Example Consider three bonds with the following characteristics Determine spot

# Example consider three bonds with the following

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ExampleConsider three bonds with the following characteristics:Determine spot rates for the 6-month (1st period), 1-year (2nd period), and 18-month (3rd period), expressed as semiannual APRs.BondMaturityCoupon Rate (Semiannual) Price16 month ࠵?1=0%\$98212 month ࠵?2=0%\$95318month ࠵?3=8%\$102
Investment Theory, COMM 371, Dr. Farid Novin Example Bond Maturity Coupon Rate (Semiannual) Price 1 6 month ࠵? 1 =0% \$98 2 3 18month 8% \$102 ࠵? 1 = ࠵? (1+ ࠵? 1 2 ) 1 Isolate ࠵? 1 1+ ࠵? 1 2 = ࠵? ࠵? 1 ࠵? 1 = 100 98 − 1 ∗ 2 = 4.0 %
Investment Theory, COMM 371, Dr. Farid Novin Example ࠵? 2 = ࠵? 2 2 (1+ ࠵? 2 2 ) 1 + ࠵? 2 2 +࠵? (1+ ࠵? 2 2 ) 2 95 = 0 (1+ ࠵? 2 2 ) 1 + 100 (1+ ࠵? 2 2 ) 2 (1 + ࠵? 2 2 ) = ( 100 95 ) 1/2 ࠵? 2 = 5.20 Bond Maturity Coupon Rate (Semiannual) Price 1 2 12 month ࠵? 2 =0% \$95 3
Investment Theory, COMM 371, Dr. Farid Novin Example Maturity Coupon Rate (Semiannual) Price 1 (6 month) 2 (12 month) 3 (18month) ࠵? 3 =8% 102 ࠵? 3 = ࠵? 3 2 (1+ ࠵? 3 2 ) 1 + ࠵? 3 2 (1+ ࠵? 3 2 ) 2 + ࠵? 3 2 +࠵? (1+ ࠵? 3 2 ) 3 102 = 4 (1+ ࠵? 3 2 ) 1 + 4 (1+ ࠵? 3 2 ) 2 + 104 (1+ ࠵? 3 2 ) 3 ⇒ ࠵? 3 = 6.58
Investment Theory, COMM 371, Dr. Farid Novin Bootstrapping Calculate the spot rates for 3 treasury securities with face values of \$100 and the following characteristics ࠵? 1 = 3% ࠵? 2 = ࠵? 2 (1+ ࠵? 1 2 ) 1 + ࠵? 2 +࠵? (1+ ࠵? 2 2 ) 2 => 100 = 2 (1+ .015) + 100+2 (1+ ࠵? 2/2 ) 2 => ࠵? 2 = 4.01% ࠵? 3 = ࠵? 3 (1+ ࠵? 1 2 ) 1 + ࠵? 3 (1+ ࠵? 2 2 ) 2 + ࠵? 3 +࠵? (1+ ࠵? 3 2 ) 3 => 100 = 2.5 (1+ .015) + 2.5 (1+ .02) 2 + 102.5 (1+ ࠵? 3 2 ) 3 Maturity Market rates Price 6-months 3% 100 12-months 4% 100 18-monts 5% 100 => ࠵? 3 = 5.00%
Investment Theory, COMM 371, Dr. Farid Novin Synthetic Replication of a Zero-Coupon BondTwo bonds with face values of \$100, are available for trading, and have the following characteristics:How can one create \$100, one year from now by trading this portfolio?Questions:(i) How do we synthetically create the one-year zero by trading in the two-year bonds?(ii) What is the no-arbitrage price or cost of this synthetic one-year zero ?MaturityCoupon Rate(Annual rate)Price2-year4%\$96.372-year8%\$103.74
Investment Theory, COMM 371, Dr. Farid Novin Synthetic Replication of a Zero-Coupon Bond Suppose that portfolio consists of n units of the first bond and m units of the second. Year Portfolio Zero-Coupon Bond 1 \$4 n + \$8 m \$100 2 \$104 n + \$108 m 0 Maturity Coupon Rate (Annual rate) Price 2-year 4% \$96.37 2-year 8% \$103.74
Investment Theory, COMM 371, Dr. Farid Novin
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