Chapter 7
ASSET LIABILITY MANAGEMENT: THE CONCEPT OF DURATION AND MANAGING A BANK’S DURATION GAP
Goal of this Chapter: To examine the concept of duration and to e how bankers u duration analysis to offt the potentially damaging effects of rising or falling market interest rates.
Key Terms Prented in this Chapter
Duration Portfolio Immunization
Duration Gap Convexity
Chapter Outline
I. Introduction: The Drawbacks of IS Gap Management and the Need for Duration II. The Concept of Duration
A.Definition of Duration
B.Calculation of Duration
C.Net Worth and Duration
D.Price Risk and Duration
E.Convexity and Duration
III. Using Duration to Hedge Against Interest-Rate Risk
A.Duration Gap
1.Dollar Weighted Duration of Asts
2.Dollar Weighted Duration of Liabilities
3.Positive Duration Gap
4.Negative Duration Gap
B.Change in the Bank’s Net Wo rth
IV. Limitations of Duration Gap Management
V. Summary of the Chapter
Concept Checks
7-1. What is duration?
Duration is a value-weighted measure of the maturity of a curity or other
income-generating ast that takes into consideration the amount and timing of all cash flows expected from the ast
7-2. How is a bank's duration gap determined?
A bank's duration gap is determined by taking the difference between the duration of a bank's asts and t he duration of its liabilities. The duration of the bank’s asts can be
determined by taking a weighted average of the duration of all of the asts in the bank’s portfolio. The weight is the dollar amount of a particular type of ast out of the total dollar amount of the asts of the bank. The duration of the liabilities can be determined in a similar manner.
7-3 What are the advantages of using duration as an ast-liability management tool as oppod to interest-nsitive gap analysis?
Interest-s ensitive 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 sin gle number which tells the bank their overall exposure to interest rate risk.
7-4 How can you tell you are fully hedged using duration gap analysis?
You are fully hedged when the dollar weighted duration of the asts 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 cour, becau the bank usually has more asts than liabilities the duration of the liabilities needs to be adjusted by the ratio of total liabilities to total asts to be entirely correct.
7-5 What are the principal limitations of duration gap analysis? Can you think of some ways of reducing the impact of the limitations?
There are veral limitations with duration gap analysis. It is often difficult to find asts and liabilities of the same duration to fit into the bank’s portfolio. In addition, some
accounts such as deposits and others don’t have well defined patterns of cash flows which makes it difficult to calculate a duration for the accounts. Duration is also affected by prepayments by customers as well as default. 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.
7-6. Suppo a bank has an average ast duration of 2.5 years and an average liability duration of 3.0 years. If the bank holds total asts of $560 million and total liabilities of $467 million, does it have a significant duration gap? If interest rates ri, what will happen to the value of the bank's net worth?
Duration Gap = D A – D L * Asts s Liabilitie = 2.5 yrs. – 3.0 yrs. ⎪⎭
⎫ ⎝⎛million $560million $467 = 2.5 years – 2.5018 years
= -0.018 years
This bank has a very slight negative duration gap; so small in fact that we could consider it insignificant. If interest rates ri, the bank's liabilities will fall slightly more in value than its asts, resulting in a small increa in net worth.深圳英语培训
7-7. Stilwater Bank and Trust Company has an average ast duration of 3.25 years and an average liability duration of 1.75 years. Its liabilities amount to $485 million, while its asts total $512 million. Suppo that interest rates were 7 percent and then ri 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 StiIwater's duration gap. This is:
Duration Gap = 3.25 yrs. – 1.75 yrs * mill.
$512mill. $485= + 1.5923 years
Then, the change in net worth if interest rates ri from 7 percent to 8 percent will be: Change in NW = ⎥⎦
⎤⎢⎣⎡++⎥⎦⎤⎢⎣⎡++mill. x$485.07)(1.01 x yrs. 1.75- - mill $512x .07)(1.01 x yrs. 3.25-
= $7.62 million.
Problems
7-1. Casio Merchants and Trust Bank, N.A., has a portfolio of loans and curities expected to generate cash inflows for the bank as follows:
Expected Cash Receipts Period in Which Receipts Are Expected
$1,385,421 Current year
ability
746,872 Two years from today
bigman
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 Payments Period in Which Payments Will be Made
$1,427,886 Current year
蔗糖的化学式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 above cash flows is 8 percent, what is the duration of the bank's portfolio of earning asts 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 ri? If interest rates fall? Given the size of the duration gap you have calculated, what type of hedging should the bank engage in? Plea be specific about the hedging transactions that are needed and their expected effects.
Solution:
Casio has an ast duration of:
$1,385,421 *1 + $746,872 * 2 + $341,555 * 3 + $62,482 * 4 + $9,871 * 5
(1 + 0.08)1 (1 + 0.08)2 (1 + 0.08)3 (1 + 0.O8)4 (1 + 0.O8)5
D A = $1,385,421 + $746,872 + $341,555 + $62,482 + $9,871
大连英语培训(1 + 0.08)1 (1 + 0.08)2 (1 + 0.08)3 (1 + 0.08)4 (1 + 0.08)5
=$3,594,1481 / $2,246,912 = 1.5996 years
Casio has a liability duration of:
$1,427,886 * 1 + $831,454 * 2 + $123,897 * 3 + $1,005 * 4
(1 + 0.08)1 (1 + 0.08)2 (1 + 0.08)3 (1 + 0.08)4
D L=
$1,427,886 + $831,454 + $123,897 + $1,005
(1 + 0.08)1 (1 + 0.08)2 (1 + 0.08)3 (1 + 0.08)4
= $3,045,808 / $2,134,047 = 1.4272 years
howfarCasio's Duration Gap = Ast Duration - Liability Duration = 1.5996 - 1.4272 = 0.1724 years.
Becau Casio's Ast Duration is greater than its Liability Duration, the bank has a positive duration gap, which means that the bank's total returns will decrea if interest rates ri becau the value of the liabilities will decline by less than the value of the asts. 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 ca, the value of the asts will ri by a greater amount than the value of the liabilities.
Given the magnitude of the duration gap, the management of Casio Merchants and Trust Bank needs to do a combination of things to clo its duration gap between asts and liabilities. It probably needs to try to shorten ast duration, lengthen liability duration, and u financial futures or options to deal with whatever ast-liability gap exists at the moment. The bank may want to consider curitization or lling some of its asts, reinvesting the cash flows in maturities that will more cloly 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 cloly match its ast maturities. Alternative Scenario 1:
Given: The discount rate applicable to Casio's cash inflows and outflows falls to 6 percent. How does
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the duration of its earning asts and liabilities change? How does this change affect the bank's nsitivity to interest rate movements?
Solution:
Casio now has an ast duration of:
$1,385,421 * 1 + $746,872 * 2 + $341,555 * 3 + $62,482 * 4 + $9,871 * 5
(1 + 0.06)1 (1 + 0.06)2 (1 + 0.06)3 (1 + 0.06)4 (1 + 0.06)5
D A =
$1,385,421 + $746,872 + $341, 555 + $62,482 + $9,871
(1 + 0.06)1 (1 + 0.06)2 (1 + 0.06)3 (1 + 0.06)4 (1 + 0.06)5
= $3,731,603 / $2,315,358 = 1.6117 years
ielts是什么意思
Casio now has a liability duration of:
$1,427,886 * 1 + $831,454 * 2 + $123,897 *3 + $1,005 * 4
(1 + 0,06)1 1 + 0.06)2 (1 + 0.06)3 (1 + 0.06)4
D L=
$1,427,886 + $831,454 + $123,897 + $1,005
(1 + 0.06)1 (1 + 0.06)2 (1 + 0.06)3 (1 + 0.06)4
清白的意思= $3,142,308 / $2,191,876 = 1.4336 years
Both the Ast Duration and the Liability Duration increa with the decline in the discount rate, with the Ast Duration increasing by more than the Liability Duration. The Duration Gap increas from 0.1724 years to 0.1781 years, making Casio more nsitive to interest rate changes.
Alternative Scenario 2:
Given: The appropriate discount rate climbs to 10 percent.
What happens to the durations of Casio's earning asts and liabilities? How does the interest rate nsitivity of Casio's total return change as a result of this upward movement in the discount rate?
Solution:
滨才教育
Casio now has an ast duration of:
