Portfolio Management II

1. Portfolio Management II William N. Goetzmann Yale School of Management, 1997

2. Overview • Asset and Liability Management • Surplus Optimization in Global Context • Technology of Interest Rate Exposure • Structured Securities in the Portfolio

3. Asset - Liability Management • Markowitz model as starting point • Insight: riskless asset return not riskless to portfolio manager with liabilities • Liabilities can be fit into the optimization framework with the appropriate assumptions

4. Institutions and Liabilities • Lending institutions • Mortgage insurers • Pension funds • Life insurance companies • Corporations • Universities • Income-oriented portfolios

5. 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

6. Mortgage Insurers • Anticipated defaults • Conditional upon interest rates • the mortgage “put” • Conditional upon economy • unemployment • regional factors

7. Pension Funds • Defined benefit plans with accrued benefit obligations [ABO] • Actuarial forecast of needs • Risk characteristics of business • Pension fund as hedge against future contributions

8. Insurance Companies • Issuers of GIC’s • Long duration liabilities • Renewals conditional upon corporate credit risk • Renewals conditional upon other forms of savings

9. Corporations • Financing for projects • Comittments for delivery • Pension liability • [Total Balance Sheet Approach] • Cash needs and receivables

10. Universities • Well-defined outflows • Periodic building activity • Anticipated future alumni giving not matched

11. Income Oriented Portfolios • Family investment trusts seeking floor on income • Fixed income managers seeking to lock-in yields

12. Surplus Optimization • Optimize over ALL assets and liabilities • Liabilities are included as a “negative” asset • Institution constrained to hold this negative asset • Outcome optimizes over asset surplus

13. Total Balance Sheet Aproach • Consider uncertainty of future business • Plan for future anticipated accruals • Use portfolio to hedge future contributions • Allow positive correlations to own stock

14. 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

15. Liability Model • Model liabilties as portfolio of riskless securities • Duration can be long, depending on life-expectancy • Covariance with equities assumed zero • NPV and expected return given by actuaries • Risk characteristics given by bond portfolio of similar duration

16. Effect of Liability Constraint • Liability constraint lowers frontier • Feasible region of frontier depends on level of funding

17. Optimization in Surplus Framework • X axis is the spread between assets and liabilities • Y axis is the volatility of the spread

18. Example: Stocks, Bonds and PBO • $120 million pension fund • Pension is overfunded by 20% • Mix between stocks and bonds • S-B cor.=.50 • B-PBO cor. =.85 • S-PBO cor. =.50 Immunized Portfolio

19. Optimal Portfolio • Choose portfolio to minimize probability of underfunding • Tradeoff between underfunding and increasng surplus

20. 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 portfolio • with a daily std. of 1% at the 95% confidence level is $100 * 1.64 * 1%

21. VAR Issues • Assets and liabilities considered • Liabilities not easily marked to market • Example: Metallgeselschaft • long oil futures position marked to market • short oil position not marked to market

22. Portfolio Value at Risk VAR = $7.6 m. 5% prob. of drop to 12.4% underfunding

23. Global Fixed Income • Role of global bonds in portfolio • Relation 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”

24. Global Assets 1970 to Present

25. Summary Statistics

26. Asset Only Optimization

27. Frontier in Surplus Framework

28. Optimum With Surplus = 0

29. 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

30. Interest Rate Exposure • Driven by Net Present Value • Perpetuity : PVt = CFt+1/r • No CF or discount rate uncertainty • Inverse value to interest rate relationship

31. Hedging Liabilities • Non-linear hedging • Duration • Convexity • Callability • Re-financing risk • Other option features • Major exposure to interest rate volatility

32. Duration • First-order approximation • VAR for interest rate sensitive portfolio • $ value * duration * 1.64 yield change

33. 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 swaps • Structured interest rate agreements

34. 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 features • May include non-linear structure

35. 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

36. Floaters & Inverse Floaters • Floaters: coupon indexed to 6 month LIBOR • Inverse floaters: fixed coupon - 6 month LIBOR

37. Lending Institution • Long-duration assets • Short duration liabilties • Profit is the spread

38. Use of Interest Rate Cap • Cap protects against rising interest rates • Covariance depends upon yields • Mean-variance does’t work

39. Insurance Company Portfolio • Long-term liabilities • E.g. 5 yr. GIC with fixed rate • Considering purchase of a floater

40. 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

41. Structured Securities in Global Context • Currency is additional dimension for hedge • Opportunities in cross-border spread differentials • Contracts allow long-term lock-ins with rates and currencies • Contracts allow asymmetric payoffs • Contracts allow maximums over markets

42. Asset-Liability Management • Asset-liability correlation is key • Emphasizes fixed income • Allows surplus optimization • Framework for VAR

43. Beyond Mean-Variance • Interest rate factor dominates • Liabilities valued by NPV • Assets for financial institutions • VAR uses duration and convexity

44. Financial Innovation • Structured note development • arose from detailed interest rate analysis • driven by additional hedging factors • Insurance for institutions • Speculation for arbitrageurs • Spreads for market makers