I must be missing something extremely simple… I followed the example on Schweser notes (book 5) for pricing a plain vanila swap. Here are the steps:
Given term, Annualized LIBOR spot rates 90 day, 0.03 180 day, 0.035 270 day, 0.04 360 day, 0.45 Notional $5,000,000.00 Calculate fixed rate, fixed payments
_ Step 1, calculate the PV factors _ term, Annualized LIBOR spot rates, PV factor 90 day 0.03 0.99256 (this is Z1) 180 day 0.035 0.98280 (this is Z2) 270 day 0.04 0.97087 (this is Z3) 360 day 0.045 0.95694 (this is Z4)
Step 2, calculate the quarterly fixed rate using the formula: C = (1 - Z4)/(Z1 + Z2 + Z3 + Z4) you get C = .011 quarterly fixed rate 0.011
Step 3, answer question quarterly rate 0.011 quarterly pay $55,163.13 yearly rate 0.044130508 (= C* 4)
As a check, I compared the fixed rate cash flows vs. the floating rate cash flows. I realize that the spot rates are used to price the swap using the LIBOR rates as of t=0. If the given LIBOR rates had indeed materialized, below is what I believe the cash flows would be. Note that since at inception the swap should have a value of 0, the fixed rate cash flows should equal the floating rate cash flows, no?
Cash Flows, fixed, floating cf, floating PV cf 90 day, $54,752.49, $37,500.00, $37,220.84 180 day, $54,214.38, $43,750.00, $42,997.54 270 day, $53,556.44, $50,000.00, $48,543.69 360 day, $52,787.69, $56,250.00, $53,827.75 Total, $215,311.00, $187,500.00, $182,589.83
The ‘fixed’ column simply takes the quarterly payment for the fixed payer of $55,163.13 and adjust by the PV (present value factor). So the NPV of the payments by the fixed payer is $215,311.
The ‘floating cf’ column is the payment I believe the floating payer would pay given the LIBOR rates materialize.
The ‘floating PV cf’ column is the ‘floating cf’ payment adjusted by the PV. So the NPV of the payments by the floating rate payer is $182,589.83.
The issue is that I was expecting both the fixed and floating payers to pay the same total PROVIDED that the LIBOR rates that were used to price the swap did in fact occur. Where is my mistake?