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Tutorial 4: Solutions

Lecture 4: Asset-liability management I

Note:

This topic has more questions than can be covered in a 1 hour tutorial session. The questions to be covered by your tutor are indicated by an asterisk (*); the rest should be viewed as extra practice problems.

Question 1. How do monetary policy actions made by the Central/Reserve Bank impact interest rates?

Through monetary actions, the Reserve Bank seeks to influence the money supply, inflation, and the level of interest rates. When the Reserve Bank finds it necessary to slow down the economy, it tightens monetary policy by raising interest rates. The normal result is a decrease in business and household spending (especially that financed by credit or borrowing). Conversely, if business and household spending decline to the extent that the Reserve Bank finds it necessary to stimulate the economy it allows interest rates to fall (an expansionary monetary policy). The drop in rates promotes borrowing and spending.

Question 2*. What is the repricing gap? On what financial performance variable does the repricing model focus? Explain.

The repricing gap is a measure of the difference between the dollar value of assets that will reprice and the dollar value of liabilities that will reprice within a specific time period, where repricing can be the result of a roll over of an asset or liability (e.g., a loan is paid off at or prior to maturity and the funds are used to issue a new loan at current market rates) or because the asset or liability is a variable rate instrument (e.g., a variable rate mortgage whose interest rate is reset every quarter based on movements in a prime rate).

The model focuses on the potential changes in the net interest income variable. In effect, if interest rates change, interest income and interest expense will change as the various assets and liabilities are repriced, that is, receive new interest rates.

Question 3. What is a maturity bucket in the repricing model?  Why is the length of time selected for repricing assets and liabilities important when using the repricing model?

The maturity bucket is the time window over which the dollar amounts of assets and liabilities are measured. The length of the repricing period determines which of the securities in a portfolio are rate-sensitive. The longer the repricing period, the more securities either mature or will be repriced, and, therefore, the more the interest rate risk exposure. An excessively short repricing period omits consideration of the interest rate risk exposure of assets and liabilities are that repriced in the period immediately following the end of the repricing period. That is, it understates the rate sensitivity of the balance sheet. An excessively long repricing period includes many securities that are repriced at different times within the repricing period, thereby overstating the rate sensitivity of the balance sheet.

Question 4*. What is the CGAP effect? According to the CGAP effect, what is the relation between changes in interest rates and changes in net interest income when CGAP is positive? When CGAP is negative?

The CGAP effect describes the relation between changes in interest rates and changes in net interest income. According to the CGAP effect, when CGAP is positive the change in NII is positively related to the change in interest rates. Thus, an FI would want its CGAP to be positive when interest rates are expected to rise. According to the CGAP effect, when CGAP is negative the change in NII is negatively related to the change in interest rates. Thus, an FI would want its CGAP to be negative when interest rates are expected to fall.

Question 5. Which of the following is an appropriate change to make on a bank’s balance sheet if it wants to increase its repricing gap.

a. Replace fixed-rate loans with rate-sensitive loans.

Yes. This change will increase RSAs, which will increase GAP.

b. Replace marketable securities with fixed-rate loans.

No. This change will decrease RSAs, which will decrease GAP.

c. Replace fixed-rate CDs with rate-sensitive CDs.

No. This change will increase RSLs, which will decrease GAP.

d. Replace equity with demand deposits.

No. This change will have no impact on either RSAs or RSLs. So, will have no impact on GAP.

e. Replace vault cash with marketable securities.

Yes. This change will increase RSAs, which will increase GAP.

Question 6. If a bank manager was quite certain that interest rates were going to rise within the next six months, how should the bank manager adjust the bank’s six-month repricing gap to take advantage of this anticipated rise? What if the manger believed rates would fall in the next six months.

When interest rates are expected to rise, a bank should set its repricing gap to a positive position. In this case, as rates rise, interest income will rise by more than interest expense. The result is an increase in net interest income. When interest rates are expected to fall, a bank should set its repricing gap to a negative position. In this case, as rates fall, interest income will fall by less than interest expense. The result is an increase in net interest income.

Question 7*. Consider the following balance sheet positions for a financial institution:

· Rate-sensitive assets = $200 million.  Rate-sensitive liabilities = $100 million

· Rate-sensitive assets = $100 million.  Rate-sensitive liabilities = $150 million

· 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.

· Rate-sensitive assets = $200 million.  Rate-sensitive liabilities = $100 million.

Repricing gap = RSA  RSL = $200  $100 million = +$100 million.

DNII = ($100 million)(0.01) = +$1.0 million, or $1,000,000.

· Rate-sensitive assets = $100 million.  Rate-sensitive liabilities = $150 million.

Repricing gap = RSA  RSL = $100  $150 million = -$50 million.

DNII = (-$50 million)(0.01) = -$0.5 million, or -$500,000.

· Rate-sensitive assets = $150 million.  Rate-sensitive liabilities = $140 million.

Repricing gap = RSA  RSL = $150  $140 million = +$10 million. DNII = ($10 million)(0.01) = +$0.1 million, or $100,000.

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

· DNII = ($100 million)(-0.01) = -$1.0 million, or -$1,000,000.

· DNII = (-$50 million)(-0.01) = +$0.5 million, or $500,000.

· DNII = ($10 million)(-0.01) = -$0.1 million, or -$100,000.

c. What conclusion can you draw about the repricing model from these results?

The FIs in parts (1) and (3) are exposed to reinvestment risk (positive gap), while the FI in part (2) is exposed to refinancing risk (negative gap). When the CGAP is positive (negative), there is a positive (negative) relation between the change in interest rates and the change in the FI’s NII.

Question 8*.    Consider the following balance sheet for MMC Bancorp (in millions of dollars):  

              Assets       Liabilities/Equity

1.  Cash and due from    $  6.25 1.  Equity capital (fixed)    $25.00

2.  Short-term consumer loans      62.50

        (1-year maturity) 2.  Demand deposits       50.00

3.  Long-term consumer loans     31.30

        (2-year maturity) 3.  One-month CDs                  37.50

4.  Three-month T-bills     37.50 4.  Three-month CDs                       50.00

5.  Six-month T-notes        43.70 5.  Three-month bankers’

         acceptances                25.00

6.  3-year T-bonds                         75.00 6.  Six-month commercial paper   75.00

7.  10-year, fixed-rate mortgages  25.00  7.  1-year time deposits  25.00

8.  30-year, floating-rate mortgages            

        (reset every nine months)      50.00 8.  2-year time deposits  50.00

9.  Premises       6.25             

                                                   $337.50                                                         $337.50

a. Calculate the value of MMC’s rate-sensitive assets, rate sensitive liabilities, and cumulative gap over the next year. What does the gap suggest?

Looking down the asset side of the balance sheet, we see the following one-year rate-sensitive assets (RSA):

1.  Short-term consumer loans: $62.50 million, which are repriced at the end of the year and just make the one-year cutoff.

2.  Three-month T-bills: $37.50 million, which are repriced on maturity (rollover) every three months.

3.  Six-month T-notes: $43.70 million, which are repriced on maturity (rollover) every six months.

4.  30-year floating-rate mortgages: $50.00 million, which are repriced (i.e., the mortgage rate is reset) every nine months. Thus, these long-term assets are RSA in the context of the repricing model with a one-year repricing horizon.

Summing these four items produces one-year RSA of $193.70 million. The remaining $143.80 million is not rate sensitive over the one-year repricing horizon. A change in the level of interest rates will not affect the interest revenue generated by these assets over the next year. The $6.25 million in the cash and due from category and the $6.25 million in premises are nonearning assets. Although the $131.30 million in long-term consumer loans, 3-year Treasury bonds, and 10-year, fixed-rate mortgages generate interest revenue, the level of revenue generated will not change over the next year since the interest rates on these assets are not expected to change (i.e., they are fixed over the next year).

Looking down the liability side of the balance sheet, we see that the following liability items clearly fit the one-year rate or repricing sensitivity test:

1. One-month CDs: $37.50 million, which mature in one months and are repriced on rollover.

2. Three-month CDs: $50 million, which mature in three months and are repriced on rollover.

3. Three-month bankers’ acceptances: $25 million, which mature in three months and are repriced on rollover.

4. Six-month commercial paper: $75 million, which mature and are repriced every six months.

5. 1-year time deposits: $25 million, which are repriced at the end of the one-year gap horizon. 

Summing these five items produces one-year rate-sensitive liabilities (RSL) of $212.5 million. The remaining $125 million is not rate sensitive over the one-year period. The $25 million in equity capital and $50 million in demand deposits do not pay interest and are therefore classified as nonpaying. The $50 million in two-year time deposits generate interest expense over the next year, but the level of the interest generated will not change if the general level of interest rates change. Thus, we classify these items as fixed-rate liabilities.

The five repriced liabilities ($37.50 + $50 + $25 + $75 + $25) sum to $212.5 million, and the four repriced assets of $62.50 + $37.50 + $43.70 + $50 sum to $193.70 million. Given this, the cumulative one-year repricing gap (CGAP) for the bank is:

CGAP = (One-year RSA) - (One-year RSL) = RSA - RSL = $193.70 million - $212.5 million =

-$18.80 million

The CGAP suggests a negative relation between the change in interest rates and the change in the FI’s NII.

b. If interest rates rise by 1 percent on both RSAs and RSLs, calculate the expected change in the net interest income for the FI

The CGAP effect suggests a reduction in reduction in net interest income of the FI when         interest rates increase

 DNII = CGAP x DR (=DR_RSA=DR_RSL)

          = (-$18.80 million) x 0.01

 = -$188,000

c. If interest rates rise by 1.2 percent on RSAs and by 1 percent on RSLs, calculate the change in the spread and what does the spread suggest? Calculate the expected change in the net interest income for the FI:

DS = DR_RSA - DR_RSL = 0.012-0.01=0.002

The spread effects suggests that there is a positive relation between the change in interest rates and the change in NII. In other words, the spread effect suggests an increase in NII when interest rates increase.

Calculate the expected change in the net interest income for the FI and explain it.

DNII = [RSA x DR_RSA] - [RSL x DR_RSL]

         = [$193.70 million x 1.2%] - [$212.5 million x 1.0%]

         = $2.3244 million - $2.125 million

         = $199,400

When interest rates increase, the expected change in NII comes from combining the spread effect (an increase in NII) and the CGAP effect (a reduction in NII)

DNII = [RSA x DR_RSA] - [RSL x DR_RSL]

DNII = RSA x [DS + DR_RSL] - [RSL x DR_RSL]

DNII = RSA x DS + [RSA – RSL] x DR_RSL

DNII = RSA x DS +  CGAPxDR_RSL   

= 193.70 x 0.002 + (-18.8) x 0.01 = 0.3874 – 0.1880 = 0.1994 = $199,400

In this case, the increase in NII because an increase in NII due to the spread effect dominates the decrease in NII due to the CGAP effect.  

Question 9. What are the reasons for not including demand deposits as rate-sensitive liabilities in the repricing analysis for a commercial bank? What is the subtle but potentially strong reason for including demand deposits in the total of rate sensitive liabilities? Can the same argument be made for passbook savings accounts?

The rate available on demand deposit accounts is zero. Although many banks are able to offer NOW accounts on which interest can be paid, this interest rate seldom is changed and thus the accounts are not really interest rate sensitive. However, demand deposit accounts do pay implicit interest in the form of not charging fully for checking and other services. Further, when market interest rates rise, customers draw down their demand deposit accounts, which may cause the bank to use higher cost sources of funds. The same or similar arguments can be made for passbook savings accounts.

Question 10. Which of the following assets or liabilities fit the one-year rate or repricing sensitivity test?

3-month U.S. Treasury bills Yes

1-year U.S. Treasury notes Yes

20-year U.S. Treasury bonds No

20-year floating-rate corporate bonds with annual repricing Yes

30-year floating-rate mortgages with repricing every two years No

30-year floating-rate mortgages with repricing every six months Yes

Overnight fed funds Yes

9-month fixed-rate CDs Yes

1-year fixed-rate CDs Yes

5-year floating-rate CDs with annual repricing Yes

Common stock No

Question 11*. What is the spread effect?

The spread effect is the effect that a change in the spread between rates on RSAs and RSLs has on net interest income as interest rates change. The spread effect is such that, regardless of the direction of the change in interest rates, a positive relation exists between changes in the spread and changes in NII. Whenever the spread increases (decreases), NII increases (decreases).

Question 12. A bank manager is quite certain that interest rates are going to fall within the next six months. How should the bank manager adjust the bank’s six-month repricing gap and spread to take advantage of this anticipated rise? What if the manger believes rates will rise in the next six months.

When interest rates are expected to fall, a bank should set its repricing gap to a negative position. Further, the manager would want to increase the spread between the return on RSAs and RSLs. In this case, as rates fall, interest income will fall by less than interest expense. The result is an increase in net interest income. When interest rates are expected to rise, a bank should set its repricing gap to a positive position. Again, the manager would want to increase the spread between the return on RSAs and RSLs. In this case, as rates rise, interest income will rise by more than interest expense. The result is an increase in net interest income.

Question 13*. A bank has the following balance sheet:

Assets Avg. Rate Liabilities/Equity       Avg. Rate

Rate sensitive    $550,000    7.75% Rate sensitive    $375,000     6.25%

Fixed rate      755,000    8.75 Fixed rate      805,000     7.50

Nonearning      265,000 Nonpaying      390,000

   Total $1,570,000    Total $1,570,000

Suppose interest rates rise such that the average yield on rate-sensitive assets increases by 45 basis points and the average yield on rate-sensitive liabilities increases by 35 basis points (1 basis point = 0.01%).

a. Calculate the bank’s CGAP and gap ratio.

 CGAP = $550,000 - $375,000 = $175,000

Gap ratio = $175,000/$1,570,000 = 11.15%

b. Assuming the bank does not change the composition of its balance sheet, calculate the resulting change in the bank’s interest income, interest expense, and net interest income.

DII = $550,000(0.0045) = $2,475

DIE = $375,000(0.0035) = $1,312.50

DNII = $2,475 - $1,312.50 = $1,162.50

c. Explain how the CGAP and spread effects influence the change in net interest income.

The CGAP effect suggests an increase net interest income because the CGAP is positive when interest rates increase. That is, interest income increases by more than interest expense, resulting in an increase in NII. The spread increased by 10 basis points. The spread effect also suggests an increase net interest income when interest rates increase. The combined effect is an increase in NII. That is given by the following calculation.

Question 14. A bank has the following balance sheet:

Assets Avg. Rate Liabilities/Equity       Avg. Rate

Rate sensitive    $550,000    7.75% Rate sensitive    $575,000     6.25%

Fixed rate      755,000    8.75 Fixed rate      605,000     7.50

Nonearning      265,000 Nonpaying      390,000

   Total $1,570,000    Total $1,570,000

Suppose interest rates fall such that the average yield on rate-sensitive assets decreases by 15 basis points and the average yield on rate-sensitive liabilities decreases by 5 basis points, (1 basis point = 0.01%).

a. Calculate the bank’s CGAP and gap ratio.

CGAP = $550,000 - $575,000 = -$25,000

Gap ratio = -$25,000/$1,570,000 = -1.59%

b. Assuming the bank does not change the composition of its balance sheet, calculate the resulting change in the bank’s interest income, interest expense, and net interest income.

DII = $550,000(-0.0015) = -$825

DIE = $575,000(-0.0005) = -$287.50

DNII = -$825 – (-$287.50) = -$537.50

c. The bank’s CGAP is negative and interest rates decreased, yet net interest income decreased. Explain how the CGAP and spread effects influenced this decrease in net interest income.

The CGAP effect suggests an increase net interest income because the CGAP was negative when interest rates decrease. That is, interest income decreases by less than interest expense, resulting in an increase in NII. The spread effect, on the other hand, suggests a decrease net interest income. The spread decreased by 10 basis points. According to the spread affect, as spread decreases, net interest income decreases. In this case, the increase in NII because an increase in NII due to the CGAP effect dominates the decrease in NII due to the spread effect.

Question 15. What are some of the weakness of the repricing model?

The repricing model has four general weaknesses: 

(1) It ignores market value effects.

(2) It ignores information regarding the distribution of assets and liabilities within time buckets. 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.

The following questions and problems are based on material in Appendix 8B to the chapter.

Question 16.  Suppose that the current one-year rate and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:

           ₁R₁ = 6%    E(₂r₁)  = 7%        E(₃r₁)  = 7.5%  E(₄r₁) = 7.85%

Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities.

₁R₁ = 6.00%

₁R₂ = [(1 + 0.06)(1 + 0.07)]^½  -  1= 6.50%

₁R₃ = [(1 + 0.06)(1 + 0.07)(1 + 0.075)]^1/3- 1 = 6.83%

₁R₄ = [(1 + 0.06)(1 + 0.07)(1 + 0.075)(1 + 0.0785)]^1/4- 1 = 7.09%

Question 17. How does the liquidity premium theory of the term structure of interest rates differ from the unbiased expectations theory?

The unbiased expectations theory asserts that long-term rates are a geometric average of current and expected short-term rates. The liquidity premium theory asserts that long-term rates are a geometric average of current and expected short-term rates plus a liquidity risk premium. The premium is assumed to increase with the maturity of the security because the uncertainty of future returns grows as maturity increases.

Question 18.  One-year Treasury bill rates and liquidity premiums for the next four years are expected to be as follows: 

₁R₁ = 5.65%

          E(₂r₁) = 6.75% L₂ = 0.05%

          E(₃r₁) = 6.85% L₃ = 0.10%

          E(₄r₁) = 7.15% L₄ = 0.12%

Using the liquidity premium hypothesis, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities.

 ₁R₁ = 5.65%

₁R₂ = [(1 + 0.0565)(1 + 0.0675 + 0.0005)]^½  -  1= 6.22%

₁R₃ = [(1 + 0.0565)(1  + 0.0675 + 0.0005)(1 + 0.0685 + 0.001)]^1/3- 1 = 6.47%

₁R₄ = [(1 + 0.0565)(1 + 0.0675 + 0.0005)(1 + 0.0685 + 0.001)(1 + 0.0715 + 0.0012)]^1/4- 1

= 6.67%