1. Sub-sovereign Credit Markets Fixed Income Securities Applications to Municipal Markets Samir El Daher The World Bank May 1999

2. 2 Fixed Income Securities Main Parameters Definitions Market Risk Liquidity Risk Credit Risk Risk/Return Analysis Structured Products/Derivatives

3. 3 Definitions l Bond is a financial asset represented by a schedule of cash flows l Amounts and timing of payments are “fixed” in advance or predictable l Difference with equities, real-estate or industrial investments

4. 4 Bond Price Formula l P = C i / (1+r) i l P is a function of the variable r as cashflows C i are constant numbers l Equation indicates that P is a decreasing function of variable r

5. 5 Market Risk l Unanticipated change in value of asset l Duration as a measure of risk of fixed income security l Measuring Duration: = - D l Duration D: Price elasticity of interest rate

6. 6 Duration -- Some Characteristics l Duration: increasing function of maturity l Duration: decreasing function of yield level l Duration: decreasing function of coupon level (ex. zero-coupon) l Duration: increasing function of frequency of coupon payments

7. 7 Duration Versus Maturity l Maturity relates to the timing of final cash-flow only l Duration includes all cash-flows time- weighted l Duration carries more information, and is more relevant, than maturity

8. 8 Case of Discount Note: Zero Coupon Bond l Discount note consists of: »one initial outlay (I 0 ) at time zero »one final payment at time n l P = l dP = - n [C n / (1+r) n ] [dr / (1+r)] l dP / P = l D = n ==> Duration = Maturity for zero coupon bond

9. 9 Example of Zero Coupon Bond l Example: P 0 = 100 / (1+ 0.065) 30 = 15 l Only in case of bond with single cashflow payment would duration and maturity be the same

10. 10 Comparison Between Duration and Maturity l Example of 8% coupon rate l Maturity 1y, 3y, 5y, 7y, 10y, 20y, 30y l Duration 1y, 2.5y, 4.2y, 5.6y, 6.8y,10y,12y l 30-Y, zero coupon bond is three times riskier than a 10-Y zero coupon l 30-Y, 8% coupon bond is only 12/6.8 = 1.75 time riskier than 10-Y coupon

11. 11 Duration of a Portfolio l Portfolio is a group of securities l Portfolio concept essential for investors for whom “munis” are part of diversified basket of investment instruments l Duration of a portfolio of securities is equal to the sum of the market-value- weighted durations of its component securities

12. 12 “Additivity” of Duration l Securities S 1, S 2, S 3,....S i,....S n l Weights in portfolio a 1, a 2, a 3,.... a i,....a n l with a i = 1 l Durations D 1, D 2, D 3,........D i,.....D n l Maturities M 1, M 2, M 3,.......M i,....M n l Average Portfolio Duration = a i D i l Average Portfolio Maturity = a i M i

13. 13 Comparing Portfolios (A) & (B): Portfolio (A) l Portfolio (A) includes 50% 10-Year note and 50% 30-Year note l 10-Year note ===> Duration 7 years l 30-Year note ===> Duration 12 years l Average Duration, Portfolio (A) (50% x 7) + (50% x 12) = 9.5 years l Average Maturity, Portfolio (A) (50% x 10) + (50% x 30) = 20 years

14. 14 Comparing Portfolios (A) & (B): Portfolio (B) l Portfolio (B) includes 100% 20-Year zero coupon note l 20-Year zero coupon note ===> Duration 20 years l Average Duration, Portfolio (B) = 100% x 20 = 20 years l Average Maturity, Portfolio (B) = 100% x 20 = 20 years

15. 15 Comparing Duration & Maturity of Portfolios (A) & (B) l Portfolio (A) and (B) have same average maturity and different durations l Average Maturity, Portfolio (A) = Average Maturity, Portfolio (B) = 20 years l Average Duration, Portfolio (B) = 20 years l Average Duration, Portfolio (A) = 9.5 years l Portfolio (B) twice as risky as Portfolio (A) for same average maturity

16. 16 Implication for Investor -- Portfolio Approach l Question: What is meaning of: “a 20-year municipal bond is “too risky” for an investor” l Answer: Meaning not clear if the 20-year bond is part of a balanced portfolio l Importance of assessing contribution of a security, or asset, within a portfolio approach [ex: fixed income and real estate (inflation hedge)]

17. 17 Example of “Balanced” Fixed Income Portfolio l One third Cash ===> Duration zero l One third 1-year bill ===> Duration 1 year l One third 20-year municipal bond ===> Duration 10 years l Average duration of portfolio: (1/3 x 0) + (1/3 x 1) + (1/3 x 10) = 3.6 years l Result might well be within risk tolerance of investor

18. 18 Liquidity Risk l Liquidity Spectrum l More liquid ---------to---------> Less Liquid l Cash, Gov Securities,........... Fixed Assets,.. l Liquidity risk is associated with existence of “ready market” where assets may be exchanged at a small difference between sale and purchase price

19. 19 Liquidity Risk l For fixed income securities, liquidity is measured by bid-ask spread in secondary markets l Bid-ask spread constitutes margin of market-makers (small 1/32nd in US) l For cash ==> bid-ask spread = 0 l For real estate ==> bid-ask spread > 6% (agent’s fee)

20. 20 Credit Risk -- Definition l Loss of value of an asset as a result of a party to a contract (seller, issuer,...) not fulfilling a contractual obligation - l Loss of value due to default: spot loss might overestimate real loss l Loss might affect principal and/or interest l Securities trading: c.o.d - Opportunity loss due to change in market value between trade date and delivery

21. 21 Credit Risk -- Estimation l Example: Fixed income Security l Years 0----(i) ----(10)------(j)----------(20) l Cashflows -----------(C 10 )-----(C j )-------(C 20 ) l Income ------------- l Actual Loss at Year-10 = (In year-10 value) l Potential Loss at time Zero = Actual Loss at Year 10 / (1+r) 10 =

22. 22 Implication for Investor -- An Example l Investor must chose 10-Y versus 20-Y l Question: If investor’s risk tolerance for a given credit is 10 years l Would investor not buy a 20-Y instrument from same credit? l Answer: Not necessarily ==> Several scenarios

23. 23 Implication for Investor -- Scenarios l 1st Scenario ===> Yield Premium (compensating for risk) l 2nd Scenario ===> Guarantee or insurance beyond 10-Y l 3rd Scenario ===> Derivatives, such as put option l 4th Scenario ===> Collateral, such as mortgage-backed security

24. 24 Guarantee or Insurance l Insurance may be full or partial (say beyond 10 years) l Case 1: Insurance may be necessary for debt acceptance l Case 2: Insurance would reduce price of debt issue and enhance liquidity (USA) l Feasibility: Interest without Insurance > Interest with Insurance + Insurance Fee

25. 25 Other Enhancement Mechanisms l Structured finance and derivatives (e.g. put option allowing maturity “reduction”) l Other non-maturity related enhancements »Collateral (revenue pledge, MBS,...) »Bank letter of credit »Other features such as convertible debt

26. 26 Example of Credit Enhancement “Zero Coupon Collateral” l Several recent cases for bullet repayment l Zero coupon “deposited” in segregated account in “highest credit quality (say US treasuries) l Zero coupon to accrue interests so as to become equivalent to face value of principal upon maturity l Definition of real cost of zero-coupon collateralized principal (ex. of calculation)

27. 27 Risk/Return Analysis -- Definitions l Return = Enhancement in market value of an asset l Risk is measure of uncertainty of outcome l Risk = volatility of returns expressed by Standard Deviation l (Example daily price changes during one year)

28. 28 Simple Risk/Return Measures l A number of ways to define and measure risk l Information Ratio = Return Standard Deviation l Sharpe Ratio = (Return - Risk-free Return) Standard Deviation

29. 29 Benchmark for Municipal Debt Security l “Risk -free” Government Securities in relevant maturity range l Y muni = Y gvn + dY n l dY n = premium that covers, inter-alia, two categories of risks: »credit risk »liquidity risk

30. 30 Risk/Return: Portfolio Approach l Long-term investors and hedgers need to know the relative risk of securities so that they may construct portfolios that match their preferences for risk and expected return l Optimize risk/return function: »For one unit of risk ===> Highest return (e.g. Foundations,...) »For one unit of return ===> Lowest risk

31. 31 Defining a Portfolio for Institutional Investors l Definition of Classes of Assets: Fixed income, equities, commodities, real- estate, currencies,... l Analyses of historical returns (over representative period, say 20 years) l Analyses of volatilities l Analyses of correlations

32. 32 Defining a Portfolio for Institutional Investors l Optimization function (e.g. “Efficient Frontier”) with iterations providing percentages for each “class” of assets ==> Asset allocation process l Example of pension fund: government securities, high yield, MBS, marketable equities, private equities, real-estate, currencies,...

33. 33 Structured Finance -- Derivatives l Main categories: Futures, Options, Swaps l Derivatives as investment vehicles: leverage l Derivatives as hedge and credit enhancement vehicles l Derivatives transfer investment risks to those (speculators) willing to assume risks l Futures, options and swaps traded over the counter (OTC) or on regulated exchanges

34. 34 Futures l Futures contract is a commitment to buy or sell a security at a future specified date and specified price l Future neutralizes price uncertainties l Example of farmer hedging crop with futures l Same result may be achieved by put option as both futures and options provide hedge

35. 35 Swaps l Swaps are arrangements between two parties l Swaps entail exchange of mutual liabilities as these come due l Swaps may involve currencies (US$/DM) l Swaps may involve interest rates (floating/fixed)

36. 36 Options l Option is a right -- not an obligation -- to buy or sell an asset at a pre-established price within a specified time period (US), or at a specified time (Europe) l Privilege to exercise such a right entails a fee, or option “premium” l Calculation of “premium” is crucial element l Option pricing models for equities and interest rate instruments

37. 37 Options l Call Option - Market position of an investor/hedger speculating that asset price would increase l Put Option - Market position of an investor/hedger speculating that asset price would decline

38. 38 Option Value -- Bond Example

39. 39 Option Parameters l Definition of “underlying” asset l Exercise or strike price l Time to expiration l “In-the-money”, “Out-of-the-money” and “At-the-money” options l Premium = Intrinsic Value + Time Value

40. 40 Option Parameters Delta  = dP/dF or Hedge Ratio (change in Price P of option to change in price F of underlying security) Gamma  = d  /dF = d 2 P/ (dF) 2 Zeta  = dP / dV (ratio of change of price to change in volatility V) Theta  = dP/dt (time dimension, time “decay”)

41. 41 Option Pricing l Call price: Increasing function of price of “underlying” relative to “strike” price l Call price: Increasing function of “time to expiration” l Call option price: Increasing function of riskless rate of return (on treasury) l Call price: Increasing function of volatility