copyright 2007 mcgraw-hill australia pty ltd ppts t/a mcgraths financial institutions, instruments...

Copyright 2007 McGraw-Hill Australia Pty Ltd PPTs t/a McGrath’s Financial Institutions, Instruments and Markets 5e by VineySlides prepared by Anthony Stanger

14-1

Chapter 14

Interest Rate

Risk Measurement


14-2

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• Revisit financial securities repricing and interest

rate risk• Describe the interest rate risk measurement

models, particularly repricing gap analysis, duration and convexity

• Outline internal and external interest rate risk management techniques


14-3

Chapter Organisation

14.1 Interest Rate Risk

14.2 Exposure Management Systems

14.3 Assets Repriced Before Liabilities Principle

(ARBL)

14.4 Pricing Financial Securities

14.5 Repricing Gap Analysis

14.6 Duration

14.7 Convexity

14.8 Interest Rate Risk Management Techniques

14.9 Summary


14-4


• Chapter 13 considered the– Macro-economic context of interest rates– Loanable funds approach to interest rate determination– Theories that explain the shape of the yield curve

• The timing and extent of interest rate changes is unknown

• Interest rate risk needs to be managed


14-5

14.1 Interest Rate Risk (cont.)

• 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


14-6

14.1 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

– Basis Occurs when pricing differentials exist between markets,

e.g. futures market and the underlying physical market


14-7





(ARBL)



14.6 Duration

14.7 Convexity


14.9 Summary


14-8


• An exposure management system involves structured procedures that enable a firm to effectively measure and manage risk, including– Forecasting– Strategies and techniques– Management reporting systems


14-9

14.2 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


14-10


• 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

Specified proportions of fixed-interest versus floating-interest debt, with remaining portion available to take advantage of forecast changes


14-11


• Strategies and techniques (cont.) 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

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


14-12


• Strategies and techniques (cont.)

Two broad interest rate risk management techniques are discussed later

• Internal methods• External methods


14-13


• 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


14-14





(ARBL)



14.6 Duration

14.7 Convexity


14.9 Summary


14-15


– Interest rate risk is the sensitivity of assets, liabilities and cash flows to changes in interest rates

– Assets repriced before liabilities (ARBL) is a risk management technique that ensures net margins and profitability are protected

– A firm should measure its ARBL interest rate sensitivity of its balance sheet assets and liabilities over a range of planning periods


14-16


– Positive ARBL gap exists when assets are repriced before liabilities and an organisation is able to benefit, e.g.

Interest rates are forecast to rise• A bank increases the interest rate received on loans (assets)

before increasing the rate paid on deposits (liabilities)• A company increases the price of its goods (assets) before or

at the same time as interest rates rise on its floating-rate loan (liability)


14-17

14.3 Assets Repriced Before Liabilities Principle (cont.)

– Negative ARBL gap exists when liabilities are repriced before assets, e.g.

Interest rates are forecast to fall• A bank lowers the interest rate paid on deposits (liabilities)

before lowering the rate received on loans (assets)

Interest rates are forecast to rise• A bank may implement strategies to reduce the negative ARBL

gap to a smaller level


14-18





(ARBL)



14.6 Duration

14.7 Convexity


14.9 Summary


14-19


• 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

maturity to days

100yield 365

365value facePrice

(14.1)


14-20

14.4 Pricing Financial Securities (cont.)

– Example 1: A company is to issue a 90-day bank bill with a face value of $500 000 yielding 9.5% per annum. What amount will the company raise on the issue?

555.75 $488373.55

000 500 18290)(0.0950 365

365000 $500Price


14-21

14.4 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, i.e. the rollover date in 90 days’ time. If the yield at the next rollover date is 9.25% per annum the company will raise:

– In this example the cost of borrowing has fallen by $294.45.

850.20 $488373.325

000 500 18290)(0.0925 365

365000 $500Price


14-22





(ARBL)



14.6 Duration

14.7 Convexity


14.9 Summary


14-23


– This is the monitoring of the interest rate sensitivities of assets and liabilities over specified planning periods

Interest rate sensitivity (or repricing gap) relates to the repricing of an asset or liability during a planning period

• Defined as rate-sensitive assets minus rate-sensitive liabilities

The longer the planning period, the more likely a security is to be rate sensitive

• e.g. a 90-day discount security is not interest rate sensitive over a 1-month planning period, but is over a 6-month planning period


14-24

14.5 Repricing Gap Analysis (cont.)

– Three groupings of assets and liabilities assist in determining the repricing gap

Interest-sensitive assets financed by interest-sensitive liabilities

• Are both sides of the balance sheet affected at the same time and to the same extent?

Fixed-rate assets financed by fixed-rate liabilities and equity• Are not exposed to interest rate risk during a planning period

as the cost of funds and return on funds is fixed

Rate-sensitive assets financed by fixed-rate liabilities or vice versa

• One side of the balance sheet is exposed to interest rate risk while the other is not


14-25



14-26



14-27


Change in profitability = Gap x change in rates x period (14.3)

= $15 billion x 0.005 x 1

= $75 million


14-28





(ARBL)



14.6 Duration

14.7 Convexity


14.9 Summary


14-29

14.6 Duration

• Duration is another tool for the measurement and management of interest rate risk exposures– It is a measure in years and 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


14-30

14.6 Duration (cont.)


14-31


– The duration calculations in Table 14.4 can also be achieved using Equation 14.5

N

t titC

N

t ti

ttC

D

1 )(1

1 )(1

)(

(14.5)

flows cash of number

decimal a as expressed yieldmaket current

due isflow cash the until periods of number the

time at flows cash of value dollar

:where

N

i

t

ttC


14-32


• Duration can also be used to ascertain the dollar impact of a change in interest rates on the value of a financial asset or security– The change in value will be proportional to the duration,

but in the opposite direction

change to forecast is or changes, rate interest the before

decimal, a as expressed yield,current the is

where

)(1

Δduration - price %Δ

r

r

r

(14.6)


14-33


– Example: Assume the funds manager has forecast that interest rates will continue to rise by another 50 basis points. The approximate change in the value of the corporate bond in Table 14.4 is:

$962.90 to$975.12 from $12.22by fall willbond thei.e.

$12.22-

0.012527- x $975.12 price

:therefore

centper 1.2527

0.012527-

)10.01(

0.00502.7559 - price %


14-34


• Duration can also be applied to a portfolio of assets and a portfolio of liabilities– Duration of a portfolio is the weighted duration of each

asset and liability in a portfolio

portfolio asset of value dollar change rate interest an before decimal, a as expressed yield,current

sliabilitieby funded assets of % being leverage, portfolioliability of duration

portfolio asset of duration :where

)(1 Δ] - [- equity in %Δ

ArkDD

rrAkDD

L

A

LA(14.7)


14-35



14-36


– Change in the value of equity = change in the value of asset portfolio + change in the value of the liability portfolio

– Limitations of duration as a measure of interest-rate risk Unrealistically assumes changes in interest rates occur

along the entire maturity spectrum, i.e. parallel shift in yield curve

Assumes yield curve is flat, i.e. yields do not vary over time Duration is a static measure at a point in time, requiring

regular recalculation to incorporate changes in cash flow, yield and maturity characteristics of assets and liabilities

Assumes linear relationship between interest rate changes and price, whereas pricing of fixed-interest securities exhibits convexity


14-37





(ARBL)



14.6 Duration

14.7 Convexity


14.9 Summary


14-38

14.7 Convexity

• Convexity is curvature in the price/yield curve of a security– This overcomes the limitation of the duration method,

which reflects a linear relationship between yield and price

– Example: A bond with a face value of $1000, coupon 5% per annum, maturing in 4 years, current yield 5% per annum, and interest rates forecast to rise by 200 basis points

The duration price approximation calculation indicates the bond price would drop from $1000 to $929.08

The bond pricing formula indicates the bond price would drop from $1000 to $932.26


14-39

14.7 Convexity (cont.)

• Convexity is curvature in the price/yield curve of a security (cont.)– The error of the duration approximation can be generalised: if

interest rates Rise, duration overestimates the change in price Fall, duration underestimates the change in price

– The problem with duration can be compensated for by adjusting for convexity, which is given by


14-40



14-41


• Convexity is curvature in the price/yield curve of a security (cont.)– The duration formula can now be adjusted to incorporate

convexity (i.e. the curvature or error)


14-42





(ARBL)



14.6 Duration

14.7 Convexity


14.9 Summary


14-43


• 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

Asset and liability repricing• E.g. seek fixed-rate funds in periods when interest rates are

rising


14-44

14.8 Interest Rate Risk Management Techniques (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

– E.g. switch from one security to another with different frequency of interest payments

Reduced reliance on interest rates• E.g. introduction of other fees on loans by a bank

Prepayment and pre-redemption conditions• E.g. early payment penalties to discourage borrowers repaying

floating-rate loans early in periods of rising interest rates


14-45

14.8 Interest Rate Risk Management Techniques (cont.)

– External methods External methods involve using off-balance-sheet strategies

• 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, options and swaps (discussed in Part 6)


14-46





(ARBL)



14.6 Duration

14.7 Convexity


14.9 Summary


14-47

14.9 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 including forecasting the future balance sheet structure and the related interest rate environment


14-48

14.9 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

copyright 2007 mcgraw-hill australia pty ltd ppts t/a mcgraths financial institutions, instruments...

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