Question

Suppose the city of Chicago issues a floating rate bond to finance a new middle school. The bond has a 5-year maturity, a par value of 10 million, and an annual coupon payment equal to 12-month LIBOR plus a spread of 1.5%. The fixed rate on a 5-year, annual settlement, 12-month LIBOR swap is 5% per year. Briefly explain how the city could use this swap to convert its floating rate bond into a synthetic fixed rate bond? For example, should the city be long or short the swap? What should be the notional principal and maturity of the swap?

Answer 1

Floating bond

n= 5 yrs

Par value = 10 million

coupon(float) = libor(12 month)+ 1.5%

coupon rate or the swap rate = 5%

The valuation of swap can be done using a simple concept:

Vswap: value of swap = B(fixed)- B(float)= difference between value of the fixed and floating rate bonds.

Since the city wants to convert from floating to fixed; it should be short on the floating bond and long on the fixed rate bond. Technically if you are paying float you will take an opposite position ie short on float and if you are paying fixed you will take an opposite position ie short on fixed.

Now using the above formula and logic we can easily deduce that since we are long on fixed and short on float effectively we are long on the swap.

The notional principal or the underlying principal is 1 million and maturity of the swap is 5 years;as stated in the question itself.