Question

If a floating rate borrower hedges their interest rate risk by entering a swap as the fixed rate payer, and the swap subsequently develops a negative value:

a. Then the swap has not been an effective hedge

b. The cost of funds for the borrower will rise

c. Then the borrower has paid lower than expected interest to their lender

d. The cost of funds will exceed the swap rate

e. Then the borrower has paid higher than expected interest to their lender

The answer is C.

Could you help please explain every option thank you

Answer 1

There are multiple complicated ways to address this. I am presenting below a simplistic and intuitive explanation for you. Please go through the same and think through it.

Please note that whenever a swap is entered into, the value of the swap at t = 0 because the fixed rate is determined in such a way the present value of all the fixed payments is equal to present value of all the payments under expected floating rate in future. This is at the time of entering into swap i.e. at t = 0.

However, subsequently, interest rates may change due to multiple factors and therefore this swap will gain value from the perspective of fixed rate payer: if floating interest rate in a period actually turns out to be higher than the expected floating rate for that period assumed at the time of entering into swap.

Similarly, this swap will lose value from the perspective of fixed rate payer: if floating interest rate in a period actually turns out to be lower than the expected floating rate for that period assumed at the time of entering into swap.

But irrespective of who gains or who loses in the swap, one thing is very clear. The outgo of the fixed rate payer is always the fixed interest rate irrespective of what happens to the interest rate actually. So, once a floating rate borrower hedges his / her interest rate risk by entering a swap as the fixed rate payer, his / her outgo and cost of borrowing has got fixed to the fixed interest rate in the swap. The increase or decrease in interest rate on the floating rate mortgage thus gets passed on to the floating rate payer in the interest rate swap.

Now that you have understood, it should not be difficult for you to figure out the validity of each of the options. Let's look into them one by one:

a. Then the swap has not been an effective hedge

This will be wrong to say. Every derivative is entered into taking a call on the future. And there is no derivative instrument that can act as a perfect hedge for the parties of the contract. A derivative is a zero sum gain. One party gains, the other loses and the sum of gain and loss is zero. The purpose of the swap is to crystallize the liability beforehand. The fixed rate payer knows in advance that his / her outgo on interest will be the fixed rate. Thus his liability is crystallized. At times he / she will gain, at times he / she will lose. So, the swap has achieved its objective and hence it's an effective hedge.

b. The cost of funds for the borrower will rise

This is wrong. The borrower is the fixed rate payer in the swap. For him / her, the cost of borrowing (fund) is fixed rate and this will not change irrespective of what happens to the interest rate in future. The increase or decrease in the floating rate will automatically pass on to the floating rate payer in the interest rate swap.

c. Then the borrower has paid lower than expected interest to their lender

This statement is true. Please try to understand this: Let's say I am the borrower and i have borrowed at a floating rate of LIBOR + 2%. LIBOR currently is say 4%. I enter into a fixed rate swap where in I am at the fixed rate payer and the counter party is floating rate payer. As per terms of swap, I pay a fixed rate F to the counter party who in turns pays me LIBOR + 2%. I use this payment of LIBOR + 2% received from the counter party to pay my interest of LIBOR + 2% on the floating rate borrowing. At the time i enter into swap, the Fixed rate, F = LIBOR currently + 2% = 4% + 2% = 6%. So on day zero, I pay 6% to the counter party as fixed rate and he / she pays me LIBOR + 2% = 6% as floating rate. A period later, let's say LIBOR increases to 5%. The swap will suddenly become negative for the counter party because he / she will now have to pay 5% + 2% = 7% but will get only F = 6% from me. But at the same time I am obligated to pay LIBOR + 2% = 5% + 2% = 7% on my floating rate borrowing. So here's how it will work:

1. I receive 7% from counter party
2. I pay 6% to the counter party
3. I use 7% received from the counter party to pay off my interest on floating rate borrowing
4. Thus i have ended up paying 6% net.
5. Thus I have paid 1% lower than expected rate of 7%.

This is exactly the point this question is trying to direct you to.

d. The cost of funds will exceed the swap rate

No, this is obviously not true. Cost of funds for me (i.e. the borrower) is fixed at F = 6% as per example above which is the swap rate of F that i entered into.

e. Then the borrower has paid higher than expected interest to their lender

No, the borrower has paid a net F = 6% against the expected rate of 7% to its lender, as per my example above.

Hope I could clear your doubts.