j. k. dietrich - fbe 432 – spring, 2002 module iii: asset-liability management week 8 – october...
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J. K. Dietrich - FBE 432 – Spring, 2002
Module III: Asset-Liability Management
Week 8 – October 14 and 16, 2002
J. K. Dietrich - FBE 432 – Spring, 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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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)
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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%
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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)
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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)
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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?
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
Balance Sheet Hedge
Income in Canada
Canadian Dollar Liability
Initial Cash Inflow is converted to US Dollars
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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%
J. K. Dietrich - FBE 432 – Spring, 2002
Comparative Advantage
A: 10% LIBOR + 0.3%
B: 11.2% LIBOR + 1%
Fixed Floating
1.2% 0.7%Difference
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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%
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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%
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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
J. K. Dietrich - FBE 432 – Spring, 2002
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