Chapter 4: Understanding Interest Rates

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Chapter 4 Understanding Interest Rates
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• 1. Measuring Interest Rates

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Present Value

• Present Value is finding value today of dollars
  received in the future
• p r1 r2 r3 . . . rn
  (1i)1 (1i)2 (1i)3
  (1i)n
• p present value
• r1 amount received 1 year from now
• r2 amount received 2 years from now
• r3 amount received 3 years from now
• rn amount received n years from now
• i interest rate (yield to maturity)

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Coupon Bond

• Formula
• r1, r2, r3, . .., rn-1 coupon (interest)
• rn coupon face value
• Example
• 100 coupon, 2 years to maturity, 1000 face
  value, 847.22 present value (price of bond)
• 847.22 100 100 1000
  (1i) (1i)2
• Solve for i
• i 20

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Consol Bond

• Formula (bond pays r forever)
• p r/i
• Example
• 100 coupon, 10 i
• p 100/.1 1000
• If raise market interest rate to 20
• p 100/.2 500
• Conclusion bond prices and interest rates are
  inversely related.

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• 2. Other Interest Rates

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Current Yield

• Formula
• i coupon
  current price of bond
• When current yield is more accurate
• Term to maturity is long
• Bond price is close to face value

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Yield on a Discount Basis

• Formula
• i (face value-pd) 360
  
  face value days to maturity
• pd discount bond price
• Why is the measure wrong?
• There are 365 days in a year
• Measures capital gain incorrectly
• Direction of bias
• Discount yield understates the true
  yield

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• 3. Interest Rates Vs.
• Rates of Return

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Rate of Return

• RET coupon pt1 pt pt
  
• RET rate of return for t to t1
• pt1 bond price at time t1
• pt bond price at time t
• Alternative formula
• RET ic g
• ic current yield
• g capital gain
• Conclusion
• Unless g 0, then RET will not equal the
  interest rate.

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Are Long Term Bonds More Risky?

• Example
• If the interest rate rises from 10 to 20, the
  price of a 1-year bond will fall by 8.3 but the
  price of a consol bond will fall by 50.
• Intuition
• The price of a long-term bond must fall more
  since the loss in interest payments is larger.
• Conclusion
• The returns on long-term bonds are
  more volatile since their prices
  are more volatile.

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• 4. Distinction Between Real and Nominal Interest
  Rates

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Nominal vs. Real Interest Rates

• Formula
• Example
• Which measure is better?
• Real interest rate is a better measure of
  economic incentives than the nominal rate.

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EndChapter 4