Question 1 A bank uses the following time buckets in its gap report: As of today, January 1st, 2010, the bank has the following interest-sensitive assets:

- $10 MM overnight placement with other financial institutions.
- 5-year linearly amortized fixed rate loan booked on June 1st, 2007 with initial principal amount of $50MM.
- 10-year Treasury bond with $100MM face value purchased at par on its issue date of March 1st, 2000.
- 3-year linearly-amortized floating rate loan booked on September 1st, 2009 with original principal amount of $60MM and paying 6m Libor + 50bps
- 10-year fixed rate bullet mortgage loan booked on June 1st, 2009 with original principal amount of $100MM.

The bank expects prepayments of 10% of outstanding principal annually over the life of the loan. The total assets in the “1d to 3m”, “3m to 1y” and “> 2y” buckets are

- $160MM, $20MM and $91MM
- $60MM, $20MM and $191MM
- $0MM, $20MM and $251MM
- $160MM, $10MM and $110MM Solution to Question 1

We slot each of the assets in the gap report as follows:

- $10 MM overnight placement is slotted in the “O/N” bucket.
- For the 5-year linearly-amortized fixed rate loan, the remaining maturity is 2 years and 5 months and the outstanding principal is $30MM. The $30MM is slotted as:
- $10MM in 5 months, which falls into the “3m to 1yr” bucket; • $10MM in 1 year and 5 months, which falls into the “1yr to 2yrs” bucket; and
- $10MM in 2 years and 5 months, which falls into the “> 2yrs” bucket.
- For the 10-year Treasury bond with $100MM face value purchased at par on its issue date of March 1st, 2000, the remaining maturity is 2 months, so the face value of $100MM is slotted in the “1 day to 3m” bucket.
- The 3-year linearly-amortized floating rate loan booked on September 1, 2009 with original principal amount of $60MM pays 6m Libor + 50bps, so as a floating rate loan it is slotted according to its next repricing date, which is March 1, 2010 – so in the “1 day to 3m” bucket.
- The 10-year bullet mortgage loan, being a fixed rate loan, is slotted in accordance with its remaining maturity, which is 9 years and 5 months; however, the bank expects prepayments of 10% of outstanding principal annually over the life of the loan, which are taken into consideration when preparing the gap report. Therefore, $10MM is considered to come due in 5 months’ time (“3m to 1 yr” bucket), $9MM (10% of the then outstanding principal of $90MM) in 1 year and 5 months (“1yr to 2 yrs” bucket), and the remaining $81MM in the “> 2 yrs” bucket. Aggregating all the positions we get the gap report here: Therefore, the correct answer is (a).

## Question 2: Assume the bank in Question 1 has the following interest-sensitive liabilities:

- $10MM of interbank money-market deposits with an average maturity of 1 month.
- $50MM of 6-month CDs issued at par on December 1, 2009.
- 5-year fixed-rate bond issued at par on January 1, 2009 with a face value of $110MM
- $100MM of demand deposits with an estimated 90% core portion and a volatile portion of

10%.

The cumulative gaps as percentages of total assets for the “1d to 3m”, “3m to 1 y” and “> 2 y” buckets are

- 40%, 50% and 20%
- 50%, 40% and 46%
- 50%, 40% and 10%
- 40%, 46% and 10% Solution to Question 2

We slot each of the liabilities in the gap report as follows:

- The $10MM of interbank money-market deposits are slotted as per their 1-month contractual

maturity, which means the “1 day to 3m” bucket. - The $50MM 6-month CDs are treated similarly. Since they were issued on December 1, their contractual maturity falls in 5 months, which corresponds to the “3m to 1yr” bucket.
- The 5-year fixed rate bond is slotted as per its remaining maturity (4 years in this case), which corresponds to the “> 2yrs” bucket.
- The $100MM demand deposits are slotted as per their volatile/core assumption, with the 10% volatile portion slotted in the “O/N” bucket, and the 90% core portion in the “> 2 yrs” bucket. Aggregating all liabilities gives: We now calculate the gaps, cumulative gaps and cumulative gaps as a percentage of total assets by aggregating assets and liabilities in the same report as follows: The cumulative gaps as percentages of total assets for the “1 day to 3m”, “3m to 1yr” and “> 2yrs” buckets are: 50%, 40% and 10% Therefore, the correct answer is (c).

## Question 3: Still using the data in Question 2 Assume the institution’s limits on cumulative gapsas percentages of total assets are as follows: Which of the following strategies assures

compliance with the limits?

- A $100MM 9×15 FRA receiving 5% and paying 6m Libor
- A 5-year interest rate swap under which

the bank pays fixed and receives 3m Libor on a notional of $100MM. - A 5-year interest rate swap under which the bank receives fixed and pays 6m Libor

on a notional of $100MM. - A 3-year interest rate swap under which the bank receives fixed and pays 1m Libor on a notional of $100MM. Solution to Question 3 We proceed to include each of these in the gap report alternatively, and calculate the resulting cumulative gaps as percentages of total assets. Here is the outcome if we use the FRA Here is the outcome if we use the 5-year pay-fixed

IRS Here is the outcome if we use the 5-year receive-fixed

IRS Here is the outcome if we use the 3-year receive-fixed

IRS Therefore, the correct answer is (d).

## Question 4: Assume the bank in Question 3 adopted the correct strategy and thus ended up with the

following gaps:

Assuming each gap amount is spread evenly

across its time bucket, the impact of a 100bps upward shift on the bank’s expected net

interest income (NII) over the next 12 months, using the Act/360 day-count convention, would

be

- $330,278
- -$330,278 c. $189,16
- -$189,167 Solution to Question 4

Since each gap amount is spread evenly across its time bucket. we can average it and assume a repricing date falling on the bucket’s mid-point. We now calculate the impact of the 100 basis point shift on expected NII over the next 12 months using the Act/360 convention. The only affected buckets are those ending within the 12-month horizon. The following table summarizes the calculation: Therefore, the correct answer is

(a). Question 5 Current zero-coupon rates (using semi-annual

compounding and Act/360 daycount convention) are shown here:

Assuming that the maximum behavioral maturity for assets and liabilities is capped at 2

years, the market value of equity and the modified duration of equity are:aa. $26,146,910 and –2.66 years

a. $26,146,910 and 2.66 years

c. $22,146,910 and –2.66 years

d. $22,146,910 and 2.66 years Solution to Question 5

WS Q5 Solution shows the necessary steps in the required calculations:

- We first calculate (cells N3:O8) the discount factors and the 6-month forward Libors to

be used in the next steps. - The market value and modified duration of each asset is calculated in the table underneath. The market value and modified duration of total assets are calculated in cells Q18:Q19.
- We repeat the same calculations for liabilities in the third table, to obtain finally the market value and modified duration for total liabilities appearing in cells P29:P30.
- The market value and modified duration of equity are programmed in cells P33:P34 and reveal values of $26,146,910 and –2.66. Therefore, the answer is (a).

## Question 6: Using the same inputs as in Question 5 and applying the Basle standardized model

The net weighted position of the banking book is:

- -$933,000
- $933,000
- -$1,075,800
- -$1,075,800 Obviously you should start from WS BIS Simple

BS and make appropriate amendments rather than go straight to the WS Q6 Solution.

Solution to Question 6 WS Q6 Solution sets forth the necessary calculations.

- We slot assets in the maturity ladder appearing in cells J21:O35. Each asset is slotted as per its repricing tenor.
- We do the same for liabilities in cells J38:N52.
- Finally we apply the Basle methodology, aggregating assets and liabilities in cells

O4:O16, then applying the weighting factors stipulated in the rules. - The net weighted position of the banking book is programmed in cell P17 and reveals a value of -$1,075,800. Therefore, the correct answer is (c)..