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Power. Point Slides for: Financial Markets and Institutions 6 th Edition By Jeff Madura Power. Point Slides for: Financial Markets and Institutions 6 th Edition By Jeff Madura Prepared by David R. Durst The University of Akron

CHAPTER 3 Structure of Interest Rates CHAPTER 3 Structure of Interest Rates

Chapter Objectives n Learn why individual interest rates differ or why security prices vary Chapter Objectives n Learn why individual interest rates differ or why security prices vary or change n Analyze theories explaining why rates vary by term or maturity, called the term structure of interest rates Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields Risk-averse investors demand higher yields For added riskiness n Risk Factors Affecting Security Yields Risk-averse investors demand higher yields For added riskiness n Risk is associated with variability Of returns n Increased riskiness generates lower security prices or higher investor required rates of return n Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields n Security yields and prices are affected by levels and Factors Affecting Security Yields n Security yields and prices are affected by levels and changes in: Default risk (also called Credit Risk) l Liquidity l Tax status l Term to maturity l Special contract provisions such as embedded options l Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields Benchmark—risk-free treasury securities for given maturity n Default risk premium Factors Affecting Security Yields Benchmark—risk-free treasury securities for given maturity n Default risk premium = risky security yield – treasury security yield of same maturity n Default risk premium = market expected default loss rate n Rating agencies set default risk ratings n Anticipated or actual ratings changes impact security prices and yields n Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields The Liquidity of a security affects the yield/price of the Factors Affecting Security Yields The Liquidity of a security affects the yield/price of the security n A liquid investment is easily converted to cash At minimum transactions cost n Investors pay more (lower yield) for liquid investment n Liquidity is associated with short-term, low default risk, marketable securities n Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields Tax status of income or gain on security impacts the Factors Affecting Security Yields Tax status of income or gain on security impacts the security yield n Investor concerned with after-tax return or yield n Investors require higher yields For higher taxed securities n Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields Yat = Ybt(1 – T) Where: Yat = after-tax yield Factors Affecting Security Yields Yat = Ybt(1 – T) Where: Yat = after-tax yield Ybt = before-tax yield T = investor’s marginal tax rate Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields Example: a taxable security that offers a beforetax yield of Factors Affecting Security Yields Example: a taxable security that offers a beforetax yield of 14 percent. The investor’s tax rate is 20 percent. Calculate the after-tax yield. Yat = 14%(1 – 0. 2) = 11. 2% n The fully taxable pre-tax equivalent corporate bond for a 11. 2% municipal bond is: Ybt = 11. 2%/(1 –. 2) = 14% n Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields n Term to maturity Interest rates typically vary by maturity. Factors Affecting Security Yields n Term to maturity Interest rates typically vary by maturity. l The term structure of interest rates defines the relationship between maturity and yield. l u. The Yield Curve is the plot of current interest yields versus time to maturity. Copyright© 2002 Thomson Publishing. All rights reserved.

Yield Curve Yield % Time to Maturity An upward-sloping yield curve indicates that Treasury Yield Curve Yield % Time to Maturity An upward-sloping yield curve indicates that Treasury Securities with longer maturities offer higher annual yields Copyright© 2002 Thomson Publishing. All rights reserved.

Yield Curve Shapes Normal Level or Flat Inverted Copyright© 2002 Thomson Publishing. All rights Yield Curve Shapes Normal Level or Flat Inverted Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields n Special Provisions l Call Feature: enables borrower to buy Factors Affecting Security Yields n Special Provisions l Call Feature: enables borrower to buy back the bonds before maturity at a specified price u. Call features are exercised when interest rates have declined u. Investors demand higher yield on callable bonds, especially when rates are expected to fall in the future Copyright© 2002 Thomson Publishing. All rights reserved.

Factors Affecting Security Yields n Special provisions l Convertible bonds u. Convertibility feature allows Factors Affecting Security Yields n Special provisions l Convertible bonds u. Convertibility feature allows investors to convert the bond into a specified number of common stock shares u. Investors will accept a lower yield for convertible bonds because investor returns include expected return on equity participation Copyright© 2002 Thomson Publishing. All rights reserved.

Estimating the Appropriate Yield n The appropriate yield to be offered on a debt Estimating the Appropriate Yield n The appropriate yield to be offered on a debt security is based on the risk-free rate for the corresponding maturity plus adjustments to capture various security characteristics Yn = Rf, n + DP + LP + TA + CALLP + COND Copyright© 2002 Thomson Publishing. All rights reserved.

Estimating the Appropriate Yield Yn = Rf, n + DP + LP + TA Estimating the Appropriate Yield Yn = Rf, n + DP + LP + TA + CALLP + COND Where: Yn = yield of an n-day security Rf, n = yield on an n-day Treasury (risk-free) security DP = default premium (credit risk) LP = liquidity premium TA = adjustment for tax status CALLP = call feature premium COND = convertibility discount Copyright© 2002 Thomson Publishing. All rights reserved.

The Term Structure of Interest Rates Theories Explaining Shape of Yield Curve Pure Expectations The Term Structure of Interest Rates Theories Explaining Shape of Yield Curve Pure Expectations Theory l Liquidity Premium Theory l Segmented Markets Theory l Copyright© 2002 Thomson Publishing. All rights reserved.

The Term Structure of Interest Rates n Pure Expectations Theory Long-term rates are average The Term Structure of Interest Rates n Pure Expectations Theory Long-term rates are average of current short-term and expected future short-term rates l Yield curve slope reflects market expectations of future interest rates l Investors select maturity based on expectations l Copyright© 2002 Thomson Publishing. All rights reserved.

The Term Structure of Interest Rates n Pure Expectations Theory Assumes investor has no The Term Structure of Interest Rates n Pure Expectations Theory Assumes investor has no maturity preferences and transaction costs are low l Long-term rates are averages of current short rates and expected short rates l u. Forward rate: market’s forecast of the future interest rate Copyright© 2002 Thomson Publishing. All rights reserved.

The Term Structure of Interest Rates Downward. Sloping Yield Curve Upward. Sloping Yield Curve The Term Structure of Interest Rates Downward. Sloping Yield Curve Upward. Sloping Yield Curve n n n Expected higher interest rate levels Expansive monetary policy Expanding economy n n n Expected lower interest rate levels Tight monetary policy Recession soon? Copyright© 2002 Thomson Publishing. All rights reserved.

The Term Structure of Interest Rates n Liquidity Premium Theory Investors prefer short-term, more The Term Structure of Interest Rates n Liquidity Premium Theory Investors prefer short-term, more liquid, securities l Long-term securities and associated risks are desirable only with increased yields l Explains upward-sloping yield curve l When combined with the expectations theory, yield curves could still be used to interpret interest rate expectations l Copyright© 2002 Thomson Publishing. All rights reserved.

The Term Structure of Interest Rates n Segmented Markets Theory explaining segmented, broken yield The Term Structure of Interest Rates n Segmented Markets Theory explaining segmented, broken yield curves l Assumes investors have maturity preference boundaries, e. g. , short-term vs. long-term maturities l Explains why rates and prices vary significantly between certain maturities l Copyright© 2002 Thomson Publishing. All rights reserved.

The Term Structure of Interest Rates n Uses of the term structure l Forecast The Term Structure of Interest Rates n Uses of the term structure l Forecast interest rates u The market provides a consensus forecast of expected future interest rates u Expectations theory dominates the shape of the yield curve l Forecast recessions u Flat or inverted yield curves have been a good predictor of recessions. See Exhibit 3. 14. l Investment and financing decisions u Lenders/borrowers attempt to time investment/financing based on expectations shown by the yield curve u Riding the yield curve u Timing of bond issuance Copyright© 2002 Thomson Publishing. All rights reserved.

Interest Rate Differential (10 -Year Rate Minus Three-Month Rate) Exhibit 3. 14 Yield Curve Interest Rate Differential (10 -Year Rate Minus Three-Month Rate) Exhibit 3. 14 Yield Curve as a Signal for Recessions 7 6 5 4 3 2 1 0 – 1 – 2 – 3 – 4 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2001 Year *The general shape of the yield curve is measured as the differential between annualized 10 -year and three-month interest rates. Recessionary periods are shaded. Copyright© 2002 Thomson Publishing. All rights reserved.

Treasury Debt Management and the Yield Curve U. S. Treasury attempts to finance federal Treasury Debt Management and the Yield Curve U. S. Treasury attempts to finance federal debt at the lowest overall cost n Treasury uses a mixture of Bills, Notes, and Bonds to finance periodic deficits and refinance outstanding securities n Treasury focuses on short-term issuance, phasing out 30 -year bonds n Treasury 10 -year bond now the standard issue n Leave the long-term issuance to private issuers n Copyright© 2002 Thomson Publishing. All rights reserved.

Historic Review of the Term Structure n Yield curves levels and shapes at various Historic Review of the Term Structure n Yield curves levels and shapes at various times indicate: l l l n Inflation expectations Level of economic activity or phase of business cycle Monetary policy at the time Usually high positive slope in short-term l l l Represents demand for liquidity Short-term securities desired; higher prices; lower rates Short-term securities provide liquidity with maturity Copyright© 2002 Thomson Publishing. All rights reserved.

Exhibit 3. 17 Yield Curves at Various Points in Time 17 16 Annualized Treasury Exhibit 3. 17 Yield Curves at Various Points in Time 17 16 Annualized Treasury Security Yields 15 February 17, 1982 14 13 January 2, 1985 12 11 10 9 August 2, 1989 8 October 22, 1996 7 October 15, 2000 6 5 September 18, 2001 4 3 2 0 5 10 15 20 Number of Years to Maturity 25 30 Copyright© 2002 Thomson Publishing. All rights reserved.

Exhibit 3. 18 Change in Term Premium Over Time 20 Percentages 15 10 5 Exhibit 3. 18 Change in Term Premium Over Time 20 Percentages 15 10 5 30 -year T-Bond Yield Three-month T-Bill Rate 0 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Year Copyright© 2002 Thomson Publishing. All rights reserved.

International Structure of Interest Rates n Capital flows to the highest expected after-tax, real International Structure of Interest Rates n Capital flows to the highest expected after-tax, real (inflation and other risk-adjusted), foreign exchange adjusted rates of return Copyright© 2002 Thomson Publishing. All rights reserved.

International Structure of Interest Rates n Yield differences between countries are related to: Expected International Structure of Interest Rates n Yield differences between countries are related to: Expected changes in forex rates l Varied expected real rates of return l Varied expected inflation rates l Varied country and business risk l Varied central bank monetary policy l Copyright© 2002 Thomson Publishing. All rights reserved.