Consider the following onformation for zero coupon bonds and a coupon bond. USE DISCRETE TIME DISCOUNTING AND COMPOUNDING Face/Par Value (Principal) of Bonds, $ $1,000 Coupon Payments per Year 2 T C Zero t: Time to Annualized Coupon Periods to Maturity Coupon, % Bond (ZCB) Maturity (year) Price (4 decimal) (2 decimal) 0.50 0.0000 $957.85 1 1.00 2 1.50 0.0000 3 2.00 0.0000 4 y: y per period PVIF: f: Spot Rate in decimal Present Value Implied One-Period %APR of $1 Forward Rate %APR (4 decimals) (4 decimals) (4 decimals) (4 decimals) ? ? ? ? 0.9210 ? ? |? 6.6052 7.0000 ? ? 0.0000 COUPON BOND Face/Par Value (Principal) of Coupn Bond $1,000 Coupon Payments per Year 2 Coupon Bond, Annual Coupon% ? Coupon Bond Time to Maturity (years) 2.00 Initially, Yield to Maturity (YTM), APR% ? Length of a period 6 Months t: Coupon PVIE: PVCF(t) y: PVIF: PVCF(t) Period# Bond Present Value Spot Rate Present Value Cash Flow, of $1 %APR of $1 CF(t) Using Coupon Using Coupon Using Spot Using Spot Bond YTM Bond YTM Rates, y's Rates, y's (4 decimal) (4 decimal) (4 decimals) (4 decimals) (4 decimals) 1.00 $59.1046 ? 2.00 0.9088 ? |? 3.00 ? I ? 4.00 7.0000 Market Price: ? No-Arb Value:? Is there an arbitrage opportunity? (YES/NO) ? What should be the Arbitrage Strategy ? Arbitrage Profit, $, for each Coupon Bond ? Arbitrage (Arb) Strategies: Coupon Stripping, Synthetic Coupon Coupon Stripping: Buy the Coupon Bond in the Market and Short Zero Coupon Bonds with Cash Flows as face value Synthetic Coupon: Short the Coupon Bond in the Market and Buy Zero Coupon Bonds with Cash Flows as face value f: Implied One-Period Forward Rate %APR (4 decimals) 6.6052 Consider the following onformation for zero coupon bonds and a coupon bond. USE DISCRETE TIME DISCOUNTING AND COMPOUNDING Face/Par Value (Principal) of Bonds, $ $1,000 Coupon Payments per Year 2 T C Zero t: Time to Annualized Coupon Periods to Maturity Coupon, % Bond (ZCB) Maturity (year) Price (4 decimal) (2 decimal) 0.50 0.0000 $957.85 1 1.00 2 1.50 0.0000 3 2.00 0.0000 4 y: y per period PVIF: f: Spot Rate in decimal Present Value Implied One-Period %APR of $1 Forward Rate %APR (4 decimals) (4 decimals) (4 decimals) (4 decimals) ? ? ? ? 0.9210 ? ? |? 6.6052 7.0000 ? ? 0.0000 COUPON BOND Face/Par Value (Principal) of Coupn Bond $1,000 Coupon Payments per Year 2 Coupon Bond, Annual Coupon% ? Coupon Bond Time to Maturity (years) 2.00 Initially, Yield to Maturity (YTM), APR% ? Length of a period 6 Months t: Coupon PVIE: PVCF(t) y: PVIF: PVCF(t) Period# Bond Present Value Spot Rate Present Value Cash Flow, of $1 %APR of $1 CF(t) Using Coupon Using Coupon Using Spot Using Spot Bond YTM Bond YTM Rates, y's Rates, y's (4 decimal) (4 decimal) (4 decimals) (4 decimals) (4 decimals) 1.00 $59.1046 ? 2.00 0.9088 ? |? 3.00 ? I ? 4.00 7.0000 Market Price: ? No-Arb Value:? Is there an arbitrage opportunity? (YES/NO) ? What should be the Arbitrage Strategy ? Arbitrage Profit, $, for each Coupon Bond ? Arbitrage (Arb) Strategies: Coupon Stripping, Synthetic Coupon Coupon Stripping: Buy the Coupon Bond in the Market and Short Zero Coupon Bonds with Cash Flows as face value Synthetic Coupon: Short the Coupon Bond in the Market and Buy Zero Coupon Bonds with Cash Flows as face value f: Implied One-Period Forward Rate %APR (4 decimals) 6.6052
