Chapter_5_H_W_Solutions

Chapter_5_H_W_Solutions - = 12.469% . 0623 . 1 ) 04135 . 1...

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1 Problem 5-13 The spot rate for year 2 can be computed as: b z 4 = 0.0301 Yield 2 = 6.02% The spot rate for year 2.5 can be computed as: b z 5 = 0.0314 Yield 2.5 = 6.28% 100 $ ) 1 ( 00 . 103 ) 02880 . 1 ( 00 . 3 ) 0275 . 1 ( 00 . 3 ) 02625 . 1 ( 00 . 3 4 4 3 2 = + + + + = z PV 100 $ ) 1 ( 125 . 103 ) 0301 . 1 ( 125 . 3 ) 02880 . 1 ( 125 . 3 ) 0275 . 1 ( 125 . 3 ) 02625 . 1 ( 125 . 3 5 5 4 3 2 = + + + + + = z PV Problem 5-13 (Continued) The spot rate for year 3 can be computed as: b z 6 = 0.03275 Yield 3 = 6.55% 100 $ ) 1 ( 25 . 103 ) 0314 . 1 ( 25 . 3 ) 0301 . 1 ( 25 . 3 ) 02880 . 1 ( 25 . 3 ) 0275 . 1 ( 25 . 3 ) 02625 . 1 ( 25 . 3 6 6 5 4 3 2 = + + + + + + = z PV Problem 5-13 (Continued) Six-year bond value of half-year cash flow spot rate the cash flow 1 3 5.25% $2.92 2 3 5.50% $2.84 3 3 5.76% $2.76 4 3 6.02% $2.66 5 3 6.28% $2.57 6 3 6.55% $2.47 7 3 6.82% $2.37 8 3 7.10% $2.27 9 3 7.38% $2.17 10 3 7.67% $2.06 11 3 7.97% $1.95 12 103 8.27% $63.34 value of the bond $90.38 Problem 5-13 (Continued) The six-month forward rate for period twelve can be computed by knowing the spot rates for periods twelve and thirteen. The bond equivalent yield is 2 x 0.06234
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Unformatted text preview: = 12.469% . 0623 . 1 ) 04135 . 1 ( ) 04295 1 ( 1 ) 1 ( ) 1 ( 12 13 12 13 12 =-+ + =-+ + = y y f Problem 5-22 Bart has two choices: With choice 1, Bart will realize the two-year spot rate and that rate is known with certainty. With choice 2, Bart will realize the one-year spot rate, but the one-year rate one year from now is unknown. The one-year forward rate is the rate that will make the two choices equal. If Bart expects that one year from now, the one year spot rate will be higher than the forward rate, then he will choose choice 2. It is not just enough to believe that one year rates will be higher in the second year than in the first year....
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