Topics to be Covered

1
Session 3

• Topics to be Covered
• Government Bonds
• Spot Rates
• Yield Curve
• Yield to Maturity

2
Spot Rates

• The yield to maturity for a bond is the interest
  rate that solves

3
Spot Rate

• In principle, there can be a different interest
  rate for each period
• The appropriate discount rate for a cash flow in
  year 1 (r1) is the one year spot rate.
• The appropriate discount rate for a cash flow in
  year n (rn) is the n-year spot rate.

4
Yield Curve

• The relationship between the interest rate and
  the maturity of the cash flow is called
• Yield Curve, or
• Term Structure of Interest Rates
• The yield to maturity of a coupon-bearing bond is
  a complex weighted average of the spot rates.

5
Example

• Consider a bond with 7 coupon (annual payments),
  100 face value, 3 years to maturity.
• Assume the spot rates are
• r1 7, r2 7.5, r3 8
• Market price
• Yield to maturity

6
Vocabulary

• Whenever a bond is issued at one yield, and
  interest rates change, the bond price will
  change.
• If the price is lower than the principal amount,
  the bond is trading at a discount (i.e. zero
  coupon bonds).
• If the price is higher than the principal amount,
  the bond trades at a premium.
• If the price equals the principal amount, the
  bond trades at par.

7
Yield Curve

• The yield curve may have different shapes.
• If interest rates on long-term bonds are higher
  than those on short-term bonds, the yield curve
  has an upward slope.
• The yield curve may also be flat, humped, or
  downward sloping.
• Determinants of the shape of the yield curve
  include
• expectations about future interest rates
• risk
• differences in preferences of borrows and lenders
  for different maturities (supply and demand).

8
Expectations of Future Rates

• Suppose you anticipate rates will increase.
• If you buy a 1-year government security, you will
  be happy with a yield of 5.
• If you invest for 5 years, will you still be
  happy with 5 per year?
• Probably not
• If you expect interest rates will go up, you will
  demand higher yields on longer-term securities.

9
Riskiness of Long-Term Bonds

• To understand how long-term bonds may be riskier
  than short-term bonds, consider the following
  example.
• Assume a flat term structure, rn10.
• For 1000, and investor could buy
• a 1-year zero coupon bond with face value
  1100.
• a 2-year zero coupon bond with face value 1210.

10
Riskiness of Long-Term Bonds

• Case 1 Interest rates shift to 15 for all
  maturities
• PV (1 year bond) 1100/(1.15) 956.52
• PV (2 year bond) 1210/(1.15)2 914.93
• Case 2 Interest rates shift to 8 for all
  maturities
• PV (1 year bond) 1100/(1.08) 1018.52
• PV (2 year bond) 1210/(1.08)2 1037.38
• The longer-term bond is much more sensitive to
  shifts in interest rates.

11
Supply and Demand

• Sometimes, investors choose to demand bonds with
  a certain maturity.
• Issuers may prefer to issue bonds with a
  different maturity.
• Differences in supply and demand affect the
  pricing of bonds (i.e., interest rates)
• Recently, the U.S. Government repurchased
  long-term securities.

12
Default Risk

• We have assumed cash flows will be paid with
  certainty.
• Except in the case of government debt, this is
  usually not truethere is default risk.
• Most people are risk averse.
• Rule A safe dollar is worth more than a risky
  one.

13
Risk and Return

• A riskier investment usually gives a higher
  return on average than a less risky investment,
  to compensate us for the extra risk.
• The average extra return is called the
• risk premium
• The higher rate is called the
• risk adjusted discount rate.

14
Risk and Return

• Once we determine
• appropriate risk adjusted discount rate, and
• estimated cash flows, then
• Use discounted cash flow (PV) formula
• where Cj expected future cash flows
• rj risk adjusted discount rate.

15
Example

• Suppose the interest rate on risk-free1-year
  bonds is 9.
• Backwoods Chemical issued bonds
• 9 coupon (annual payment)
• 1000 face value
• 1 year maturity
• What should be the price of these bonds?

16
Example

• If the notes are risk-free, discount at 9.
• Suppose the notes are risky.
• 20 chance Backwoods will default, no cash flows.
• Investors demand 2 risk premium.

17
Example

• The expected cash flow is
• (0.8)(1,090) (0.2)(0) 872
• The risk adjusted discount rate is
• rf risk premium 0.09 0.02 0.11
• The price should be

18
Example

• An investor who buys the bond for 785.59 will
  receive a promised yield of
• However, if the borrower defaults, the actual
  yield will be less.

19
Ratings

• Standard and Poors and Moodys are two rating
  agencies that classify bonds by risk category.
• Bonds rated BB/Ba or lower are Speculative
  Grade/Junk Bonds.
• Bonds rated BBB/Baa or higher are Investment
  Grade.
• Yields on bonds and the spread between yields on
  bonds of different risk vary over time.