Term Structure of Interest Rates

1
Term Structure of Interest Rates

• PRM Study Group Session 2
• Date August 9, 2007

2
Overview

• Compounding methods
• Term structure of interest rates
• Yield curve bootstrapping
• Spot and forward rates

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Compounding Methods

• Continuous vs. discrete compounding
• Example 5 P.A. on 100 principal

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Periodic Compounding
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Effective Yield

• APR Annual Percentage Rate Nominal Rate (ie.
  5 p.a. )
• APY Annual Percentage Yield Effective Yield
• Effective Yield APR if n 1
• Effective Yield gt APR if n gt 1

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Effective Yield
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Types of Interest Rates

• Treasury Rates
• Japanese Treasury rates are the rates at which
  the Japanese Govt can borrow in yen
• Termed Risk-free rate because assume no default
  risk as govt can print money to meet its
  obligation

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Types of Interest Rates

• LIBOR Rates
• London Interbank Offer Rate
• If more banks want to borrow funds than lend
  funds, LIBOR increase
• In practice, LIBOR is the risk-free rate because
  financial institute borrow and lend in this
  market.

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Term Structure of Interest Rates

• A plot of yields to maturity of zero-coupon bonds
  with annual compounding vs. maturity
• Also called zero-coupon Yield Curve
• YTM of a n-year zero-coupon bond n-year spot
  rate

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Term Structure of Interest Rates

• Given 1) face value, 2) zero-coupon bond price,
  and 3) compounding frequency
• Solve for zero-coupon bond yields spot rates

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Yield Curve Bootstrapping

• Can be bootstrapped using zero-coupon bond prices
  or coupon paying bonds cash flows
• Assumption linear between two maturities

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Yield Curve Bootstrapping

• Bond Price Sum(PV Coupon) PV face value
• Spot rates are built-up one by one

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Forward Rates

• Yield to maturity of a bond in the future
• Given the price of the bond in the future, you
  can obtain the forward rates
• Forward rates are the interest rates implied by
  current spot rates for periods of time in the
  future

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Forward Rate

• Spot rate
• 3-year spot rate YTM of 3-year zero-coupon bond
• Short rate 1 period forward rate
• 1-year short rate at the end of year 2

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Forward Rates

• Given 1) future bond prices, 2) todays spot
  prices, 3) compounding frequency
• Solve forward rates