Chapter 4 Understanding Interest Rates

1
Chapter 4 Understanding Interest Rates
2
Chapter 4 Understanding Interest Rates

• Measuring interest rates
• Yield on a discounts
• The distinction between interest rates and
  returns
• The distinction between real and nominal rates

3
Measuring Interest Rates

• Present Value
• A dollar paid to you one year from now is less
  valuable than a dollar paid to you today
• We can deposit money into a savings account and
  earn interest

4
Simple Loan

• The lender provides the borrower with an amount
  of funds (principal)
• The borrower repays the principal and an interest
  payment at maturity
• Interest Rate

5
Discounting the Future
6
Discounting the Future

• The process of calculating todays value of
  dollars received in the future
• If you are promised 100 of cash flow for certain
  10 years from now, it would not be as valuable
  today because you could invest it and earn more
  than the initial 100.

7
Simple Present Value
8
Four Types of Credit Market Instruments

• Simple Loan
• Fixed Payment Loan (Fully Amortized Loan)
• The lender provides the borrower with funds that
  must be repaid by making the same payment every
  period
• Coupon Bond
• Pays a fixed amount every year and then a
  specified final amount (face or par value) is
  repaid at maturity
• Discount Bond
• Is bought below face value, at maturity receive
  the face value

9
Yield to Maturity

• The interest rate that equates the present value
  of cash flow payments received from a debt
  instrument with its value today
• It is considered the most accurate measure of
  interest rates

10
Simple Loan

• For the case of the simple loan, calculating the
  yield to maturity is the same as the present
  value

11
Simple Loan Yield to Maturity
12
Fixed Payment Loan

• These loans are mortgages and other installment
  type loans
• The borrower makes the same payment to the bank
  every month
• To calculate yield to maturity we equate todays
  value of the loan to all future payments

13
Fixed Payment Loan Yield to Maturity
14
Coupon Bond

• Not very popular today
• Got their name because the bond holder would have
  to mail in a coupon to receive their payment
• The bond is calculated by adding up the present
  value of all coupon payments and the face value
• A coupon bond is describe by its coupon rate
• i.e. if you get 100 coupon and it has a 1,000
  face value it is considered a 10 (100/1,000)
  coupon bond

15
Coupon Bond Yield to Maturity
16

• When the coupon bond is priced at its face value,
  the yield to maturity equals the coupon rate
• The price of a coupon bond and the yield to
  maturity are negatively related
• The yield to maturity is greater than the coupon
  rate when the bond price is below its face value

17
Consol or Perpetuity

• A bond with no maturity date that does not repay
  principal but pays fixed coupon payments forever

18
Discount Bond

• U.S. Treasury Bills
• Yield to Maturity is calculated similarly to the
  simple loan
• Thus, the interest rate is calculated by
• Where PV is the purchase price today and CF is
  the face value

19
Discount Bond
20
Discount Bond Yield to Maturity
21
Bond Prices

• The bond price and interest rate are negatively
  related
• As the interest rate increases
• Future coupon and final bond payments are worth
  less when discounted back to the present
• The opportunity cost of buying the bond
  increases, thus you pay less for the bond

22
Yield on a Discount Basis
23
Yield on a Discount Basis

• Notice it uses the percent change of the face
  value, YTM uses percent change of the price
• Secondly, it uses only 360 days not 365 days
• Thus it understates the interest rate
• The percent change is also smaller (price value)
• The denominator is larger under the yield on a
  discount

24
Rate of Return and Interest Rates

• The return equals the yield to maturity only if
  the holding period equals the time to maturity
• An increase in interest rates is associated with
  a fall in bond prices, resulting in a capital
  loss only if the time to maturity is longer than
  the holding period
• i.e. dont buy the bond when interest rates are
  expected to increase
• The more distant a bonds maturity, the greater
  the size of the percentage price change
  associated with an interest-rate change

25
Rate of Return
26
Rate of Return and Interest Rates

• The more distant a bonds maturity, the lower the
  rate of return that occurs as a result of an
  increase in the interest rate
• Even if a bond has a substantial initial interest
  rate, its return can be negative if the interest
  rate rises
• If the bond is sold before the maturity date, the
  return on the bond is different than the YTM

27
(No Transcript)
28
Interest-Rate Risk

• Prices and returns for long-term bonds are more
  volatile than those for shorter-term bond
• Interest rate increases hold short term bonds
• Interest rate decreases hold long term bonds
• There is no interest-rate risk for any bond whose
  time to maturity matches the holding period

29
Real and Nominal Interest Rates

• Nominal interest rate makes no allowance for
  inflation
• Real interest rate is adjusted for changes in
  price level so it more accurately reflects the
  cost of borrowing
• Ex ante real interest rate is adjusted for
  expected changes in the price level
• Ex post real interest rate is adjusted for actual
  changes in the price level

30
Fisher Equation
31
Returns

• So far we have only considered nominal returns
• A big reason for an increase in interest rates
  are due to higher levels of inflation
• Recently, the U.S. has experienced negative real
  interest rates.
• Only way to avoid inflation risk is to purchase
  U.S. Treasury Bonds that are indexed to
  inflation.
• TIPS Treasury Inflation Protected Securities

32
(No Transcript)