Finance 4000

Money and Capital Markets

Fifth class

• What determines interest rate differentials?

  
  
  

• Examples

  
  
  

  • Federal government bonds have lower yields than those issued by private agents

    
    
    

  • Private agents' bonds have different yields

    
    
    

    • lower bond rating -- e.g. baa versus aaa -- implies higher yield to maturity

      
      
      

    • FHA 30 years bonds in between aaa and baa bonds

      
      
      

  • State and local bonds have a lower yield than federal government bonds

    
    
    

  • These differentials vary over time

• Default risk

  
  
  

  • At least partly explains

    
    
    

    • yields on private bonds relative to federal bonds

      
      
      

    • baa yield relative to aaa yield

      
      
      

  • default risk -- the chance that payments will not be made as promised in the bond

    
    
    

  • Risk premium

    
    
    

    • Compensation for bearing risk

      
      
      

    • Defined as the interest rate on the bond minus the risk-free rate

      
      
      

    • Usually measured as the interest rate on the bond minus the interest rate on federal bonds

      
      
      

      • Federal bonds have no nominal default risk -- risk-free nominal rate
        • does not mean that they have a risk-free real yield to maturity
        • Do TIPS have a risk-free real yield to maturity?

          
          
          
          
          

• How does default risk become reflected in the price?

  
  
  

  • Assume bonds are substitutes

    
    
    

  • How does the price of bonds come to reflect the perceived default risk in equilibrium?

    
    
    

    • Demand and supply

      
      
      

    • What if someone has a different opinion than is reflected in the market price of the bonds?

      
      
      

• Taxes

  
  
  

  • How does the tax-free status of interest on state and local bonds become reflected in the price?

    
    
    

    • Demand and supply

      
      
      

      • Assume bonds are substitutes

        
        
        

      • Ignore default risk on state and local bonds

        
        
        

    • Whose tax rate is reflected in the difference in yields on state and local bonds relative to Treasury securities?

      
      
      

• Liquidity premiums?

  
  
  

  • Liquidity premium is the extra rate of return for holding a less liquid bond

    
    
    

  • Widely-traded Treasury securities probably are the most liquid securities

    
    
    

  • Effects of changes in liquidity

    
    
    

  • 1987

    
    
    

  • Recent?

    
    
    

    • Long Term Capital Management unwinding positions

• The term structure of interest rates

  
  
  

• Yield curves for nominal Treasury bonds and TIPS

  
  
  

  • A yield curve shows how the yield to maturity of a bond varies as the term to maturity varies

    
    
    

    • bonds that are identical other than term to maturity

      
      
      

• General observations about bond yields

  
  
  

  • Yields on bonds with different maturities tend to go up and down together. There is a large common factor in bond yields.

    
    
    

  • When short-term interest rates are low, the yield curve is more likely to slope up. When short-term interest rates are high, the yield curve is more likely to slope down.

    
    
    

  • On average, shorter-term bonds have a lower yield than longer-term bonds.

• Explanations of the term structure

  
  
  

  • Expectations hypothesis

    
    
    

    • The yield curve reflects expectations of future short-term interest rates

      
      
      

  • Segmented markets theory

    
    
    

    • Relative bond yields depend only on relative demand and supply

      
      
      

  • Preferred habitat theory

    
    
    

    • Different holders and issuers of bonds prefer different maturities but different maturities are substitutes

      
      
      

    • Liquidity preference theory

      
      
      

      • Everything else the same, holders of bonds prefer shorter-term bonds than issuers want to issue

        
        
        

    • The expectations hypothesis is fundamental for the preferred habitat and liquidity preference theories

• A T-period bond yield always can be broken down into T single-period interest rates

  
  
  

  • This is independent of any theory of the term structure

    
    
    

• Example -- two period bond

  
  
  

  • Issuer is borrowing for two periods

    
    
    

  • Discount bond

    
    
    

  • Two-period bond yield is i₂ when issued

    
    
    

    • Bond yield is 10 percent per year

      
      
      

    • Initial amount borrowed and lent is $100

      
      
      

    • Pays (1.10)²$100=$121 two years later

      
      
      

    • Can decompose this into two one-year loans

• • Borrow $100 for first year

    
    
    

    • What interest rate?

      
      
      

      • Interest rate at which one-year loans currently being made

        
        
        

        • Suppose that interest rate is 10 percent also

          
          
          

        • Implies that $110 would be paid back at the end of the year

• • Suppose borrow $110 for second year

    
    
    

    • This is a forward loan

      
      
      

      • A loan contracted today for a date in the future

        
        
        

      • contract for a date forward in time

        
        
        

    • What interest rate?

      
      
      

      • Denote it by

        
        
        

        • forward rate starting in period 1 and ending in period 2

          
          
          

          • Know that two-year loans today are at 10 percent
          • Know that one-year loans today are at 10 percent

            
            
            

          • 10 percent would seem sensible

            
            
            

      • 

        
        
        

      • 

        
        
        

• Expectations hypothesis of the term structure

  
  
  

  • Implicit forward interest rates equal expectations of future one-period rates

    
    
    

    • Let be the expected interest for period 1 to 2

      
      
      

    • 

      
      
      

  • Why?

    
    
    

    • Suppose the people respond to expected earnings -- profits from alternative strategies

      
      
      

    • If the expected return from holding two successive 1-period bonds is greater than the expected return from holding one 2-period bond, then hold two 1-period bonds with higher return

      
      
      

    • If the expected return from holding one 2-period bond were greater than holding two successive 1-period bonds, then hold the 2-period bond with higher return

      
      
      

    • Other ways to profit if can sell short the 1-period or 2-period bond

• • Basic point of expectations hypothesis

    
    
    

    • People care about the periods when they borrow or make loans

      
      
      

    • People do not care about the term to maturity of bonds that they buy and sell to borrow and lend

      
      
      

  • Implications for interpreting term structure of interest rates

    
    
    

    • forward rates

      
      
      

    • bond yields

• Segmented-markets hypothesis

  
  
  

  • Agents care about term to maturity of bonds

    
    
    

    • Saving for retirement, buy long term bond

      
      
      

    • Financing a plant, issue long term bond

      
      
      

    • Saving for a house, buy short term bond

      
      
      

    • Financing inventory, issue short term bond

      
      
      

    • Nothing else going on

      
      
      

  • Implications for term structure of interest rates

    
    
    

    • Relative bond yields are a function of relative demand and supply

      
      
      

• Preferred habitat hypothesis

  
  
  

  • People have to be paid to change the maturity of their assets and liabilities but a finite payment will induce them to change

    
    
    

  • Implication for term structure

    
    
    

    • Bond yields are a function of expectations and relative demand and supply

      
      
      

  • Problem

    
    
    

    • Pretty vacuous

      
      
      

    • Why higher yield on long-term bonds?

      
      
      

      • Just happens to be

        
        
        

      • Could be the opposite

        
        
        

• Liquidity preference hypothesis

  
  
  

  • In general, people prefer to hold short-term bonds

    
    
    

    • Due to interest-rate risk

      
      
      

    • Ignores reinvestment risk or assumes a very particular structure of preferences of issuers and holders of bonds

      
      
      

  • Implication for term structure

    
    
    

    • On average, term structure slopes upward even though the average expected change is zero

      
      
      

    • When the term structure slopes upward, interest rates may be expected to increase
      • If increase greater than liquidity premium
      • Have to estimate liquidity premium

        
        
        

    • When the term structure is flat, interest rates are expected to decrease

      
      
      

    • When the term structure slopes downward, interest rates are expected to decrease