bond prices zero-coupon bonds: promise a single future payment, e.g., a u.s. treasury bill. fixed...
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Bond Prices
Zero-coupon bonds: promise a single future payment, e.g., a U.S. Treasury Bill.
Fixed payment loans, e.g., conventional mortgages.
Coupon Bonds: make periodic interest payments and repay the principal at maturity, e.g., U.S. Treasury Bonds and most corporate bonds.
Consols: make periodic interest payments forever, never repaying the principal that was borrowed, e.g., British consols.
Bond Prices
Zero-Coupon Bonds or Discount Bonds
Price of a $100 face value zero-coupon bond
Where i = interest rate
n = time until the payment is made
ni)1(
100$
Bond Prices Zero-Coupon Bonds or Discount Bonds
Examples. Assume i=4%
Price of a One-Year Treasury Bill.
Price of a Six-Month Treasury Bill
06.98$)04.01(
1002/1
Bond PricesFixed Payment Loans
Value of a Fixed Payment Loan =
ni
ntFixedPayme
i
ntFixedPayme
i
ntFixedPayme
)1()1()1( 2
Bond PricesCoupon Bond
nnCB i
FaceValue
i
entCouponPaym
i
entCouponPaym
i
entCouponPaymP
)1()1(......
)1()1( 21
Bond PricesConsols
i
PaymentCoupon Yearly PConsol
Bond YieldsYield to Maturity
Price of One-Year 5 percent Coupon Bond =
The value of i that solves this equation is the yield to maturity
)1(
100$
)1(
5$
ii
Bond YieldsYield To Maturity
• If the price of the bond is $100, then the yield to maturity equals the coupon rate.
• Since the price rises as the yield falls, when the price is above $100, the yield to maturity must be below the coupon rate.
– If you pay more than the face value for a bond, you are earning less than the coupon rate.
Bond Yields
Paid Price
Payment CouponYearly YieldCurrent
Bond Yields Relationship Between a Bond’s Price and
Its Coupon Rate, Current Yield and Yield to Maturity
Bond Price < Face Value Coupon Rate < Current Yield < Yield to
Maturity
Bond Price = Face Value Coupon Rate = Current Yield = Yield to
Maturity
Bond Price > Face Value Coupon Rate > Current Yield > Yield to
Maturity
Bond YieldsHolding Period Return:
the return to holding a bond and selling it before maturity.
The holding period return can differ from the yield to maturity when you do not hold the bond to maturity.
Bond YieldsExample:
10 year bond (Face value=$100) and a 6% coupon rate. Sold one year later.
• If the interest rate in one year is 5%, one year holding period return =
1311.100$
11.13$
100$
100$11.107$
100$
6$
Bond YieldsIf the interest rate in one year is 7%
One year holding Period return =
or -.52%
0052.100$
52$.
100$
100$48.93$
100$
6$
Bond Market and Interest Rates
One Year Zero-coupon (discount) Bond.
P
Pi or
iP
100$
1
100$
Bond Market and Interest Rates
Bond Market and Interest Rates
Factors that shift Bond Supply
• An increase in the government’s borrowing increases the quantity of bonds outstanding, shifting the bond supply curve to the right.
• As business conditions improve, the bond supply curve shifts to the right.
• An increase in expected inflation shifts the bond supply curve to the right.
Bond Market and Interest Rates
Factors that Shift Bond Demand to Right
• An increases in wealth.
• A fall in expected inflation.
• If the return on bonds rises relative to the return on alternative investments, the demand for bonds increases.
• If a bond becomes less risky relative to alternative investments, the demand for the bond increases.
• When a bond becomes more liquid relative to alternatives, the demand for the bond increases.
Bond Market and Interest Rates
Bonds and Risk
Sources of Bond Risk
• Default Risk
• Inflation Risk
• Interest-Rate Risk