Bonds, Bond Prices and the Determination of Interest Rates

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Chapter 6

• Bonds, Bond Prices and the Determination of
  Interest Rates

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Bonds and Interest Rates Topics

• Types of bonds and their prices
• Measures of bond yields
• Supply and demand in the bond market
• Why bonds are risky

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1. Types of Bonds

• 1.1. Zero-coupon or discount bond
• Promise a single payment on a future date
• Treasury bill
• 1.2. Fixed-payment loan
• Sequence of fixed payments
• Mortgage or car loan
• 1.3. Coupon bond
• periodic interest payments principal repayment
  at maturity
• U.S. Treasury Bonds and most corporate bonds
• 1.4. Consol (Consolidated Stock perpetuities )
• periodic interest payments forever, principal
  never repaid
• U.K. government has some outstanding

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1.1 Bond Prices Zero-Coupon or Discount
Bonds

• Price of 100 face value zero-coupon bond
• Where i is the interest rate in decimal form and
  n is time until the payment is made in the same
  time units as the interest rate

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1.1 Bond Prices Zero-Coupon or Discount
Bonds

• Assume i5
• Price of a One-Year Treasury Bill.
• Price of a Six-Month Treasury Bill

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1.1 Bond Prices Zero-Coupon or Discount
Bonds

• Given maturity (n), the price of a bond and
  the interest rate move in opposite directions

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1.2 Bond Prices Fixed Payment Loans

• Value of a Fixed Payment Loan
• Value is the sum of the present value of the
  payments.
• The interest rate rises and the value of the
  fixed-payment loan move in opposite directions.

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1.3 Bond Prices Coupon Bonds

• Price of Coupon Bond
• Present value of coupon payments
• Present value of face value

The interest rate rises and the price of the
coupon bond move in opposite directions.
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1.4 Bond Prices Consols

• Why? Page 124, footnote 2

The interest rate rises and the price of the
consol move in opposite directions.
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2. Bond Yields Definition

• The interest rate or return to an investor ,
  implicit in the bonds price.

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2.1 Bond Yields Yield to Maturity

• Price of 1yr 5 Coupon Bond
• Price of Coupon Bond X (1 i) 105
• Yield to maturity The value of i that solves
  this equation.

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Bond Yields Yield to Maturity

• If Bond Price 100 (par), Yield to maturity
  the coupon rate
• If Bond Price gt100 (par), Yield to maturity lt
  the coupon rate
• If Bond Price lt100 (par), Yield to maturity gt
  the coupon rateBond Price ? ? Yield to maturity?

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2.2 Bond Yields Current Yield
Current Yield Part of the Return arising
solely from the coupon payments.
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Bond Yields Current Yield

• Example
• 1yr, 5 coupon bond selling for 99
• Current Yield , or 5.05
• Note
• Yield to maturity
  , i 0.0606, or 6.06

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Bond Yields Comparisons
Relationship among Coupon Rate, Current Yield,
Yield to Maturity
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2.3 Bond Yields Holding Period Returns

• The holding period return is the return to
  holding a bond and selling it before maturity.
• Holding period return can differ from the yield
  to maturity.

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2.3 Bond Yields Holding Period Returns

• Examples
• 10 year bond
• 6 coupon rate
• Purchase at face value, 100
• Hold for one year and then sell it

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2.3 Bond Yields Holding Period Returns

• What if the interest rate falls to 5 (Pb
  107.11)
• 1yr Holding Period Return
• 1-yr Holding Period Return 13.11

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2.3 Bond Yields Holding Period Returns

• What if the interest rate rises to 7
• 1yr Holding Period Return
• 1-yr Holding Period Return ?0.52

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2.3 Bond Yields Holding Period Returns

• Holding Period Return
• Current Yield Capital Gain (as a )

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• A bond mutual fund reports great returns much
  higher than interest rates were
• Whats going on?
• Chances are interest rates fell, so the holding
  period return gt interest rate

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3. Bond Market Determination of Interest
Rates

• Consider
• 1yr, Zero-coupon (discount) Bond

Know P ? compute i. Focus on how market
determines P.
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3.1 Bond Market Supply

• The Bond supply curve is the relationship
  between the price and the quantity of bonds
  people are willing to sell, all other things
  being equal.

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3.1 Bond Market Supply

• Investor Higher the price, the more tempting it
  is to sell a bond they currently hold.
• Company seeking to finance a project Higher
  the price at which they can sell bonds, the
  cheaper it is to borrow.
• Conclusion Supply curve slopes up.
• For a 100 one-year zero-coupon bond, the
  supply will be higher at 95 than it will be at
  90, all other things being equal.

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3.2 Bond Market Demand

• The bond demand curve is the relationship
  between the price and quantity of bonds that
  investors demand, all other things being equal.

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3.2 Bond Market Demand

• InvestorsThe lower the price bondholders must
  pay for a fixed-dollar payment on a future date,
  the more likely they are to buy a bond
• Conclusion Demand curve slopes down
• For a 100 one-year zero-coupon bond, the
  demand will be higher at 90 than it will be at
  95, all other things being equal.

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3.3 Bond Market Equilibrium

• Supplyslopes up
• Demandslopes down
• Equilibrium supplydemand

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3.4 Bond Market Shifting the Supply
Curve

• These all shift supply to the right
• Increase in the governments borrowing.
• An improvement in business conditions
• Increase in expected inflation
• Each of these lowers bond prices, increasing
  interest rates.

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3.4 Bond Market Shifting the Supply
Curve
When borrowers desire for funds increases, the
supply curve shifts to the right. This lowers
bond prices, raising interest rates.
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3.5 Bond Market Shifting the Demand
Curve

• These all shift demand to the right
• An increases in wealth shift
• Reduction in expected inflation
• Fall in expected future interest rates
• Rise in expected return on bonds relative to
  alternatives.
• Fall in riskiness of bonds relative to
  alternatives
• Increase in bond liquidity relative to
  alternatives
• Each of these raises bond prices, lowering
  interest rates.

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3.5 Bond Market Shifting the Demand
Curve
When bonds become more attractive for investors,
the demand curve shifts to the right. This
raises bond prices, lowering interest rates.
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Factors that Shift Bond Demand to the Right (I)
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Factors that Shift Bond Demand to the Right (II)
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3.6 Bond Market Examples

• Increases in Expected Inflation
• Business-Cycle Downturn

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3.6.1 Bond Market Increase in Expected
Inflation
1) Shift S right 2) Shifts D right Drives P
down, increasing the interest rates
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3.6.2 Bond Market Business-Cycle
Downturn

• Shift S left
• Shift D left
• Drives P up,
• decreasing i.

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• There are times when investors
• Flee risky bonds
• Buy Treasury bonds
• Fall 1998
• Russia defaulted
• Investors got worried about all risky bonds
• Demand for Treasury bonds rose.

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4. Why Bonds are Risky

• Default Risk Issuer may not make promised
  payments
• Inflation Risk
• Inflation could turn out to be greater than
  expected.
• Interest-Rate Risk Interest rate may rise
  between the time of purchase and the time you
  sell the bond.

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• Loans to students at truck-driving school are
  risky.
• Lenders face high default risk.
• How do you find borrowers who stop making paying?

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• Inflation creates risk that nominal return will
  be less than you expected.
• If i6 and ?6 ? r0!
• TIPS Treasury Inflation Protection Securities
• Pay a real interest rate
• Plus change in the CPI