yale school of management portfolio management ii william n. goetzmann yale school of management,...

Yale School of Management

Portfolio Management II

William N. Goetzmann

Yale School of Management, 1997

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Overview

Asset and Liability ManagementSurplus Optimization in Global ContextTechnology of Interest Rate ExposureStructured Securities in the Portfolio

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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

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Institutions and Liabilities

Lending institutionsMortgage insurersPension fundsLife insurance companiesCorporationsUniversitiesIncome-oriented portfolios

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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