6. Arbitrage: Consider a hypothetical Payment in Kind (PIK) bond of XYZ Corporation. The bond has 2 years to maturity, a face value of $1000, and has an annual coupon rate of 10%. Coupons are paid annually. XYZ has the right to pay the first coupon either in cash or in additional PIK bonds - i.e., the bond holder may get either $100 in cash or 10 additional PIK bonds for every 100 bonds she has. The second coupon must however be paid in cash along with the face value at the end of two years. The PIK bonds are risk free and trade at par while the yield curve is flat at 9% -- risk free 1 year and 2 year zero coupon bonds trade at a yield to maturity of 9%. Suppose you can buy and short sell (borrow and sell) the PIK and zero coupon bonds without transactions costs. You forecast that the yield to maturity on one year zero coupon bonds one year from now will either stay at 9% or change to 8.5% or 9.5%. a) Assume XYZ always pays the first coupon in cash, what should be the price of the bond? b) Given your forecast on future interest rate (as stated in the problem), show that there is an arbitrage opportunity. (Hint: will XYZ pay cash or additional PIK bonds in each of the future interest rate scenarios?) c) Assuming that your forecast holds, construct a portfolio of the PIK bonds and one year and two year zeros such that you get positive cash flow today and no negative cash flows in the future. Show the cash flow table with net cash flows and cumulative cash flows over time. 6. Arbitrage: Consider a hypothetical Payment in Kind (PIK) bond of XYZ Corporation. The bond has 2 years to maturity, a face value of $1000, and has an annual coupon rate of 10%. Coupons are paid annually. XYZ has the right to pay the first coupon either in cash or in additional PIK bonds - i.e., the bond holder may get either $100 in cash or 10 additional PIK bonds for every 100 bonds she has. The second coupon must however be paid in cash along with the face value at the end of two years. The PIK bonds are risk free and trade at par while the yield curve is flat at 9% -- risk free 1 year and 2 year zero coupon bonds trade at a yield to maturity of 9%. Suppose you can buy and short sell (borrow and sell) the PIK and zero coupon bonds without transactions costs. You forecast that the yield to maturity on one year zero coupon bonds one year from now will either stay at 9% or change to 8.5% or 9.5%. a) Assume XYZ always pays the first coupon in cash, what should be the price of the bond? b) Given your forecast on future interest rate (as stated in the problem), show that there is an arbitrage opportunity. (Hint: will XYZ pay cash or additional PIK bonds in each of the future interest rate scenarios?) c) Assuming that your forecast holds, construct a portfolio of the PIK bonds and one year and two year zeros such that you get positive cash flow today and no negative cash flows in the future. Show the cash flow table with net cash flows and cumulative cash flows over time
