Duration Exposure (equity & liabilities)

CFA Level III
#1

In response a question, and analyst makes a statement:

“By entering into the swap, the duration of the company’s long term liabilities will become smaller, causing the value of the firm’s equity to become more sensitive to interest rate changes.” For context, it’s a floating rate payer swap, so the first part of the statement makes a lot of sense to me.

The second part of the statement is also true, but I got it wrong.

I am getting hung up on this concept of equity duration. The answer key explains that a swap will not change a firm’s total duration, so if liabilty duration declines, equity duration must increase to offset it.

But why???

#2

Because the asset duration is unchanged.

Think of this: The firm entered the swap and it’s liability duration reduced but asset duration wasn’t altered.

We also know that equity = Assets - Liabilities. So when the interest rates increase, the liabilities will decrease by a smaller amount (after the reduced duration) but the assets will decrease by a larger amount because asset duration is still the same.

Net effect is that the larger asset decrease and smaller liability decrease will decrease the firms equity.

So you can see that equity has a higher duration for that reason.

#3

Can u pls tell which side of the swap is the company on ? Isnt taking a floating rate payer side in the swap gonna increase the duration of the liabilities ???

#4

^This.

Also, assuming they entered as a fixed rate payer

AD(A) = LD(L) + ED(E) where A = assets, L = liabilities, E = equities and D = duration. ST L means LT E.

Think a bank.

#5

Good catch. My mistake. The company was a fixed rate payer.

#6

Thanks, 1recho. The super simplistic example of a bank with all assets and liabilities in fixed income securities gets me to understand it. The duration of the asset porfolio would remain unchanged even if the liabilities did.

Same goes for machinery in an industrial company.