© 2006 Thomson Business and Professional Publishing. All rights reserved. T H I R D E D I T I O N PowerPoint Presentation by Charlie Cook The University.

© 2006 Thomson Business and Professional Publishing. All rights reserved. T H I R D E D I T I O N PowerPoint Presentation by Charlie Cook The University of West Alabama Interest Rates Chapter 4 Unit II Financial Markets and Instruments

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–2 Fundamental Issues 1.Why must we compute different interest yields? 2.How does risk cause market interest rates to differ? 3.Why do market interest rates vary with differences in financial instruments’ terms to maturity? 4.What is the real interest rate? 5.What interest rates are the key indicators of financial market conditions?

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–3 Calculating Interest Yields: Key Terms Principal:  The amount of credit extended when one makes a loan or purchases a bond. Interest:  The payment, or yield, received for extending credit by holding any financial instrument. Interest rate:  The percentage return, or percentage yield, earned by the holder of a financial instrument.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–4 Different Concepts of Interest Yield Coupon return: (C) A fixed interest return that a bond yields each year. Coupon return gets its name from so-called Bearer Bonds, where the owner clipped the coupon from the bond and Sends coupon to issuer, who returns coupon payment Registered Bonds-(more common) the issuer:  Keeps records of ownership  Automatically sends coupon payment to bondholder

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–5 Different Concepts of Interest Yield Nominal yield: (r n )  The coupon return on a bond divided by the bond’s face value; r n =C/F.  Where F equals the face value.  Example from book: say the bond has a face value of $10,000 and an annual coupon payment of $600, then the nominal yield is 600/10000 =.06 or 6 percent.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–6 Different Concepts of Interest Yield Since the current price of a bond in the secondary market is usually different from its face value, we often look at the current yield of a bond: Current yield: ( r c )  The coupon return on a bond divided by the bond’s market price; r c =C/P. where P equals the current market price of the bond. Say the current price of this bond is $9,000, then the current yield is 600/$9,000 =.067 or 6.7 percent.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–7 Different Concepts of Interest Yields (cont’d) Yield to maturity:  The rate of return on a bond if it is held until it matures, which reflects the market price of the bond, the bond’s coupon return, and any capital gain from holding the bond to maturity. Capital gain:  An increase in the value of a financial instrument at the time it is sold as compared with its market value at the date it was purchased.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–8 Calculating Discounted Present Value First lets look at future values, then find the discounted present value. Compounding Future Values  What is the future value of money lent (or borrowed) today?  (1) AMOUNT REPAID = PRINCIPAL + INTEREST  The amount of interest can be found as: (2) INTEREST = PRINCIPAL x INTEREST RATE Substitute from 2 into 1 gives:

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–9 Future values AMOUNT REPAID = PRINCIPAL + ( PRINCIPAL x INTEREST RATE ) AMOUNT REPAID = PRINCIPAL x ( 1 + r ) Where r equals the interest rate. In terms of an equation, we have V 1 = V 0 ( 1 + r ) Where V 1 = the funds to be received by the lender at the end of one year ( a future value) V 0 = the funds lent now( the present value)

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–11 What would be the future value in 2 years? Let V 2 = value after 2 years V 2 = V 0 + r V 0 + r(V 0 + r V 0 ) = V 0 + r V 0 + rV 0 + r 2 V 0 = V 0 + 2r V 0 + r 2 V 0 = V 0 ( 1 + 2r + r 2 ) V 2 = V 0 ( 1 + r ) 2 PS, don’t worry about showing this on tests!!

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–13 Example, future values You put $10,000 into a cd that matures in 10 years. Assuming all interest is reinvested, what will the cd be worth if the interest rate is 5%? 10%? V 10 = V 0 ( 1 + r ) 10 = 10,000 (1 +.05) 10 = $16,289 At 10% we have 10,000 (1 +.10) 10 = 25,937

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–14 Calculating Discounted Present Value Now go from future value to Discounted present value: Discounting is backward-looking What is the PRESENT VALUE of money to be received (or paid) in the future? Solving our future value equation for V 0 gives: V 0 = V n / (1 + r ) n

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–15 Example: Present values You just had a baby: how much would you have to invest today at 5% interest in order to have $100,000 for the baby’s college in 18 years? At 10%?

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–16 Example continued V 0 = V n / (1 + r ) n = 100,000 (1 +.05) 18 =$41,545 V 0 = V n / (1 + r ) n = 100,000 (1 +.10) 18 =$17,985

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–17 Calculating Discounted Present Value  Discounted present value gives you the value today of a payment to be received at a future date.  For one year from now, the present value equals the payment one year from now/(1+ r)  Discounted present value of payment to be received n years in the future:  Payment n years from now/(1+ r) n

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–18 Present value Why do we care about present value? For one thing, the price that traders should be willing to pay for various financial instruments, such as bonds, that have future payments, is the present value of that bond.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–19 Present value Most bonds mature in 10 years or more, have a face or par value (F) of $1,000 per bond or some multiple of $1,000, make equal interest payments over the term to maturity, called coupon payments, and then repay the face value at maturity.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–20 Calculating Discounted Present Value Example from the text: market value of a 3-year bond with a $600 annual coupon, $10,000 face value, and the current rate of interest is 5%. To find the present value or price people should be willing to pay, we need to discount the coupon payments in the first 2 years as well as the coupon and face value payment in the last year. Present value or the price of this 3 year bond is calculated as: = $600/(1.05) + $600/(1.05) 2 + $10,600/(1.05) 3 = $571.43 + $544.22 + $9,156.68 = $10,272.33.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–21 Calculating Discounted Present Value In general, the formula is: P = C 1 / ( 1 + r ) 1 + C 2 / ( 1 + r ) 2 + … + C n / ( 1 + r ) n + F / ( 1 + r ) n P = the price (present value) of the bond C = the coupon payment on the bond (C1 in year 1, C2 in year 2 etc. F = the face or par value of the bond r = the interest rate n = the number of years to maturity (on a three -year bond, n=3)

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–22 Compounded Annual Interest Rate Year3%5%8%10%20% 1.971.952.926.909.833 2.943.907.857.826.694 3.915.864.794.751.578 4.889.823.735.683.482 5.863.784.681.620.402 6.838.746.630.564.335 7.813.711.583.513.279 8.789.677.540.466.233 9.766.645.500.424.194 10.744.614.463.385.162 Present Values of a Future Dollar Table 4–1

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–23 Calculating the Yield to Maturity Perpetuity:  A bond with an infinite term to maturity.  Perpetuity price = C/r. Simple rule:  Prices of existing bonds are inversely related to changing market interest rates.  Higher interest rates causes bond prices to fall.  In a sense, stocks (equities) are similar to perpetuities, since they have no maturity date.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–24 Yields On Treasury Bills Published T-bill rates:  Are based on a fictitious 360-day year calculated from the equation: where F= face or par value, P is the price paid, and n is the number of days to maturity.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–25 Yields On Treasury Bills Coupon yield equivalent: (uses a 365 day year)  An annualized T-bill rate (that can be compared with annual yields on other financial instruments) is calculated from the equation:

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–27 Interest Rates on Money Market Instruments Table 4–2 SOURCE: Board of Governors of the Federal Reserve System, H.15 (519) Statistical Release, June 13, 2005.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–28 Some web sites for bonds http://www.investinginbonds.com/ All financial instruments are somewhat substitutable for one another, but not perfect substitutes: they can differ in risk, liquidity, tax treatment, and term to maturity.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–29 The Risk Structure of Interest Rates Risk structure of interest rates:  The relationship among yields on financial instruments that have the same maturity but differ because of variations in default risk, liquidity, and tax rates. Default risk:  The chance that an individual or a firm that issues a financial instrument may be unable to honor its obligations to repay the principal and/or to make interest payments.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–30 The Risk Structure of Interest Rates Compare say, US government bonds with Corporate bonds: which has less default risk and why?

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–31 The Risk Structure… (cont’d) Risk premium:  The amount one instrument’s yield exceeds the yield of another instrument because the first instrument is riskier and less liquid than the second. Rating securities  Investment-grade securities: Bonds with relatively low default risk.  Junk bonds: Bonds with relatively high default risk.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–32 The Risk Structure… (cont’d) Bonds rated by Moody’s and Standard and Poors Liquidity differences: generally less liquid instruments are seen as riskier and thus have a higher rate of return. Usually this liquidity premium is added into the risk premium. Tax considerations  Municipal bond earnings are not taxed, and thus have a lower rate of return than say Treasury bonds.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–33 Long-Term Bond Yields Figure 4–1 SOURCE: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin, various issues. 12

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–34 Municipal and Treasury Bond Yields Figure 4–2 SOURCE: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin, various issues.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–35 The Term Structure of Interest Rates Term structure of interest rates:  The relationship among yields on financial instruments with identical risk, liquidity, and tax characteristics but differing terms to maturity. Yield curve:  A chart depicting the relationship among yields on bonds that differ only in their terms to maturity.  Often focus on one type of security, like treasuries, in order to hold other factors constant.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–38 Shapes of yield curves 1. Upward sloping, higher yield for longer term to maturity, most usual case. 2. Downward sloping, lower yield for longer term to maturity, known as an inverted yield curve. 3. Horizontal, same yield for differing term to maturity.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–39 Question is, what can explain these shapes? Several theories, including: 1. Segmented market hypothesis 2. Expectations theory 3. Preferred habitat and liquidity premium theory.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–40 Segmented Markets Theory Segmented markets theory:  A theory of the term structure of interest rates that views bonds with differing maturities as nonsubstitutable, so their yields differ because they are determined by supply and demand in separate markets.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–41 Segmented Markets Theory This can explain why yield curve is not horizontal: however 2 drawbacks to this theory: 1. Treasury bond rates do move together, thus suggesting some substitutability. 2. Cannot explain why the yield curve is normally upward sloping.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–42 Treasury Security Yields Figure 4–4 SOURCES: Board of Governors of the Federal Reserve System, Federal Reserve Bulletin (various issues) and G.13 (415) Statistical Release.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–43 Expectations Theory Expectations theory:  Explains how expectations about future yields can cause yields on instruments with different maturities to move together.  It can provide insight into why the yield curve may systematically slope upward or downward:  An upward-sloping yield curve indicates a general expectation by savers that short-term interest rates will rise.  A downward-sloping yield curve indicates a general expectation that short-term interest rates will decline.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–44 Expectations Theory Theory holding that the long-term interest rate is the average of the present short- term rate and the short-term rates expected to prevail over the term to maturity of the long-term security.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–45 Expectations theory Consider a 2 year horizon: can either buy a 2 year bond now, or a one year bond now and then another one year bond. Other things equal, you should be indifferent between these 2 if the expected rate of return was the same. Start with a simple average (technically should use a geometric average due to compounding, but to simplify we will omit this.)

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–46 Let R = current yield on a 2 year bond Let r 1 = current yield on a 1 year bond Let r 2 e = expected yield on a 1 year bond a year from now If R = (r 1 + r 2 e ) / 2, then should be indifferent between the 2.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–47 Example Say r 1 =.02, and r 2 e =.04, then R =.03. R = (.02 +.04) / 2 =.03. Note that this gives an upward sloping yield curve.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–49 Suppose rates are expected to fall… Say r 1 =.02, and r 2 e =.01, then R =.015. R = (.02 +.01) / 2 =.015. Note that this gives a downward sloping yield curve.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–53 Expectations theory Strengths, Weaknesses of expectations theory  Strength: Able to explain upward or downward yield curves  Weakness: Yield curves usually slope upward, which implies people expect higher rates: yet in the long run interest rates sometimes rise, sometimes fall. Thus expectations theory seems incomplete.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–54 The Preferred Habitat Theory Preferred habitat theory:  A modification of the expectations theory of the term structure of interest rates that views bonds as imperfectly substitutable, so yields on longer-term bonds must be greater than those on shorter-term bonds even if short-term interest rates are not expected to rise or fall.  By this view, many borrowers and lenders have preferred maturities, which creates a degree of market segmentation between short-term and long- term markets.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–55 The Preferred Habitat Theory (cont’d) Term premium:  An amount by which the yield on a long-term bond must exceed the yield on a short-term bond to make individuals willing to hold either bond if they expect short-term bond yields to remain unchanged.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–56 The Preferred Habitat Theory (cont’d) Using books example, suppose that r 1 =.04, and r 2 e =.04, in other words people expect the one year rate to remain at 4 percent. Suppose the term premium is.005 or one half a percent. This gives the 2 year bond rate to be: R =.005 + (.04 +.04) / 2 =.045. Thus the 2 year rate is 4.5%, the one year is 4%, and we have an upward sloping yield curve.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–57 The Preferred Habitat Theory (cont’d) To get a horizontal yield curve by this theory, need some slight expected delcine in rates. r 1 =.04, and r 2 e =.03, in other words people expect the one year rate to fall to 3.0 percent. Again, if the term premium is.005 or one half a percent, we have R =.005 + (.04 +.03) / 2 =.040. Thus the 2 year rate is 4.0%, the one year is 4%, and we have a horizontal yield curve.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–58 The Preferred Habitat Theory (cont’d) To get a downward sloping curve by this theory, need a larger drop in expected interest rates. r 1 =.04, and r 2 e =.02, in other words people expect the one year rate to fall to 2.0 percent. Again, if the term premium is.005 or one half a percent, we have R =.005 + (.04 +.02) / 2 =.035. Thus the 2 year rate is 3.5%, the one year is 4%, and we have a downward sloping yield curve.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–60 Nominal versus Real Rates of Interest Nominal interest rate:  A rate of return in current-dollar terms that does not reflect anticipated inflation.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–61 Nominal versus Real Rates of Interest Real interest rate:  The anticipated rate of return from holding a financial instrument after taking into account the extent to which inflation is expected to reduce the amount of goods and services that this return could be used to buy. where r r is the real rate of interest, r is the nominal rate, and π e is the expected rate of inflation.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–62 Nominal versus Real Rates of Interest While the real interest rate is of great importance to an individual in deciding how much to save, it is safe to use nominal rates to choose among different instruments since inflation affects all of these.

© 2006 Thomson Business and Professional Publishing. All rights reserved.4–63 Key Interest Rates in the Global Economy Federal funds rate:  A short-term (usually overnight) interest rate on interbank loans in the United States. Prime rate:  The interest rate that American banks charge on loans to the most creditworthy business borrowers. London Interbank Offer Rate (LIBOR):  The interest rate on interbank loans traded among six large London banks.  International equivalent of the U.S. federal funds rate

© 2006 Thomson Business and Professional Publishing. All rights reserved. T H I R D E D I T I O N PowerPoint Presentation by Charlie Cook The University.

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© 2006 Thomson Business and Professional Publishing. All rights reserved. T H I R D E D I T I O N PowerPoint Presentation by Charlie Cook The University.

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