9 Interest Rates Learning Objectives - PowerPoint Presentation

1. 9Interest Rates

2. Learning ObjectivesOur goal in this chapter is to discuss the many different interest rates that are commonly reported in the financial press.We will also:Find out how different interest rates are calculated and quoted, andDiscuss theories of what determines interest rates. 1. Money market prices and rates. 2. Rates and yields on fixed-income securities. 3. Treasury STRIPS and the term structure of interest rates. 4. Nominal versus real interest rates. 5. Forward rates2

3. Comparative Performance of Stocks and Bonds (1997-2008)3

4. What Stocks Have to Offer – Bonds as Alternative ChoiceThe Advantages of Stock OwnershipStocks typically outperform bonds, and usually by a wide margin.Over the last century, stocks earned annual returns roughly double that of the returns provided by high-grade corporate bonds.Stocks provide protection from inflation because over time their returns exceed the inflation rate.Stocks are easy to buy and sell.Costs associated with trading stocks are modest.The Disadvantages of Stock OwnershipStocks are subject to various types of risk and therefore, stock returns are highly volatile and very hard to predict, so it is difficult to consistently select top performers.Stocks generally distribute less current income compared to other investment alternatives.Bonds pay more current income and do so with much greater certainty.4

5. The Current Income of Stocks and Bonds(Source: Data from Federal Reserve Board of Governors and http://www.multpl.com/s-p-500-dividend-yield/table.)5

6. U.S. Interest Rate History, 1800-20146

7. Yield Spreads 7

8. Auction Results for a 30-Year Treasury Bond8

9. Money Market Rates, I.Prime rate - The basic interest rate on short-term loans that the largest commercial banks charge to their most creditworthy corporate customers.Discount rate - The interest rate that the Fed offers to commercial banks for overnight reserve loans.Federal funds rate - Interest rate that banks charge each other for overnight loans of $1 million or more.Banker’s acceptance - A postdated check on which a bank has guaranteed payment. Commonly used to finance international trade transactions.Call money rate - The interest rate brokerage firms pay for call money loans from banks. This rate is used as the basis for customer rates on margin loans.Commercial paper - Short-term, unsecured debt issued by the largest corporations.9

10. Money Market Rates, II.U.S. Treasury bill (T-bill) - A short-term U.S. government debt instrument issued by the U.S. Treasury.London Interbank Offered Rate (LIBOR) - Interest rate that international banks charge one another for overnight Eurodollar loans.Euro LIBOR refers to deposits denominated in euros—the common currency of 12 European Union countries.EURIBOR is an interest rate that also refers to deposits denominated in euros. However, EURIBOR is based largely on interest rates from the interbank market for banks in the European Union.HIBOR is an interest rate based on Hong Kong dollars. Hibor is the interest rate among banks in the Hong Kong interbank market.Eurodollars - U.S. dollar denominated deposits in banks outside the United States. 10

11. Interest rates : Market data from WSJ11

12. Money Market Prices and RatesA Pure Discount Security is an interest-bearing asset:It makes a single payment of face value at maturity.It makes no payments before maturity.There are several different ways market participants quote interest rates.Bank Discount BasisBond Equivalent Yields (BEY)Annual Percentage Rates (APR)Effective Annual Rates (EAR)12

13. The Bank Discount BasisThe Bank Discount Basis is a method of quoting interest rates on money market instruments. It is commonly used for T-bills, commercial papers, and banker’s acceptances.It is based on the instrument’s par value and the amount of the discount.It is often called a discount yield and it is the required rate of return. The formula is:Note that we use 360 days in a year in this (and many other) money market formula.The term “discount yield” here simply refers to the quoted interest rate. Don’t confuse it with the Fed’s discount rate.13

14. Example: Calculating a Price Using a Bank Discount RateSuppose a banker’s acceptance that will be paid is 90 days has a face value of $1,000,000.If the discount yield is 5%, what is the current price of the banker’s acceptance?The difference between $1 million and $987,500 is $12,500, which is the discount , the interest earned over the 90-day period.14

15. Treasury Bill Quotes (online at www.wsj.com)15

16. Treasury Bill Prices:November 2, 2015Figure 9.3 shows a T-bill that expires April 7, 2016.It has 156 days to maturity.The bid discount is 0.178% (you use this to calculate the bid price, i.e., the price you will receive for the T-bill).Prices are quoted for $1,000,000 face values.Verify that the askprice is $999,272.00.16

17. Bond Equivalent YieldsBond Equivalent Yields (BEY) are another way to quote an interest rate.A calculation for restating semi-annual, quarterly, or monthly discount-bond or note yields into an annual yield.The BEY allows fixed-income securities whose payments are not annual to be compared with securities with annual yields. The BEY is the yield that is quoted in newspapers. You can convert a bank discount yield to a bond equivalent yield using this formula: Note that this formula is correct only for maturities of six months or less. Moreover, if February 29 occurs within the next 12 months, use 366 days.17

18. Example I: Bond Equivalent YieldFigure 9.3 shows a T-bill that expires April 7, 2016.It has 156 days to maturity.The bid discount is 0.178%.What is the Bond Equivalent (bid) Yield?There is not much difference at this low interest rate.Suppose, the bid discount was 6.00% for this 156-day T-bill. What is the BEY in this case? (6.2457%)Remember to multiply before you subtract.18

19. Example II: Calculating T-bill Prices Using Bond Equivalent YieldWe can calculate a Treasury bill asking price using the “asked” yield, which is a bond equivalent yield.Look at Figure 9.3 for the T-bill that expires on April 7, 2016.It has 156 days to maturity.The reported ask yield is 0.170%.Note: The bill’s ask price differs from a previous slide by about $1.95 due to rounding of the reported asked yield. The ask yield is really 0.17046% (verify using the BEY formula)The error is bigger for higher interest rates.19

20. More Ways to Quote Interest Rates“Simple” interest basis - Another method to quote interest rates. Calculated just like annual percentage rates (APRs). Used for CDs.The bond equivalent yield on a T-bill with less than six months to maturity is also an APR.An APR understates the true interest rate, which is usually called the effective annual rate (EAR).Alternatively, the EAR is the annualized rate you would get, had you used the annual compounding frequency.20

21. Converting APRs to EARsIn general, if we let m be the number of periods in a year, an APR can be converted to an EAR as follows:EARs are sometimes called effective annual yields, effective yields, or annualized yields.21

22. Example: The BEY on a T-bill is Really Just an APRWhat is the EAR of this T-bill’s BEY (aka APR)?Earlier, using the bid discount rate, we calculated a bid price for an 83-day T-bill to be $991,607.78.At maturity, this T-bill will be worth $1,000,000.You will earn $8,392.22 of interest on an investment of $991,607.78 over 83 days, a return of 0.846325%.In a 365-day year, there are 365/83 = 4.3976 periods of 83 days in length.0.846325 times 4.3976 is 3.7218%. This is the bond equivalent (bid) yield that we calculated before (that we rounded to 3.72%). Note: The Wall Street Journal rounds ask yields 2 decimal places.22Note that when interest rates are low, the APR will be close to the EAR.

23. Example: Converting Credit Card APRs to EARsSome Credit Cards quote an APR of 18%.18% is used because 18 = 12 times 1.50That is, the monthly rate is really 1.50%.What is the EAR?Ouch.23

24. Using Excel to Calculate T-bill Prices and Yields24

25. Rates and Yields on Fixed-Income SecuritiesSo far, we have focused on short-term interest rates, where “short-term” means one year or less. When issued, money market securities have a maturity of less than one year.When issued, fixed-income securities have a maturity of greater than one year.Fixed-income securities include long-term debt contracts from a wide variety of issuers:The U.S. government,Real estate purchases (mortgage debt),Corporations, andMunicipal governments25

26. The Treasury Yield CurveBecause of its sheer size, the leading world market for debt securities is the market to U.S. Treasury securities. The Treasury yield curve is a plot of Treasury yields against maturities.It is fundamental to bond market analysis, because it represents the interest rates for default-free lending across the maturity spectrum.26

27. Example: The Treasury Yield Curve27

28. The Term Structure of Interest Rates, I.The term structure of interest rates is the relationship between time to maturity and the interest rates for default-free, pure discount instruments.The term structure is sometimes called the “zero-coupon yield curve” to distinguish it from the Treasury yield curve, which is based on coupon bonds.Maturity premium is the difference between the required yield on long- and short-term securities of the same characteristics except maturity.It can be positive, negative, or zero.28

29. The Term Structure of Interest Rates, II.The term structure can be seen by examining yields on U.S. Treasury STRIPS.STRIPS are pure discount instruments created by “stripping” the coupons and principal payments of U.S. Treasury notes and bonds into separate parts,which are then sold separately.The term STRIPS stands for Separate Trading of Registered Interest and Principal of Securities.29

30. U.S. Treasury STRIPSAn asked yield for a U.S. Treasury STRIP is an APR, calculated as two times the true semiannual rate.Recall:Therefore, for STRIPS:M is the number of years to maturity.30

31. U.S. Treasury STRIPS31

32. Example: Pricing U.S. Treasury STRIPS, I.Let’s verify the price of the August 2017 Strip.The ask quote is 62.162, or $62.162.The ask YTM is 4.86%.Matures in about 10 years from the time of the quote.Close (considering the two-decimal rounding of the ask YTM).32

33. Example: Pricing U.S. Treasury STRIPS, II.Let’s calculate the YTM from the quoted price.Close again (reported ask YTM was 4.86%--using the actual days to maturity. We used “about 10 years.”).33

34. Treasury Yield Curves34

35. 35

36. Normal Yield CurveThis is the yield curve shape that forms during normal market conditions, wherein investors generally believe that there will be no significant changes in the economy.During such conditions, the market expects long-term fixed income securities to offer higher yields than short-term fixed income securities. Short-term instruments is generally perceived to hold less risk than long-term instruments; the farther into the future the bond's maturity, the more time and, therefore, uncertainty the bondholder faces before being paid back the principal. To invest in one instrument for a longer period of time, an investor needs to be compensated for undertaking the additional risk. 36

37. Flat Yield CurveThese curves indicate that the market environment is sending mixed signals to investors.During such an environment, it is difficult for the market to determine whether interest rates will move significantly in either direction farther into the future. Usually occurs when the market is making a transition that emits different but simultaneous indications of what interest rates will do. In other words, there may be some signals that short-term interest rates will rise and other signals that long-term interest rates will fall. When the yield curve is flat, investors can maximize their risk/return tradeoff by choosing fixed-income securities with the least risk, or highest credit quality. In the rare instances wherein long-term interest rates decline, a flat curve can sometimes lead to an inverted curve.37

38. Inverted Yield CurveThese yield curves are rare, and they form during extraordinary market conditions wherein the expectations of investors are completely the inverse of those demonstrated by the normal yield curve. the market currently expects interest rates to decline as time moves farther into the future, which in turn means the market expects yields of long-term bonds to decline bonds with maturity dates further into the future are expected to offer lower yields than bonds with shorter maturities. 38

39. Inverted Yield CurveRemember, also, that as interest rates decrease, bond prices increase and yields decline. You may be wondering why investors would choose to purchase long-term fixed-income investments when there is an inverted yield curve, which indicates that investors expect to receive less compensation for taking on more risk. Some investors, however, interpret an inverted curve as an indication that the economy will soon experience a slowdown, which causes future interest rates to give even lower yields. Before a slowdown, it is better to lock money into long-term investments at present prevailing yields, because future yields will be even lower.39

40. Dynamic Yield Curvehttp://stockcharts.com/freecharts/yieldcurve.html40

41. Yields on 10-Year versus 90-Day Treasury Securities: Term Spread41

42. Inverted Yield Curve = Prognosis for Recession?42

43. Nominal versus Real Interest RatesNominal interest rates are interest rates as they are observed and quoted, with no adjustment for inflation.the percentage change in the amount of money you haveReal interest rates are adjusted for inflation effects. the percentage change in the amount of stuff you can actually buy.Real interest rate = nominal interest rate – inflation rateorNominal rate = real interest rate + inflation rate43

44. Two Kinds of Interest Rates: Nominal vs. Real RatesExample: Suppose we have $1000, and Diet Coke costs $2.00 per six pack. We can buy 500 six packs. Now suppose the rate of inflation is 5%, so that the price rises to $2.10 in one year. We invest the $1000 and it grows to $1100 in one year. What’s our return in dollars? In six packs?Dollars. Our return is ($1100 - $1000)/$1000 = $100/$1000 = .10. The percentage increase in the amount of green stuff is 10%; our return is 10%. Nominal RateSix packs. We can buy $1100/$2.10 = 523.81 six packs, so our return is (523.81 - 500)/500 = 23.81/500 = 4.76% The percentage increase in the amount of brown stuff is 4.76%; our return is 4.76%. Real Rate44

45. The Fisher EffectThe Fisher Effect defines the relationship between real rates, nominal rates and inflation(1 + R) = (1 + r)(1 + h), whereR = nominal rater = real rateh = expected inflation rateApproximationR = r + hIf we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?R = (1.1)(1.08) – 1 = .188 = 18.8%Approximation: R = 10% + 8% = 18%45

46. Nominal versus Real Interest RatesThe Fisher Hypothesis asserts that the general level of nominal interest rates follows the general level of inflation.According to the Fisher hypothesis, interest rates are, on average, higher than the rate of inflation.46

47. Inflation Rates and T-bill Rates,1950 through 201447

48. Real T-bill Rates, 1950 through 201448

49. Inflation-Indexed Treasury Securities, I.Recently, the U.S. Treasury has issued securities that guarantee a fixed rate of return in excess of realized inflation rates. These inflation-indexed Treasury securities:pay a fixed coupon rate on their current principal adjust their principal semiannually according to the most recent inflation rate Suppose an inflation-indexed note has just been issued.Its coupon rate is 2% and has an initial principal of $1,000. Inflation is 1.5% since the note was issued. What is the coupon payment, six months later?49

50. Inflation-Indexed Treasury Securities, I.Recently, the U.S. Treasury has issued securities called Treasury Inflation Protected Securities (TIPS) that guarantee a fixed rate of return in excess of realized inflation rates – that is, they are indexed to inflation in order to protect investors from the negative effects of inflation.Their par value rises with inflation and falls with deflation, as measured by the CPI. TIPS pay interest twice a year, at a fixed coupon rate on their current principalBut, principal are adjusted semiannually according to the most recent inflation rate. So, like the principal, interest payments rise with inflation and fall with deflation.When a TIP matures, you are paid the adjusted principal or original principal, whichever is greater.TIPS can be purchased directly from the government through the TreasuryDirect system in $100 increments with a minimum investment of $100 and are available with 5-, 10-, and 20-year maturities.You can hold a TIPS until it matures or sell it in the secondary market before it matures.50

51. Example: TIPSSuppose an inflation-indexed note is issued with a coupon rate of 3.5% and an initial principal of $1,000. Six months later, the note will pay a coupon of $1,000 × (3.5%/2) = $17.50. Assuming 2 percent inflation over the six months since issuance, the note’s principal is then increased to $1,000 × 102% = $1,020. Six months later, the note pays $1,020 × (3.5%/2) = $17.85Its principal is again adjusted to compensate for recent inflation.51

52. Inflation-Indexed Treasury Securities, II.52

53. Traditional Theories of the Term StructureExpectations TheoryThe term structure of interest rates reflects financial market beliefs about future interest rates.Observed long-term rate is a function of today’s short-term rate and expected future short-term rates.Long-term and short-term securities are perfect substitutes.Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term rates.53

54. Traditional Theories of the Term StructureMaturity Preference (Liquidity Premium) Theory:Long-term bonds are more risky, and therefore, long-term interest rates contain a maturity premium necessary to induce lenders into making longer term loans.Investors will demand a premium for the risk associated with long-term bonds.The yield curve has an upward bias built into the long-term rates because of the risk premium.Forward rates contain a liquidity premium and are not equal to expected future short-term rates.54

55. Traditional Theories of the Term StructureMarket Segmentation Theory: Debt markets are segmented by maturity, so interest rates for various maturities are determined separately in each segment.Investors have specific needs in terms of maturity.Yield curve reflects intersection of demand and supply of individual maturities.55

56. Problems with Traditional TheoriesExpectations TheoryThe term structure is almost always upward sloping, but interest rates have not always risen.It is often the case that the term structure turns down at very long maturities.Maturity Preference TheoryThe U.S. government borrows much more heavily short-term than long-term.Many of the biggest buyers of fixed-income securities, such as pension funds, have a strong preference for long maturities.Market Segmentation TheoryThe U.S. government borrows at all maturities.Many institutional investors, such as mutual funds, are more than willing to move maturities to obtain more favorable rates.There are bond trading operations that exist just to exploit perceived premiums, even very small ones.56

57. Modern Term Structure Theory, I.Long-term bond prices are much more sensitive to interest rate changes than short-term bonds. This is called interest rate risk.So, the modern view of the term structure suggests that:NI = RI + IP + RPIn this equation: NI = Nominal interest rate RI = Real interest rate IP = Inflation premium RP = Interest rate risk premium57

58. Modern Term Structure Theory, II.58

59. Modern Term Structure Theory, III.The previous equation showed the component of interest rates on default-free bonds that trade in a liquid market.Not all bonds do.Therefore, a liquidity premium (LP) and a default premium (DP) must be added to the previous equation:NI = RI + IP + RP + LP + DP59

60. Forward Ratesr1 = current market rate for one-yearr2 = current market rate for two-yearf1,1 = the implied one-year forward rate at the end of one year60

61. Example61

62. Forecasting Interest Rates62

63. Forecasting Interest Rates63

64. Downward Sloping Spot Yield Curve Zero-Coupon Rates Bond Maturity 12% 1 11.75% 2 11.25% 3 10.00% 4 9.25% 564

65. Forward Rates Downward Sloping Yield Curve1yr Forward Rates 1yr [(1.1175)2 / 1.12] - 1 = 0.1150062yrs [(1.1125)3 / (1.1175)2] - 1 = 0.1025673yrs [(1.1)4 / (1.1125)3] - 1 = 0.0633364yrs [(1.0925)5 / (1.1)4] - 1 = 0.063008 65

66. Useful Internet Siteswww.money-rates.com (for the latest money market rates)www.gmacfs.com (the General Motors Acceptance Corp.)www.bba.org.uk (learn more about LIBOR)www.sifma.org (information on fixed income securities)www.bloomberg.com (current U.S. Treasury rates)www.smartmoney.com/bonds (view a “living yield curve”)www.fanniemae.com (one of three mortgage security websites)www.ginniemae.gov (one of three mortgage security websites)www.freddiemac.com (one of three mortgage security websites)www.publicdebt.treas.gov (information on STRIPS; other U.S. debt)66