Lesson 5: Interest Rate Risk

Question 1

Consider the following balance sheet positions for a financial institution:

1) Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million
2) Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million
3) Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million

a. Calculate the repricing gap and the impact on net interest income of a 1 percent increase in interest rates for each position.

Answer 1

1) Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million.
Repricing gap = RSA - RSL = $200 -$100 million = +$100 million.
∆NII = ($100 million)(0.01) = +$1.0 million, or $1,000,000.

2) Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million.
Repricing gap = RSA - RSL = $100 -$150 million = -$50 million.
∆NII = (-$50 million)(0.01) = -$0.5 million, or -$500,000.

3)Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million.
Repricing gap = RSA - RSL = $150 -$140 million = +$10 million.
∆NII = ($10 million)(0.01) = +$0.1 million, or $100,000.

Question 2

Consider the following balance sheet positions for a financial institution:

1) Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million
2) Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million
3) Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million

b. Calculate the impact on net interest income on each of the above situations assuming a 1 percent decrease in interest rates.

Answer 2

1) ∆NII = ($100 million)(-0.01) = -$1.0 million, or -$1,000,000.
2) ∆NII = (-$50 million)(-0.01) = +$0.5 million, or $500,000.
3) ∆NII = ($10 million)(-0.01) = -$0.1 million, or -$100,000.

Question 3

c. What conclusion can you draw about the repricing
model from these results? (Use answers from pt.A given below)

1) Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million. Repricing gap = RSA - RSL = $200 -$100 million = +$100 million.
∆NII = ($100 million)(0.01) = +$1.0 million, or $1,000,000.

2) Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million. Repricing gap = RSA - RSL = $100 -$150 million = -$50 million.
∆NII = (-$50 million)(0.01) = -$0.5 million, or -$500,000.

3)Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million. Repricing gap = RSA - RSL = $150 -$140 million = +$10 million.
∆NII = ($10 million)(0.01) = +$0.1 million, or $100,000.

Answer 3

The FIs in parts (1) and (3) are exposed to interest rate declines (positive repricing gap), while the FI in part (2) is exposed to interest rate increases. The FI in part (3) has the lowest interest rate risk exposure since the absolute value of the repricing gap is the lowest, while the opposite is true for the FI in part (1).

(Below for reference)
1) Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million. Repricing gap = RSA - RSL = $200 -$100 million = +$100 million.
∆NII = ($100 million)(0.01) = +$1.0 million, or $1,000,000.

2) Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million. Repricing gap = RSA - RSL = $100 -$150 million = -$50 million.
∆NII = (-$50 million)(0.01) = -$0.5 million, or -$500,000.

3)Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million. Repricing gap = RSA - RSL = $150 -$140 million = +$10 million.
∆NII = ($10 million)(0.01) = +$0.1 million, or $100,000.

Question 4

What are some of the weakness of the repricing model? How have large banks solved the problem of choosing the optimal time period for repricing? What is runoff cash flow, and how does this amount affect the repricing model’s analysis?

Answer 4

The repricing model has four general weaknesses:

1. It ignores market value effects
2. It does not take into account the fact that the dollar value of rate-sensitive assets and liabilities within a bucket are not similar. Thus, if assets, on average, are
   repriced earlier in the bucket than liabilities, and if interest rates fall, FIs are subject to reinvestment risks.
3. It ignores the problem of runoffs. That is, that some assets are prepaid and some liabilities are withdrawn before the maturity date.
4. It ignores income generated from off-balance-sheet activities.

Large banks are able to reprice securities every day using their own internal models so reinvestment and
repricing risks can be estimated for each day of the year. Runoff cash flow reflects the assets that are repaid before maturity and the liabilities that are withdrawn unexpectedly. To the extent that either of these amounts is significantly greater than expected, the estimated interest rate sensitivity of the FI will be
in error.

Question 5

Identify and discuss three criticisms of using the duration gap model to immunise the portfolio of a financial institution.

Answer 5

The three criticisms are:

1. Immunisation is a dynamic problem because duration changes over time. Thus, it is necessary to rebalance the portfolio as the duration of the assets and liabilities change over time.
2. Duration matching can be costly because it is not easy to restructure the balance sheet periodically, especially for large FIs.
3. Duration is not an appropriate tool for immunising portfolios when the expected interest rate changes are large because of the existence of convexity. Convexity
   exists because the relationship between security price changes and interest rate changes is not linear, which is assumed in the estimation of duration. Using convexity
   to immunise a portfolio will reduce the problem.