FRM 2008 Practice PII question 27 - + maturity gap and increased r

[fullofquestions]

QUESTION
If interest rates rise, a bank with a positive maturity gap will experience:
a. A gain in equity capital.
b. A loss of equity capital.
c. Either a gain or a loss of equity capital.
d. No change in equity capital.
Answer: b
a. Incorrect. The Bank will experience a loss of equity capital. See explanation in ‘b’ below.
b. Correct. A loss of equity capital. If the maturity gap is positive, the assets have a longer weighted-
average maturity than the liabilities. If rates rise, the value of the liabilities will fall by less than the
value of the assets, and equity capital will decrease.
c. Incorrect. The Bank will experience a loss of equity capital. See explanation in ‘b’ above.
d. Incorrect. The Bank will experience a loss of equity capital. See explanation in ‘b’ above.


Why are liabilities considered here? The answers clearly mention 'equity capital' and NOT 'debt capital'. Furthermore, even if we compare equity with liabilities, why do they both fall? Say one of my liabilities is a loan. If interest rates increase, I have to pay more in terms of interest, therefore my liability increases. Most assets will gain value if interest rates go up. Could someone explain the why values go down? I guess it really depends on what kind of equity we are talking about. Also, I realize that we are discussing Assets - Liabilities and the fact that the maturity of the assets is greater than that of the liabilities.

 

[hsuwang]

Hello,
The way I think about this is:
Asset = Liability + Equity,
and so liability has to be considered here because if the assets have a longer weighted-average maturity than the liabilities, then when rates increase, the value of the assets will decline more than the liability (maturity gap=asset's average maturity - liability's average maturity), and so in order to equate asset with liability "plus" equity, this means equity value has to drop.

Don't know if this is of much help..

Thanks!

 

[David Harper CFA FRM]

FoQ - To add to Jack's answer, we worked this question a bit here:http://forum.bionicturtle.com/threads/asset-liability-gap.1565

David

 

[dadalee1102]

I hope anyone here or David can help me with understanding this fundemental concept: why both asset and liability decreases when interest rate increases?
What's the fundemental reason that causes both asset and liability on bank's book to decrease when interest rate increases?

Thank you so much in advance!

Btw, David, I tried to click on the link you provided above, but it no longer work.

 

[David Harper CFA FRM]

Hi dadallee, I restored the link (to http://forum.bionicturtle.com/threads/asset-liability-gap.1565), old links were broken in our forum upgrade last year.

I'm not sure that it matters greatly to contrast asset vs liability; both decrease for the same fundamental reason that the value (aka, price) of a fixed-rate bond decreases when the yield (rate) increases. For example, if the current yield is flat (all maturities) at 3.0%, then a way-too-simple bank might make a long-term (long-duration) loan of $100 (par or principal) that earns a coupon of 2.0%; this bank's asset will have a value greater than >> par of $100, since coupon >> yield. To fund the asset, it might issue a bond that pays a 3% coupon, so it's liability bond has a price of $100 since yield = coupon.

If yields increase, as economically both are effectively bonds that pay fixed-rate coupons, the price (value) of both decrease. The key link is the fixed-rate coupons which give both assets/liabilities positive duration. (floating rate notes would not change very much in value; their duration in ~ zero). On the asset side, as yields increase, the same 3% coupon is received yet the market rate has increased (lowering the value). On the liability side, the same 3% coupon is owed, even as the market rate has increased, lowering the mark-to-market price of an obligation.

Both are due to the effect of the discount rate on a stream of obligations: PV = cash flow(1)/discounted + cash flow (2)/discounted + ....
higher yields -- > higher discount rates --> lower PV of the cash flow. I hope that helps,

 

[dadalee1102]

Hi David,
thank you so much, the concept is more clear to me now!

 

[Backwardation]

QUESTION
If interest rates rise, a bank with a positive maturity gap will experience:
a. A gain in equity capital.
b. A loss of equity capital.
c. Either a gain or a loss of equity capital.
d. No change in equity capital.
Answer: b
a. Incorrect. The Bank will experience a loss of equity capital. See explanation in ‘b’ below.
b. Correct. A loss of equity capital. If the maturity gap is positive, the assets have a longer weighted-
average maturity than the liabilities. If rates rise, the value of the liabilities will fall by less than the
value of the assets, and equity capital will decrease.
c. Incorrect. The Bank will experience a loss of equity capital. See explanation in ‘b’ above.
d. Incorrect. The Bank will experience a loss of equity capital. See explanation in ‘b’ above.


Why are liabilities considered here? The answers clearly mention 'equity capital' and NOT 'debt capital'. Furthermore, even if we compare equity with liabilities, why do they both fall? Say one of my liabilities is a loan. If interest rates increase, I have to pay more in terms of interest, therefore my liability increases. Most assets will gain value if interest rates go up. Could someone explain the why values go down? I guess it really depends on what kind of equity we are talking about. Also, I realize that we are discussing Assets - Liabilities and the fact that the maturity of the assets is greater than that of the liabilities.

Hi,

the DGAP includes both, the Duration of assets and liabilites as it calculated as: D(assets) - D(liab.) * (TA/TD)
If the DGAP is positive, this means that the average Duration of assets exceeds the average Duration of liabilities, which implies that Assets are more sensitive to interest rate changes (basic concept of Duration). So if rates rise, the value of both (assets AND liabilities) will fall, but the assets will drop by a higher amount (because they are more rate sensitive). Hence, if assets drop more than liabilities, the equity capital must decline as a result.
On the other hand, a negative DGAP (which is rare in practice business models) would imply an increase in equity if rates increase, because liabilities would fall more than assets, leading to a "profit" which will increase equity.

The calculation becomes more difficult if yu include embedded options: in practice banks have postive DGAPs, but are not able to generate profits of rates fall, because then mortgages tend to prepaid and bonds with the option are called.

Maybe one question which arises to me: The question says "Maturity Gap". I would not interpret this as DGAP but as the normal GAP which would vary inversly in their result. Or do you use Maturity Gap as Duration GAP?