Term Structure of Interest Rates: Relationship with the Business Cycle

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Term Structure of Interest RatesRelationship
with the Business Cycle
Typical Shapes
Yield
Peak
Normal Expansion
Trough
Maturity
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Short-Term Interest Rates Examples

• t-bill yield, e.g., 91-day rate ? issued by
  government
• bank rate ? central bank rate lending to banks
• bankers acceptance (BAs), e.g., 3-month ?
  guaranteed by chartered banks
• commercial paper, e.g., 3-month ? corporate
  borrowing (typically unsecured)
• prime rate ? chartered bank lending to best
  customers
• typically move together (but not lockstep)
• . . . Problem 1 and 3

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Bonds Nomenclature

• A COUPON BOND is a combination of an annuity (the
  annual or semi-annual coupon payments) and a zero
  coupon bond (with face value due at maturity).
• Example
• 15 year bond with 8 coupons (paid semi-annually)
  and 1000 par value.
• This coupon bond pays to the holder, 40 every
  six months for fifteen years
• At the end of fifteen years, the principal amount
  of 1000 is repaid with the final coupon payment
  of 40.

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Zero Coupons Bond

• A ZERO COUPON BOND, only pays the holder the
  principal or face value at maturity
• No interim payments (or coupons) are due prior to
  maturity,
• At maturity the entire face value is repaid
• The holder will typically have purchased this
  zero coupon bond for less than the face value
• Quite simply, a zero coupon bond is a
• ZERO COUPON BOND

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Zero Coupon Bonds Pricing
Price P (1r)T

• Where P is the bonds principle (or par value) due
  upon maturity, r is the required return and T is
  the time to maturity
• Example 91-day T-bill with 100 par value. The
  required return is 2 over this (one) 91-day
  period

Price 100 98.04 (10.02)
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Zero Coupon Bond Yields

• The yield to maturity (YTM) on a bond is simply
  the IRR for the bond
• Example
• The average bid price on 91-day T-bills is
  98.352 (i.e., this is the price today for the
  bills that will provide a cash flow of 100 in 91
  days)
• what is the YTM or IRR or T-bill rate?

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Zero Coupon Bond Yields contd.

• NPV 0 -C0 C1/(1r)
• 0 -98.352 100/(1r)
• (1r) 100/98.352
• r 1.0168 1
• r .0168 or 1.68 which is a 91-day rate
• Using a spreadsheet
• RATE(1, 0, -98.352, 100) 0.0168

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Zero Coupon Bond Yields contd.

• What rate would be quoted?
• By convention, annualize (using simple interest)
• 1.68 x (365/91) 6.72
• What is the effective annual rate of return?
• (1.0168)365/91 1 0.0691 or 6.91

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Coupon Bond Pricing
Example 15 year bond with 8 coupons (paid
semi-annually) and 1000 par value. Suppose, the
required return is 5 every six months

Price 40 x 1- (1.05)-30 1000
846.28 0.05
(1.05)30
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Coupon Bond Yields

• What is the YTM of a 2-year bond which has a
  price today of 100 and pays semi-annual coupons
  of 5 (i.e., has a coupon rate of 10)?
• NPV 0 -C0 C1/(1r) C2/(1r)2
  C3/(1r)3 C4/(1r)4 PRINC/(1r)4
• 0 -100 5/(1r) 5/(1r)2 5/(1r)3
  5/(1r)4 100/(1r)4
• r 5
• Excel rate (4, 5, -100, 100) or Goalseek
• Quoted Bond yield (annualized) 10
• Effective annual rate 1.052 -1 .1025 or 10.25

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Bond Chart Example

• Issuer coupon maturity ask
  price ask yield
• US Govt 6.00 Oct 08 99.0625 3.33
• Problems 5 6

current price ()
coupon rate is 6 of 100 face 3 paid every 6
months
current YTM ()
final coupon and 100 face paid then
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Term Structure of Interest RatesInterest Rate
Forecasting

• . . . Problem 4 (equivalent)
• Assume the 2 year rate is 1 higher than the 1
  year rate and you have a two year horizon.
• You have 2 strategies
• 1. Put a 1000 into a bond with a 2 yr. maturity
• 2. Put a 1000 into a 1 year bond, which you will
  roll over at the end of one year?

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Key Learning Points

• Term structure of interest rates
• Expectations hypothesis and forward rates
• Real and nominal interest rates
• Inflation
• Real and nominal cash flows
• Bond yields
• Yields are inversely related to bond prices
• Long maturity bonds are most sensitive to changes
  in yields