Module III: Asset-Liability Management

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Module III Asset-Liability Management

• Week 7 February 23, 2006

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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

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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

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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

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Normal Distribution and Risk
Less than 1 Probability
67 Probability
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Cumulative Distribution and VaR
Value at Risk (VaR)
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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

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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

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Duration as Time Measure

• In 1930s, 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)

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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 (1yield to maturity)
• can be redefined using term structure of yields
  (Fisher-Weil duration noted d2)

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Duration Calculations

• Duration can be calculated for bonds
• For level-payment loans (e.g. mortgages)

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Duration is an Approximation
Derivative is used in calculating duration
Price (Par1.0)
Actual price change
Change predicted by duration
0
Yield to Maturity
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Summary Properties of Duration

• Can be interpreted as price elasticity or
  weighted average payment period
• Note when c0 that d1 M
• When M is infinite d1 (1i)/i
• Duration measure effects on values of parallel
  shift in interest rates
• Other economic risks are not assessed

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Duration of Portfolios

• Portfolio durations (of assets and liabilities)
  can be measured as
• Alternatively, total portfolio asset risk can be
  expressed

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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 717
  to 719 in text)

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Current and 2003-5 Yield Curves
Source FRBoard Release H15
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Asset Liability ManagementDefinitions

• 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

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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 firms 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

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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 stocks 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

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Stylized Example

• Suppose Citibanks cash flows are negatively
  related to interest rate movements but increase
  with the Yen/ rate. Define
• C 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

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Regression Measuring Risk

• The firm estimates a two-factor model (using
  regression analysis) of the form
• The term e 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

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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

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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?

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Balance Sheet Hedge

• Consider taking a long-term liability in Canadian
  dollars to offset the (risky) income in Canadian
  dollars from UALs 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

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Balance Sheet Hedge
Income in Canada
Initial Cash Inflow is converted to US Dollars
Canadian Dollar Liability
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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

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Interest Rate SwapPlain vanilla, LIBOR_at_5.5
1/2 5 fixed
Company A (receive floating)
Company B (receive fixed)
2.5mm
2.75mm
1/2 6-month LIBOR
Notional Amount 100 mm
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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

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Comparative Advantage
Fixed Floating
A 10 LIBOR 0.3
B 11.2 LIBOR 1
Difference
1.2 0.7
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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

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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

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Interest Rate Swap
LIBOR1
9.95
A
B
10
LIBOR
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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

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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

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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

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Swap Bank Intermediary
Bank fees are 0.1
LIBOR1
A
B
9.95
Bank
9.90
10
LIBOR
LIBOR- 0.05
Even with fees, both parties are still better off
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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

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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

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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 IBMs 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

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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

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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

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Next Week March 2, 2006

• Review Wall Street Journal tables on interest
  rates, futures, swaps, options
• Review this weeks discussion to identify areas
  needing clarification before midterm
• Read and prepare case Union Carbide Corporation
  Interest Rate Risk Management and identify
  issues in the case you have questions about