J. K. Dietrich - FBE 432 – Spring, 2002 Module III: Asset-Liability Management Week 8 – October...

J. K. Dietrich - FBE 432 – Spring, 2002

Module III: Asset-Liability Management

Week 8 – October 14 and 16, 2002


Risk Management Measure and manage sources of variation in

value or cash flows from– Interest rates– Exchange rates– Input and product prices– Unexpected casualty losses

Several approaches are available– Balance sheet management, insurance,

derivatives


Micro- versus macro-risks

Micro-risks are associated with specific cash flow risks, such as commodity prices or exchange rates in specific contracts

Macro-risks are the net overall risks from all sources of cash flows, including revenues and operating and financial costs

Define and measure both macro and micro risks first


Risk Measurement: Portfolios Standard deviation of returns () is a standard

risk measure– If returns are normal, 67% of the time return is

within , 95% within 2x – Risk is conceptually symmetric (not good, bad)

Cumulative probability of default or other bad income is alternative but related concept for all distributions (not just normal)

Value at Risk (VAR) looks at probability of bad outcomes, e.g. equity wiped out


Normal Distribution and RiskStandard Normal Probability

0.00000

0.00500

0.01000

0.01500

0.02000

0.02500

-4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00

Standard Deviations from Mean

Pro

bab

ilit

y

Probability

67% Probability

Less than 1% Probability


Cumulative Distribution and VaR

0.00000

0.10000

0.20000

0.30000

0.40000

0.50000

0.60000

0.70000

0.80000

0.90000

1.00000

-4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00

Series1

Value at Risk (VaR)


Asset Risks: Interest Rate Risk Risk to the value of an asset (or liability) to interest-

rate variability is often described in terms of risk sensitivity measures

A very common measure is asset bond price elasticity

This is called duration denoted d1, which is widely used by bond traders and analysts and is often available on quote sheets

)1(%

%1 yield

priced


Example of Duration

Assume a 10-year 8% coupon bond is priced at 12% yield to maturity and has value of 77.4 and duration of 6.8

If yields changed immediately from 12% to 10%, that is a 2/112 or 1.8% change in gross yield

The bond price should change about 1.8% * 6.8 = 12.1%


Duration as Time Measure

In 1930’s, Macauley noted that maturity was not relevant measure of timing of payments of bonds and defined his own measure, duration, a time measure

The definition of duration is (p. 717):

PV

3)C(PV2)C(PV1)C(PVDuration 321


Duration has two interpretations Elasticity of bond prices with respect to

changes in one plus the yield to maturity Weighted average payment date of cash

flows (coupon and interest) from bonds Duration measure

– Can be modified to be a yield elasticity by dividing by (1+yield to maturity)

– can be redefined using term structure of yields (Fisher-Weil duration noted d2)


Duration Calculations

Duration can be calculated for bonds:

For level-payment loans (e.g. mortgages):

1M)i1(

1cM

pi

1M

i

i1d

1)i1(

M

i

i1d

M


Duration is an Approximation

Yield to Maturity

Pri

ce (

Par

=1.

0)

0

p

i

Derivative is used in calculating duration

Change predicted by duration

i

Actual price change


Summary: Properties of Duration

Can be interpreted as price elasticity or weighted average payment period

Note when c=0 that d1= M

When M is infinite d1= (1+i)/i

Duration measure effects on values of parallel shift in interest rates

Other economic risks are not assessed


Duration of Portfolios

Portfolio durations (of assets and liabilities) can be measured as:

Alternatively, total portfolio asset risk can be expressed:

ii

33

22

11

p

A

AdAdAdd

i

ip Ad)yield1(%Value$RiskPortfolio


Duration and Interest-Rate Risk

Duration can be used to manage value risks of parallel shifts in a flat term structure

Hedge three types of value risk– Holding-period yield risk– Balancing asset and liability risks– Immunization risk to equity from changes in

asset and liability values Last two are different (see example on

pages 718 to 720 in text)


U-Shaped Yield Curves 2000-01Yield Curve 2000-2001

3

3.5

4

4.5

5

5.5

6

6.5

7

0.25 0.5 1 2 3 5 7 10 20 30

Maturity

Yie

ld t

o M

atu

rity

6/30/2000 1/1/2001


Current Term StructureYield Curve September 20, 2002

0

1

2

3

4

5

6

0 2 4 6 8 10 12 14 16 18 20

Time to Maturity

Yie

ld t

o M

atu

rity


Asset Liability Management:Definitions

Approach to balance sheet management including financing and balance sheet composition and use of off-balance sheet instruments

Assessment or measurement of balance sheet risk, especially to interest rate changes

Simulation of earnings performance of a portfolio or balance sheet under a variety of economic scenarios


Value versus Cash-Flow Risk Duration measures sensitivity of value of assets

and liabilities to changes in interest rates Cash flows may change due to changes in a

number of factors, including interest rates Ultimately a firm’s value comes from cash flows,

and those come from operations and depend on current and future investment needs

A Framework for Risk Management (Froot, Scharfstein, Stein, HBR Nov-Dec/1994) emphasize importance of cash-flow risks


Factor Model Risk Measures

The general factor model expresses the portfolio (or firm) returns (or cash flows) as a linear function of a number of factors

Example: the familiar CAPM market model is a single-factor model– The stock’s return is expressed as a linear

function of the market factor– But many industrial firms and banks are also

exposed to significant interest rate risk


Stylized Example

Suppose Citibank’s cash flows are negatively related to interest rate movements but increase with the Yen/$ rate. DefineC = cash flow, millions of U.S. dollars a month

Fcurr = the percentage change in the Yen/$ exchange rate, monthly

Fint = the change in LIBOR, monthly


Regression Measuring Risk The firm estimates a two-factor model

(using regression analysis) of the form:

The term represents idiosyncratic or unsystematic risks and the coefficients are the factor loadings

Sign (positive or negative) indicates whether firm has long or short exposure to risk

int2curr10 FFC


Hedging Balance Sheet Risk

Hedging on balance sheet– Assets and liabilities chosen to offset risks– Changing mismatches of assets and/or

liabilities through swaps– Floating rate securities with short re-pricing

intervals have little interest-rate risk Hedging off balance sheet

– Futures, forward contracts, and options


Balance Sheet Hedges

Example: United Airlines receives income in Canadian dollars from its operations in Canada

In 1997-98, the Canadian dollar depreciated against the US Dollar.

How can United hedge its currency risk from Canadian operations?


Balance Sheet Hedge Consider taking a long-term liability in

Canadian dollars to offset the (risky) income in Canadian dollars from UAL’s operations in Canada– A bank loan or bond issue (in Canada or

Eurobonds denominated in Canadian dollars), generates cash which can be converted to US dollars

– Interest obligations are met from Canadian income


Balance Sheet Hedge

Income in Canada

Canadian Dollar Liability

Initial Cash Inflow is converted to US Dollars


Swaps

Exchange of future cash flows based on movement of some asset or price– Interest rates– Exchange rates– Commodity prices or other contingencies

Swaps are all over-the-counter contracts Two contracting entities are called counter-parties Financial institution can take both sides


Interest Rate Swap:Plain vanilla, [email protected]%

Company A(receive floating)

Company B(receive fixed)

Notional Amount$100 mm

$2.5mm$2.75mm

1/2 5% fixed

1/2 6-month LIBOR


Example: Interest Rate Swap

Two companies want to borrow $10 million with a 5 year duration

Company A, a financial institution, can borrow at fixed rate of 10%; B can borrow at a 11.2% fixed rate

Company A can borrow at a floating rate of 6 month LIBOR + 0.3%; B can borrow at a floating rate of 6 month LIBOR + 1%


Comparative Advantage

A: 10% LIBOR + 0.3%

B: 11.2% LIBOR + 1%

Fixed Floating

1.2% 0.7%Difference


Preferences

Company A prefers floating interest debt while B wants to lock in a fixed rate

However, A has a comparative advantage in the fixed rate market while B has a comparative advantage in the floating rate market


Swap Mechanics

Suppose A borrows at 10% fixed and B borrows at LIBOR + 1%, and then the two companies swap flows

Company A pays B interest at 6-month LIBOR on $10 million

Company B pays A interest at 9.95% per annum on $10 million


Interest Rate Swap

A B

LIBOR

9.95%10

%

LIBOR+1%


Both Parties are Better Off

Cost to A:– 10% to outside bank - 9.95% from B + LIBOR

= LIBOR + 0.05%– Cost saving is 25 basis points per year

Cost to B:– LIBOR + 1% to outside bank - LIBOR from A

+ 9.95% to A = 10.95%– Cost saving is 25 basis points per year


Swaps: Some fine points

The source of the gain is the fact that the two firms have different comparative advantages; even though A has an absolute advantage, there are still gains from trade

The total gain is 0.25% + 0.25% = 0.5% = 1.2% - 0.7%, the difference in the relative borrowing costs


Swaps in Practice

Note that a swap does not involve the exchange of principals– All that is swapped is the cash flows

To guard against default, the deal will typically be structured with an intermediary (usually a large bank) between the two parties


Swap: Bank Intermediary

A B

LIBOR

9.95%10%

LIBOR+1%

Bank

Even with fees, both parties are still better off

LIBOR- 0.05%

9.90%

Bank fees are 0.1%


Swaps in Practice

The intermediary will charge fees for acting as a clearing house and guaranteeing the payments

As long as these fees are below 0.5%, all parties can be made better off

If the deal is put together by the intermediary, it is not necessary for either firm to know the trade counter-party


Swaps in Practice

Many interest rate swaps also involve currency swaps or commodity swaps

Recently, the swap market has grown so rapidly that dealers will act as counterparties


Dealer Quotations for Swaps Example:

– IBM can issue fixed rate bonds at 7.0% per annum. IBM wants a floating rate obligation believing rates will fall.

– An OTC dealer gives IBM a fixed rate quote of 60 basis points over treasuries to be exchanged for 6-month LIBOR on a 5 year swap

– If 5-year treasuries are at 5.53%, this quote means that you can get 6-month LIBOR by paying 6.13% (= 5.53% +0.60) fixed rate.

– In IBM’s case, it would thus get 6.13% from the counterparty (or dealer) and would have to pay 6-month LIBOR, plus the 7.0% on its original debt

– All-in costs are approximately LIBOR+ 0.87%


The Value of Swaps

Swaps are beneficial because they allow hedging with one contract since they typically involve cash flows over several years

There are no losers; financial engineering results in value creation

The source of this value is in overcoming segmented markets


Issues in Hedging

Micro-hedging versus macro-hedging– Accounting– Regulation

Assumptions underlying hedging– Market liquidity– Covariance structure (second moments)

Notorious examples– PNC, IG Metall, Bankers Trust, Orange Cy,

Long-Term Capital Mgmt (LTCM), BancOne


Next Week – Oct. 21 & 23, 2002

Read New York Times articles on LTCM Review this week’s discussion to identify

areas needing clarification Read and prepare case Union Carbide

Corporation Interest Rate Risk Management and identify issues in the case you have questions about

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J. K. Dietrich - FBE 432 – Spring, 2002 Module III: Asset-Liability Management Week 8 – October...

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