# Overall sensitivity of portfolio

Vignette says: Bazlamit states that by entering into an interest rate swap in which we receive a floating rate in return for paying a fixed rate of interest, we can hedge against rising interest rates and stabilize cash outflows. The swap will also reduce sensitivity of overall position to changes in interest rates. The italics part of the above sentence is incorrect. Answer says that the swap converts variable loan to a fixed loan. Because the duration of the fixed loan will exceed the duration of variable rate loan, interest rate sensitivity of overall position increases. If we enter a swap as receive floating, pay fixed, this is a negative (short) duration position. Why does this increase overall duration?

When you add swap to your loan position you subtract swap duration (duration of pay-fixed swap is negative number as you mentioned):

D_loan = D_float - D_pay_fixed_swap = D_float - ( D_float - D_fixed ) = D_fixed

You start with floating loan which has near 0 duration and convert it via swap into fixed loan with duration equal to swap maturity times 75% per CFAI convention which is much higher positive number so your interest rate sensitivity of overall position increases.

I understand that the duration of a pay fixed/receive floating swap is higher than the pay floating/receive fixed. And here for sensitivity we need to look at the size of the duration number, not the sign (which for pay fixed/receive floating is negative). Is that correct?

Anyone able to please confirm: Here for sensitivity we need to look at the size of the duration number, not the sign (which for pay fixed/receive floating is negative)? Since pay fixed swap has higher duration than pay floating, we now have a more sensitive portfolio?

That’s what it looks like. It’s sensitivity in general they’re talking about I think.

You are correct, sign is not important for sensitivity since sensitivity is magnitude of price variation with change in price so absolute value of duration determines how sensitive your position. Sign will change if position is asset or liability but magnitude of price change is the same.

Anyone else care to comment? I know this is a year old now, but the answer seems to take the perspective of the creditor and NOT the borrower. In this case, Viewmont’s overall sensitivity to changes in interest rates has decreased since cash flows are now fixed.