Question

Consider hypothetical Callable bond (C) and Putable bond of XYZ Corporation. All bonds in this question are risk free. Both bonds have 2 years to maturity, face values of $1000, and annual coupon rates of 10%. Coupons are paid annually. The callable bond (C) can be called at par, only at the end of the first period (right after the coupon payment). Similarly, the putable bond (P) can be put at par, only at the end of the first period (right after the coupon payment). The callable bond and the putable bond are now traded at $970 and $1020, respectively. The 1-year and 2-year T-strips both trade at a yield to maturity of 10% (Effective Annual Yield). Suppose you can buy and short sell (borrow and sell) C, P and T-strips without transactions costs. You forecast that interest rate will change in the future - one year from now, the yield to maturity on one year T-strips at that time will not be 10% for sure. a) If the callable bond will never be called and putable bond never be put, what should be their current prices? (5 points) Note that the assumption in part a) does NOT carry over to part b). b) Show that there is an arbitrage opportunity. (15 points)

Answer 1

a) copoun rate = 10% , Fcae value of both the bond = $1000.00

Duration = 2 years for both the bond

Copoun amount = 10%*1000=$100

We need to calculate Yield to Maturity after one year

YTM For callable bond:

YTM =[Interest +( Issue price - current price)/Duration]/[(Issue price + current price )/2] *100

=[100+(1000-970)/1] / [(1000+970)/2] * 100

= 13.20% approx

Current price of callable bond = 100PVIFA(13.20%,2) + 1000PVIF(13.20%,2)

= $(100*1.6638 + 1000*.780)

= $946.38 approx

Puttable Bond:

Issue price = $1000 Cuurent price = $1020

Copoun amount = 10%*1000

= $100

YTM For puttable bond:

YTM = [100+(1000-1020)/1] / [(1000+1020)/2]*100

= 7.92%

Current price of puttable bond = 100 PVIFA(7.92%,2) + 1000PVIF(7.92%,2)

=$( 100*1.7852 + 1000*.8586)

= $(178.52 + 858.60)

= $1037.12 approx