Chapter 14 - McGraw Hill Higher Education

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Chapter 14
Interest Rate
Risk Measurement
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Learning Objectives
• Describe interest rate risk and its forms
• Identify the components of an interest rate
risk exposure management system
• Explain the interest rate risk management
principle of asset repricing before liabilities
• Describe the interest rate risk measurement
models repricing gap analysis, duration
(and convexity)
• Outline internal and external interest rate
risk management techniques
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Chapter Organisation
14.1
14.2
14.3
14.4
Introduction
Interest Rate Risk
Exposure Management Systems
Assets Repriced Before Liabilities
Principle (ARBL)
14.5 Pricing Financial Securities
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Chapter Organisation (cont.)
14.6
14.7
14.8
14.9
Repricing Gap Analysis
Duration
Convexity
Interest Rate Risk Management
Techniques
14.10 Summary
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14.1 Introduction
• Chapter 13 considered the
– Macro-economic context of interest rates
– Loanable funds approach to interest rate
determination
– A number of theories that explain the shape of
the yield curve
• Unknown is the timing and extent of
interest rate changes
• Interest rate risk needs to be managed
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Chapter Organisation
14.1
14.2
14.3
14.4
Introduction
Interest Rate Risk
Exposure Management Systems
Assets Repriced Before Liabilities
Principle (ARBL)
14.5 Pricing Financial Securities
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14.2 Interest Rate Risk
• Interest rate risk takes two forms
– Reinvestment risk

–
Impact of a change in interest rates on a firm’s future
cash flows
Price risk


Impact of a change in interest rates on the value of a
firm’s assets and liabilities
An inverse relationship exists between interest rates
and security prices i.e. a rise in interest rates results in
a fall in the value of an asset or liability, or vice versa
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14.2 Interest Rate Risk (cont.)
• Interest rate risk exposures may also be
described as
–
Direct

–
Reinvestment and price risk
Indirect

Relate to the future actions of market participants e.g.
a rise in interest rates causes borrowers to seek new
loans elsewhere and/or repay existing loans
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14.2 Interest Rate Risk (cont.)
• Interest rate risk exposures may also be
described as (cont.)
–
Basis

Occurs when pricing differentials exist between
markets e.g. futures market and the underlying
physical market
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Chapter Organisation
14.1
14.2
14.3
14.4
Introduction
Interest Rate Risk
Exposure Management Systems
Assets Repriced Before Liabilities
Principle (ARBL)
14.5 Pricing Financial Securities
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14.3 Exposure Management
Systems
• An exposure management system involves
structured procedures that enable a firm to
effectively measure and manage risk,
including
–
–
–
Forecasting
Strategies and techniques
Management and reporting systems
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14.3 Exposure Management
Systems (cont.)
• Forecasting
– A firm needs to understand factors that will
impact upon risk exposures and its environment

A firm must know the current structure of its balance
sheet and forecast future changes in its assets,
liabilities and equities with regard to
•
•
•
Future business activity growth
Future interest rates
Future financing needs, and use of debt financing
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14.3 Exposure Management
Systems (cont.)
• Strategies and techniques
– The strategies and techniques used relate to the
types of interest cash flows associated with a
firm’s assets and liabilities, and include

Monitoring and adjusting the maturity structure of
assets and liabilities, taking into account the term
structure of interest rates
•
Maturity structure is the relative proportion of assets
and liabilities maturing at different time intervals
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14.3 Exposure Management
Systems (cont.)
• Strategies and techniques (cont.)
– The strategies and techniques used relate to the
types of interest cash flows associated with a
firm’s assets and liabilities, and include (cont.)

Specified proportions of fixed-interest versus floatinginterest debt
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14.3 Exposure Management
Systems (cont.)
• Strategies and techniques (cont.)
– The strategies and techniques used relate to the
types of interest cash flows associated with a
firm’s assets and liabilities, and include (cont.)

Liability diversification—where a firm raises funds from
a range of different sources, thereby reducing its
exposure to potential interest changes in a particular
market
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14.3 Exposure Management
Systems (cont.)
• Strategies and techniques (cont.)
– Two broad interest rate risk management
techniques, internal and external methods, are
discussed later
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14.3 Exposure Management
Systems (cont.)
• Management reporting
– Policies and procedures need to provide clear
instructions on





The type of information to be reported
Frequency of reports
Report hierarchy
Delegation and staff responsible to act on the reports
The need for audit and review of policies and
procedures
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Chapter Organisation
14.1
14.2
14.3
14.4
Introduction
Interest Rate Risk
Exposure Management Systems
Assets Repriced Before Liabilities
Principle (ARBL)
14.5 Pricing Financial Securities
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14.4 Assets Repriced Before
Liabilities Principle (ARBL)
• Repricing of assets and liabilities is essential
in interest rate risk measurement and
management
–
Positive ARBL gap exists when assets are
repriced before liabilities

For e.g., if interest rates are forecast to rise
•
•
A bank increases the interest rate on loans (assets)
before increasing the rate on deposits (liabilities)
A firm increases the price of its goods before or at the
same time as interest rates rise on its loan
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14.4 Assets Repriced Before
Liabilities Principle (ARBL)
(cont.)
• Repricing of assets and liabilities is essential
in interest rate risk measurement and
management (cont.)
–
Negative ARBL gap exists when liabilities are
repriced before assets

For e.g., if interest rates are forecast to fall
•
A bank lowers the interest rate on deposits (liabilities)
before lowering the rate on loans (assets)
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14.4 Assets Repriced Before
Liabilities Principle (ARBL)
(cont.)
• A firm should measure its ARBL interest
rate sensitivity of its balance sheet assets
and liabilities over a range of planning
periods
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Chapter Organisation
14.1
14.2
14.3
14.4
Introduction
Interest Rate Risk
Exposure Management Systems
Assets Repriced Before Liabilities
Principle (ARBL)
14.5 Pricing Financial Securities
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14.5 Pricing Financial
Securities
• The effect of interest rate risk on the price
of discount securities and fixed-interest
corporate/government bonds can be
demonstrated using calculations discussed
in Chapters 9, 10 and 12
face value  365
Price 
 yield

365  
 days to maturity 
 100

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(14.1)
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14.5 Pricing Financial
Securities (cont.)
–
Example 1: A company is to issue a ninety-day bank bill, with a
face value of $500,000 yielding 9.5 per cent per annum. What
amount will the company raise on the issue?
$500 000  365
Price 
365  (0.0950 90)
182 500 000

373.55
 $488 555.75
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14.5 Pricing Financial
Securities (cont.)
–
Example 1 (cont.): If the company has a rollover facility in place
for this bill, it is exposed to interest-rate risk at the next
repricing date, the rollover date, in ninety-days time. If the yield
at the next rollover date is 9.25 per cent per annum the
company will xxx.
$500 000  365
Price 
365  (0.0925  90)
182 500 000

373.325
 $488 850.20
–
In this example the cost of borrowing has fallen by $294.45.
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Chapter Organisation (cont.)
14.6
14.7
14.8
14.9
Repricing Gap Analysis
Duration
Convexity
Interest Rate Risk Management
Techniques
14.10 Summary
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14.6 Repricing Gap Analysis
• Repricing gap analysis is the monitoring of
the interest rate sensitivities of assets and
liabilities over specified planning periods
–
Interest rate sensitivity relates to the repricing
of an asset or liability within the planning period

The longer the planning period, the more likely a
security is to be rate sensitive
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14.6 Repricing Gap Analysis
(cont.)
• The repricing gap is rate sensitive assets
minus rate sensitive liabilities
–
Three groupings of assets and liabilities assist in
determining the repricing gap



Interest-sensitive assets financed by interest-sensitive
liabilities
Fixed-interest assets financed by fixed-interest
liabilities and equities
Interest-sensitive assets financed by fixed-interest
liabilities
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14.6 Repricing Gap Analysis
(cont.)
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14.6 Repricing Gap Analysis
(cont.)
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14.6 Repricing Gap Analysis
(cont.)
Change in profitability = Gap x change in rates x period (14.3)
= $15 billion x 0.005 x 1
= $75 million
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Chapter Organisation (cont.)
14.6
14.7
14.8
14.9
Repricing Gap Analysis
Duration
Convexity
Interest Rate Risk Management
Techniques
14.10 Summary
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14.7 Duration
• Duration is another tool for the
measurement and management of interest
rate risk exposures
–
–
It is a measure in years, that considers the
timing and present values of cash flows
associated with a financial asset or liability
Duration is calculated as the weighted average
time over which cash flows occur, where
weights are the relative present values of the
cash flows
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14.7 Duration (cont.)
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14.7 Duration (cont.)
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14.7 Duration (cont.)
• Duration can also be used to determine the
dollar impact of a change in interest rates
on the price of a security using equation
14.5
C ( n)

(1  i )
D
C

(1  i )
N
i
n
t 1
N
t
t 1
n
(14.5)
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14.7 Duration (cont.)
• Duration can also be used to determine the
dollar impact of a change in interest rates
on the price of a security using equation
14.5
(14.5 [cont.])
where :
C  dollar value of cash flows at time t
t
n  the number of periods until the cash flow is due
i  current maket yield expressed as a decimal
N  number of cash flows
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14.7 Duration (cont.)
• The duration of a portfolio of securities is
the weighted duration of each asset or
liability in the portfolio
–
Given a forecasted change in interest rates, the
dollar change in the equity position of a firm can
be calculated from equation 14.6
 Δr% 
% price  - duration

 (1  r ) 
where r is the current yield before
the interest rate changes, or is forecast to change.
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(14.6)
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14.7 Duration (cont.)
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Chapter Organisation (cont.)
14.6
14.7
14.8
14.9
Repricing Gap Analysis
Duration
Convexity
Interest Rate Risk Management
Techniques
14.10 Summary
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14.8 Convexity
• Convexity is curvature in the price/yield curve
–
–
This overcomes the limitation of the duration method
which reflects a linear relationship between yield and
price
Convexity is illustrated in the following example


A 2% interest rate change on one-year, two-year and threeyear bonds that have a face value of $1000 and pay a fixed
annual coupon of 8% p.a.
Figure 14.1 illustrates that the percentage change in price
relationships for the one, two and year bonds is not linear,
but convex
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14.8 Convexity (cont.)
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14.8 Convexity (cont.)
• Figure 14.2 indicates the difference in the price of
the following bond using the duration and
convexity approaches, assuming a forecast interest
rate rise of 2%
–
$1000 bond paying 5% coupon pa, maturing in four
years, currently yielding 5% p.a.
• The problem with duration can be compensated for
by adjusting for convexity
% price = - duration [r%] + 0.5(convexity)(r2)
(14.8)
(1+r)
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14.8 Convexity (cont.)
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Chapter Organisation (cont.)
14.6
14.7
14.8
14.9
Repricing Gap Analysis
Duration
Convexity
Interest Rate Risk Management
Techniques
14.10 Summary
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14.9 Interest Rate Risk
Management Techniques
• Interest rate risk management techniques
also include internal and external methods
–
Internal methods involve the restructuring of a
firm’s balance sheet and associated cash flows

Asset and liability portfolio restructuring
•
E.g. a funds manager sells part of its bond portfolio and
invests the funds in shares or property
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14.9 Interest Rate Risk
Management Techniques
(cont.)
• Interest rate risk management techniques
also include internal and external methods
(cont.)
–
Internal methods (cont.)

Asset and liability repricing
•
E.g. seek fixed-rate funds in periods when interest rates
are rising
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14.9 Interest Rate Risk
Management Techniques
(cont.)
• Interest rate risk management techniques
also include internal and external methods
(cont.)
–
Internal methods (cont.)

Cash flow timing
•
Change the timing of cash flows to minimise the effect
of interest rate changes or to take advantage of
forecast rate movements by
• E.g. switching from one security to another with
different frequency of interest payments
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14.9 Interest Rate Risk
Management Techniques
(cont.)
• Interest rate risk management techniques
also include internal and external methods
(cont.)
–
Internal methods (cont.)

Reduced reliance on interest rates
•
E.g. introduction of other fees on loans by a bank
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14.9 Interest Rate Risk
Management Techniques
(cont.)
• Interest rate risk management techniques
also include internal and external methods
(cont.)
–
Internal methods (cont.)

Prepayment and pre-redemption conditions
•
E.g. early payment penalties to discourage borrowers
repaying floating-rate loans early in periods of rising
interest rates
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14.9 Interest Rate Risk
Management Techniques
(cont.)
• Interest rate risk management techniques
also include internal and external methods
(cont.)
–
External methods

External methods involve strategies outside the
balance sheet
•
Primarily involve the use of derivative products allowing
a party to lock in a price today that will apply at a
specified future date i.e. futures contracts, forward rate
agreements, interest options and swaps
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Chapter Organisation (cont.)
14.6
14.7
14.8
14.9
Repricing Gap Analysis
Duration
Convexity
Interest Rate Risk Management
Techniques
14.10 Summary
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14.10 Summary
• Interest rate risk is the sensitivity of the value of
balance sheet assets and liabilities and cash flow to
movements in interest rates
• Interest rate risk exists in the form of reinvestment
risk and price risk
• A firm must establish an effective interest rate
exposure management system
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14.10 Summary (cont.)
• ARBL is a basic principle of interest rate risk
management
• Models for measuring interest rate risk include
repricing gap analysis, duration (and convexity)
• A range of internal and external interest rate risk
management techniques exist
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