Sub-sovereign Credit Markets

Fixed Income Securities Applications to Municipal

Markets

Samir El DaherThe World Bank

May 1999

2

Fixed Income SecuritiesMain Parameters

• Definitions

• Market Risk

• Liquidity Risk

• Credit Risk

• Risk/Return Analysis

• Structured Products/Derivatives

3

Definitions

Bond is a financial asset represented by a schedule of cash flows

Amounts and timing of payments are “fixed” in advance or predictable

Difference with equities, real-estate or industrial investments

4

Bond Price Formula

P = Ci / (1+r)i

P is a function of the variable r as cashflows Ci are constant numbers

Equation indicates that P is a decreasing function of variable r

i

5

Market Risk

Unanticipated change in value of asset Duration as a measure of risk of fixed

income security Measuring Duration: = - D Duration D: Price elasticity of interest

rate

dP

P

dr

r1

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Duration -- Some Characteristics

Duration: increasing function of maturity Duration: decreasing function of yield

level Duration: decreasing function of coupon

level (ex. zero-coupon) Duration: increasing function of

frequency of coupon payments

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Duration Versus Maturity

Maturity relates to the timing of final cash-flow only

Duration includes all cash-flows time-weighted

Duration carries more information, and is more relevant, than maturity

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Case of Discount Note:Zero Coupon Bond

Discount note consists of:» one initial outlay (I0) at time zero

» one final payment at time n P = dP = - n [Cn / (1+r)n] [dr / (1+r)]

dP / P = D = n ==> Duration = Maturity for zero

coupon bond

ndr

r1

C

r

n

n( )1

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Example of Zero Coupon Bond

Example: P0 = 100 / (1+ 0.065)30 = 15 Only in case of bond with single

cashflow payment would duration and maturity be the same

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Comparison Between Duration and Maturity

Example of 8% coupon rate Maturity 1y, 3y, 5y, 7y, 10y, 20y, 30y Duration 1y, 2.5y, 4.2y, 5.6y, 6.8y,10y,12y 30-Y, zero coupon bond is three times

riskier than a 10-Y zero coupon 30-Y, 8% coupon bond is only 12/6.8 =

1.75 time riskier than 10-Y coupon

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Duration of a Portfolio

Portfolio is a group of securities Portfolio concept essential for investors

for whom “munis” are part of diversified basket of investment instruments

Duration of a portfolio of securities is equal to the sum of the market-value-weighted durations of its component securities

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“Additivity” of Duration

Securities S1, S2, S3,....Si,....Sn

Weights in portfolio a1, a2, a3,.... ai,....an

with ai = 1

Durations D1, D2, D3,........Di,.....Dn

Maturities M1, M2, M3,.......Mi,....Mn

Average Portfolio Duration = ai Di

Average Portfolio Maturity = ai Mi

i

i

i

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Comparing Portfolios (A) & (B): Portfolio (A)

Portfolio (A) includes 50% 10-Year note and 50% 30-Year note

10-Year note ===> Duration 7 years 30-Year note ===> Duration 12 years Average Duration, Portfolio (A)

(50% x 7) + (50% x 12) = 9.5 years Average Maturity, Portfolio (A)

(50% x 10) + (50% x 30) = 20 years

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Comparing Portfolios (A) & (B): Portfolio (B)

Portfolio (B) includes 100% 20-Year zero coupon note

20-Year zero coupon note ===> Duration 20 years

Average Duration, Portfolio (B) = 100% x 20 = 20 years

Average Maturity, Portfolio (B) = 100% x 20 = 20 years

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Comparing Duration & Maturity of Portfolios (A) & (B)

Portfolio (A) and (B) have same average maturity and different durations

Average Maturity, Portfolio (A) = Average Maturity, Portfolio (B) = 20 years

Average Duration, Portfolio (B) = 20 years Average Duration, Portfolio (A) = 9.5 years Portfolio (B) twice as risky as Portfolio (A)

for same average maturity

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Implication for Investor -- Portfolio Approach

Question: What is meaning of: “a 20-year municipal bond is “too risky” for an investor”

Answer: Meaning not clear if the 20-year bond is part of a balanced portfolio

Importance of assessing contribution of a security, or asset, within a portfolio approach [ex: fixed income and real estate (inflation hedge)]

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Example of “Balanced” Fixed Income Portfolio

One third Cash ===> Duration zero One third 1-year bill ===> Duration 1 year One third 20-year municipal bond ===>

Duration 10 years Average duration of portfolio:

(1/3 x 0) + (1/3 x 1) + (1/3 x 10) = 3.6 years Result might well be within risk tolerance of

investor

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Liquidity Risk

Liquidity Spectrum More liquid ---------to---------> Less Liquid Cash, Gov Securities, ........... Fixed Assets,.. Liquidity risk is associated with existence of

“ready market” where assets may be exchanged at a small difference between sale and purchase price

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Liquidity Risk

For fixed income securities, liquidity is measured by bid-ask spread in secondary markets

Bid-ask spread constitutes margin of market-makers (small 1/32nd in US)

For cash ==> bid-ask spread = 0 For real estate ==> bid-ask spread > 6%

(agent’s fee)

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Credit Risk -- Definition

Loss of value of an asset as a result of a party to a contract (seller, issuer,...) not fulfilling a contractual obligation -

Loss of value due to default: spot loss might overestimate real loss

Loss might affect principal and/or interest Securities trading: c.o.d - Opportunity loss due

to change in market value between trade date and delivery

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Credit Risk -- Estimation

Example: Fixed income Security Years 0----(i) ----(10)------(j)----------(20) Cashflows -----------(C10)-----(Cj)-------(C20) Income -------------<---Forgone Income---> Actual Loss at Year-10 = (In

year-10 value) Potential Loss at time Zero = Actual Loss at

Year 10 / (1+r)10 =

C

r

j

jj ( )1

C

r

r

j

jj ( )

( )

1

1 10

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Implication for Investor --An Example

Investor must chose 10-Y versus 20-Y Question: If investor’s risk tolerance for a

given credit is 10 years Would investor not buy a 20-Y instrument

from same credit? Answer: Not necessarily ==> Several

scenarios

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Implication for Investor -- Scenarios

1st Scenario ===> Yield Premium (compensating for risk)

2nd Scenario ===> Guarantee or insurance beyond 10-Y

3rd Scenario ===> Derivatives, such as put option

4th Scenario ===> Collateral, such as mortgage-backed security

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Guarantee or Insurance

Insurance may be full or partial (say beyond 10 years)

Case 1: Insurance may be necessary for debt acceptance

Case 2: Insurance would reduce price of debt issue and enhance liquidity (USA)

Feasibility: Interest without Insurance > Interest with Insurance + Insurance Fee

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Other Enhancement Mechanisms

Structured finance and derivatives (e.g. put option allowing maturity “reduction”)

Other non-maturity related enhancements» Collateral (revenue pledge, MBS,...)» Bank letter of credit » Other features such as convertible debt

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Example of Credit Enhancement“Zero Coupon Collateral”

Several recent cases for bullet repayment Zero coupon “deposited” in segregated account

in “highest credit quality (say US treasuries) Zero coupon to accrue interests so as to

become equivalent to face value of principal upon maturity

Definition of real cost of zero-coupon collateralized principal (ex. of calculation)

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Risk/Return Analysis -- Definitions

Return = Enhancement in market value of an asset

Risk is measure of uncertainty of outcome

Risk = volatility of returns expressed by Standard Deviation

(Example daily price changes during one year)

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Simple Risk/Return Measures

A number of ways to define and measure risk

Information Ratio = Return Standard

Deviation Sharpe Ratio = (Return - Risk-free Return)

Standard Deviation

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Benchmark for Municipal Debt Security

“Risk -free” Government Securities in relevant maturity range

Ymuni = Ygvn + dYn

dYn = premium that covers, inter-alia, two categories of risks: » credit risk» liquidity risk

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Risk/Return: Portfolio Approach

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

Optimize risk/return function:» For one unit of risk ===> Highest return (e.g.

Foundations,...)» For one unit of return ===> Lowest risk

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Defining a Portfolio for Institutional Investors

Definition of Classes of Assets: Fixed income, equities, commodities, real-estate, currencies,...

Analyses of historical returns (over representative period, say 20 years)

Analyses of volatilities Analyses of correlations

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Defining a Portfolio for Institutional Investors

Optimization function (e.g. “Efficient Frontier”) with iterations providing percentages for each “class” of assets ==> Asset allocation process

Example of pension fund: government securities, high yield, MBS, marketable equities, private equities, real-estate, currencies,...

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Structured Finance -- Derivatives

Main categories: Futures, Options, Swaps Derivatives as investment vehicles: leverage Derivatives as hedge and credit enhancement

vehicles Derivatives transfer investment risks to those

(speculators) willing to assume risks Futures, options and swaps traded over the

counter (OTC) or on regulated exchanges

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Futures

Futures contract is a commitment to buy or sell a security at a future specified date and specified price

Future neutralizes price uncertainties Example of farmer hedging crop with futures Same result may be achieved by put option as

both futures and options provide hedge

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Swaps

Swaps are arrangements between two parties

Swaps entail exchange of mutual liabilities as these come due

Swaps may involve currencies (US$/DM) Swaps may involve interest rates

(floating/fixed)A B

11%

9.95%

LIBORLIBOR+2%

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Options

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)

Privilege to exercise such a right entails a fee, or option “premium”

Calculation of “premium” is crucial element Option pricing models for equities and interest

rate instruments

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Options

Call Option - Market position of an investor/hedger speculating that asset price would increase

Put Option - Market position of an investor/hedger speculating that asset price would decline

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Option Value -- Bond Example

-5

0

5

10

15

20

25

70 80 90 100 110 120 130

Terminal Bond Price ($)

Pro

fit

($)

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Option Parameters

Definition of “underlying” asset Exercise or strike price Time to expiration “In-the-money”, “Out-of-the-money” and

“At-the-money” options Premium = Intrinsic Value + Time Value

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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 = d2P/ (dF)2

Zeta = dP / dV (ratio of change of price to change in volatility V)

Theta = dP/dt (time dimension, time “decay”)

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Option Pricing

Call price: Increasing function of price of “underlying” relative to “strike” price

Call price: Increasing function of “time to expiration”

Call option price: Increasing function of riskless rate of return (on treasury)

Call price: Increasing function of volatility