Swaps! Apr2018 P1 Q4 ii)

[Logarithm n Blues]

Hi Forum,

I'm a bit confused by this answer and I just want to see if someone can help me get my head around what's happening.
The question asks:

An insurance company’s liabilities are sensitive to interest rates. The company wishes
to reduce its exposure to interest rate risk via the use of swaps.
(ii) Explain how:
(a) These swaps could be valued in the company’s accounts.
(b) Their values will move if future interest rates are lower than expected.

In the examiners' report answer is the following..

If anticipated future interest rates become lower than expected at the inception of the swap, the value of the asset held by the insurer will decrease, but this will offset the increase in their other assets (assuming the durations match) making the impact less volatile on the liabilities side.. [5]

and im having trouble interpreting and understanding this.

I thought through the answer as follows:

• The stated problem is that the liabilities are sensitive to interest rate changes. I guess that this means that there are some long term liabilities and when interest rates fall these liabilities are discounted by lower interest rates and so the present value of the liabilities increases. I'm guessing that the increase in liabilities is larger than the increase in asset values otherwise the assets would already be offseting the liabilities and there would not be a problem. If the assets already move much more than the liabilities then I would say that the issue was that the assets are sensitive to interest rates, not the liabilities.
  
• Therefore the insurer is exposed to the risk of low interest rates.
• Therefore the insurer would naturally take the leg of the swap where they would be paying out at a floating rate of interest and receiving a fixed rate of interest. This way when interest rates are low they would benefit and this would offset the problem with volatile liabilities.
• So if future interest rates are lower than expected then the insurer is now holding a swap contract where they pay only low floating rate values but they are still receiving the same fixed rate values. Surely this contract looks great to the insurer and has positive value?
• So I would say that the value of the swap INCREASES when rates are low, and that this helps to offset the increasing value of liabilities (by adding volatility to the assets in order to more closely match. the assets already increase in value but not by enough!)

To me the examiner's answer looks like it deals with a problem with a volatile asset portfolio and not liabilities that are sensitive to interest rates. I'm also not sure I understand what they mean by "making the impact less volatile on the liabilities side". Surely the swap doesn't affect the liabilities? it just affects the assets which may end up better matched against the liabilities?
Or are we talking about discretionary liabilities? in which case this still feels odd to me given the set up of the question?

Any help or pointers would be appreciated.

 

[mugono]

Hi Forum,

I'm a bit confused by this answer and I just want to see if someone can help me get my head around what's happening.
The question asks:


In the examiners' report answer is the following..



and im having trouble interpreting and understanding this.

I thought through the answer as follows:

• The stated problem is that the liabilities are sensitive to interest rate changes. I guess that this means that there are some long term liabilities and when interest rates fall these liabilities are discounted by lower interest rates and so the present value of the liabilities increases. I'm guessing that the increase in liabilities is larger than the increase in asset values otherwise the assets would already be offseting the liabilities and there would not be a problem. If the assets already move much more than the liabilities then I would say that the issue was that the assets are sensitive to interest rates, not the liabilities.
  
• Therefore the insurer is exposed to the risk of low interest rates.
• Therefore the insurer would naturally take the leg of the swap where they would be paying out at a floating rate of interest and receiving a fixed rate of interest. This way when interest rates are low they would benefit and this would offset the problem with volatile liabilities.
• So if future interest rates are lower than expected then the insurer is now holding a swap contract where they pay only low floating rate values but they are still receiving the same fixed rate values. Surely this contract looks great to the insurer and has positive value?
• So I would say that the value of the swap INCREASES when rates are low, and that this helps to offset the increasing value of liabilities (by adding volatility to the assets in order to more closely match. the assets already increase in value but not by enough!)

To me the examiner's answer looks like it deals with a problem with a volatile asset portfolio and not liabilities that are sensitive to interest rates. I'm also not sure I understand what they mean by "making the impact less volatile on the liabilities side". Surely the swap doesn't affect the liabilities? it just affects the assets which may end up better matched against the liabilities?
Or are we talking about discretionary liabilities? in which case this still feels odd to me given the set up of the question?

Any help or pointers would be appreciated.

Hi,

I actually think you have the right sort of idea.

Part ii of the question makes reference to the liabilities. I'd therefore be inclined, initially, to talk about the swap with respect to the liabilities.

As you say, a reduction in interest rates would increase the value of the liabilities.

An insurer who wanted to remove the risk of declining rates could enter into a swap arrangement where they received the fixed leg and paid the floating leg. The swap would increase / fall in value when rates fell / increased, and would offset partially, fully or by more the opposite movement in the value of liabilities. It would depend on how well the swap performed as a hedge for the liabilities.

The overall impact on the company (ie after allowing for the other assets held) will depend on how well matched the assets ('swap' plus other assets) and liabilities are.

A swap that has a positive / negative value can be considered an asset / liability.
The swap will have a negative value for the insurer were rates to increase.

Hope that helps.

 

[Lindsay Smitherman]

Here's another way to look at this, and perhaps this is how the Examiners were thinking about it.

According to the question, the insurance company’s liabilities are sensitive to interest rates and it wants to reduce its exposure to interest rate risk by using swaps.

We don't have any information as to exactly what that sensitivity is, and the direction of adverse interest rate movement for the insurer is not stated. (Although lower rates would generally increase liabilities through discounting, higher rates can also increase liabilities eg some types of guaranteed benefits.)

So we could interpret this as the insurer wanting to be immunised against changes in interest rates, rather than specifically hedging against the impact of lower future interest rates. So potentially the swap could be arranged for the insurer to pay fixed and receive floating - to reduce uncertainty. [This is equivalent to the position which would be taken for a longevity swap, which hedges longevity risk within annuity liabilities, say: the insurer pays fixed and receives floating.]

For the holder in that position (ie paying fixed, receiving floating) the value of the swap would reduce when interest rates fall.

It sounds like you are understanding nicely how swaps actually work and would be valued, and that's what's important here. It would make very little difference to how well an answer would score if you were thinking about it from the opposite position.

Hope that helps.

 

[Logarithm n Blues]

Thanks both.
Happy to know that my understanding seems to be okay.