Week 7 – Interest Rate Risk.pdf

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Week 7 – Interest Rate RiskChapter 14

Mark W. Werman

125.220

Learning objectives

• To consider the economy’s and business cycle’s impacts on

• interest rates

• To analyse the business cycle and its impacts

• To learn how to monitor and to use basic business indicators as aguide to financial decision making

• To be familiar with some common methods of forecasting interestrates

• To learn the major financial risks faced by financial institutions andthe management techniques used to deal with these risks, inparticular interest rate risk and duration

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Introduction

• Interest rates change:

– Central banks control inflation using open market operations tocontrol inflation

– Increase cash rate to slow economy down

– Lower cash rate to stimulate the economy

• Change in interest rate creates uncertainty

– Why will it increase

– When will it increase - unknown (uncertainty)

– How does it affect us?

– How much will interest rates change?

• Eco. Indicators – makes forecasting hard i.e. housingmarket strong and rural sector weak

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Introduction

• Why must interest rate risk be managed?

– Interest rate changes represent:

• Change in the cost of borrowing

• Return on investment

• Affect the value of financial assets and liabilities

• Risk – relates to uncertainty – the probability that anoutcome will be different from that which has beenforecast

• Something will occur that has not been taken intoaccount

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Origins of modern risk management

• After the events of the1930s, laws were passed to limitactivities of FIs so that regulators set prices & costs

• ⇒ FIs usually profitable & few failed.

• With interest rate rises in 70s, depositors withdrew fundsfrom FIs in order to find higher returns.

• Because of regulations, FIs unable to respond changesin the economy

• 1980’s government many of the restrictions on FIsloosened or removed (Regan, Thatcher, etc

• called deregulation...

• e.g. interest rate controls in July 1984

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Origins

• 1980s saw volatility of such financial variables as interest rates

• & exchange rates ↑.• Volatility refers to average change in price (e.g. exchange rates

• or interest rates) which occur over a specific time interval – e.g. NZ$1= 0.87 US & $1=0.82 US over a week.

• With the abandonment of fixed exchange rate regime in the 70s,thefloating exchange rates regime has been accompanied by increasedvolatility due to a number of influences

• fluctuation in commodity prices

• stresses in global financial system

• large current account deficits run by some countries

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Origins

• 1980’s Savings and Loan Crisis in the US

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Origins

• L/T volatility of cash S/T interest rates ↑since their use assole instrument of monetary policy in many countries.

• As well, longer-term interest rates have become morevolatile over S/T horizons due to impact of deregulation.

– removals of ceilings on interest rates more sensitiveto changes

– marketing of govt. securities by tender increasedsensitivity to change

• L/T interest rates are related to S/T rates & reliance of

monetary policy on S/T rates has added to long-runvolatility

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Origins

• Period of deregulation coincided with & was encouraged

by rapid developments in technology & innovation inproducts that FIs offer.

• All these changes exposed FIs to risks that needmanaging.

• FI managers must devote considerable time & resourcesto managing the various risks

E.g. A bank has a asset and liability managementcommittee (ALCO) i.e. risk management committee for thispurpose

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Consequence

• Majority of business are exposed to interest raterisks therefore it must be managed

• Try to forecast future interest rate changes butthere is still uncertainty

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Performance and risk in FinancialInstitutions

• All types of FIs must actively manage their organisations to obtainan adequate return on equity cap ital.

• For a bank, return is managed by prudent setting of prices on loans& deposits and control of operating expenses.

• Two measures often used to report firm’s performance

– 1. return on assets (ROA= profit/dollar of total assets

– 2. return on equity (ROE)= profit/dollar of equity capital

• Norm for banks’ ROA - less than 1% on assets.

• ROE for banks - much higher

• Second aspect - control of risk

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Risk

• Risk is defined as the chance that actual outcome will

differ from expected outcome.• It equals uncertainty (usually of a loss).

• Risk is assumed to arise out of variability

• Example:

– if an asset’s return has no variability, it has no risk.

– So the security T bill is considered to have no risk

– So used as a proxy for a risk-free asset

• The risk of a distribution can be assessed.

• Commonly used measure is standard deviation

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The modern FI faces several risks toconsider, measure & control

• Interest rate risk

• Credit (default) risk

• Off-balance sheet risks

• Operational/technology risk

• Liquidity risk

• Foreign exchange risk

• Country/sovereign risk

• For a bank, the first two are major risk

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14.1 Interest rate risk

• Chapter 13 considered the:

– macro-economic context of interest rates

– loanable funds approach to interest ratedetermination

– theories that explain the shape of the yield curve

• The timing and extent of interest rate changes isunknown

• Interest rate risk needs to be managed

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• During and after the GFC, interest rate risk were an

important topic

• As credit risks emerged during 2007 and 2008, interestrates rose sharply

• Sharp and sudden rises in interest rates exposed manyindividuals and firms to higher borrowing costs

• The identification and management of interest rate risk isimportant for firms and financial institutions

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Interest Rate Risk For FIs

• Sensitivity of future cash flows & value of assets or liabilities-(forborrower their liabilities or lender their investments) to uncertainchanges in interest rates

• For FIs the deposits of FIs often have different maturity & liquiditycharacteristics than the securities (loans in the case of a bank) theysell.

• The mismatching of maturities of assets & liabilities ⇒FIs exposed torisk of lower than expected net interest income.

• Two important aspects of interest rate risk:

• 1. refinancing risk

• 2. reinvestment risk

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• Interest rate risk takes two forms

1.Reinvestment risk

• Impact of a change in interest rates on a firm’s future

cash flows

2. Price risk

• Impact of a change in interest rates on the value of afirm’s assets and liabilities

• An inverse relationship exists between interest ratesand security prices; i.e. a rise in interest rates resultsin a fall in the value of an asset or liability, or viceversa

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Example

• Example

• : Consider an FI that issues 1-yr maturity liabilities (deposits) toprovide funds for their assets (term loans) with 2-yr maturity (i.e.maturity of assets longer than maturity of liabilities

0 Liabilities 1

0 Assets 1 2

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Example

• Cost of funds (liabilities) is 9% pa & return on assets is 10% ⇒over 1year FI can lock in profit spread of 1% by borrowing S/T(1 yr.) &lending long-term (2 yr).

• Uncertainty for year 2 if interest rates stay the same, FI canrefinance its liabilities at 9% & lock in profit of 1%.

• If interest rates ↑& FI can only borrow new 1 yr liabilities at 11%,then spread is negative (-1%).

• Whenever FI holds longer term assets relative to liabilities, itpotentially exposes itself to refinancing risk

• - risk that cost of re-borrowing funds is more than returns earned onasset investment.

• Classic example: US Savings & Loans banks in 1980s – loanedmoney at 8.5% and borrowing costs over 15%

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Example

• Example:

• Or, suppose FI issues securities (borrows funds) at 9% pa for 2 yrs& invested the funds in assets that yield 10% for 1 yr. (has 1-yrloans) i.e. maturity of assets smaller than maturity of liabilities.

0 Assets 1

0 Liabilities 1 2

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Example

• FI still locks in one-year profit of 1%. At the end of first

year, asset matures & funds have to be reinvested. Ifinterest rates ↓so that return on assets is 8%, then FIfaces a loss in second year of 1%.

• FI is exposed to reinvestment risk - the risk that thereturns on the funds to be reinvested will fall below thecost of the funds.

• Recent example

: banks operating in Euromarkets (overseasmarkets) that borrowed fixed-rate while investing infloating-rate loans

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Market Value risk

• In addition to potential refinancing or reinvestment risk affecting itsnet interest income, an FI faces market value risk (price risk) onassets or liabilities.

• Rising interest rates increase discount rates on future cash flows &the market value (price) of that asset or liability ↓. FIs also faceprice or market risk on its assets and any securities it holds

• Price risk is:

• Price or market risk arises from the important relationship betweeninterest rates & prices of financial assets

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Example

• Market risk Example of debt security: Pricing of fixed-interest security e.g. 2 yr bond coupon 8.0% p.a.,parvalue $1,000 with semi-annual interest payments,current market rates 8%

• Bond sells at par because the YTM = coupon rate

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1 1 1

T t

t T t

C Fv price

r r

1 2 3 4

40 40 40 40 1,0001,000

1.04 1.04 1.04 1.04 price

Change in YTM

• If the firm is seen as more risky i.e. if market expects

10% or comparable current market instruments are nooffering 10%...

• Then

• = $964.54 at discount

• Price of bond moves to a discount so bond buyers canearn comparable yields to other market instruments.

• S/T & L/T debt securities such as bonds show differentsensitivity to interest rates.

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2 3 4

40 40 40 1,040

1.05 1.05 1.05 1.05 price


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For the same coupon

• Example:

• (i) For 2-year bond, 8% pa semi-annual coupon, face value $1,000 &market interest rates are 8%

• Price is ______.• (ii) For 10-year bond, 8% pa semi-annual coupon, face value $1,000

and market interest rates are 8%

• Price is ______.

• Now interest rates change to 10%,

• 2-year bond price is now $964.54

• 10-year bond is now $875.38

• So for bonds with the same coupon interest rate, ____ bondschange proportionately more in price than ____ bonds for a giveninterest rate change. But at maturi ty what happens?

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For the same maturity: Example

• (i) for 10-year bond, 8% pa semi-annual coupon,

• face value $1,000 & market rates 8% pa, price is $1,000

• (ii) for 10-year bond, 4% pa semi-annual coupon, facevalue $1,000 & market rates 8%, price is $728.19

• Now interest rates change to 10% pa

• For (i) price is now $875.38 = 12.5% change

• For (ii) price is now $626.13 = 13% change

• So for bonds with the same time to maturity, price

volatility of a ______coupon bond is ________ than thatof a ______ coupon bond.

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• Interest rate risk exposures may also be described as:

– Direct

• Reinvestment and price risk

– Indirect

• Relating to the future actions of market participants,e.g. a rise in interest rates causes borrowers to seeknew loans elsewhere and/or repay existing loans

– Basic

• Occurs when pricing differentials exist betweenmarkets, e.g. futures market and the underlyingphysical market

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14.2 Exposure management systems

• An exposure management system involves structuredprocedures that enable a firm to effectively measure and

manage risk, including:

– Forecasting

– Strategies and techniques

– Management reporting systems

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• Forecasting – Need to know and understand the market

– A firm needs to understand factors that will impactupon risk exposures and its environment

• A firm must know the current structure of itsbalance sheet and

• forecast future changes in its assets, liabilities andequities with regard to:

– future business activity growth

– future interest rates

– future financing needs and use of debt financing (futurecost of capital)

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• Strategies and techniques

– The strategies and techniques used relate to the types ofinterest cash flows associated with a firm’s assets andliabilities, and include:

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

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• Monitoring and adjusting the maturity structure

of assets and liabilities, taking into account theterm structure of interest rates

– Maturity structure is the relative proportion ofassets and liabilities maturing at different timeintervals

• Liability diversification—where a firm raisesfunds from a range of different sources, therebyreducing its exposure to potential interest changesin a particular market

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14.2 Exposure management systems (cont.)


• Two broad interest rate risk managementtechniques are discussed later

– 1. Internal methods

– 2. External methods

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• Management reporting

– Policies and procedures need to provide clearinstructions on:

• the type of information to be reported

• frequency of reports

• report hierarchy

• delegation and staff responsible to act on thereports

• the need for audit and review of policies andprocedures

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14.4 Pricing financial securities

• The effect of interest rate risk on the price of discountsecurities and fixed-interest corporate/government bonds

can be demonstrated using calculations discussed inChapters 9, 10 and 12

maturitytodays

100yield 365

365valuefacePrice

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1 Fv

pricert


– Example 1: A company is to issue a 90-day bank billwith a face value of $500 000, yielding 9.5% perannum.

– What amount will the company raise on the issue?

555.75$488

373.55000500182

90)(0.0950365365000$500Price

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– Example 1: If the company has a rollover facility in

place for this bill, it is exposed to interest rate risk atthe next repricing date, i.e. the rollover date in 90days’ time. If the yield at the next rollover date is

9.75% per annum the company will raise:

– Note: cost of borrowing increased by $294.09

261.66$488373.775

000500182

90)(0.0975365365000$500

Price

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Pricing – fixed interest security

• Where:

• I = current yield

• n= number of period that cash flows occur

• Pmt periodic fixed coupon payment

• Fv – face value

• k= fraction of the elapsed interest period

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1 11 1

n

n k i price pmt Fv i ii

Example

• A funds manager is holding a corporate bond in an investmentportfolio, The bond has a face value of $1,000,000 and pays 10%per annum half-yearly coupon and matures on December 31, 2018.

Assume today is 20 May 2013 and the current yield on similarinvestments is 12% per annum. What is the value of the bond?

• Semi-annual coupon payment = $50,000

• FV = $1,000,000

• I = 0.06 (12%/2)

• n= 12 (6*2)

• k= 140/181 (Jan 31, Feb 28, Mar 31, April 30 And May 20 = 140days

• $958,397.46

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14.5 Repricing gap analysis

• 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 repricingof an asset or liability during a planning period

• Defined as rate-sensitive assets minus rate-sensitiveliabilities

– The longer the planning period, the more likely a security is to berate sensitive

• E.g. a 90-day discount security is not interest ratesensitive over a one-month planning period, but it wouldbe over a six-month planning period

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• Three groupings of assets and liabilities assist in determining therepricing gap (matching principle)

1. 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?

2. Fixed-rate assets financed by fixed-rate liabilities and equity

• Are not exposed to interest rate risk during a planning periodas the cost of funds and return on funds is fixed

3. Rate-sensitive assets financed by fixed-rate liabilities or viceversa

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

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• Change in profitability = Gap x change in rates xperiod

• = $15 billion x 0.005 x 1

• = $75 million

Re-pricing gap analysis

• Monitors the sensitivity of a balance sheet (assets andliabilities) to interest rate changes over specific planningperiods. Example 1 month and 6 month periods

• Example a 3 month term deposit is not rate sensitive in aone-month planning period

• Re-pricing gap is the interest rate risk and is measuredas rate-sensitive assets minus rate-sensitive liabilities

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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 andpresent values of cash flows associated with afinancial asset or liability

– Duration is calculated as the weighted average timeover which cash flows occur, where weights are therelative present values of the cash flows

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Duration

• It is a measurement of how long, in years, ittakes for the price of a bond to be repaid by its

internal cash flows.

• Important measure for investors;

– Bonds with higher durations carry more risk and havehigh volatility than bonds with lower risk

• Remember – price relationship to yield

• Yield Price

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14.6 Duration

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

N

t t

i

t C

N

t t i

t t

C

D

1 )(1

1 )(1

)(

flowscashof number

decimalaasexpressedyieldmarketcurrentdueisflowcashtheuntilperiodsof number the

timeatflowscashof valuedollar

where

N

i

t

t t

C

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14.6 Duration

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Duration: $1,000 bond, 9.00%pa, fixed annual coupon, 3 yrs

to maturity current yield 10%


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• Example: Assume the funds manager has forecastthat interest rates will continue to rise by another50 basis points. The approximate change in the

value of the corporate bond in Table 14.4 is:

$962.90to$975.12from$12.22byfallw illbondthei.e.

$12.22

0.012527x$975.12price

therefore

7%252.1

012527.0

0.10)1(

0.0050.7559]2[ price%

14.6 Duration (cont.)

14.6 Duration

Year (t) Cash flows $ PVIF @ 12% Presentvalue PVCF

Weighted cfT*PVCF

1 $110.00 0.8929 98.22 98.22

2 $110.00 0.7972 87.69 175.38

3 $110.00 0.7118 78.30 234.90

4 $1,110.00 0.6355 705.41 2,821.64

969.62 3,330.14

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Duration: $1,000 Bond, 11.00%pa fixed annual coupon, 4 yrs to maturity,current yield 12% pa

Duration = weighted cash flows/present value (price) = 3,330.14/969.62 =3.4345 years

Duration

• The approximate change in the four year bond is: four

year bond:

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0.0050% price [3.4345]

(1 0.10)

0.015333

1.5333%

therefore

price $969.62 x 0.015333

$14.87

i.e. the bond will fall by $14.87 from $969.62 to $954.75


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14.6 Duration

• Duration can also be used to ascertain the dollar impactof 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

changeto forecastisor changes,rateinterestthebefore

decimal, a as expressedyield,currenttheis

where

)(1

Δdurationprice% Δ

r

r

r

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14.6 Duration

• Duration can also be applied to a portfolio of assets anda portfolio of liabilities

– Duration of a portfolio is the weighted duration ofeach asset and liability in a portfolio

portfolioassetof valuedollar

changerateinterestanbeforedecimal,aasexpressedyield,currentsliabilitiebyfundedassetsof %beingleverage,

portfolioliabilityof duration

portfolioassetof duration

where

)(1

Δ][equityin% Δ

A

r

k

D

D

r

r Ak DD

L

A

L A

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14.6 Duration

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Duration – zero coupon bond

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Duration – vanilla bond

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Duration will always be less than its time to maturity

Duration of an asset and liability portfolio

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%1

A L

r in equity D D k A

r


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Duration

• Where:

• = duration of asset portfolio

• = duration of liability portfolio

• k = leverage being the proportion of assets funded by liabilities

• r = current yield

• A dollar value of the portfolio

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A D

L D

%

1 A L

r in equity D D k A

r

Example: Basic facts

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4.690

2.520

$35 / $50 0.70

0.08

0.01

$50

$35

A

L

D years

D years

k mil mil

r

changeinr

A mil

L mil

Change in value of asset portfolio

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0.01

% 4.6900 0.043426 4.3426%1 0.08

:

$50,000,000* 0.043426

$2,171, 296.30

$47,828,703.70

inasset portfolio

Therefore

in asset portfolio

valueof assets


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Change in value of liability portfolio

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0.01% 2.5200 0.023333 2.3333%

1 0.08

:

$35,000,000* 0.023333

$816,666.67

$34,183,333.33

inliability portfolio

Therefore

in asset portfolio

valueof assets

Change in value of equity

• Or Value of assets $47,828,703.70 – the value of

liabilities $34,183,333.33 = value of equity$13,645,370.37

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0.01% 4.6900 2.5200 *0.70 * $50, 000, 000

1 0.08

0.012.9260*$50,000,000 $1,354,629.63

(1 0.08)

:

$13,645,370.37 $15,000,000

inequity

Therefore

value of equity from

New balance sheet

• Liabilities are now 71.47 per cent of the firms capitalstructure

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Assets $47,828,703.70 Liabilities $34,183,333.33

Equity $13,645,370.37


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14.6 Duration

• Change in the value of equity = change in the value of assetportfolio - 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 theentire 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 regularrecalculation to incorporate changes in cash flow, yield andmaturity characteristics of assets and liabilities

– Assumes linear relationship between interest rate changes andprice, whereas pricing of fixed-interest securities exhibitsconvexity

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Duration

• Measure of interest rate risk

• Comparative measure of risk securities that havedifferent yields, cash-flow structures and terms ofmaturity

• It is the weighted average over time over which cashflows occur, where the weights are relative present valueof cash flows

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Duration

• Duration calculation:

– Identify periodic cash flows

– Calculate the present value of those cash flows basedupon current market yields

– Multiple by the relevant time period (t) to obtain theweighted cash flows

– Divide the total of the weighted cash flows by thepresent value of the security

– = duration

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Duration

• Comparing:

– Asset with the lowest duration has the lowest level of interestrate risk

• Used to calculate change in value:

• Used to calculate change in equity of a portfolio:

• D A – duration of assets, D l - duration of liabilities, A isassets and k leverage % of assets funded by liabilities

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%

1

r price duration

r

1 A l

r in equity D D k A

r

14.8 Interest rate risk management techniques

• 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 andinvests the funds in shares or property

• Asset and liability repricing

– E.g. seeking fixed-rate funds in periods when interestrates are rising

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– 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 forecastrate movements

» E.g. switching from one security to another withdifferent frequency of interest payments

• Reduced reliance on interest rates

– E.g. the introduction of other fees on loans by a bank

• Prepayment and pre-redemption conditions

– E.g. early payment penalties to discourage borrowersfrom repaying floating-rate loans early in periods of risinginterest rates

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– External methods

• External methods involve using off-balance-sheet

strategies – These involve primarily the use of derivative products

allowing a party to lock in a price today that will apply ata specified future date; i.e. futures contracts, forward rateagreements, options and swaps (discussed in Part 6)

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14.9 Summary

• Interest rate risk is the sensitivity of the value of balance-sheet assets and liabilities and cash flow to movementsin interest rates

• Interest rate risk exists in the form of reinvestment riskand price risk

• A firm must establish an effective interest rate exposuremanagement system, including forecasting the future

balance-sheet structure and the related interest rateenvironment

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14.9 Summary

• ARBL is a basic principle of interest rate riskmanagement

• A range of internal and external interest rate riskmanagement techniques exist

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Documents

Week 7 – Interest Rate Risk.pdf