Dgap Calculation

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Review Questions

5.1 What is asset-liability management?

Asset/liability management is the coordinated management of the entire portfolio of a financial institution. It considers both the acquisition of funds from various sources and the allocation of funds to profitable investments. The traditional focus of ALM has been on net interest income. However, it also considers market values, via duration. Finally, simulations allow other aspects of risk management to be brought into the ALM process.

5.1 Given the following information:
Assets$RateLiabs & Equity$Rate
RSA $3,00010.0%RSL $2,0008.0%
NonRSA 1,500 9.0NonRSL 2,0007.0
Nonearning500Equity1,000
$5,000 $5,000

a. Calculate the expected net interest income at current interest rates and assuming no change in the composition of the portfolio. What is the net interest margin? b. Assuming that all interest rates rise by 1 percentage point, calculate the new expected net interest income and net interest margin.

a. Net interest income = $3,000 (.10) + $1,500 (.09) - $2,000 (.08) - $2,000 (.07)
= $435 - $300
= $135
Net interest margin = $135/$4,500 = 0.03 or 3.0%

c. Net interest income = $3,000(0.11) +$1,500(0.09) - $2,000(0.09) - $2,000 (.07) = $145

Net interest margin = $145/$4,500 = 0.0322 = 3.22%

(Note only rate sensitive items are impacted by the change in interest rates)

5.2 Given the following information:

ABC National Bank ($ Millions)

Assets Liabilities and Equity

RSA $200(12%)RSA$300(6%)

NonRSA 400(11%)NonRSA 300(5%)
Nonearn100 Equity100
Total$700Total$700

a. What is the dollar gap? net interest income? net interest margin? How much will net interest income change if interest rates fall by 200 basis points? b. What changes in portfolio composition would you recommend to management if you expected interest rates to increase. Be specific.

a. The gap is $-100 ($200 - $300).

The net interest income is:
= ($200) (12%) + ($400) (11%) – ($300) (6%) – ($300) (5%) = $24 + $44 - $18 - $15
= $35.
As such, the net interest margin is $35/$600 = 5.8%.

If interest rates change (fall) by 200 basis points, the net interest income would be: = ($200) (10%) + ($400) (11%) – ($300) (4%)( - ($300) (5%) = $20 + $44 - $12 - $15
= $37.
This compares with a net interest income of $35 before the change in interest rates.

b. Given the existing portfolio, an increase in interest rates will reduce net interest income. To prevent this from happening, management could shift $100 from nonrate- sensitive assets to rate-sensitive assets, or it could shift $100 from rate-sensitive liabilities to nonrate-sensitive liabilities. This would reduce the gap to zero. If it moved more than $100, it could create a positive gap and benefit from rising interest rates.

4. A bank recently purchased at par a $1 million issue of Commonwealth government securities. The bond has a duration of 3 years and pay 6% annual interest. How much would the bond’s price change if interest rates fell from 6% to 5%? If interest rates rose from 6% to 7%? What would your answer be if the duration of the bond was 6 years?

The price change if interest rates fell from 6% to 5% would be:

% Change in Net Worth=- Dur Gap (change in i / 1+i)
= –(3) [pic]
= [pic] + 2.83%.

If interest rates increased from 6% to 7%, the price change would be:

% Change in Net Worth =–(3) [pic]
= - 2.83%.

If the duration of the bond were 6 years, the percentage change in price would be double that just calculated:

% Change in Net Worth = 2 x 2.83 or +5.66% for the decline in rates and – 5.66% for the increase in rates.

5.9 The balance sheet of Capital Bank appears as follows:

AssetsLiabilities and...
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