Interest Rate Swap and Duration

Pain Vanilla Swap

1. Same currency (So no exchange of principal)
2. Fixed vs Float

Fixed rate payer with floating loans pays

NP*(Days/360)*(Fixed rate + loan spread)

Now, the fixed rate payers supposed to pay the same amount of rate every period. But no! Because # of days are usually different!

Floating rate payer with fixed loans pays

NP*(Days/360)*(Float Rate + fixed loan rate – fixed swap rate)

Floating rate loans is also called floating rate notes (FRN)

Duration = – %change of value/%change of rate

%change of value = – Duration * % change of rate

*** -ve is important!, and duration is usually positive in bonds

Fixed rate instrument has larger duration (+ve), has low cash flow risk but larger market value risk

Floating rate instrument has smaller duration (+ve), has high cash flow risk but low market value risk

Fixed rate payer/ floating rate receiver has

-Duration_Fixed + Duration_float = -ve duration (meaning interest rate increase will increase portfolio value)

Floating rate payer /Fixed

rate receiver has

Duration_Fixed – Duration_float = +ve duration

Equity = Asset – Liabilities

D(E)=D(A)-D(L)

Modify portfolio V_P duration (MD_P to MD_T) using swap:

V_P*(MD_T) = V_P*(MD_P) + NP*(MD_S)