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Yale School of Management
Portfolio Management II
William N. Goetzmann
Yale School of Management, 1997
Yale School of Management
Overview
Asset and Liability ManagementSurplus Optimization in Global ContextTechnology of Interest Rate ExposureStructured Securities in the Portfolio
Yale School of Management
Asset - Liability Management
Markowitz model as starting pointInsight: riskless asset return not riskless to
portfolio manager with liabilitiesLiabilities can be fit into the optimization
framework with the appropriate assumptions
Yale School of Management
Institutions and Liabilities
Lending institutionsMortgage insurersPension fundsLife insurance companiesCorporationsUniversitiesIncome-oriented portfolios
Yale School of Management
Lending Institutions
Thrifts with short-term liabilities classic mis-match in duration of assets and
liabilities
Mortgage banks with pre-commitments locked-in mortgage rates represent liability possibly complicated option features
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Mortgage Insurers
Anticipated defaultsConditional upon interest rates
the mortgage “put”
Conditional upon economy unemployment regional factors
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Pension Funds
Defined benefit plans with accrued benefit obligations [ABO]
Actuarial forecast of needsRisk characteristics of businessPension fund as hedge against future
contributions
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Insurance Companies
Issuers of GIC’sLong duration liabilitiesRenewals conditional upon corporate credit
riskRenewals conditional upon other forms of
savings
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Corporations
Financing for projectsComittments for deliveryPension liability
[Total Balance Sheet Approach]
Cash needs and receivables
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Universities
Well-defined outflowsPeriodic building activityAnticipated future alumni giving not
matched
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Income Oriented Portfolios
Family investment trusts seeking floor on income
Fixed income managers seeking to lock-in yields
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Surplus Optimization
Optimize over ALL assets and liabilitiesLiabilities are included as a “negative”
assetInstitution constrained to hold this negative
assetOutcome optimizes over asset surplus
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Total Balance Sheet Aproach
Consider uncertainty of future businessPlan for future anticipated accrualsUse portfolio to hedge future contributionsAllow positive correlations to own stock
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Defining the Liability
Pension fund example: ABO
Actuarial forecast of future cash outflows to current beneficieries
Simple assumptions Cash - flows are
riskless Cash flows are known -35.0
-30.0
-25.0
-20.0
-15.0
-10.0
-5.0
0.0
1997
2000
2003
2006
2009
2001
2
2001
5
2001
8
2002
1
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Liability Model
Model liabilties as portfolio of riskless securities
Duration can be long, depending on life-expectancy
Covariance with equities assumed zeroNPV and expected return given by actuariesRisk characteristics given by bond portfolio of
similar duration
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Effect of Liability Constraint
Liability constraint lowers frontier
Feasible region of frontier depends on level of funding
Mean Return
Std. Of Return
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Optimization in Surplus Framework
X axis is the spread between assets and liabilities
Y axis is the volatility of the spread
Expected Surplus
Std. Of Surplus
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Example: Stocks, Bonds and PBO
$120 million pension fund
Pension is overfunded by 20%
Mix between stocks and bonds
S-B cor.=.50B-PBO cor. =.85S-PBO cor. =.50
Standard Deviation (Risk)
Expected SurplusEfficient Frontier
Bonds
Stocks
0.00 13.883.00 6.00 9.00
20.85
26.90
22.00
24.00
26.00
Immunized Portfolio
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Optimal Portfolio
Choose portfolio to minimize probability of underfunding
Tradeoff between underfunding and increasng surplus
Threshold Surplus = 20Stocks (42.2%)
Bonds (57.8%)
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Value at Risk
How much do I expect to lose 1 in 20 times?
The minimum value of potential loss for a given portfolio at a given time horizon at a given probability level.
E.G. VAR for a $100 million portfoliowith a daily std. of 1% at the 95%
confidence level is $100 * 1.64 * 1%
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VAR Issues
Assets and liabilities consideredLiabilities not easily marked to marketExample: Metallgeselschaft
long oil futures position marked to market short oil position not marked to market
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Portfolio Value at Risk
Surplus
DensityThreshold Surplus = 20: Normal Distribution
-0.37 47.817.00 14.00 21.00 28.00 35.00
0.00
0.06
0.02
0.04
5% prob. of drop to 12.4%underfunding
VAR = $7.6 m.
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Global Fixed Income
Role of global bonds in portfolioRelation to other assets
moderate correlation to U.S. bonds currency risk may or may not be hedged
Relation to liabilities lower covariance with U.S. liabilities avoids “home country bias”
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Global Assets 1970 to Present
Time
Index ValuesCumulative Wealth
16.52
N/A
10.88
N/A18.55
24.83
Dec1969
Dec1995
Dec1970
Dec1975
Dec1980
Dec1985
Dec1990
0.8
30
1
10
Europe Gvt Port TR Japan Corp TR U.S. Bond Port TRWorld Bond Port TR S&P 500 TR MSCI EAFE TR
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Summary Statistics
Risk (STD)
Return (AM)Risk vs. Return
4% 24% 6% 8% 10% 12% 14% 16% 18% 20% 22%
7%
16%
8%
9%
10%
11%
12%
13%
14%
15%
Europe Gvt Port TR
Japan Corp TR
U.S. Bond Port TR
World Bond Port TR
S&P 500 TR
MSCI EAFE TR
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Asset Only Optimization
Standard Deviation (Risk)
Expected ReturnEfficient Frontier
MSCI EAFE TR
S&P 500 TR
U.S. Bond Port TR
World Bond Port TR
0.00 22.903.00 6.00 9.00 12.00 15.00 18.00
9.46
15.34
10.00
12.00
14.00
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Frontier in Surplus Framework
Standard Deviation (Risk)
Expected SurplusEfficient Frontier
MSCI EAFE TR
S&P 500 TR
U.S. Bond Port TR
World Bond Port TR
0.00 23.573.00 6.00 9.00 12.00 15.00 18.00
-0.54
5.34
0.00
2.00
4.00
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Optimum With Surplus = 0Threshold Surplus = 0
World Bond Port TR (44.2%)
S&P 500 TR (48.9%)
MSCI EAFE TR (6.9%)
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Limits to Portfolio Risk Tools
Mean-variance limits symmetric return distribution covariance captures exposure no options
Beta risk model limits assumes linearity in factor exposure
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Interest Rate Exposure
Driven by Net Present Value Perpetuity : PVt = CFt+1/r
No CF or discount rate uncertaintyInverse value to interest rate relationship
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Hedging Liabilities
Non-linear hedging Duration Convexity
CallabilityRe-financing riskOther option featuresMajor exposure to
interest rate volatility
Value
Interest Rate
Assets
Liabilities
100% Funded
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Duration
First-order approximation
VAR for interest rate sensitive portfolio
$ value * duration * 1.64 yield change
Value
Interest Rate100% Funded
Modified Duration:-D/(1+y)
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Interest-Rate Risk Control Tools for Asset /Liability Management
Forward and futures contracts allow a lock-in of an interest rate
Options protection of down-side or premium capture
Swaps Change exposure fixed/floating
Options on futures or swapsStructured interest rate agreements
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Structured Notes
Interest rate agreements with conditions customized to buyer’s specifications
Payments often indexed to some financial variable i.e. a derivative.
May include currency featuresMay include non-linear structure
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Caps, Floors & Collars
Interest rate cap payment when rate
exceeds ceiling
Interest rate floor payment when rate
falls below floor
Interest rate collar buy a cap and sell a
flooor
Rate
CF
CF
CF
CF
Rate Rate
Rate
CAP FLOOR
COLLAR FIXED
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Floaters & Inverse Floaters
Floaters: coupon indexed to 6 month LIBOR
Inverse floaters: fixed coupon - 6 month LIBOR
CF
CF
Rate
Inverse Floater
Floater
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Lending Institution
Long-duration assetsShort duration
liabiltiesProfit is the spread
Liabilities
Y
V
Assets
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Use of Interest Rate Cap
Cap protects against rising interest rates
Covariance depends upon yields
Mean-variance does’t work
Liabilities
Y
V
Assets + Rate Cap
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Insurance Company Portfolio
Long-term liabilities E.g. 5 yr. GIC with
fixed rate
Considering purchase of a floater
Y
V
GIC
Floater
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Portfolio with Interest-Rate Floor
Floor pays when rates drop
Allows increase when rates rise
Equivalent to a package of options
Mean-variance doesn’t work Y
V
GIC
Floater + Floor
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Structured Securities in Global Context
Currency is additional dimension for hedgeOpportunities in cross-border spread
differentialsContracts allow long-term lock-ins with
rates and currenciesContracts allow asymmetric payoffsContracts allow maximums over markets
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Asset-Liability Management
Asset-liability correlation is key
Emphasizes fixed incomeAllows surplus optimizationFramework for VAR
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Beyond Mean-Variance
Interest rate factor dominatesLiabilities valued by NPVAssets for financial institutionsVAR uses duration and convexity
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Financial Innovation
Structured note development arose from detailed interest rate analysis driven by additional hedging factors
Insurance for institutionsSpeculation for arbitrageurs Spreads for market makers