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• In this case:

A*]i)(1

i[*DGAP- ΔEquity

91.12$000,1$*]10.1

01.[*1.42- ΔEquity

Duration Gap

TA

TL * D - D Dgap LA

An Immunized Portfolio

• To immunize the value of equity from rate changes in the example, the bank would need to:– decrease the asset duration by 1.42 years or – increase the duration of liabilities by 1.54

years– DA / ( TA/TL)

= 1.42 / ($920 / $1,000) = 1.54 years

1 Par Years Market$1,000 % Coup Mat. YTM Value Dur.

AssetsCash 100$ 100$ Earning assets

3-yr Commercial loan 700$ 12.00% 3 12.00% 700$ 2.696-yr Treasury bond 200$ 8.00% 6 8.00% 200$ 4.99 Total Earning Assets 900$ 11.11% 900$ Non-cash earning assets -$ -$

Total assets 1,000$ 10.00% 1,000$ 2.88

LiabilitiesInterest bearing liabs.

1-yr Time deposit 340$ 5.00% 1 5.00% 340$ 1.003-yr Certificate of deposit 300$ 7.00% 3 7.00% 300$ 2.816-yr Zero-coupon CD* 444$ 0.00% 6 8.00% 280$ 6.00 Tot. Int Bearing Liabs. 1,084$ 6.57% 920$ Tot. non-int. bearing -$ -$ Total liabilities 1,084$ 6.57% 920$ 3.11

Total equity 80$ 80$

Immunized Portfolio

DGAP = 2.88 – 0.92 (3.11) ≈ 0

1 Par Years Market$1,000 % Coup Mat. YTM Value Dur.

AssetsCash 100.0$ 100.0$ Earning assets

3-yr Commercial loan 700.0$ 12.00% 3 13.00% 683.5$ 2.696-yr Treasury bond 200.0$ 8.00% 6 9.00% 191.0$ 4.97 Total Earning Assets 900.0$ 12.13% 874.5$ Non-cash earning assets -$ -$

Total assets 1,000.0$ 10.88% 974.5$ 2.86

LiabilitiesInterest bearing liabs.

1-yr Time deposit 340.0$ 5.00% 1 6.00% 336.8$ 1.003-yr Certificate of deposit 300.0$ 7.00% 3 8.00% 292.3$ 2.816-yr Zero-coupon CD* 444.3$ 0.00% 6 9.00% 264.9$ 6.00 Tot. Int Bearing Liabs. 1,084.3$ 7.54% 894.0$ Tot. non-int. bearing -$ -$ Total liabilities 1,084.3$ 7.54% 894.0$ 3.07

Total equity 80.0$ 80.5$

Immunized Portfolio with a 1% increase in rates

Immunized Portfolio with a 1% increase in rates

• Equity changed by only $0.5 with the immunized portfolio versus $25.0 when the portfolio was not immunized.

• Why was the change not zero?

Book Value Market Value Book Yield Duration*

LoansPrime Based Ln $ 100,000 $ 102,000 9.00%Equity Credit Lines $ 25,000 $ 25,500 8.75% -Fixed Rate > I yr $ 170,000 $ 170,850 7.50% 1.1Var Rate Mtg 1 Yr $ 55,000 $ 54,725 6.90% 0.530-Year Mortgage $ 250,000 $ 245,000 7.60% 6.0Consumer Ln $ 100,000 $ 100,500 8.00% 1.9Credit Card $ 25,000 $ 25,000 14.00% 1.0Total Loans $ 725,000 $ 723,575 8.03% 2.6Loan Loss Reserve $ (15,000) $ 11,250 0.00% 8.0 Net Loans $ 710,000 $ 712,325 8.03% 2.5InvestmentsEurodollars $ 80,000 $ 80,000 5.50% 0.1CMO Fix Rate $ 35,000 $ 34,825 6.25% 2.0US Treasury $ 75,000 $ 74,813 5.80% 1.8 Total Investments $ 190,000 $ 189,638 5.76% 1.1

Fed Funds Sold $ 25,000 $ 25,000 5.25% -Cash & Due From $ 15,000 $ 15,000 0.00% 6.5Non-int Rel Assets $ 60,000 $ 60,000 0.00% 8.0 Total Assets $ 100,000 $ 100,000 6.93% 2.6

Savings Bank Value of Equity Market Value/Duration Report as of 12/31/06

Most Likely Rate Scenario-Base Strategy

Ass

ets

Book Value Market Value Book Yield Duration*

DepositsMMDA $ 240,000 $ 232,800 2.25% -Retail CDs $ 400,000 $ 400,000 5.40% 1.1Savings $ 35,000 $ 33,600 4.00% 1.9NOW $ 40,000 $ 38,800 2.00% 1.9DDA Personal $ 55,000 $ 52,250 8.0Comm'l DDA $ 60,000 $ 58,200 4.8 Total Deposits $ 830,000 $ 815,650 1.6TT&L $ 25,000 $ 25,000 5.00% -L-T Notes Fixed $ 50,000 $ 50,250 8.00% 5.9Fed Funds Purch - - 5.25% -NIR Liabilities $ 30,000 $ 28,500 8.0 Total Liabilities $ 935,000 $ 919,400 2.0

Equity $ 65,000 $ 82,563 9.9 Total Liab & Equity $ 1,000,000 $ 1,001,963 2.6

Off Balance Sheet Notionallnt Rate Swaps - $ 1,250 6.00% 2.8 50,000

Adjusted Equity $ 65,000 $ 83,813 7.9

Savings Bank Value of Equity Market Value/Duration Report as of 12/31/06

Most Likely Rate Scenario-Base Strategy

Liab

ilitie

s

Duration Gap for Savings Bank Equity

• Market Value of Assets– $1,001,963

• Duration of Assets– 2.6 years

• Market Value of Liabilities– $919,400

• Duration of Liabilities– 2.0 years

Duration Gap for Savings Bank Equity

• Duration Gap– = 2.6 – ($919,400/$1,001,963)*2.0

= 0.765 years

• Example:– A 1% increase in rates would reduce equity by

$7.2 million= 0.765 (0.01 / 1.0693) * $1,001,963

• Recall that the average rate on assets is 6.93%

Effective “Duration” of Equity

• By definition, duration measures the percentage change in market value for a given change in interest rates– Thus, a bank’s duration of equity measures

the percentage change in equity that will occur with a 1 percent change in rates:

• Effective duration of equity 9.9 yrs. = $8,200 / $82,563

Asset/Liability Sensitivity and DGAP

• Funding GAP and Duration GAP are NOT directly comparable– Funding GAP examines various “time buckets”

while Duration GAP represents the entire balance sheet.

• Generally, if a bank is liability (asset) sensitive in the sense that net interest income falls (rises) when rates rise and vice versa, it will likely have a positive (negative) DGAP suggesting that assets are more price sensitive than liabilities, on average.

Strengths and Weaknesses: DGAP and EVE-Sensitivity Analysis

• Strengths– Duration analysis provides a comprehensive

measure of interest rate risk– Duration measures are additive

• This allows for the matching of total assets with total liabilities rather than the matching of individual accounts

– Duration analysis takes a longer term view than static gap analysis

Strengths and Weaknesses: DGAP and EVE-Sensitivity Analysis

• Weaknesses– It is difficult to compute duration accurately– “Correct” duration analysis requires that each

future cash flow be discounted by a distinct discount rate

– A bank must continuously monitor and adjust the duration of its portfolio

– It is difficult to estimate the duration on assets and liabilities that do not earn or pay interest

– Duration measures are highly subjective

Speculating on Duration GAP

• It is difficult to actively vary GAP or DGAP and consistently win– Interest rates forecasts are frequently wrong– Even if rates change as predicted, banks

have limited flexibility in vary GAP and DGAP and must often sacrifice yield to do so

Gap and DGAP Management Strategies Example

• Cash flows from investing $1,000 either in a 2-year security yielding 6 percent or two consecutive 1-year securities, with the current 1-year yield equal to 5.5 percent.

0 1 2

$60 $60

Two-Year Security

0 1 2

$55 ?

One-Year Security & then another One-Year Security

Gap and DGAP Management Strategies Example

• It is not known today what a 1-year security will yield in one year.

• For the two consecutive 1-year securities to generate the same $120 in interest, ignoring compounding, the 1-year security must yield 6.5% one year from the present.

• This break-even rate is a 1-year forward rate, one year from the present:

• 6% + 6% = 5.5% + x so x must = 6.5%

Gap and DGAP Management Strategies Example

• By investing in the 1-year security, a depositor is betting that the 1-year interest rate in one year will be greater than 6.5%

• By issuing the 2-year security, the bank is betting that the 1-year interest rate in one year will be greater than 6.5%

Yield Curve Strategy• When the U.S. economy hits its peak, the

yield curve typically inverts, with short-term rates exceeding long-term rates.– Only twice since WWII has a recession not

followed an inverted yield curve

• As the economy contracts, the Federal Reserve typically increases the money supply, which causes the rates to fall and the yield curve to return to its “normal” shape.

Yield Curve Strategy• To take advantage of this trend, when the

yield curve inverts, banks could:– Buy long-term non-callable securities

• Prices will rise as rates fall

– Make fixed-rate non-callable loans• Borrowers are locked into higher rates

– Price deposits on a floating-rate basis– Lengthen the duration of assets relative to

the duration of liabilities

Interest Rates and the Business CycleThe general level of interest rates and the shape

of the yield curve appear to follow the U.S. business cycle.

In expansionary stages rates rise until they reach a peak as the Federal Reserve tightens credit availability.

Time

ExpansionContraction

Expansion

Long-TermRates

Short-TermRatesPeak

Trough

DATE WHEN 1-YEAR RATE FIRST EXCEEDS 10-YEAR RATE

LENGTH OF TIME UNTIL START OF NEXT RECESSION

Apr. ’68 20 months (Dec. ’69)Mar. ’73 8 months (Nov. ’73)Sept. ’78 16 months (Jan. ’80)Sept. ’80 10 months (July ’81)Feb. ’89 17 months (July ’90)Dec. ’00 15 months (March ’01)

The inverted yield curve has predicted the last five recessions

In contractionary stages rates fall until they reach a trough when the U.S. economy falls into recession.