Interest Rates

1
Interest Rates

• Chapter 4

2
Valuing Debt

• In 1945, U.S. Treasury bills offered a return of
  0.4. At their 1981 peak, they offered a return
  of over 17.
• Why does the same security offer radically
  different yields at different times?

3
Valuing Debt

• In January 2000, the U.S. Treasury could borrow
  for 1 year at an interest rate of 6.2, but it
  had to pay a rate of about 7 for 20-year loans.
  
• Why do bonds maturing at different dates offer
  different rates of interest?

4
Valuing Debt

• In January 2000, the U.S. government could issue
  long-term bonds at a rate of about 7.
• You could not have borrowed at that rate. Why
  not?

5

• INTEREST RATES SERVE AS A
• YARDSTICK FOR COMPARING
• DIFFERENT TYPES OF
• SECURITIES AND MATURITIES.

6
5 Major Sources of Rate Differences in Bonds

• Term to maturity
• Default risk
• To default on a bond is to fail to pay the
  interest when interest is due or to fail to pay
  the principal at maturity
• Bond ratings
• Tax treatment
• The value of the tax factors to the investor
  depends on the investors marginal income tax
  rate
• After tax yieldBefore tax yield (1-T)

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• Marketability
• time required to effect the sale
• spread between the current market price and
  realized price at the time of the sale.
• Special features
• call option.
• put option.
• convertible option.

8
Characteristics of Bonds

• Details contained in the indenture.
• Administered through a trustee.
• Secured versus unsecured.
• Mortgage/debenture
• Senior or junior or subordinated.
• Call features.
• Bond rating.

9
Types of Bonds

• Coupon/Zero-coupon bonds
• Municipal bonds
• Revenue/General Obligation
• Junk bonds
• Consols
• Eurobonds/Foreign bonds

10
Sources of Bond Information

• http//www.moodys.com
• http//www.bondsonline.com/
• http//www.wsj.com
• http//bonds.yahoo.com

11
Bond Features

• When a corporation (or government) wants to
  borrow money, it often sells a bond.
• An investor gives the corporation money for the
  bond.
• The corporation promises to give the investor
• Regular coupon payments every period until the
  bond matures.
• The face value of the bond when it matures.

12
The Bond Pricing Formula

• C1 C2 C3
  Cn Fn
• P
• (1 r)1 (1 r)2 (1 r)3
  (1 r)T
• The price of the bond today is the present value
  of all future cash flows (coupon payments and
  principal).

13
The Bond-Pricing Equation
14
Bond Features

• Consider a bond with three years to maturity, a
  coupon rate of 8, and a 1000 face value. If
  the current market rate is 10, what is the price
  of the bond.
• 80 80 1080
  
• P
• (1.10)1 (1.10)2 (1.10)3
• P80(0.9091)80(0.8264)1080(0.7513)
• P950.24

15
Bond Rates and Yields

• The coupon rate is the annual dollar coupon
  expressed as a percentage of the face value.
• Coupon rate 80/1000 8.0
• The current yield is the annual coupon divided by
  the price
• Current yield 80/950.24 8.42
• The yield to maturity is the rate that makes
  the price of the bond just equal to the present
  value of its future cash flows.
• YTM 10

16
Example

• Bond A has 4 years remaining to maturity.
  Interest is paid annually the bond has a 1,000
  par value and the coupon interest rate is 9.
• What is the current yield and yield to maturity
  at a current market price of 829?
• What is the current yield and yield to maturity
  at a current market price of 1,104?

17
Par, Premium and Discount Bonds

• If a bonds coupon rate is equal to the market
  rate of interest (the bonds yield), the bond
  will always sell at par.
• Bonds selling at below par are called discount
  bonds.
• Bonds selling above par are called premium bonds.

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Pure Discount Bond

• Zero-coupon bonds pay no coupon payment but
  promise a single payment at maturity.
• Value of a pure discount bond
• P F / (1 r)T

19
Perpetual Bonds

• A consol pays coupons forever. It never matures.
• PC/r

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Bond Pricing Theorem I

• Bond prices and market interest rates move in
  opposite directions.

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Bond Pricing Theorem II

• When coupon rate YTM, price par value.
• When coupon rate gt YTM, price gt par value
  (premium bond)
• When coupon rate lt YTM, price lt par value
  (discount bond)

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Bond Pricing Theorem III

• A bond with longer maturity has higher relative
  () price change than one with shorter maturity
  when interest rate (YTM) changes. All other
  features are identical.

23
Bond Pricing Theorem IV

• A lower coupon bond has a higher relative ()
  price change than a higher coupon bond when
  interest rate (YTM) changes. All other features
  are identical.

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Coupon Rate and Bond Price Volatility
Consider two otherwise identical bonds. The
low-coupon bond will have much more volatility
with respect to changes in the discount rate
25
Interest Rate Risk

• Price Risk.
• Reinvestment Risk.
• Price Risk versus Reinvestment Risk.
• Duration.

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Interest Rate Risk Example

• Suppose you buy three securities
• A one-year bill with a face value of 10,000.
• A 5-year strip with a face value of 10,000.
• A 30-year strip with a face value of 10,000.
• The market interest rate is 6, so their prices
  are
• T-bill P10,000/1.069,434
• 5-year strip P10,000/(1.06)57,473
• 30-year strip P10,000/(1.l06)301,741

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Example, continued

• After a year, you need your money and you must
  liquidate your portfolio. Suppose market rates
  have risen from 6 to 8.
• T-bill P10,000
• 5-year strip P10,000/(1.08)47,350
• 30-year strip P10,000/(1.08)291,073

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Reinvestment-Rate Risk

• Suppose that you do not need your money after one
  year but want to leave it invested until you
  retire in 30 years.
• On the 30-year strip, the holding-period yield
  equals the market yield at the time you bought
  the bond.
• How much you make on the other two investments
  will depend on how you reinvest the money when
  the bond matures.

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Reinvestment-Rate Risk

• Reinvestment-rate risk
• the risk associated with reinvestment at
  uncertain interest rates.
• Considerations
• What is your time horizon?
• Do you want to play it safe?
• Do you think interest rates will rise or fall?

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Lessons

• If you hold a bill or strip to maturity, the
  holding-period yield will equal the market yield
  at the time that you bought it.
• If you sell a bill or strip before maturity, the
  holding-period yield depends on the market yield
  at the time of the sale.
• The higher the market yield at the time of the
  sale, the lower the market price.
• The greater the bills or the strips remaining
  time to maturity, the greater the sensitivity of
  its market price to market yield.

32
Return Versus Yield to Maturity

• Rate of return measures the cash flows received
  during a period relative to the amount invested
  at the beginning
• For a bond held for one year, the return is
  computed as follows

33
Nominal versus Real Rates

• The real rate of interest is the fundamental
  long-run interest rate in the economy. It is
  called the real rate of interest because it is
  determined by the real output of the economy.
• It is estimated to be on average about 3 percent.
  It varies between 2 and 4 percent.
• The nominal rate of interest is the observed rate
  of interest.
• Nominal rate Real rate Inflation

34
Calculating Interest Rates

• Nominal Versus Real Interest Rates
• Nominal Interest RatesMoney amount of interest
  received
• Real Interest RatesPurchasing power of interest
  received
• Real interest rate is the nominal interest
  adjusted for inflation

Real interest rate Nominal rate Inflation rate

• Where
• ex-ante is based on the expected rate of
  inflation
• ex-post is based on the actual or realized rate
  of inflation

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Supply and Demand Determine the Interest Rate

• Interest rate is price of credit or borrowing
  money
• Market for Credit or Loanable Funds
• Supply of FundsUpward sloping, lenders are
  willing to extend more credit at higher interest
  rates
• Demand for FundsDownward sloping, borrowers are
  willing to borrow less at higher interest rates
• EquilibriumIntersection of supply and demand, no
  tendency to change

36
Why Does the Interest Rate Fluctuate

• U.S. Treasury bond yields change day to day
• Movement along a single curveChanges in the
  interest rate results in a movement along a
  single demand or supply curve
• Shifts of a CurveChange in determinants of
  supply or demand (other than interest rate)
  causes the respective curve to shift
• Changes in EquilibriumShift of either the supply
  or demand curve will reflect a change in the
  equilibrium interest rate

37
Borrowing (Demand)

• Business firms
• finance inventory or buy capital equipment
• Households
• buy cars, consumer goods, or homes
• State and local government
• provide infrastructure or public services
• Federal government
• finance Federal Budget Deficit
• INCREASES IN BORROWING
• SHIFT DEMAND TO RIGHT AND RAISE INTEREST RATES

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Lending or Credit (Supply)

• Financial institutions or individuals lend to
  market
• Government authorities may restrict lending by
  banks
• Ability of individuals to lend depends on their
  savingsless savings results in lower amount of
  lending
• DECREASES IN LENDING
• SHIFT SUPPLY TO LEFT AND RAISE INTEREST RATE

39
The Importance of Expectations

• Effect of a change in expectations of increasing
  inflation
• DemandBorrowers increase demand since they will
  be repaying in depreciated dollars and desire to
  purchase before the prices increase
• SupplyLenders decrease supply since they will be
  repaid with money of diminished purchasing power
• SHIFTS OF THE DEMAND AND SUPPLY CURVE WILL CAUSE
  THE INTEREST RATE TO INCREASE

40
The Importance of Expectations

• Self-fulfilling Prophesies
• If individuals and institutions expect inflation
  and interest rates to increase, they will alter
  behavior that causes the higher rates that were
  anticipated

41
Cyclical and Long-term Trends in Interest Rates

• Level of interest rates tends to rise during
  cyclical expansion and fall during recessions.
• During economic expansion
• Firms and households increase borrowingdemand
  curve right
• FED usually tightens credit during
  expansionsupply curve left

42
Cyclical and Long-term Trends in Interest Rates

• Level of interest rates on upward long-term trend
  between 1950 and 1981
• Large federal budget deficit forced US Treasury
  to increase borrowingpushing up interest rates
• Expectations of increasing inflation
• Since 1981 rates have trended downward
• Federal deficits continued to increase in 1980s
• Expectations of lower inflation has been major
  reason for fall of interest rates.