Prentice Hall 41 of 53 3.5 Learning Objective Explain the difference between interest rates and rates of return © 2012 Pearson Education, Inc Publishing as Prentice Hall 42 of 53 Return The total earnings from a security; for a bond, the coupon payment plus the change in the price of the bond Rate of return, R The return on a security as a percentage of the initial price; for a bond, the coupon payment plus the change in the price of a bond divided by the initial price For example, for a bond with a $1,000 face value and a coupon rate of 8%: If the end-of-year price was $1,271.81, then, the rate of return for the year was:   If the end-of-year price was $812.61, then, the rate of return for the year was:   Interest Rates and Rates of Return © 2012 Pearson Education, Inc Publishing as Prentice Hall 43 of 53 A General Equation for the Rate of Return A general equation for the rate of return on a bond for a holding period of one year is:     Three important points to note: For the current yield, the calculation uses the initial price If you sell the bond, you have a realized capital gain or loss If you not sell the bond, your gain or loss is unrealized Neither the current yield nor the yield to maturity may be a good indicator of the rate of return because they ignore your capital gain or capital loss Interest Rates and Rates of Return © 2012 Pearson Education, Inc Publishing as Prentice Hall 44 of 53 Interest-Rate Risk and Maturity Interest-rate risk The risk that the price of a financial asset will fluctuate in response to changes in market interest rates • Bonds with fewer years to maturity will be less affected by a change in market interest rates • At the end of one year, the yield to maturity on similar bonds has risen to 10% The table shows that the longer the maturity of your bond, the lower (more negative) your return after one year of holding the bond With a maturity of 50 years, your rate of return for the first year of owning your bond will be -33.7% Interest Rates and Rates of Return © 2012 Pearson Education, Inc Publishing as Prentice Hall 45 of 53 3.6 Learning Objective Explain the difference between nominal interest rates and real interest rates © 2012 Pearson Education, Inc Publishing as Prentice Hall 46 of 53 Nominal interest rate An interest rate that is not adjusted for changes in purchasing power Real interest rate An interest rate that is adjusted for changes in purchasing power • Inflation causes the purchasing power of both the interest income and the principal to decline • Because lenders and borrowers don’t know what the actual real interest rate will be during the period of a loan, they must estimate an expected real interest rate • The expected real interest rate, r, equals the nominal interest rate, i, minus the expected rate of inflation, • Therefore, the nominal interest rate equals the real interest rate plus the expected inflation rate: i = r + e e π   π Nominal Interest Rates versus Real Interest Rates © 2012 Pearson Education, Inc Publishing as Prentice Hall 47 of 53 Nominal Interest Rates versus Real Interest Rates © 2012 Pearson Education, Inc Publishing as Prentice Hall 48 of 53 Figure 3.1 Nominal and Real Interest Rates, 1981–2010 In this figure, the nominal interest rate is the interest rate on three-month U.S Treasury bills The actual real interest rate is the nominal interest minus the actual inflation rate, as measured by changes in the consumer price index The expected real interest rate is the nominal interest rate minus the expected rate of inflation as measured by a survey of professional forecasters When the U.S economy experienced deflation during 2009, the real interest rate was greater than the nominal interest rate.• Nominal Interest Rates versus Real Interest Rates © 2012 Pearson Education, Inc Publishing as Prentice Hall 49 of 53 • It is possible for the nominal interest rate to be lower than the real interest rate For this outcome to occur, the inflation rate has to be negative, meaning that the price level is decreasing rather than increasing Deflation A sustained decline in the price level • In January 1997, the U.S Treasury started issuing indexed bonds to address investors’ concerns about the effects of inflation on real interest rates With these bonds, called TIPS (Treasury Inflation Protection Securities), the Treasury increases the principal as the price level increases Nominal Interest Rates versus Real Interest Rates © 2012 Pearson Education, Inc Publishing as Prentice Hall 50 of 53 Figure 3.2 TIPS as a Percentage of All Treasury Securities TIPS (Treasury Inflation Protection Securities) were an increasing percentage of all U.S Treasury securities until 2009.• Nominal Interest Rates versus Real Interest Rates © 2012 Pearson Education, Inc Publishing as Prentice Hall 51 of 53 Answering the Key Question At the beginning of this chapter, we asked the question: “Why interest rates and the prices of financial securities move in opposite directions?” We have seen in this chapter that the price of a financial security equals the present value of the payments an investor will receive from owning the security When interest rates rise, present values fall, and when interest rates fall, present values rise Therefore, interest rates and the prices of financial securities should move in opposite directions © 2012 Pearson Education, Inc Publishing as Prentice Hall 52 of 53 AN INSIDE LOOK AT POLICY Higher Interest Rates Increase Coupons, Decrease Capital Gains Wall Street Journal, Coupon Clipping: Playing a Calmer Corporate-Bond Market • As this chapter explained, as interest rates rise, bond prices fall The table below illustrates why this is so • The price of Treasury bills paid in December 1998 was $4.353 less than the face value of the bills This represented an interest rate of 4.6% • The price paid in April 2010 was about only $0.49 less than the face value, which represented an interest rate of only 0.5% • Investors expected increases in interest rates in the latter part of 2010 Higher interest rates would mean higher coupon payments on new bonds, but lower bond prices would reduce the opportunity for capital gains © 2012 Pearson Education, Inc Publishing as Prentice Hall 53 of 53 ... interest paid by the issuer of the bond to the buyer • The coupon rate is the value of the coupon expressed as a percentage of the par value of the bond • The current yield is the value of the coupon... mean by the payments in the Mets’ contract being “backloaded”? What does he mean by the “true value” of the contract? How would backloading the payments affect the true value of the contract? The. .. that most financial transactions involve payments in the future; the interest rate provides a link between the financial present and the financial future The Interest Rate, Present Value, and Future