Goals of This Chapter: The purpose of this chapter is to explore the options bankers have today for dealing with risk - especially the risk of loss due to changing interest rates - and to see how a bank's management can coordinate the management of its assets with the management of its liabilities in order to achieve the institution's goals.
Key Topic In This Chapter
Asset, Liability, and Funds Management
Market Rates and Interest Rate Risk
The Goals of Interest Rate Hedging
Interest-Sensitive Gap Management
Duration Gap Management
Limitations of Interest Rate Risk Management Techniques
Chapter Outline
I. Introduction: The Necessity for Coordinating Bank Asset and Liability Management Decisions
II. Asset-Liability Management Strategies
A. Asset Management Strategy
B. Liability Management Strategy
C. Funds Management Strategy
III. Interest Rate Risk: One of the Greatest Management Challenges
A. Forces Determining Interest Rates
B. The Measurement of Interest Rates
1. Yield to Maturity
2. Bank Discount Rate
C. The Components of Interest Rates
1. Risk Premiums
2. Yield Curves
3. The Maturity Gap and the Yield Curve
D. Responses to Interest Rate Risk
IV. One of the Goals of Interest-Rate Hedging: Protect the Net Interest Margin
A. The Net Interest Margin
B. Interest-Sensitive Gap Management as a Risk- Management Tool
1. Asset-Sensitive Position
2. Liability-Sensitive Position
3. Dollar Interest-Sensitive Gap
4. Relative Interest Sensitive Gap
5. Interest Sensitivity Ratio
6. Computer-Based Techniques
7. Cumulative Gap
8. Strategies in Gap Management
C. Problems with Interest-Sensitive GAP Management
V. The Concept of Duration as a Risk-Management Tool
A. Definition of Duration
B. Calculation of Duration
C. Net Worth and Duration
D. Price Sensitivity to Changes in Interest Rates and Duration
E. Convexity and Duration
VI. Using Duration to Hedge Against Interest Rate Risk
A. Duration Gap
1. Dollar Weighted Duration of Assets
2. Dollar Weighted Duration of Liabilities
3. Positive Duration Gap
4. Negative Duration Gap
B. Change in the Bank's Net Worth
VII The Limitations of Duration Gap Management
VIII. Summary of the Chapter
Concept Checks
7-1. What do the following terms mean: Asset management? Liability management? Funds management?
Asset management refers to a banking strategy where management has control over the allocation of bank assets but believes the bank's sources of funds (principally deposits) are outside its control. The key decision area for management was not deposits and other borrowings but assets.
Liability management is a strategy of control over bank liabilities by varying interest rates offered on borrowed funds.
Funds management combines both asset and liability management approaches into a balanced liquidity management strategy.
7-2. What factors have motivated financial institutions to develop funds management techniques in recent years?
The necessity to find new sources of funds in the 1970s and the risk management problems encountered with troubled loans and volatile interest rates in the 1970s and 1980s led to the concept of planning and control over both sides of a bank's balance sheet -- the essence of funds management.
7-3. What forces cause interest rates to change? What kinds of risk do financial firms face when interest rates change?
Interest rates are determined, not by individual banks, but by the collective borrowing and lending decisions of thousands of participants in the money and capital markets. They are also impacted by changing perceptions of risk by participants in the money and capital markets, especially the risk of borrower default, liquidity risk, price risk, reinvestment risk, inflation risk, term or maturity risk, marketability risk, and call risk.
Financial institutions can lose income or value no matter which way interest rates go. Rising interest rates can lead to losses on security instruments and on fixed-rate loans as the market values of these instruments fall. Falling interest rates will usually result in capital gains on fixed-rate securities and loans but an institution will lose income if it has more rate-sensitive assets than liabilities. Rising interest rates will also cause a loss to income if an institution has more rate-sensitive liabilities than rate-sensitive assets.
7-4. What makes it so difficult to correctly forecast interest rate changes?
Interest rates cannot be set by an individual bank or even by a group of banks; they are determined by thousands of investors trading in the credit markets. Moreover, each market rate of interest has multiple components--the risk-free interest rate plus various risk premium. A change in any of these rate components can cause interest rates to change. To consistently forecast market interest rates correctly would require bankers to correctly anticipate changes in the risk-free interest rate and in all rate components.
Another important factor is the timing of the changes. To be able to take full advantage of their predictions, they also need to know when the changes will take place.
7-5. What is the yield curve, and why is it important to know about its shape or slope?
The yield curve is the graphic picture of how interest rates vary with different maturities of loans viewed at a single point in time (and assuming that all other factors, such as credit risk, are held constant).
The slope of the yield curve determines the spread between long-term and short-term interest rates. In banking most of the long-term rates apply to loans and securities (i.e., bank assets) and most of the short-term interest rates are attached to bank deposits and money market borrowings. Thus, the shape or slope of the yield curve has a profound influence on a bank's net interest margin or spread between asset revenues and liability costs.
7-6. What is it that a lending institution's wishes to protect from adverse movements in interest rates?
A financial institution wishes to protect both the value of assets and liabilities and the revenues and costs generated by both assets and liabilities from adverse movements in interest rates.
7-7. What is the goal of hedging?
The goal of hedging in banking is to freeze the spread between asset returns and liability costs and to offset declining values on certain assets by profitable transactions so that a target rate of return is assured.
7-8. First National Bank of Bannerville has posted interest revenues of $63 million and interest costs from all of its borrowings of $42 million. If this bank possesses $700 million in total earning assets, what is First National's net interest margin? Suppose the bank's interest revenues and interest costs double, while its earning assets increase by 50 percent. What will happen to its net interest margin?
Net Interest
=
$63 mill. - $42 mill.
= 0.03 or 3 percent
Margin
$700 mill.
If interest revenues and interest costs double while earning assets grow by 50 percent, the net interest margin will change as follows:
($63 mill. - $42 mill.) * 2
= 0.04 or 4 percent
$700 mill. * (1.50)
Clearly the net interest margin increases--in this case by one third.
7-9. Can you explain the concept of gap management?
Gap management requires the management to perform analysis of the maturities and repricing opportunities associated with interest-bearing assets and with interest-bearing liabilities. When more assets are subject to repricing or will reach maturity in a given period than liabilities or vice versa, the bank has a GAP between assets and liabilities and is exposed to loss from adverse interest-rate movements based on the gap's size and direction.
7-10 When is a financial firm asset sensitive? Liability sensitive?
A financial firm is asset sensitive when it has more interest-rate sensitive assets maturing or subject to repricing during a specific time period than rate-sensitive liabilities. A liability sensitive position, in contrast, would find the financial institution having more interest-rate sensitive deposits and other liabilities than rate-sensitive assets for a particular planning period.
Commerce National Bank reports interest-sensitive assets of $870 million and
Interest-sensitive liabilities of $625 million during the coming month. Is the bank asset sensitive or liability sensitive? What is likely to happen to the bank's net interest margin if interest rates rise? If they fall?
Because interest-sensitive assets are larger than liabilities by $245 million the bank is asset sensitive.
If interest rates rise, the bank's net interest margin should rise as asset revenues increase by more than the resulting increase in liability costs. On the other hand, if interest rates fall, the bank's net interest margin will fall as asset revenues decline faster than liability costs.
7-12. Peoples' Savings Bank, a thrift institution, has a cumulative gap for the coming year of + $135 million and interest rates are expected to fall by two and a half percentage points. Can you calculate the expected change in net interest income that this thrift institution might experience? What change will occur in net interest income if interest rates rise by one and a quarter percentage points?
For the decrease in interest rates:
Expected
Change in = $135 million * (-0.025) = -$3.38 million
Net Interest Income
For the increase in interest rates:
Expected Change
in Net Interest = $135 million * (+0.0125) = +$1.69 million
Income
7-13 How do you measure the dollar interest-sensitive gap? The relative interest-sensitive gap? What is the interest-sensitivity ratio?
The dollar interest-sensitive gap is measured by taking the repriceable (interest-sensitive) assets minus the repriceable (interest-sensitive) liabilities over some set planning period. Common planning periods include 3 months, 6 months and 1 year. The relative interest-sensitive gap is the dollar interest-sensitive gap divided by some measure of bank size (often total assets).
The interest-sensitivity ratio is just the ratio of interest-sensitive assets to interest sensitive liabilities. Regardless of which measure you use, the results should be consistent. If you find a positive (negative) gap for dollar interest-sensitive gap, you should also find a positive (negative) relative interest-sensitive gap and an interest sensitivity ratio greater (less) than one.
7-14 Suppose Carroll Bank and Trust reports interest-sensitive assets of $570 million and interest-sensitive liabilities of $685 million. What is the bank's dollar interest-sensitive gap? Its relative interest-sensitive gap and interest-sensitivity ratio?
Dollar Interest-Sensitive Gap = Interest-Sensitive Assets - Interest Sensitive Liabilities
= $570 - $685 = -$115
Relative Gap
=
$ IS Gap
=
-$115
= -0.2018 or -20.18 percent
Bank Size
$570
Interest-Sensitivity
=
Interest-Sensitive Assets
=
$570
= .8321
Ratio
Interest-Sensitive Liabilities
$685
7-15 Explain the concept of weighted interest-sensitive gap. How can this concept aid management in measuring a financial institution's real interest-sensitive gap risk exposure?
Weighted interest-sensitive gap is based on the idea that not all interest rates change at the same speed. Some are more sensitive than others. Interest rates on bank assets may change more slowly than interest rates on liabilities and both of these may change at a different speed than those interest rates determined in the open market.
In the weighted interest-sensitive gap methodology, all interest-sensitive assets and liabilities are given a weight based on their speed (sensitivity) relative to some market interest rate. Fed Funds loans, for example, have an interest rate which is determined in the market and which would have a weight of 1. All other loans, investments and deposits would have a weight based on their speed relative to the Fed Funds rate. To determine the interest-sensitive gap, the dollar amount of each type of asset or liability would be multiplied by its weight and added to the rest of the interest-sensitive assets or liabilities. Once the weighted total of the assets and liabilities is determined, a weighted interest-sensitive gap can be determined by subtracting the interest-sensitive liabilities from the interest-sensitive assets.
This weighted interest-sensitive gap should be more accurate than the unweighted interest-sensitive gap. The interest-sensitive gap may change from negative to positive or vice versa and may change significantly the interest rate strategy pursued by the bank.
7-16. What is duration?
Duration is a value- and time-weighted measure of maturity considers the timing of all cash inflows from earning assets and all cash outflows associated with liabilities. Duration measures the average time needed to recover the funds committed to an investment. It is a direct measure of price risk.
7-17. How is a financial institution's duration gap determined?
A bank's duration gap is determined by taking the difference between the duration of a bank's assets and the duration of its liabilities. The duration of the bank's assets can be determined by taking a weighted average of the duration of all of the assets in the bank's portfolio. The weight is the dollar amount of a particular type of asset out of the total dollar amount of the assets of the bank. The duration of the liabilities can be determined in a similar manner. The duration of the liabilities is then adjusted to reflect that the bank has fewer liabilities than assets.
7-18. What are the advantages of using duration as an asset-liability management tool as opposed to interest-sensitive gap analysis?
Interest-sensitive gap only looks at the impact of changes in interest rates on the bank's net income. It does not take into account the effect of interest rate changes on the market value of the bank's equity capital position. In addition, duration provides a single number which tells the bank their overall exposure to interest rate risk.
7-19. How can you tell you are fully hedged using duration gap analysis?
You are fully hedged when the dollar weighted duration of the assets portfolio of the bank equals the dollar weighted duration of the liability portfolio. This means that the bank has a zero duration gap position when it is fully hedged. Of course, because the bank usually has more assets than liabilities the duration of the liabilities needs to be adjusted by the ratio of total liabilities to total assets to be entirely correct.
7-20. What are the principal limitations of duration gap analysis? Can you think of some way of reducing the impact of these limitations?
There are several limitations with duration gap analysis. It is often difficult to find assets and liabilities of the same duration to fit into the financial-service institution's portfolio. In addition, some accounts such as deposits and others don't have well defined patterns of cash flows which make it difficult to calculate duration for these accounts.
Duration is also affected by prepayments by customers as well as default. Duration gap models assume that a linear relationship exists between the market values (prices) of assets and liabilities and interest rates, which is not strictly true. Finally, duration analysis works best when interest rate changes are small and short and long term interest rates change by the same amount. If this is not true, duration analysis is not as accurate.
7-21. Suppose that a thrift institution has an average asset duration of 2.5 years and an average liability duration of 3.0 years. If the thrift holds total assets of $560 million and total liabilities of $467 million, does it have a significant leverage-adjusted duration gap? If interest rates rise, what will happen to the value of its net worth?
Duration Gap = DA - DL * = 2.5 yrs. - 3.0 yrs.
= 2.5 years - 2.5018 years
= -0.0018 years
This bank has a very slight negative duration gap; so small in fact that we could consider it insignificant. If interest rates rise, the bank's liabilities will fall slightly more in value than its assets, resulting in a small increase in net worth.
7-22. Stilwater Bank and Trust Company has an average asset duration of 3.25 years and an average liability duration of 1.75 years. Its liabilities amount to $485 million, while its assets total $512 million. Suppose that interest rates were 7 percent and then rise to 8 percent. What will happen to the value of the Stilwater bank's net worth as a result of a decline in interest rates?
First, we need an estimate of Stilwater's duration gap. This is:
Duration Gap = 3.25 yrs. - 1.75 yrs * = + 1.5923 years
Then, the change in net worth if interest rates rise from 7 percent to 8 percent will be:
Change in NW =
= -$7.62 million.
Problems
7-1. A government bond is currently selling for $1,150 and pays $75 per year in interest for 14 years when it matures. If the redemption value of this bond is $1,000, what is its yield to maturity if purchased today for $1,150?
The yield to maturity equation for this bond would be:
Using a financial calculator the YTM =5.9%
7-2. Suppose the government bond described in problem 1 above is held for five years and then the savings institution acquiring the bond decides to sell it at a price of $975. Can you figure out the average annual yield the savings institution will have earned for its five-year investment in the bond?
$1,150 = + + + ++
Using a financial calculator, the HPY is 3.7%
7-3. U.S. Treasury bills are available for purchase this week at the following prices (based upon $100 par value) and with the indicated maturities:
a. $98.50, 182 days.
b. $97.50, 270 days.
c. $99.25, 91 days.
Calculate the bank discount rate (DR) on each bill if it is held to maturity. What is the equivalent yield to maturity (sometimes called the bond-equivalent or coupon equivalent yield) on each of these Treasury Bills?
The discount rates and equivalent yields to maturity (bond-equivalent or coupon-equivalent yields) on each of these Treasury bills are:
Discount Rates Equivalent Yields to Maturity
a.
b.
c.
7-4. Clarksville Financial reports a net interest margin of 2.75 percent in its most recent financial report with total interest revenues of $95 million and total interest costs of $82 million. What volume of earning assets must the bank hold? Suppose the bank's interest revenues rises by 5 percent and its interest costs and earnings assets increase by 9 percent. What will happen to Clarksville's net interest margin?
The relevant formula is:
Net Interest Margin = .0275 =
Then Earning Assets = $473 million.
If revenues rise by 5 percent and costs and earnings assets rise by 9 percent net interest margin is:
Net Interest Margin =
=
= 0.0201 or 2.01 percent.
7-5. If a credit union's net interest margin, which was 2.50 percent, increases 15 percent and its total assets, which stood originally at $625 million, rise by 20 percent, what change will occur in the bank's net interest income?
The correct formula is:
.025 * (1+.15) =
Net Interest Income = 0.02875 * $750 million
= $21.5625 million.
7-6. The cumulative interest-rate gap of Jamestown Savings Bank increases 75 percent from an initial figure of $22 million. If market interest rates rise by 25 percent from an initial level of 4.5 percent, what change will occur in this thrift's net interest income?
The key formula here is:
Change in the = Change in interest rates (in percentage points) * cumulative gap
Net Interest = (0.045 * .25) x ($22 mill.) * (1+.75)
Income = .43
Thus, the bank's net interest income will drop by 57 percent.
7-7. Old Settlers State Bank has recorded the following financial data for the past three years (dollars in millions):
Current Year
Previous Year
Two Years Ago
Interest revenues
$80
$82
$84
Interest expenses
66
68
70
Loans (Excluding nonperforming)
400
405
400
Investments
200
195
200
Total deposits
450
425
475
Money market borrowings
100
125
75
What has been happening to the bank's net interest margin? What do you think caused the changes you have observed? Do you have any recommendations for Old Settlers management team?
Net interest margin (NIM) = Net Interest Income/Earning Assets, where
Net Interest Income = Net Interest Revenues - Net Interest Expenses
Earning Assets = Loans + Investments
NIM (Current) = ($80-66)/ (400 + 200) = 14/600 = 0.0233 or 2.33%
NIM (previous) = ($82-68)/ (405 + 195) = 14/600 = 0.0233 or 2.33%
NIM (Two years ago) = ($84-70)/ (400 + 200) = 14/600 = 0.0233 or 2.33%
The net interest margin is steady in all the three years As interest revenues and expenses are varying simultaneously.There is no fluctuation in the net interest margin.
7-8 The First National Bank of Spotsburg finds that its asset and liability portfolio contains the following distribution of maturities and repricing opportunities:
Coming
Week
Next
30 Days
Next
31-90 Days
More Than
90 Days
Loans
$210
$300
$475
$525
Securities
+21
+26
40
70
Total IS Assets
$231
$326
$515
$595
Transaction Dep.
$350
$ ---
$ ---
$ ---
Time Accts.
100
276
196
100
Money Mkt. Borr.
136
140
100
50
Total IS Liab.
$586
$416
$296
$150
GAP
- $355
- $90
$219
+ $445
Cumulative GAP
- $355
- $445
- $226
$219
First National has a negative gap in the nearest period and therefore would benefit if interest rates fell. In the next period it has a slightly negative gap and would therefore benefit of interest rate rose. However, its cumulative gap is still negative. The third period is positive gap and hence the bank would benefit if interest rates rises. In the final period the gap is positive and the bank would benefit if interest rates rose. Its cumulative gap is slightly positive and also shows that rising interest rates would be beneficial to the bank overall.
7-9 Fluffy Cloud Savings Bank currently has the following interest-sensitive assets and liabilities on its balance sheet with the interest-rate sensitivity weights noted.
Interest-Sensitive Assets
Index
Interest-Sensitive Liabilities
Index
Federal fund loans $50
1.00
Security holdings $50
1.20
Interest-bearing deposits $250
.75
Loans and leases $310.8
1.45
Money-market borrowings $85
.95
What is the bank's current interest-sensitive gap? Adjusting for these various interest-rate sensitivity weights what is the bank's weighted interest-sensitive gap? Suppose the federal funds interest rate increases or decreases one percentage point. How will the bank's net interest income be affected (a) given its current balance sheet makeup and (b) reflecting its weighted balance sheet adjusted for the foregoing rate-sensitive indexes?
Solution:
Dollar IS Gap
=
ISA - ISL
=
($50 + $50 + $310.8) - ($250 + $85)
= $410.8 - $335
= $75.8
Weighted IS Gap
=
[(1)($50) + (1.20)(50) + (1.45) (310.8)]
-
[(.75)($250) + (.95)($85)]
=
$50 + $60 + $450.66
-
$187.5 + $80.75
=
$560.66
-
$268.25
=
$292.41
a.) Change in Bank's Income = IS Gap * Change in interest rates
= ($75.8) (.01) = $.76 million
Using the regular IS Gap; net income will change by plus or minus $760,000
b.) Change in Bank's Income = Weighted IS Gap * Change in interest rates
= ($292.41) (.01) = $2.9241
Using the weighted IS Gap; net income will change by plus or minus $2,924,100
7-10 Twinkle Savings Association has interest-sensitive assets of $325 million, interest-sensitive liabilities of $325 million, and total assets of $500 million. What is the bank's dollar interest-sensitive gap? What is Twinkle's relative interest-sensitive gap? What is the value of its interest-sensitivity ratio? Is it asset sensitive or liability sensitive? Under what scenario for market interest rates will Twinkle experience a gain in net interest income? A loss in net interest income?
Dollar Interest-Sensitive Gap = ISA - ISL = $325 - $325 = $0
Relative Interest-Sensitive Gap
=
ISA - ISL
=
$0
= 0
Bank Size
$500
Interest-Sensitivity Ratio
=
ISA
=
$325
= 1
ISL
$325
Here the interest sensitivity Gap is zero as the interest sensitive assets are equal to interest sensitive liabilities. Twinkle Savings Association is relatively insulated from interest rate risk. interest revenues from assets and funding costs will change at the same rate. The interest-sensitive gap is zero, and the net interest margin is protected regardless of which way interest rates go.
7-11 Richman Bank,, N.A., has a portfolio of loans and securities expected to generate cash inflows for the bank as follows:
Expected Cash Inflows of Principal & Interest Payments
Annual Period in Which Cash Receipts Are Expected
$1,500,675
Current year
746,872
Two years from today
341,555
Three years from today
62,482
Four years from today
9,871
Five years from today
Deposits and money market borrowings are expected to require the following cash outflows:
Expected Cash Outflows of Principal $ Interest Payments
Annual Period during Which Payments must be Made
$1,595,786
Current year
831,454
Two years from today
123,897
Three years from today
1,005
Four years from today
-----
Five years from today
If the discount rate applicable to the previous cash flows is 5 percent, what is the duration of the Richman's portfolio of earning assets and of its deposits and money market borrowings? What will happen to the bank's total returns, assuming all other factors are held constant, if interest rates rise? If interest rates fall? Given the size of the duration gap you have calculated, in what type of hedging should Richman engage? Please be specific about the hedging transactions that are needed and their expected effects.
Richman has asset duration of:
$1,500,675*1 + $746,872 * 2 + $341,555 * 3 + $62,482 * 4 + $9,871 * 5
(1 + 0.05)1 (1 + 0.05)2 (1 + 0.05)3 (1 + 0.05)4 (1 + 0.05)5
DA = $1,500,675 + $746,872 + $341,555 + $62,482 + $9,871
(1 + 0.05)1 (1 + 0.05)2 (1 + 0.05)3 (1 + 0.05)4 (1 + 0.05)5
= $3, 874,844.66/ $2,453,101.35 = 1.5796 years
Richman has a liability duration of:
$1,595786 * 1 + $831,454 * 2 + $123,897 * 3 + $1,005 * 4
(1 + 0.05)1 (1 + 0.05)2 (1 + 0.05)3 (1 + 0.05)4
DL=
$1,595,786+ $831,454 + $123,897 + $1,005
(1 + 0.05)1 (1 + 0.05)2 (1 + 0.05)3 (1 + 0.05)4
= $3,352,490.69 / $2,381,803.18 = 1.4075 years
Richman's Duration Gap = Asset Duration - Liability Duration = 1.5796 - 1.4075 = 0.1720years.
Because Richman's Asset Duration is greater than its Liability Duration, the bank has a positive duration gap, which means that the bank's total returns will decrease if interest rates rise because the value of the liabilities will decline by less than the value of the assets. On the other hand, if interest rates were to fall, this positive duration gap will result in the bank's total returns increasing. In this case, the value of the assets will rise by a greater amount than the value of the liabilities.
Given the magnitude of the duration gap, the management of Richman Bank, needs to do a combination of things to close its duration gap between assets and liabilities. It probably needs to try to shorten asset duration, lengthen liability duration, and use financial futures or options to deal with whatever asset-liability gap exists at the moment. The bank may want to consider securitization or selling some of its assets, reinvesting the cash flows in maturities that will more closely match its liabilities' maturities. The bank may also consider negotiating some interest-rate swaps to change the cash flow patterns of its liabilities to more closely match its asset maturities.
7-12. Given the cash inflow and outflow figures in Problem 11 for Richman Bank, N.A., suppose that interest rates began at a level of 5 percent and then suddenly rise to 5.75 percent. If the bank has total assets of $5 billion and total liabilities of $4.5 billion, by how much would the value of Richman's net worth change as a result of this movement in interest rates? Suppose, on the other hand, that interest rates decline from 5 percent to 4.5 percent. What happens to the value of Richman's net worth in this case and by how much in dollars does it change? What is the size of its duration gap?
From Problem #11 we find that Richman's average asset duration is 1.5796 years and average liability duration is 1.4075 years. If total assets are $5 billion and total liabilities are $4.5 billion, then Richman has a duration gap of:
Duration Gap = 1.5796 - 1.4075 *
= 1.5796 - 1.26675
= 0.3128
The change in Casio's net worth would be:
Change in Value of Net Worth = [-DA * * A] - [- DL * * L]
If interest rates fall from 5 percent to 4.5 percent,
Change in NW =
= + $7,447.16
7-13. Watson Thrift Association reports an average asset duration of 7 years, an average liability duration of 3.25 years. In its latest financial report, the association recorded total assets of $1.8 billion and total liabilities of $1.5 billion. If interest rates began at 6 percent and then suddenly climbed to 7.5 percent, what change (in percentage terms) wills this bond's price experience if market interest rates change as anticipated?
The key formula is:
Change in net worth = [-DA * * A] - [- DL ** L]
For the change in interest rates from 6 to 7.5 percent, Watson's net worth will change to:
Change in Net Worth =
= -$178.30 million + $68.99 million
= -$109.31 million
On the other hand, if interest rates decline from 6 to 5 percent we have:
Change in Net Worth =
= + $118.87 mill. - $45.99 mill.
= + $72.88 million
7-14. A financial firm holds a bond in its investment portfolio whose duration is 13.5 years. Its current market price is $950. While market interest rates are currently at 7 percent for comparable quality securities, a decrease in interest rates to 6.75 percent is expected in the coming weeks. What changes (in percentage terms) will this bond's price experience if market interest rates change as anticipated?
Solution:
This bond's price will increased by 3.15 percent or its price will rise to $971.965.
7-15. A savings bank's weighted average asset duration is 10 years. Its total liabilities amount to $925 million, while its assets total 1 billion dollars. What is the dollar-weighted duration of the bank's liability portfolio if it has a zero leverage - adjusted duration gap ?
Given the bank has a duration gap equal to zero:
Duration Gap =
7-16 Blue Moon National Bank holds assets and liabilities whose average durations and dollar amounts are as shown in this table:
Asset and Liability Items
Avg.Duration(yrs)
$ Amount
Investment Grade Bonds
12.00
$65.00
Commercial Loans
4.00
$400.00
Consumer Loans
8.00
$250.00
Deposits
1.10
$600.00
Nondeposit Borrowings
0.25
$50.00
What is the weighted average duration of New Phase's asset portfolio and liability portfolio? What is the leverage-adjusted duration gap?
7-17 A government bond currently carries a yield to maturity of 7 percent and a market price of $1161.68. If the bond promises to pay $100 in interest annually for five years, what is its current duration?
7-18 Clinton National Bank holds $15 million in government bonds having a duration of 7 years. If interest rates suddenly rise from 6 percent to 7 percent, what percentage change should occur in the bonds' market price?
Or -6.6 percent
