Ch05-Interest Rate Risk Management

Chapter 05: Interest Rate Risk Management

Lectured by: PEOU Rithjayasedh, MFin (Melb)

Content

�  Interest Risk Measurement

�  Maturity Model (Homework)

�  Duration Model

�  Repricing Model

�  Convexity

�  Managing Interest Rate Risk

2

Introduction

�  MM theory suggests that: “The firm should find the NPV of the prospective real asset first as if it is being financed exclusively by stockholders; and if it is positive, then the appropriate asset financing should take advantage of existing financial market imperfections.”

�  This resource allocation process seems to work well with a non-financial firm, but not a financial firm or a bank.

� Why?

3

Introduction �  The bank’s assets are as much financial as its liabilities. But

more fundamentally, as we saw in Chapter 2, the basic premise for the existence of banks is rooted in financial market inefficiencies, and this premise is at odds with the MM theory.

�  Indeed, such inefficiencies signify a joint consideration of investment and financing decisions, and the computation of the cost of capital (as suggested by, for instance, MM) as a cutoff rate becomes less meaningful for a bank than for the non-financial firm.

�  Furthermore, any investment project cannot be considered in isolation or by itself. Instead, its impact on the owners must be analyzed in the context of other investments of the firm.

4

Introduction �  Bank management practice that focuses on joint consideration

of (a) investment-financing decisions, and (b) an investment proposal with existing investments (rather than the proposal in itself ) is consistent with the above conceptual implications.

�  Hence, this chapter concentrates on bank management practice that emphasizes asset-liability management, rather than consideration of a single project.

�  In turn, the asset-liability management practice has highlighted the risk (rather than return) dimension. Its objective has been to optimize three components of risk: liquidity risk, credit risk, and interest rate risk.

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Interest Risk Measurement

�  Given the mix of a bank’s assets and liabilities, interest rate changes may raise or lower the spread or net interest income as well as the market value of assets and liabilities, and thereby affect the equity value.

�  Interest Rate Risk is defined as the risk incurred by a financial institution when the maturities of its assets and liabilities are mismatched.

�  Interest rate risk is primarily measured in terms of the volatility of (a) net interest income, or (b) the bank’s value due to changes in the interest rates.

6

Interest Risk Measurement

�  There are three conventional methods for measuring and managing interest rate risk. These are maturity model, duration model and repricing model.

�  However, the two commonly employed conventional methods for measuring and managing interest rate risk are the gap/repricing models and duration models.

�  The gap model focuses on net interest income as the target measure of bank performance, while the duration models target primarily the market value of bank equity

7

Repricing Model �  (Funding) Gap model can be called “the repricing model.”

�  The repricing model is essentially a book value accounting cash flow analysis on the repricing gap between the interest earned on an FI’s assets and the interest paid on its liabilities over some particular period.

�  The objective of this approach is to stabilize or increase the expected net interest income (NII).

�  At a given point, NII is managed by dividing the planning period into several intervals, and for each interval a gap is determined, where the gap is the difference between the dollar amount of rate-sensitive assets (RSAs) and the dollar amount of rate-sensitive liabilities (RSLs).

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Repricing Model

�  The US Federal Reserve requires US commercial banks to report quarterly (on schedule RC-J of the call report) the repricing gaps for assets and liabilities with these maturities: (1) One day,

(2) More than one day to three months, (3) More than three months to six months, (4) More than six months to twelve months,

(5) More than one year to five years, and (6) More than five years.

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Repricing Model

�  Rate sensitivity in this context means the time to repricing of the asset or liability. More simply it means how long the FI manager has to wait to change the posted interest rates on any asset or liability.

�  While the cumulative gap over the whole balance must by definition be zero, the advantage of the repricing model lies in its information value and its simplicity in pointing to an FI’s net interest income exposure (or earnings exposure) to interest rate changes at different maturity buckets.

10

Repricing Model

�  Specifically, let: �  ΔNIIi = Change in NII in the ith bucket. �  GAPi = The dollar sizze of the gap between the

book value of assets and liabilities in maturity bucket i.

�  ΔRi = The change in the level of interest rates impacting assets and liabilities in the ith bucket.

�  Formula: ΔNIIi = GAPi x ΔRi = (RSAi – RSLi) x ΔRi

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Repricing Model

12

Assets Liabilities Gaps

(1) One day $20 $30 -10

(2) More than one day to three months 30 40 -10

(3) More than three months to six months 70 85 -15

(4) More than six months to twelve months 90 70 +20

(5) More than one year to five years 40 30 +10

(6) More than five years 10 5 +5

$260 $260 0

Repricing Model

�  The one-day gap indicates a negative $10 million difference between assets and liabilities being repriced in one day.

�  Assets and liabilities that are repriced each day are likely to be interbank borrowings and loans or repurchase agreements.

�  Thus, this gap indicates that a rise in the overnight rate would lower the bank’s net interest income because the bank has more rate sensitive liabilities and assets in this bucket.

13

Repricing Model

�  In the first bucket, the gap is negative $10 million and the overnight rate rises by 1 percent so that the annualized change in the bank’s future net interest income is:

ΔNIIi = GAPi x ΔRi

ΔNIIi= (-$10 million) x 0.01 = -$100,000

�  The financial institution manager can also estimate cumulative gaps (CGAP) over various repricing categories or buckets.

14

Repricing Model

�  A common cumulative gap of particular interest is the one-year repricing gap estimated from the table above as:

CGAP = (-$10) + (-$10) + (-$15) + $20 = -$15

�  If ΔRi is the average rate change affecting assets and liabilities that can be repriced within a year, the cumulative effect on the bank’s net interest income is:

ΔNIIi = CGAP x ΔRi = (-$15) x (0.01) = -$150,000

15

Repricing Model

�  Bank management uses the above gap information against expectations of interest rate changes either to hedge net interest income or to speculatively change the size of the gap for each time interval.

�  Hedging removes the volatility of net interest income by either changing the dollar amount of assets and liabilities sensitive to interest rate changes or using less traditional instruments such as forwards, futures, option contracts, and interest rate swaps.

16

Repricing Model

�  Speculation focuses on improving profitability in the wake of the anticipated interest rate change. If the anticipated change does not materialize, profitability is likely to worsen.

�  For example, if management expects an interest rate increase in a given time interval, it may move its gap in the positive direction, that is, decrease the maturity of its assets and/or increase the maturity of its liabilities belonging to longer time intervals.

17

Repricing Model

18

Repricing Model

�  Strength of Repricing Model

�  Its calculations are easy.

�  Its results are readily understandable.

�  Many asset/liability software programs are available to produce a gap report and analyze a bank’s general interest rate sensitivity.

19

Repricing Model �  Weakness of Repricing Model

�  It ignores the market value effect.

�  It ignores the time value of money within each interval; thus assets and liabilities may mature at the “front” or the “back” of an interval and are still lumped together without differentiation within that interval.

�  It assumes a parallel shift in the term structure of interest rates.

�  It ignores the problem of runoffs, which is periodic cash flow of interest and principal amortization payments on long-term assets.

20

Duration Model �  Duration is the weighted-average time to maturity of a series of

cash flows, using the relative present values of the cash flows as the weights.

�  A general formula for duration

�  Where:

�  CFt = Cash flow received on the security at end of period t

�  N = The last period in which the cash flow is received

�  DFt = The discount factor = (1 / (1+R)t, where R is the yield or current level of interest rates in the market

�  PVt = The present value of the cash flow at the end of period t, which equals CFt x DFt

21

D =CFt

t=1

N

∑ ×DFt × t

CFtt=1

N

∑ ×DFt=

PVtt=1

N

∑ × t

PVtt=1

N

∑

5.1.2. Duration Gap Analysis

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t CFt DFt PVt PVt x t

Half a year 40 0.9434 37.74 18.87

One year 40 0.8900 35.60 35.60

One year and a half 40 0.8396 33.58 50.37

Two years 1,040 0.7921 823.78 1,647.56

930.70 1,752.40

D =

1, 752.40930.70

=1.88years

�  For example:

�  Suppose the annual coupon rate is 8 percent, the face value is $100, and the annual yield to maturity, R, is 12 percent.

�  See table below for the calculation of the duration of a two-year bond.


�  The Economic Meaning of Duration

�  Duration is the a DIRECT measure of the interest rate sensitivity or elasticity of an asset or liability.

�  In other words, the larger the numerical value of D that is calculated for an asset or liability, the more sensitive the price that asset or liability is to changes or shocks in interest rates.

�  Formula:

�  Meaning: The economic interpretation of the Equation is that the number D is the interest-elasticity or sensitivity of the security’s price to small interest rate change.

23

dPP= −D dR

1+ R"

#$

%

&' or dP

P= −D dR

1+ 12R

"

#

$$$

%

&

'''


�  Immunizing the whole Balance Sheet of an FI

�  To estimate the overall duration gap, we determine first the duration of an FI’s asset portfolio and the duration of its liability. These can be calculated as:

�  And:

�  Where:

24

DL = X1LD1L + X2LD2

L +…+ XnLDnL

⇒ΔLL= −DL

ΔR(1+ R)

⇒ΔL = −DL ⋅L ⋅ΔR(1+ R)

X1 j + X2 j +…+ Xnj =1 and j = A,L

DA = X1AD1A + X2AD2

A +…+ XnADnA

⇒ΔAA= −DA

ΔR(1+ R)

⇒ΔA = −DA ⋅A ⋅ΔR(1+ R)



�  From the Balance Sheet:

25

A = L +EAnd: ΔA = ΔL +ΔEOr: ΔE = ΔA−ΔL

⇒ΔE = −DA ⋅A ⋅ΔR

(1+ R)%

&'

(

)*− −DL ⋅L ⋅

ΔR(1+ R)

%

&'

(

)*

⇒ ΔE = −DA ⋅A+DL ⋅L[ ] ΔR(1+ R)

⇒ΔE = − DA ⋅A−DL ⋅L[ ] ΔR(1+ R)

⇒ΔE = − DA ⋅AA+DL ⋅

LA

%

&'(

)*⋅A ⋅ ΔR

(1+ R)

Duration Gap Model: ΔE = − DA +DLk[ ] ⋅A ⋅ ΔR(1+ R)



�  From the Balance Sheet:

�  This gap is measured in years and reflects the degree of duration mismatch in an FI’s balance sheet. Specifically, the larger this gap in absolute terms, the more exposed the FI is to interest rate shocks.

�  .

�  The size of the FI, A: The larger the scale of the FI, the larger the dollar size of the potential net worth exposure from any given interest rate shock.

�  The larger the shock, the greater the FI’s exposure. 26

Duration Gap Model: ΔE = − DA +DLk[ ] ⋅A ⋅ ΔR(1+ R)

The leverage adjusted duration gap = DA −DLk

The size of the interest rate shock = ΔR 1+ R( )


�  Example:

�  The following is the ABC Bank’s simplified balance sheet:

A = $100 million; L = $80 million; E = $20 million

�  Suppose that: Asset Duration (DA) = 6; Liability Duration (DL) = 4; Interest rate change (Δr) = 1%; Current Interest Rate (r) = 10%

�  The adjusted duration gap will be:

�  The change in the bank’s equity value will be as follows:

�  A 1% interest rate increase will reduce the equity value by $2.55 mln.

27

28

Repricing Vs. Duration Model

�  A comparison between the duration and gap analyses is instructive:

�  A positive gap or d-gap responds favorably, for instance, to a positive interest rate change.

�  Duration analysis concentrates on the stockholders’ equity value; the gap approach only looks at net earnings for stockholders.

�  Duration measures are additive. Hence the bank can match assets with liabilities, instead of matching individual accounts.

�  The d-gap method takes a longer-term viewpoint.

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Convexity �  In the duration and gap analysis, we focused on interest rate risk that

would arise from the parallel shift of the term structure of interest rate.

�  In many instances, the term structure does not have a parallel shift. In fact, the slope of the term structure changes at different rates because the change in interest rates for different maturities is not constant

�  Convexity reflects the rate of change in the bond price increase (decrease) as a result of the rate of change in the interest rate decrease (increase).

�  A larger value of convexity suggests greater sensitivity of the bond price to a given change in its interest rate.

�  A smaller convexity value means less bond price sensitivity to its interest rate change..

30

Managing Interest Rate Risk

�  Basic immunization procedure in gap versus d-gap models

�  Gap Model (Gap = o)

�  Calculate periodic gaps over short time intervals.

�  If the gap is positive, rate-sensitive assets should be decreased, or rate-sensitive liabilities should be increased, through a combination of actions such as the following:

�  Match funding of re-priceable assets with similar re-priceable liabilities so that periodic gaps approach zero.

�  Match funding of long-term assets with short term, interest-sensitive liabilities in the positive-gap slots.

�  Use off-balance sheet transactions, such as financial futures and interest rate swaps, to construct “synthetic” securities for hedging purposes.

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�  Basic immunization procedure in gap versus d-gap models (Cont’d)

�  Duration Model (D-gap = 0)

�  In the duration model, calculation of the adjusted d-gap is required. If it is positive, the duration of assets is greater than the leverage-weighted duration of liabilities. Hence, a combination of strategies is possible:

�  Decrease the duration of assets.

�  Increase the duration of liabilities.

�  Increase debt ratio.

32


�  Strategies of interest rate risk management can be implemented by two categories of actions: balance sheet related; and those belonging to the off-balance sheet category.

�  Balance sheet-related actions attempt to change the bank’s interest rate sensitivity by altering various components of the assets and liabilities on the balance sheet.

�  These actions are basic tools for interest rate risk management and have been extensively used by banks.

�  Off-balance sheet strategies involve more recent financial instruments, such as financial futures and interest rate swaps.

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5.4. Managing Interest Rate Risk

34

End of chapter 05!

Lectured by: PEOU Rithjayasedh, MFin (Melb)

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Ch05-Interest Rate Risk Management