Sample Data (Table 4

# Sample Data (Table 4 - 4 5.0 6.2 = R3,4 5 5.3 6.5 = R4,5 6...

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Sample Data (Table 4.3, page 86) Bond Time to Annual Bond Principal Maturity Coupon Price (dollars) (years) (dollars) (dollars) 100 0.25 0 97.5 100 0.50 0 94.9 100 1.00 0 90.0 100 1.50 8 96.0 100 2.00 12 101.6 1

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The Bootstrap Method to Compute Zero Rates STOP here and compute zero rates for maturities of 3 months, 6 months, 1 year, 1.5 years, and 2 years. 2
Zero Curve Calculated from the Data (Figure 4.1, page 88) Zero Rate (%) Maturity (yrs) 10.127 10.469 10.53 6 10.68 1 10.808 3 9 10 11 12 0 0.5 1 1.5 2 2.5

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Forward Rates The forward rate is the future zero rate implied by today’s term structure of interest rates 4
Calculation of Forward Rates (Use zero rates in Table 4.5, page 89) STOP here and compute forward rates for years 2, 3, 4, and 5. Zero Rate for Forward Rate an n -year Investment for n th Year Year ( n ) (% per annum) (% per annum) 1 3.0 2 4.0 3 4.6 4 5.0 5 5.3 5

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Forward Rates Table 4.5, page 89 Zero Rate for Forward Rate an n -year Investment for n th Year Year ( n ) (% per annum) (% per annum) 1 3.0 2 4.0 5.0 = R1,2 3 4.6 5.8 = R2,3

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Unformatted text preview: 4 5.0 6.2 = R3,4 5 5.3 6.5 = R4,5 6 Formula for Forward Rates • Suppose that the zero rates for time periods T1 and T2 are R1 and R2 with both rates continuously compounded. • The forward rate for the period between times T1 and T2 is 7 R T R T T T 2 2 1 1 2 1--Upward vs Downward Sloping Yield Curve • If the yield curve is upward (downward) sloping, the forward rate is always above (below) the zero-coupon. – The zero-coupon is the average of forward rates. • If the yield curve is upward (downward) sloping, coupon bond yield is always below (above) the zero-coupon. – Some coupon payments are before maturity and the discount rates are lower than those applying at maturity. • For an upward sloping yield curve: Forward Rate > Zero Rate > Bond Yield • For a downward sloping yield curve Bond Yield > Zero Rate > Forward Rate 8...
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Sample Data (Table 4 - 4 5.0 6.2 = R3,4 5 5.3 6.5 = R4,5 6...

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